From 66c3bbfa94d8a41e58adf154be25e6d86fee8e30 Mon Sep 17 00:00:00 2001 From: "martial.simon" Date: Sun, 13 Apr 2025 19:54:19 +0200 Subject: init: initial commit --- PVCM/Jupyter + numpy.md | 1 + PVCM/Rappels matrices.md | 67 + PVCM/cama.md | 364 + PVCM/cama/.jupyter/custom/custom.css | 74 + PVCM/cama/.jupyter/custom/custom.js | 44 + PVCM/cama/.jupyter/jupyter_lab_config.py | 3 + PVCM/cama/.jupyter/jupyter_notebook_config.py | 3 + .../workspaces/auto-d-8a94.jupyterlab-workspace | 1 + PVCM/cama/.jupyter/labconfig/page_config.json | 3 + PVCM/cama/.jupyter/migrated | 1 + PVCM/cama/en/_Table of contents.ipynb | 236 + PVCM/cama/en/data | 1 + PVCM/cama/en/images | 1 + PVCM/cama/en/ma1 Jupyter.ipynb | 344 + PVCM/cama/en/ma1 np01 Numpy Introduction.ipynb | 932 + PVCM/cama/en/ma1 np02 Filtres.ipynb | 411 + PVCM/cama/en/ma1 np03 Manipulations.ipynb | 821 + PVCM/cama/en/ma1 np05 Notation Einstein.ipynb | 318 + .../ma1 np06 Linalg pour le calcul matriciel.ipynb | 425 + PVCM/cama/en/ma1 np90 petits exercices.ipynb | 430 + PVCM/cama/en/ma20 Rappels sur les matrices.ipynb | 530 + .../en/ma21 Transformations isometriques.ipynb | 458 + PVCM/cama/en/ma22 Changement de repere.ipynb | 697 + PVCM/cama/en/ma24 Vectors propres.ipynb | 807 + PVCM/cama/en/ma25 Drones -- Exercice.ipynb | 294 + .../en/ma26 Vecteurs propres -- Exercices.ipynb | 305 + PVCM/cama/en/ma30 ACP.ipynb | 460 + .../ma31 Syst\303\250me d'\303\251quations.ipynb" | 799 + .../en/ma32 Conditionnement d'une matrice.ipynb | 589 + PVCM/cama/en/ma34 ACP -- Exercice.ipynb | 295 + ...35 Syst\303\250me matriciel -- Exercices.ipynb" | 190 + .../ma40 M\303\251thodes it\303\251ratives.ipynb" | 416 + .../ma41 Convergence de Jacobi avec inertie.ipynb | 1144 + ...rrelaxation pour Gauss-Seidel -- Exercice.ipynb | 335 + ...ptimisation - M\303\251thode du gradient.ipynb" | 36389 +++++++++++++++++++ .../ma51 x.T A x sur un maillage en Numpy .ipynb | 32043 ++++++++++++++++ ...u gradiant pour syst\303\250me matriciel.ipynb" | 31856 ++++++++++++++++ .../en/ma53 Notations du produit scalaire.ipynb | 99 + ... pour r\303\251soudre Ax = b -- Exercice.ipynb" | 182 + ...303\251thode du gradient conjugu\303\251.ipynb" | 405 + ...\303\250me matriciel non lin\303\251aire.ipynb" | 502 + ...a62 Gradient conjugu\303\251 -- Exercice.ipynb" | 409 + "PVCM/cama/fr/_Table des mati\303\250res.ipynb" | 236 + PVCM/cama/fr/data/Ab.npz | Bin 0 -> 32756866 bytes PVCM/cama/fr/data/Acoo.npz | Bin 0 -> 99808 bytes PVCM/cama/fr/data/cours.mplstyle | 13 + PVCM/cama/fr/data/mouse.npy | Bin 0 -> 336 bytes ...303\251lations_d'une_ACP_norm\303\251e.svg.png" | Bin 0 -> 15578 bytes PVCM/cama/fr/images/cercle_trigo.svg | 355 + PVCM/cama/fr/images/drone_boat.png | Bin 0 -> 326692 bytes PVCM/cama/fr/images/gradient.png | Bin 0 -> 115482 bytes PVCM/cama/fr/images/nasa-x57-pression.jpg | Bin 0 -> 316766 bytes PVCM/cama/fr/ma1 Jupyter.ipynb | 346 + PVCM/cama/fr/ma1 np01 Numpy Introduction.ipynb | 933 + PVCM/cama/fr/ma1 np02 Filtres.ipynb | 411 + PVCM/cama/fr/ma1 np03 Manipulations.ipynb | 823 + PVCM/cama/fr/ma1 np05 Notation Einstein.ipynb | 323 + .../ma1 np06 Linalg pour le calcul matriciel.ipynb | 426 + PVCM/cama/fr/ma1 np90 petits exercices.ipynb | 529 + PVCM/cama/fr/ma20 Rappels sur les matrices.ipynb | 531 + .../fr/ma21 Transformations isometriques.ipynb | 458 + PVCM/cama/fr/ma22 Changement de repere.ipynb | 697 + PVCM/cama/fr/ma24 Vectors propres.ipynb | 807 + PVCM/cama/fr/ma25 Drones -- Exercice.ipynb | 295 + .../fr/ma26 Vecteurs propres -- Exercices.ipynb | 305 + PVCM/cama/fr/ma30 ACP.ipynb | 461 + .../ma31 Syst\303\250me d'\303\251quations.ipynb" | 799 + .../fr/ma32 Conditionnement d'une matrice.ipynb | 589 + PVCM/cama/fr/ma34 ACP -- Exercice.ipynb | 295 + ...35 Syst\303\250me matriciel -- Exercices.ipynb" | 190 + .../ma40 M\303\251thodes it\303\251ratives.ipynb" | 417 + .../ma41 Convergence de Jacobi avec inertie.ipynb | 1182 + ...rrelaxation pour Gauss-Seidel -- Exercice.ipynb | 336 + ...ptimisation - M\303\251thode du gradient.ipynb" | 36389 +++++++++++++++++++ .../ma51 x.T A x sur un maillage en Numpy .ipynb | 32043 ++++++++++++++++ ...u gradiant pour syst\303\250me matriciel.ipynb" | 31807 ++++++++++++++++ .../fr/ma53 Notations du produit scalaire.ipynb | 99 + ... pour r\303\251soudre Ax = b -- Exercice.ipynb" | 182 + ...303\251thode du gradient conjugu\303\251.ipynb" | 365 + ...\303\250me matriciel non lin\303\251aire.ipynb" | 502 + ...a62 Gradient conjugu\303\251 -- Exercice.ipynb" | 409 + PVCM/notebooks_cama.tgz | Bin 0 -> 11371712 bytes 82 files changed, 227237 insertions(+) create mode 100755 PVCM/Jupyter + numpy.md create mode 100755 PVCM/Rappels matrices.md create mode 100755 PVCM/cama.md create mode 100644 PVCM/cama/.jupyter/custom/custom.css create mode 100644 PVCM/cama/.jupyter/custom/custom.js create mode 100644 PVCM/cama/.jupyter/jupyter_lab_config.py create mode 100644 PVCM/cama/.jupyter/jupyter_notebook_config.py create mode 100644 PVCM/cama/.jupyter/lab/workspaces/auto-d-8a94.jupyterlab-workspace create mode 100644 PVCM/cama/.jupyter/labconfig/page_config.json create mode 100644 PVCM/cama/.jupyter/migrated create mode 100644 PVCM/cama/en/_Table of contents.ipynb create mode 120000 PVCM/cama/en/data create mode 120000 PVCM/cama/en/images create mode 100644 PVCM/cama/en/ma1 Jupyter.ipynb create mode 100644 PVCM/cama/en/ma1 np01 Numpy Introduction.ipynb create mode 100644 PVCM/cama/en/ma1 np02 Filtres.ipynb create mode 100644 PVCM/cama/en/ma1 np03 Manipulations.ipynb create mode 100644 PVCM/cama/en/ma1 np05 Notation Einstein.ipynb create mode 100644 PVCM/cama/en/ma1 np06 Linalg pour le calcul matriciel.ipynb create mode 100644 PVCM/cama/en/ma1 np90 petits exercices.ipynb create mode 100644 PVCM/cama/en/ma20 Rappels sur les matrices.ipynb create mode 100644 PVCM/cama/en/ma21 Transformations isometriques.ipynb create mode 100644 PVCM/cama/en/ma22 Changement de repere.ipynb create mode 100644 PVCM/cama/en/ma24 Vectors propres.ipynb create mode 100644 PVCM/cama/en/ma25 Drones -- Exercice.ipynb create mode 100644 PVCM/cama/en/ma26 Vecteurs propres -- Exercices.ipynb create mode 100644 PVCM/cama/en/ma30 ACP.ipynb create mode 100644 "PVCM/cama/en/ma31 Syst\303\250me d'\303\251quations.ipynb" create mode 100644 PVCM/cama/en/ma32 Conditionnement d'une matrice.ipynb create mode 100644 PVCM/cama/en/ma34 ACP -- Exercice.ipynb create mode 100644 "PVCM/cama/en/ma35 Syst\303\250me matriciel -- Exercices.ipynb" create mode 100644 "PVCM/cama/en/ma40 M\303\251thodes it\303\251ratives.ipynb" create mode 100644 PVCM/cama/en/ma41 Convergence de Jacobi avec inertie.ipynb create mode 100644 PVCM/cama/en/ma42 Surrelaxation pour Gauss-Seidel -- Exercice.ipynb create mode 100644 "PVCM/cama/en/ma50 Optimisation - M\303\251thode du gradient.ipynb" create mode 100644 PVCM/cama/en/ma51 x.T A x sur un maillage en Numpy .ipynb create mode 100644 "PVCM/cama/en/ma52 M\303\251thode du gradiant pour syst\303\250me matriciel.ipynb" create mode 100644 PVCM/cama/en/ma53 Notations du produit scalaire.ipynb create mode 100644 "PVCM/cama/en/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" create mode 100644 "PVCM/cama/en/ma60 M\303\251thode du gradient conjugu\303\251.ipynb" create mode 100644 "PVCM/cama/en/ma61 Syst\303\250me matriciel non lin\303\251aire.ipynb" create mode 100644 "PVCM/cama/en/ma62 Gradient conjugu\303\251 -- Exercice.ipynb" create mode 100644 "PVCM/cama/fr/_Table des mati\303\250res.ipynb" create mode 100644 PVCM/cama/fr/data/Ab.npz create mode 100644 PVCM/cama/fr/data/Acoo.npz create mode 100644 PVCM/cama/fr/data/cours.mplstyle create mode 100644 PVCM/cama/fr/data/mouse.npy create mode 100644 "PVCM/cama/fr/images/500px-Cercle_des_cor\303\251lations_d'une_ACP_norm\303\251e.svg.png" create mode 100644 PVCM/cama/fr/images/cercle_trigo.svg create mode 100644 PVCM/cama/fr/images/drone_boat.png create mode 100644 PVCM/cama/fr/images/gradient.png create mode 100644 PVCM/cama/fr/images/nasa-x57-pression.jpg create mode 100644 PVCM/cama/fr/ma1 Jupyter.ipynb create mode 100644 PVCM/cama/fr/ma1 np01 Numpy Introduction.ipynb create mode 100644 PVCM/cama/fr/ma1 np02 Filtres.ipynb create mode 100644 PVCM/cama/fr/ma1 np03 Manipulations.ipynb create mode 100644 PVCM/cama/fr/ma1 np05 Notation Einstein.ipynb create mode 100644 PVCM/cama/fr/ma1 np06 Linalg pour le calcul matriciel.ipynb create mode 100644 PVCM/cama/fr/ma1 np90 petits exercices.ipynb create mode 100644 PVCM/cama/fr/ma20 Rappels sur les matrices.ipynb create mode 100644 PVCM/cama/fr/ma21 Transformations isometriques.ipynb create mode 100644 PVCM/cama/fr/ma22 Changement de repere.ipynb create mode 100644 PVCM/cama/fr/ma24 Vectors propres.ipynb create mode 100644 PVCM/cama/fr/ma25 Drones -- Exercice.ipynb create mode 100644 PVCM/cama/fr/ma26 Vecteurs propres -- Exercices.ipynb create mode 100644 PVCM/cama/fr/ma30 ACP.ipynb create mode 100644 "PVCM/cama/fr/ma31 Syst\303\250me d'\303\251quations.ipynb" create mode 100644 PVCM/cama/fr/ma32 Conditionnement d'une matrice.ipynb create mode 100644 PVCM/cama/fr/ma34 ACP -- Exercice.ipynb create mode 100644 "PVCM/cama/fr/ma35 Syst\303\250me matriciel -- Exercices.ipynb" create mode 100644 "PVCM/cama/fr/ma40 M\303\251thodes it\303\251ratives.ipynb" create mode 100644 PVCM/cama/fr/ma41 Convergence de Jacobi avec inertie.ipynb create mode 100644 PVCM/cama/fr/ma42 Surrelaxation pour Gauss-Seidel -- Exercice.ipynb create mode 100644 "PVCM/cama/fr/ma50 Optimisation - M\303\251thode du gradient.ipynb" create mode 100644 PVCM/cama/fr/ma51 x.T A x sur un maillage en Numpy .ipynb create mode 100644 "PVCM/cama/fr/ma52 M\303\251thode du gradiant pour syst\303\250me matriciel.ipynb" create mode 100644 PVCM/cama/fr/ma53 Notations du produit scalaire.ipynb create mode 100644 "PVCM/cama/fr/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" create mode 100644 "PVCM/cama/fr/ma60 M\303\251thode du gradient conjugu\303\251.ipynb" create mode 100644 "PVCM/cama/fr/ma61 Syst\303\250me matriciel non lin\303\251aire.ipynb" create mode 100644 "PVCM/cama/fr/ma62 Gradient conjugu\303\251 -- Exercice.ipynb" create mode 100755 PVCM/notebooks_cama.tgz (limited to 'PVCM') diff --git a/PVCM/Jupyter + numpy.md b/PVCM/Jupyter + numpy.md new file mode 100755 index 0000000..c5ae773 --- /dev/null +++ b/PVCM/Jupyter + numpy.md @@ -0,0 +1 @@ +Cf notebook \ No newline at end of file diff --git a/PVCM/Rappels matrices.md b/PVCM/Rappels matrices.md new file mode 100755 index 0000000..5775637 --- /dev/null +++ b/PVCM/Rappels matrices.md @@ -0,0 +1,67 @@ +# Question 1 + +$$ +A = \begin{pmatrix} +1 & 0 & 2 \\ +2 & -1 & 1 \\ +0 & -2 & 1 +\end{pmatrix} = (A_{ij}) +;\; +b = \begin{pmatrix} +-1 \\ +0 \\ +2 +\end{pmatrix} +$$ +$$ +X = Ab = \begin{pmatrix} +1 & 0 & 2 \\ +2 & -1 &1 \\ +0 & -2 & 1 +\end{pmatrix} +\begin{pmatrix} +-1 \\ +0 \\ +2 +\end{pmatrix} += \begin{pmatrix} +3 \\ +0 \\ +2 +\end{pmatrix} +$$ +$$ +\begin{pmatrix} +3 & 1 & 2 \\ +1 & 4 & 3 \\ +0 & 0 & 1 +\end{pmatrix} +\begin{pmatrix} +-2 \\ +0 \\ +2 +\end{pmatrix} += \begin{pmatrix} +-2 \\ +4 \\ +2 +\end{pmatrix} +$$ +# Question 2 +### Matrice de rotation + +$$ +R = \begin{pmatrix} +\cos \theta & -\sin \theta \\ +\sin \theta & \cos \theta +\end{pmatrix} +$$ +### Matrice orthogonale + +$$A^TA = Id$$ +0 + +### Matrice de passage + + +Stage ds secteur + large que annonce \ No newline at end of file diff --git a/PVCM/cama.md b/PVCM/cama.md new file mode 100755 index 0000000..21e49cf --- /dev/null +++ b/PVCM/cama.md @@ -0,0 +1,364 @@ +# Notes pour Cama + +Je m'excuse par avance pour les fautes d'orthographe, +pour ce qui est du contenu numpy, je me relis le plus possible +mais les risques de fautes est toujours présent, dans le doute, +consultez la man page + +## Tips sympa + +### Accéder à une man page en exam :D + +Dans un terminal python: +```py +>>> import numpy as np +>>> import numpy.linalg as lin # format généralement utilisé sur moodle +>>> help(np. 'appuyer sur tab pour voir les propositions') +>>> # Par exemple : +>>> help(np.arange) # affiche la man page de la fonction arange +>>> help(lin) # affiche la man page du module linalg +>>> help(np.float32) # information sur la classe en question +``` + +Cette man page est votre amie, chérissez la. +Il aussi notable que beaucoup de fonctions sont directement applicables +sur les objets numpy, +Par exemple: + +```py +# A est un array numpy +A.sum() +# est strictement équivalent à +np.sum(A) +``` + +CEPENDANT, certaines méthodes sont propres à certaines structures. +Donc, si vous ne trouvez pas la méthode cherchée avec l'aide de 'help(np. ...)' +Essayez de regarder la man page de la structure de donnée avec laquelle vous +travaillez (par exemple 'help(np.ndarray)') + +## Récap des cours + +### ma1 np01: Intro Numpy + +#### Les dtypes: +* bool +* int, int8/16/32/64 +* uint, uint8/16/32/64 +* float, float8/16/32/64 +* complex, complex64/128 +Dans le doute, vous pouvez utiliser la fonction 'type()' de python + +#### Les tableaux/matrices/tensor: + +##### Les basics : + +```py +pyton_list = [...] +a = np.array(python_list) # création avec une list python +a = np.arange(4, dtype=np.uint8) # array([0,1,2,3]) de type uint8 +a.dtype # uint8 +b = a.astype('float32') # crée une copie de a où les éléments sont convertis en float32 +b.nbytes # = 16 car 4 éléments de 4 bytes +b[0].itemsize # = 4 car un float fait 4 bytes +b.reshape(2,2) # un tableau 2x2 de floats (voir man page pour plus de precisions) +b.flatten() # transforme b en un tableau 1d +c = np.empty((2,2), dtype=float) # (2,2) correspond aux dimensions du tableau sortant +# de plus empty signifie que les valeurs ne sont pas initialisées => plus rapide + +# Alternatives à empty et arrange: +c = np.zeros((2,2), dtype=float) # remplis avec des 0 +c = np.ones((2,2), dtype=complex) # remplis avec des 1 +c = np.full((2,2), 3.2) # remplis avec des 3.2 +c = np.random.random(size=(3,4)) # créer une matrice (tableau 2d) 3x4 avec des valeurs aléatoires +# Regardez help(np.random. 'tab') pour voir les différentes fonctions et choisir +# la loi aléatoire qui nous est utile +np.random.permutation() # mélange le tableau +# cas où l'on veut permuter tous les éléments du tableau indépendamment de la dimention +np.random.permutation(c.flatten()).reshape(c.shape) +id = np.identity(10) # matrice identité 10x10 +np.fromfunction(f, shape=(3,4), dtype=int) # créer un tableau à partir d'une fonction +# ici le tableau est de dimension 2, f devra prendre 2 paramètre (par ex, def f(i,j): ...) +``` + +##### Les essentiels: +```py +# Gestion de la forme +a = np.arange(8) +b = a.reshape(2,2,2) # check l'organisation du tableau sur le notebook +b.flat[index] # TRES PRATIQUE, permet d'indexer comme ci b était 1d +# .flat revient à faire un flatten puis reshape avec la shape d'origine +b.shape # = (2,2,2) + +# Opération des bases sur tableaux: + +A = np.array([[1,2], [3,4]]) +A+1 # fait +1 sur tous les éléments +A*3 # fait *3 sur tous les éléments ... +A*A # <=> np.square(A), produit d'Hadamard +A @ A # <=> A.dot(A), produit matricielle +A+A # <=> addition matricielle +A.T # <=> A.transpose() + +# Les opérations mathématiques de bases: +np.round(A) # arrondie +np.sqrt(A) # racine carrée +np.sin(A) # applique la fonction sinus sur tous les éléments de A +# possède des fonctions trigonométrique, hyperboliques, exposant, log ... +``` + +##### Les essentiels 2 (jsp pas comment nommer des titres): +```py +A = np.arange(10) # = [0,1,2, ..., 9] +np.sum(A) # somme sur les élém de A +np.prod(A) # produit sur les élém de A +np.mean(A) # moyenne de A +np.average(A) # moyenne pondérée de A +np.min(A) # valeur min de A +np.max(A) # valeur max de A +np.argmin(A) # indice de la valeur min de A +np.argmax(A) # indice de la valeur min de A +np.maximum(arr1, arr2) # pour avoir le tableau des maximums entre 2 tableaux ou entre un tableau et une valeur, +np.minimum(arr1, arr2) # pour avoir le tableau des maximums entre 2 tableaux ou entre un tableau et une valeur, +np.cumsum(A) # si A = [e_0, e_1, ..., e_n] alors cumsum = [e_0, e0+e1, e_0+e_1+e2, ..., somme de e_0 à e_n] +np.cumprod(A) # comme cumsum mais on travaille avec des produits +np.diff(A) # pour avoir l'écart avec l'élément suivant (utile pour calculer une dérivée). +``` + +### ma1 np02: Filtres + +Bon, les listes en python (/array numpy car fonctionne de la même manière), niveau indexage, on peut faire un peu n'importe quoi +Je vais présenter les fonctionnalités de bases mais n'hésitez pas à voir ca de votre côté avec vos propres exemples + +#### Les bases: + +Ce qu'on peut mettre entre les '[]' d'une liste/array: + +* un entier i; si positif correspond au ième indice, si négatif on commence par la fin du tableau (tab[-1] = tab[len(tab) - 1] aka le dernier elem) +* une liste d'indice [i, j, k]; tab[[i,j,k]] renvoie un tableau avec les éléments aux indices i, j et k +* une séquence 'debut:fin:saut'; debut inclut, fin exclut (comme pour les boucles for), permet par exemple de récupérer tous les indices impaires en faisant tab[1::2] +* un tableau de booléen de même taille que le tableau souhaité; si tab = [1,2,3], faire tab[[True, True, False]] donnera [1,2]. !! ATTENTION !! cette notation ne fonctionne pas avec les listes python (pas de soucis concernant les arrays numpy) + +```py +# les exemples données sont ceux du notebook +a = np.arange(12).reshape(3,4) +print(a, '\n') +# [[ 0 1 2 3] +# [ 4 5 6 7] +# [ 8 9 10 11]] +print(a[1, :], '\n') # 2nd line +# [4 5 6 7] +print(a[0:2, 0:2], '\n') # top left sub-matrix +# [[ 0 1] +# [4 5] +print(a[::2, -1], '\n') # even lines, last column +# [3 11] +print(a[:, [0,-1]]) # first and last column +# [[ 0 3] +# [ 4 7] +# [ 8 11]] + +# ATTENTION +a[i][j] +# et +a[i,j] +# Peuvent sembler similaires, et dans le cas des entiers c'est généralement le +# cas, (du moins je n'ai pas trouvé de contre exemple) +# Cependant, lorsque l'on travaille avec d'autres outils que les indices brutes +# (par exemple les ':') les notations ne sont plus équivalentes; +a[:, j] != a[:][j] # je vous conseille de travailler avec la notation [,] +# c'est généralement la plus pratique mais prenez ce que vous comprenez le mieux +``` + +#### Les filtres logiques + +Ces filtres vont créer des tableaux de booléens, comme dit ci-dessus, +ces tableaux sont utiles pour numpy mais ils ne sont pas utilisables sur les +listes python + +```py +a = np.array([i for i in range(5)] +# a = array([0,1,2,3,4]) +filtre = (a%2==0) # les parenthèses sont préférables mais pas obligatoires +# filtre = array([True, False, True, False, True]) +a[filtre] # = array([0,2,4]) + +# filtre étant un tableau, on peut déterminer certaines info sur a: +filtre.sum() # cmb d'élément de a vérifie la condition de filtre +filtre.any() # vérifie si au moins une valeur est à true +filtre.all() # vérifie si toutes les valeurs sont à true +filtre.prod() == 0 # vérifie si un cas est faux +filtre.sum() == 0 # vérifie si tous les cas sont faux + +# On peut biensur faire des opérations sur les éléments de a qui respectent les conditions d'un filtre, par exemple: +a[filtre ^ True] += 1 # ajoute 1 à tous les nombres impaires +# l'opérateur ^ est l'opérateur Xor +# filtre ^ True => transforme les True en False et vice versa + +# on peut aussi utiliser les opérateurs booléens | et & (or, and) +# => nécessite des '()' entre chaque segment, i.e: +filtre = a>2 & a%2==0 # non valide +filtre = (a>2) & (a%2==0) # valide +``` + +#### La fonction where + +Permet de réaliser un ternaire sur chaque élément d'un tableau + +```py +np.where(a > 5, a, 0) # a if a > 5 else 0 +# On peut donc utiliser des filtres comme premier param +``` + +### ma1 np03: Manipulation + +Cette partie est très bien expliquée sur le notebook, de plus cette partie +comporte bcp de fonctions, la man page est très bien détaillée avec des exemples pertinents. +Tout ca pour vous dire que j'ai la flemme de faire des exemples pour chacune des fonctions +Je vais me contenter de faire un listing des fonctions qui supportent les axes pour passer +plus de temps sur les nouvelles fonctions + +#### Les axes: + +Un tableau a des axes qui correspondent aux axes d'un repère dans l'espace. L'ordre des axes est celui de l'inclusion des crochets. En 2D un tableau de tableau est un tableau de lignes avec chaque ligne qui est un tableau 1D de valeurs. L'ordre est donc lignes puis colonnes (contrairement à l'axes (𝑥,𝑦) + +dans l'espace). En 3D l'ordre est ligne, colonne, profondeur si on désire avoir une image, sinon c'est 0, 1 et 2. + +De très nombreuses opérations sur les tableaux se font suivant un des axes du tableau aussi il est important de comprendre ce que sont les axes. (oui c'est un copié collé du cours j'en ai rien à foutre) + +#### Les fonctions 'classiques' qui supportent les axes: + +* arithmétiques : sum, prod, cumsum, cumprod +* statistiques : min, max, argmin, argmax, mean (moyenne), average (moyenne pondérée), std (écart type), var, median, percentile, quantile +* autres : gradiant, diff, fft (ps: dans le court il est noté 'gradiant' mais je crois que c'est 'gradient', car help(np.gradiant) n'existe simplement pas) + + +#### Les fonctions de manipulations (enfin): + +Les nouveautés: + +```py +# Application de fonctions + +array_ = np.arange(2*4*3).reshape((2,4,3)) +np.apply_along_axis(function_name, axis=-1, arr=array_) +# applique function_name sur le dernier axe de array_, le dernier axe va donc disparaitre +array_.max(axis=(1,2)) # on peut spécifier plusieurs axes +np.apply_over_axes(...) # s'applique sur plusieurs axes + +# Réorganisation d'un tableau + +np.moveaxis(array_,2,0) # permet de déplacer un axe (wow) +array_.shape # égale à (3,2,4) +array_.swapaxes(1,2) # je crois que vous avez compris (sinon help(np.swapaxes)) +array_.transpose((2,0,1)) # met l'axe 2 en place 0, 0 en place 1 et 1 en place 2 +# transpose réorganise les axes comme on veut, on peut faire un peu ce qu'on veut avec +np.flip(array_, n) # où n est un entier positif, cette ligne est équivalente à: +# a[:,:,..,::-1,:,..,:] avec ::-1 en nième position => permet d'inverser les valeurs +# d'un tableau suivant un axe +np.roll(array_, 2, axis=1) # fait glisser les éléments de 2 indices le long de l'axe 1 +array_.T # transposée de array_ + +#Concaténation: +a = np.zeros((2,3)) +b = np.ones((2,3)) +np.concatenate((a,b), axis=0) +# deplus, vous pouvez directement utiliser les fonctions vstack/row_stack ou hstack/column_stack +# ou dstack (travail en profonduer) pour travailler sur des axes spécifiques + +# Empilage +# A la différence de la concaténation, l'empilage ajoute une dimension. Empiler est utile +# pour stocker un paquet de tableaux 2D, des images par exemple, dans un tableau 3D +np.stack((a,b)) +# stack() possède un paramèter axis au besoin + +#Découpage: +e,f = np.split(c, 2, 1) # split en 2 le long de l'axe 1 +# split est la fonction inverse de la concaténation, comme concatenate, split possède les +# variantes : hsplit, vsplit et dsplit (découpe suivant les axes 0, 1 et 2) +``` + +### ma1 np05 (rip np04): Notation d'Einstein + +Pour être 100% honnête je ne maitrise que très peu cette notation qui relève +très clairement de la magie noire. +Voici une très bonne vidéo qui récapitule cette notation en 5min: +https://www.youtube.com/watch?v=ULY6pncbRY8 +Une autre vidéo, avec un peu plus d'exemple est qui est tout aussi bien: +https://www.youtube.com/watch?v=pkVwUVEHmfI&t=785s + +La man page de help est aussi très complète. +La manière de faire la plus simple reste d'écrire un pseudo code avec des boucles for, +puis de re-écrire avec la notation Einstein. + +#### Formule essentiels + exemple + +Rappel: Voici la formule pour calculer C[i,j], avec C = A @ B où +A est de dimension i*k et B de dimension k*j: +$$C_{ij} = \sum_1^k A_{ik} \times B_{kj}$$ + + +| Signature de einsum | Équivalent NumPy | Description | +|---------------------|-----------------|-------------| +| `('i->', v)` | `sum(v)` | Somme des valeurs du vecteur v | +| `('i,i->i', u, v)` | `u * v` | Multiplication des vecteurs u et v élément par élément | +| `('i,i', u, v)` | `inner(u, v)` | Produit scalaire de u et v | +| `('i,j', u, v)` | `outer(u, v)` | Produit dyadique de u et v | +| `('ij', A)` | `A` | Renvoie la matrice A | +| `('ji', A)` | `A.T` | Transposée de A | +| `('ii->i', A)` | `diag(A)` | Diagonale de A | +| `('ii', A)` | `trace(A)` | Somme de la diagonale de A | +| `('ij->', A)` | `sum(A)` | Somme des valeurs de A | +| `('ij->j', A)` | `sum(A, axis=0)` | Somme des colonnes de A | +| `('ij->i', A)` | `sum(A, axis=1)` | Somme des lignes de A | +| `('ij,ij->ij', A, B)` | `A * B` | Multiplication des matrices A et B élément par élément | +| `('ij,ji->ij', A, B)` | `A * B.T` | Multiplication des matrices A et B transposée élément par élément | +| `('ij,jk', A, B)` | `dot(A, B)` | Produit scalaire de A et B | +| `('ij,jk->ij', A, B)` | `inner(A, B)` | Produit intérieur de A et B | +| `('ij,jk->ijk', A, B)` | `A[:, None] * B` | Chaque ligne de A multipliée par B | +| `('ij,kl->ijkl', A, B)` | `A[:, :, None, None] * B` | Chaque valeur de A multipliée par B | + +### ma1 np06 : Linalg + +On attaque la partie chiante; faire des maths. +Il n'y a pas énormément de fonctions dans le module linalg à connaitre mais au vu +des exercies d'entrainement vous devez connaitre le sens mathématiques des objets avec +lequels vous travaillez. + +#### Petits rappels: + +```py +A = np.array([[1,2],[3,4]]) +B = np.array([[1,2],[3,4]]) +A @ B # produit matriciel <=> A.dot(B) +A * B # produit d'Hadamard +``` + +#### De l'algèbre linéaire youpi ! + +```py +b = np.array([17,37]) +x = lin.solve(A,b) # résoud un système d'équation linéaire (matricielle ou scalaire) +# x = [3. , 7.] +A @ x # = [17. 37.] = b +lin.inv(A) # matrice inverse +# x = lin.inv(A).dot(b) +A.T # ca ne change pas c'est toujours la transposée + +# Extractions: +np.diag(A) # renvoie la diagonale de la matrice +np.tril(A) # matrice triangulaire inférieur (l pour lower) +np.triu(A) # matrice triangulaire supérieur +np.tri(3) # créer une matrice 3*3 triangulaire avec des 0 et des 1 +Q,R = lin.qr(A) # alors là ... jsp +lin.eig(A) # donne valeurs propres et vecteurs propres de A +lin.det(A) # determinant de A +lin.norm(A) # norme 2 +lin.norm(A, 1) # norme 1 +lin.cond(A, 2) # conditionnement, encore une fois jsp ce que c'est... pour le 2, je sais encore moins +``` + +Voilà voilà, si vous pensez qu'il manque qlq chose n'hésitez pas à me le faire remonter. +Je ne me répéterais jamais assez mais il y a surement des fautes (surtout niveau orthographe), +pensez bien à toujours regarder la man page si vous avez le moindre doute, sinon demandez moi +directement :) diff --git a/PVCM/cama/.jupyter/custom/custom.css b/PVCM/cama/.jupyter/custom/custom.css new file mode 100644 index 0000000..6034bbd --- /dev/null +++ b/PVCM/cama/.jupyter/custom/custom.css @@ -0,0 +1,74 @@ + + diff --git a/PVCM/cama/.jupyter/custom/custom.js b/PVCM/cama/.jupyter/custom/custom.js new file mode 100644 index 0000000..4b280ad --- /dev/null +++ b/PVCM/cama/.jupyter/custom/custom.js @@ -0,0 +1,44 @@ +import json +import os +import re +import ipykernel +import requests +from notebook.notebookapp import list_running_servers +from urllib.parse import urljoin +from IPython.display import display, Markdown + +def get_notebook_path(): + """ + Return the full path of the jupyter notebook. + """ + session = requests.Session() + session.trust_env = False + kernel_id = re.search('kernel-(.*).json', + ipykernel.connect.get_connection_file()).group(1) + servers = list_running_servers() + if + for ss in servers: + response = session.get(f"{ss['url']}api/sessions", + params={'token': ss['token']}) + for nn in json.loads(response.text): + if nn['kernel']['id'] == kernel_id: + try: + return os.envion['HOME_URL'] + 'notebooks/' + nn['notebook']['path'] + except: + return ss['url'] + 'notebooks/' + nn['notebook']['path'] + +def PreviousNext(url1, url2): + section = get_notebook_path() + section = section.replace('notebooks','tree') + section = section[:section.rfind('/')] + toc = "http://python3.mooc.lrde.epita.fr/notebooks/Table%20des%20mati%C3%A8res.ipynb" + text = 200 * "  " + text += "
" + text += f'{url1[url1.rfind("/")+1:-6]}' +# text += f'  ← △ →  ' + text += f'  ← △ →  ' + text += f'{url2[url2.rfind("/")+1:-6]}' + text += '

' + text += ' ' + return text + diff --git a/PVCM/cama/.jupyter/jupyter_lab_config.py b/PVCM/cama/.jupyter/jupyter_lab_config.py new file mode 100644 index 0000000..f846fdf --- /dev/null +++ b/PVCM/cama/.jupyter/jupyter_lab_config.py @@ -0,0 +1,3 @@ +c = get_config() #noqa +c.ServerApp.token = "" +c.ServerApp.password = "" diff --git a/PVCM/cama/.jupyter/jupyter_notebook_config.py b/PVCM/cama/.jupyter/jupyter_notebook_config.py new file mode 100644 index 0000000..993ec12 --- /dev/null +++ b/PVCM/cama/.jupyter/jupyter_notebook_config.py @@ -0,0 +1,3 @@ +c = get_config() +c.NotebookApp.token = '' +c.NotebookApp.password = '' diff --git a/PVCM/cama/.jupyter/lab/workspaces/auto-d-8a94.jupyterlab-workspace b/PVCM/cama/.jupyter/lab/workspaces/auto-d-8a94.jupyterlab-workspace new file mode 100644 index 0000000..764992d --- /dev/null +++ b/PVCM/cama/.jupyter/lab/workspaces/auto-d-8a94.jupyterlab-workspace @@ -0,0 +1 @@ +{"data":{"layout-restorer:data":{"main":{"dock":{"type":"tab-area","currentIndex":0,"widgets":[]}},"down":{"size":0,"widgets":[]},"left":{"collapsed":false,"visible":true,"current":"filebrowser","widgets":["filebrowser","running-sessions","@jupyterlab/toc:plugin","extensionmanager.main-view"],"widgetStates":{"jp-running-sessions":{"sizes":[0.25,0.25,0.25,0.25],"expansionStates":[false,false,false,false]},"extensionmanager.main-view":{"sizes":[0.3333333333333333,0.3333333333333333,0.3333333333333333],"expansionStates":[false,false,false]}}},"right":{"collapsed":true,"visible":true,"widgets":["jp-property-inspector","debugger-sidebar"],"widgetStates":{"jp-debugger-sidebar":{"sizes":[0.2,0.2,0.2,0.2,0.2],"expansionStates":[false,false,false,false,false]}}},"relativeSizes":[0.09334586746090842,0.9066541325390917,0],"top":{"simpleVisibility":true}}},"metadata":{"id":"auto-d"}} \ No newline at end of file diff --git a/PVCM/cama/.jupyter/labconfig/page_config.json b/PVCM/cama/.jupyter/labconfig/page_config.json new file mode 100644 index 0000000..1703a8a --- /dev/null +++ b/PVCM/cama/.jupyter/labconfig/page_config.json @@ -0,0 +1,3 @@ +{ + "lockedExtensions": {} +} \ No newline at end of file diff --git a/PVCM/cama/.jupyter/migrated b/PVCM/cama/.jupyter/migrated new file mode 100644 index 0000000..bfbcba1 --- /dev/null +++ b/PVCM/cama/.jupyter/migrated @@ -0,0 +1 @@ +2024-02-28T14:34:18.590584+00:00 \ No newline at end of file diff --git a/PVCM/cama/en/_Table of contents.ipynb b/PVCM/cama/en/_Table of contents.ipynb new file mode 100644 index 0000000..e8f2e13 --- /dev/null +++ b/PVCM/cama/en/_Table of contents.ipynb @@ -0,0 +1,236 @@ + +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + +"## Table of contents.ipynb\n", +"* [ma1 Jupyter](ma1%20Jupyter.ipynb)\n", +" - Using Jupyter\n", +" - Cell manipulation\n", +" - Configuration\n", +" - IPython\n", +" - Completion and help\n", +" - Shell under IPython\n", +" - Magic commands\n", +"* [ma1 np01 Numpy Introduction](ma1%20np01%20Numpy%20Introduction.ipynb)\n", +" - NumPy - N-dimensional Array manipulations library\n", +" - Creating an array\n", +" - By redefining its shape\n", +" - Mixing values\n", +" - Basic Operations\n", +" - Browse an array\n", +" - Think vector\n", +"* [ma1 np02 Filtres](ma1%20np02%20Filtres.ipynb)\n", +" - Filter by indices\n", +" - Logical filters\n", +" - A filter = a logical condition\n", +" - `where` to handle non-filter values\n", +" - Update a table with a filter\n", +"* [ma1 np03 Manipulations](ma1%20np03%20Manipulations.ipynb)\n", +" - The axes\n", +" - Arranging a table\n", +" - Reorder axes\n", +" - Changing the order of array elements\n", +" - Aggregation\n", +" - Concatenation\n", +" - Stacking\n", +" - Splitting\n", +" - From Python to Numpy\n", +" - Pandas too\n", +"* [ma1 np05 Notation Einstein](ma1%20np05%20Notation%20Einstein.ipynb)\n", +" - Introduction to Einstein Notation\n", +" - Practical Application\n", +"* [ma1 np06 Linalg pour le calcul matriciel](ma1%20np06%20Linalg%20pour%20le%20calcul%20matriciel.ipynb)\n", +" - Linalg (linear algebra)\n", +" - Basic operations\n", +" - Extraction\n", +" - Matrix operations\n", +"* [ma1 np90 petits exercices](ma1%20np90%20petits%20exercices.ipynb)\n", +" - Numpy - Exercises\n", +" - Square Matrix\n", +" - Vector Norm\n", +" - Sub-Matrix\n", +" - Random Vector\n", +" - Trace\n", +" - Matrix of Multiples of 3\n", +" - Count of 9s\n", +" - Column with the Smallest Average\n", +" - ChessSum\n", +" - 2 Minimums\n", +" - Rows in Order\n", +" - Unique Values\n", +" - Magic Tensor\n", +" - Tensor Slices\n", +"* [ma20 Rappels sur les matrices](ma20%20Rappels%20sur%20les%20matrices.ipynb)\n", +" - Vector\n", +" - Matrices and linear maps\n", +" - Determinant of a matrix\n", +" - Standards\n", +" - Norm of a vector\n", +" - Norm of a matrix\n", +" - Properties\n", +"* [ma21 Transformations isometriques](ma21%20Transformations%20isometriques.ipynb)\n", +" - Isometric transformations\n", +" - Rotation matrix centered at (0,0)\n", +" - Properties\n", +" - Axial Symmetry\n", +" - Translation\n", +" - Exercise 1.1\n", +"* [ma22 Changement de repere](ma22%20Changement%20de%20repere.ipynb)\n", +" - Matrice de passage\n", +" - Vecteurs dans le nouveau repère\n", +" - Matrice de passage vue comme une transformation\n", +" - Points dans le nouveau repère\n", +" - Notre souris dans le nouveau repère\n", +" - Exercice -- Et l'inverse ?\n", +" - Une application linéaire transposée dans le nouveau repère\n", +"* [ma24 Vectors propres](ma24%20Vectors%20propres.ipynb)\n", +" - $A^n \\textbf{x}$\n", +" - Vecteurs propres et valeurs propres\n", +" - Le cas des matrices de rotation\n", +" - Symétrie axiale horizontale\n", +" - Diagonalisation d'une matrice\n", +"* [ma25 Drones -- Exercice](ma25%20Drones%20--%20Exercice.ipynb)\n", +" - Drone show\n", +" - Figure 1\n", +" - Figure 2\n", +" - Figure 3\n", +"* [ma26 Vecteurs propres -- Exercices](ma26%20Vecteurs%20propres%20--%20Exercices.ipynb)\n", +" - Cas d'utilisation des valeurs et vecteurs propres\n", +" - Fibonnacci\n", +" - Google page rank\n", +" - Approche itérative\n", +" - Un autre approche\n", +"* [ma30 ACP](ma30%20ACP.ipynb)\n", +" - Principal component analysis (PCA)\n", +" - A cloud of dots\n", +" - Covariance matrix\n", +"* [ma31 Système d'équations](ma31%20Système%20d'équations.ipynb)\n", +" - Systèmes matriciels\n", +" - Résolution d'un système matriciel\n", +" - Méthode du pivot de Gauss\n", +" - Complexité du pivot de Gauss\n", +" - Décomposition LU (Lower, Upper)\n", +" - Gauss Jordan\n", +" - Comparaison de la vitesse de méthodes\n", +" - Erreurs d'arrondi\n", +" - Solution au problème d'arrondi dans le cas du pivot de Gauss\n", +"* [ma32 Conditionnement d'une matrice](ma32%20Conditionnement%20d'une%20matrice.ipynb)\n", +" - Conditionnement d'une matrice\n", +" - Pourquoi ?\n", +" - Perturbons la matrice\n", +" - Propriétés\n", +" - Préconditionnement\n", +"* [ma34 ACP -- Exercice](ma34%20ACP%20--%20Exercice.ipynb)\n", +" - Exercise: 3D point cloud\n", +" - Experience Data\n", +" - Calculations to find the characteristics of our cloud\n", +"* [ma35 Système matriciel -- Exercices](ma35%20Système%20matriciel%20--%20Exercices.ipynb)\n", +" - Vector Programming\n", +" - Partial Gaussian pivot method\n", +" - Choleski factorization\n", +" - Improve Jacobi\n", +"* [ma40 Méthodes itératives](ma40%20Méthodes%20itératives.ipynb)\n", +" - Numerical simulation\n", +" - Iterative Methods\n", +" - Jacobi method\n", +" - Why does the 2nd case work?\n", +" - Calculation time\n", +"* [ma41 Convergence de Jacobi avec inertie](ma41%20Convergence%20de%20Jacobi%20avec%20inertie.ipynb)\n", +" - Add inertia to Jacobi\n", +" - Let's program inertia for Jacobi\n", +" - Let's study convergence\n", +" - Let's test other matrices with this algorithm\n", +" - Exercise 20.1\n", +" - Normalize\n", +"* [ma42 Surrelaxation pour Gauss-Seidel -- Exercice](ma42%20Surrelaxation%20pour%20Gauss-Seidel%20--%20Exercice.ipynb)\n", +" - Exercise ma21\n", +" - Gauss-Seidel\n", +" - Gauss-Seidel overrelaxation\n", +" - Let's program overrelaxed Gauss-Seidel\n", +" - The good case\n", +" - Study by $w$\n", +"* [ma50 Optimisation - Méthode du gradient](ma50%20Optimisation%20-%20Méthode%20du%20gradient.ipynb)\n", +" - Optimization problem\n", +" - Optimization problem with constraint\n", +" - The gradient method\n", +" - Study of the convergence of the gradient\n", +"* [ma51 x.T A x sur un maillage en Numpy ](ma51%20x.T%20A%20x%20sur%20un%20maillage%20en%20Numpy%20.ipynb)\n", +" - Let's calculate ${\\bf x}^T \\, A \\, {\\bf x} $ with Numpy\n", +" - Test case with A = 2 Id\n", +" - A real case\n", +" - Let's optimize\n", +" - Using a J function and a loop\n", +" - Using `np.tensordot`\n", +" - Conclusion\n", +"* [ma52 Méthode du gradiant pour système matriciel](ma52%20Méthode%20du%20gradiant%20pour%20système%20matriciel.ipynb)\n", +" - Gradient et dérivée\n", +"- A x = b seen as an optimization problem\n", +" - Calculation of derivative\n", +" - Definition\n", +" - Calculate the derivative of J along a direction\n", +" - A symmetrical\n", +" - Gradient and derivative\n", +"* [ma53 Notations du produit scalaire](ma53%20Notations%20du%20produit%20scalaire.ipynb)\n", +" - Writings of the scalar product\n", +" - ${\\bf v} \\,.\\, {\\bf w}$\n", +" - ${\\bf v}^T \\, {\\bf w}$\n", +" - $<{\\bf v}, {\\bf w}>$\n", +"* [ma54 Gradient pour résoudre Ax = b -- Exercice](ma54%20Gradient%20pour%20résoudre%20Ax%20=%20b%20--%20Exercice.ipynb)\n", +" - The gradient method to solve A x = b\n", +" - Introduce inertia\n", +" - Optimal value of µ\n", +"* [ma60 Méthode du gradient conjugué](ma60%20Méthode%20du%20gradient%20conjugué.ipynb)\n", +" - Conjugate gradient method\n", +" - Generate a base of $ℝ^n$\n", +" - The $A {\\bf x} = {\\bf b}$ case\n", +" - Calculation of $μ^k$\n", +" - Property\n", +" - 2nd attempt\n", +" - Let's work in the base of $\\nabla J({\\bf x}^i)$\n", +" - New calculation of μ\n", +"* [ma61 Système matriciel non linéaire](ma61%20Système%20matriciel%20non%20linéaire.ipynb)\n", +" - Système matriciel non linéaire\n", +" - La méthode du point fixe\n", +" - La méthode du point fixe pour résoudre $A({\\bf x}) \\, {\\bf x} = {\\bf b}$\n", +" - Test\n", +" - Appliquons l'inertie\n", +" - La méthode de Newton-Raphson\n", +"* [ma62 Gradient conjugué -- Exercice](ma62%20Gradient%20conjugué%20--%20Exercice.ipynb)\n", +" - Programmer le gradient conjugué\n", +" - Comparons avec le gradient simple\n", +" - Perfs\n", +" - Nombre d'iteration dans les 2 cas\n", +" - Un cas réel\n", +" - Comparaison gradient simple et conjugué\n", +" - Comparaison avec `lin.solve` de Scipy\n", +" - Le gradient conjugué de Scipy (avec Lapack)\n", + + "" + ]}], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.7" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} + diff --git a/PVCM/cama/en/data b/PVCM/cama/en/data new file mode 120000 index 0000000..e72e676 --- /dev/null +++ b/PVCM/cama/en/data @@ -0,0 +1 @@ +../fr/data \ No newline at end of file diff --git a/PVCM/cama/en/images b/PVCM/cama/en/images new file mode 120000 index 0000000..b84b47e --- /dev/null +++ b/PVCM/cama/en/images @@ -0,0 +1 @@ +../fr/images \ No newline at end of file diff --git a/PVCM/cama/en/ma1 Jupyter.ipynb b/PVCM/cama/en/ma1 Jupyter.ipynb new file mode 100644 index 0000000..01e5c96 --- /dev/null +++ b/PVCM/cama/en/ma1 Jupyter.ipynb @@ -0,0 +1,344 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Using Jupyter\n", + "\n", + "#### Cells\n", + "\n", + "A Jupyter sheet is made up of cells that you can guess if you click on the text. There are different\n", + "cell types that you choose with the drop-down menu in the middle of the icons at the top of the page:\n", + "\n", + "* Python code (default)\n", + "* rich text ([Markdown](https://en.wikipedia.org/wiki/Markdown))\n", + "* plain text (useful for deactivating a code cell)\n", + "\n", + "You can add\n", + "a cell with the + symbol at the top of the page, delete a cell with the scissors, move a cell with the arrows and edit it by double-clicking on it. We will see that we execute the cells to obtain the result of the written code. All this can be found on the menu\n", + "`Cell`.\n", + "\n", + "#### Kernel\n", + "\n", + "Jupyter takes its name from 3 languages, namely Julia, Python and R. Today the list of languages ​​that can be\n", + "to use in a Jupyter sheet is much longer but in all cases you need a kernel which makes the interface\n", + "between Jupyter and the language. In the case of Python the core is iPython. We choose it when creating the sheet\n", + "and we can interact with it using the `Kernel` menu.\n", + "\n", + "The other menus are more classic and do not require explanation (forget `Widget`).\n", + "\n", + "#### Note\n", + "\n", + "If you do not know Python or Jupyter, it is advisable to come back here after reading the first chapter .\n", + "\n", + "## Cell manipulation\n", + "\n", + "#### Status and execution\n", + "\n", + "* A cell can have 3 states:\n", + " * not selected (no frame around the cell)\n", + " * selected (blue frame or blue bar on the left)\n", + " * selected and in edit mode (change of background color and sometimes green frame)\n", + "* Clicking selects a cell (or even puts it directly into edit mode for calculation cells)\n", + "* Double click selects and enters editing mode (on a text area, Markdown syntax appears)\n", + "* Enter like clicking allows you to activate the edition when Esc allows you to close the edition mode.\n", + "* To make Python recompute the result of a cell\n", + " * Shift+Enter does the calculation and moves to the next cell\n", + " * Crtl+Enter does the calculation and stays on the cell\n", + " * Alt+Enter does the calculation and then adds an empty cell.\n", + "\n", + "#### Display\n", + " \n", + " * `[out]` To hide the results, end the last line of the cell with `;`.\n", + " * `[In]` To hide a cell, use 'Hide input' from nbextessions (see config in the Edit menu)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(2)\n", + "1+1; # remove the ; to see the difference" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Configuration\n", + "\n", + "Jupyter has many commands to manipulate your note sheet and of course it is possible to\n", + "set keyboard shortcuts.\n", + "\n", + "To display the list of commands (the *command palette*) click on the small keyboard in the icon bar.\n", + "With Chrome, you can display this command palette with Ctrl+Shift+P.\n", + "\n", + "To display and define your keyboard shortcuts you can go to the help menu or type `shortcut` in\n", + "the command palette.\n", + "\n", + "For example, for my use I redefined the cell type change with\n", + "\n", + "* Crtl+1 for Code mode\n", + "* Crtl+2 for Markdown mode\n", + "* Crtl+3 for Raw mode (uninterpreted data)\n", + "\n", + "This works when the cell is selected but not in edit mode (so blue frame or blue bar)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Exercise\n", + "\n", + "Choose your shortcuts to switch from one mode to another then switch the cell below to Code mode and execute it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "print('$qsD!Me+nsodd= 1l lre3W$'[-2:2:-2])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Cell manipulation shortcuts are good to know or redefine when you start using Jupyter seriously." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## IPython\n", + "\n", + "When using Python in Jupyter, we rely on [IPython](https://ipython.org/) which enriches Python.\n", + "\n", + "This gives the following functionality:\n", + "\n", + "* Completion by pressing Tab\n", + "* Help with `?` and `??` for even more help with objects (or even code)\n", + "* [Shell access](https://ipython.readthedocs.io/en/stable/interactive/shell.html) with `!`\n", + "* Magic commands" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Completion and help\n", + "\n", + "`a`Tab will give a list including `abs`" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "For the help examples, you must launch the cells to see the result." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "abs?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "To close the help window click on the cross at the top right of the window or use Esc.?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mot = \"Coucou\"\n", + "mot.split?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Shell under IPython" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "!pwd" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "vlib = '/var/lib/'\n", + "res = !ls $vlib\n", + "res = res.grep('lib')\n", + "for f in res:\n", + " print(f)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(type(res))\n", + "res??" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Magic commands\n", + "\n", + "Magic commands improve the use of Python. They start with\n", + "\n", + " * `%` and apply to the line\n", + " * `%%` and apply to the cell (when it makes sense)\n", + "\n", + "The first magic command to run is `%quickref` to get the list of iPython possibilities." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%quickref" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Here is a selection of some magic commands:\n", + " \n", + "* `%time` to get the time the line takes (`%%time` for the execution time of the cell).\n", + "* `%timeit` is like `%time` but it restarts the line several times to get a more accurate estimate\n", + "* `%prun` to run the line through the Python profiler and see where it's taking time\n", + "* `%matplotlib inline` so that the graphs are displayed in the Jupyter page\n", + "* `%load` to load a Python file into the cell (comments %load once executed)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "!echo 'print(\"coucou\")' > /tmp/prog.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%load /tmp/prog.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import scipy.linalg as lin\n", + "\n", + "%prun lin.solve(np.random.random([3000,3000]), np.random.random(3000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "{{ PreviousNext('Introduction.ipynb','../lesson1 Python basics/00 - Premiers calculs.ipynb') }}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma1 np01 Numpy Introduction.ipynb b/PVCM/cama/en/ma1 np01 Numpy Introduction.ipynb new file mode 100644 index 0000000..bf30835 --- /dev/null +++ b/PVCM/cama/en/ma1 np01 Numpy Introduction.ipynb @@ -0,0 +1,932 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# NumPy - N-dimensional Array manipulations library\n", + "\n", + "[NumPy](https://docs.scipy.org/doc/numpy/user/index.html) is a toolkit for scientific program development. It\n", + "provides multidimensional arrays that are simple to manipulate and **efficient** (which Python lists are not).\n", + "\n", + "Numpy's syntax is also used in other languages like R or Julia. In AI, TensorFlow, PyTorch and JAX use also this syntax." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np # np is the convention" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Unlike lists, __tables have all their values of the same type__.\n", + "\n", + "## Creating an array" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 2 3]\n", + " [4 5 7]]\n", + "shape: (2, 3)\n", + "type: \n" + ] + } + ], + "source": [ + "a = np.array([[1,2,3], [4,5,7]]) # 2D array built from a list\n", + "print(a)\n", + "print(\"shape: \",a.shape)\n", + "print(\"type: \",type(a[0,0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### dtype: the choice of weapons\n", + "\n", + "When doing scientific calculation it is important to choose the type of tables to optimize memory, errors, speed.\n", + "\n", + "NumPy offers the following types:\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
Data typeDescription
boolBoolean (True or False) stored as a byte
intPlatform integer (usually either int32 or int64)
int8Byte (-128 to 127)
int16Integer (-32768 to 32767)
int32Integer (-2147483648 to 2147483647)
int64Integer (9223372036854775808 to 9223372036854775807)
uint8Unsigned integer (0 to 255)
uint16Unsigned integer (0 to 65535)
uint32Unsigned integer (0 to 4294967295)
uint64Unsigned integer (0 to 18446744073709551615)
floatShorthand for float64.
float16Half precision float: sign bit, 5 bits exponent,\n", + "10-bit mantissa
float32Single precision float: sign bit, 8 bits exponent,\n", + "23-bit mantissa
float64Double precision float: sign bit, 11 bits exponent,\n", + "52-bit mantissa
complexShorthand for complex128.
complex64Complex number, represented by two 32-bit floats (real\n", + "and imaginary components)
complex128Complex number, represented by two 64-bit floats (real\n", + "and imaginary components)
" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [0 1 2 3] uint8\n", + "x = [254 1 2 3] uint8\n", + "y = [254. 1. 2. 3.] float32\n" + ] + } + ], + "source": [ + "x = np.arange(4, dtype= np.uint8) # arange is the numpy version of range to produce an array\n", + "print(\"x =\", x, x.dtype)\n", + "\n", + "x[0] = -2 # 0 - 2 = max -1 for unsigned int\n", + "print(\"x =\", x, x.dtype)\n", + "\n", + "y = x.astype('float32') # conversion\n", + "print(\"y =\", y, y.dtype)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We can know the memory size (in bytes) occupied by an element of the array:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "4\n" + ] + }, + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(x[0].itemsize)\n", + "print(y[0].itemsize)\n", + "y.nbytes" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Predefined methods\n", + "\n", + "There is also the possibility to create an empty or predefined array of the dimension of your choice using\n", + "[predefined creation methods](https://docs.scipy.org/doc/numpy/reference/routines.array-creation.html):" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Empty float:\n", + " [[2.42350504e-316 0.00000000e+000]\n", + " [4.94065646e-324 nan]]\n", + "Float zeros:\n", + " [[0. 0.]\n", + " [0. 0.]]\n", + "Complex ones:\n", + " [[1.+0.j 1.+0.j 1.+0.j]\n", + " [1.+0.j 1.+0.j 1.+0.j]]\n", + "Full of 3.2:\n", + " [[3.2 3.2]\n", + " [3.2 3.2]]\n", + "La matrice suivante est affichée partiellement car trop grande : \n", + "[[1. 0. 0. ... 0. 0. 0.]\n", + " [0. 1. 0. ... 0. 0. 0.]\n", + " [0. 0. 1. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 1. 0. 0.]\n", + " [0. 0. 0. ... 0. 1. 0.]\n", + " [0. 0. 0. ... 0. 0. 1.]]\n" + ] + } + ], + "source": [ + "a = np.empty((2,2), dtype=float) # empty do not set any value, it is faster\n", + "print(\"Empty float:\\n\", a)\n", + "\n", + "print(\"Float zeros:\\n\", np.zeros((2,2), dtype=float)) # matrix filled with 0\n", + "\n", + "print(\"Complex ones:\\n\", np.ones((2,3), dtype=complex)) # matrix filled with 1\n", + "\n", + "print(\"Full of 3.2:\\n\", np.full((2,2), 3.2))\n", + "\n", + "print(\"La matrice suivante est affichée partiellement car trop grande : \")\n", + "print(np.identity(1000)) # identity matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### With random values\n", + "\n", + "The sub-library [`np.random`](https://docs.scipy.org/doc/numpy/reference/routines.random.html) provides methods for generating arrays of random values." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Random integers < 10:\n", + " [[7 5 7 2]\n", + " [6 7 0 8]\n", + " [6 3 8 3]]\n", + "Random reals between 0 and 1 :\n", + " [[0.45228105 0.39674551 0.02142443 0.14342572]\n", + " [0.95223097 0.85798264 0.85777533 0.28784271]\n", + " [0.5142878 0.36823048 0.87704756 0.44096786]]\n" + ] + } + ], + "source": [ + "print(\"Random integers < 10:\\n\", np.random.randint(10, size=(3,4))) # can also choose a min\n", + "\n", + "print(\"Random reals between 0 and 1 :\\n\", np.random.random(size=(3,4)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We can choose the law of distribution (uniform law by default)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.44216124, 2.5586318 , 4.28770816],\n", + " [2.16814785, 1.82332334, 4.53031302]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "loc = 3\n", + "scale = 1.5\n", + "np.random.normal(loc, scale, size=(2,3)) # Gauss distribution" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### By redefining its shape\n", + "\n", + "A classic case for testing is to create a small multidimensional array with different values.\n", + "For this the simplest is to put 0,1,2,...,N in the boxes of our form table (3,4) for example.\n", + "This is done with `arange` which we have already seen to generate the values and `reshape` to have the desired form:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "arr = np.arange(3*4).reshape((3,4))\n", + "arr" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "arr[1, 0]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Attention, the numbering of the boxes of a table is carried out with nested loops. It is always the last dimension which varies most quickly. In 3D this means that going from one element to the next varies the last index (along z). This does not correspond to the human way of filling a cube (we tend to stack 2D arrays). In \n", + "regular use this is not a problem, it is\n", + "only weird when printing tests to check.\n", + "\n", + "```\n", + " human Numpy\n", + "   ┌─┬─┐ ┌─┬─┐\n", + "┌─┬─┐│5│ ┌─┬─┐│3│\n", + "│0│1│┼─┤ │0│2│┼─┤\n", + "├─┼─┤│7│ ├─┼─┤│7│\n", + "│2│3│┴─┘ │4│6│┴─┘\n", + "└─┴─┘ └─┴─┘\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[0, 1],\n", + " [2, 3]],\n", + "\n", + " [[4, 5],\n", + " [6, 7]]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.arange(8).reshape(2,2,2) # a[0,1,0] is 2 and a[0,1,1] is 3\n", + "A" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The reverse of reshape is `flatten()` which reshape a multi-dimensional array into a 1-dimensional array. We can also use `flat` to have a 1D view on the array without reshaping it." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5\n", + "(2, 2, 2)\n" + ] + } + ], + "source": [ + "print(A.flat[5])\n", + "print(A.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Mixing values\n", + "\n", + "If we want to work with the values of an array taken in a random order then we can mix\n", + "the table with `np.random.permutation()`. Attention the permutation is carried out on the elements of the first level of the array, `A[:]`, i.e. arrays\n", + "if the array is multi-dimensional (an array of arrays)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11],\n", + " [ 0, 1, 2, 3]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = np.arange(12).reshape(3,4)\n", + "np.random.permutation(data) # permutes lines only" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "If you want to mix all the values ​​you have to flatten the table and give it back its shape:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[10, 3, 11, 8],\n", + " [ 4, 1, 2, 7],\n", + " [ 0, 9, 6, 5]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = np.random.permutation(data.flatten()).reshape(data.shape) # it works because flatten returns a copy\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### With its own function\n", + "\n", + "We can also create an array with a function that gives the value of the array for each index (i, j):" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, -1, -2, -3],\n", + " [ 2, 1, 0, -1],\n", + " [ 4, 3, 2, 1]])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def f(i,j):\n", + " return 2*i - j\n", + "\n", + "np.fromfunction(f, shape=(3,4), dtype=int)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Basic Operations\n", + "\n", + "Numpy makes it possible to apply the usual operations to all the elements of the array:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A + 1:\n", + " [[2 3]\n", + " [4 5]] \n", + "\n", + "2 A + Id:\n", + " [[3. 4.]\n", + " [6. 9.]] \n", + "\n", + "A * A (element-wise product):\n", + " [[ 1 4]\n", + " [ 9 16]] \n", + "\n", + "A @ A (matrix or dot product):\n", + " [[ 7 10]\n", + " [15 22]]\n" + ] + } + ], + "source": [ + "A = np.array([[1,2], [3,4]])\n", + "\n", + "print(\"A + 1:\\n\", A + 1, '\\n')\n", + "print(\"2 A + Id:\\n\", 2 * A + np.identity(2), '\\n')\n", + "print(u\"A * A (element-wise product):\\n\", A * A, '\\n') # or np.square(A)\n", + "print(u\"A @ A (matrix or dot product):\\n\", A @ A) # or A.dot(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "You can transpose an array with `.T`. It does nothing with a 1D array, to make a horizontal vector or a vertical vector, you have to write it in 2D:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 3 5]] \n", + "\n", + " [[1]\n", + " [3]\n", + " [5]] \n", + "\n", + "Guess what v + v.T means:\n", + " [[ 2 4 6]\n", + " [ 4 6 8]\n", + " [ 6 8 10]]\n" + ] + } + ], + "source": [ + "v = np.array([[1,3,5]])\n", + "print(v, '\\n\\n', v.T, '\\n')\n", + "print(\"Guess what v + v.T means:\\n\", v + v.T)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Trigonometric functions and other usual mathematical functions are also available." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.841, 0.909],\n", + " [ 0.141, -0.757]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.set_printoptions(precision=3) # set printing precision for reals\n", + "np.sin(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Finally Numpy offers a set of methods to perform calculations on array elements:\n", + "\n", + "* `sum()` to sum all elements\n", + "* `mean()` to get the average of the elements and `average()` to get the weighted average,\n", + "* `prod()` to multiply all elements,\n", + "* `min()` and `max()` to get the minimum value and the maximum value,\n", + "* `argmin()` and `argmax()` to have the array indices of the minimum and maximum value,\n", + "* `cumsum()` and `cumprod()` for cumulative addition and multiplication,\n", + "* `diff()` to get the gap with the next element (useful to calculate a derivative).\n", + "\n", + "Each `A.sum()` method also exists as a `np.sum(A)` function." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.argmax()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 1, 1])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.diff(A.flatten())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Browse an array\n", + "\n", + "The natural way to browse all the elements of a multi-dimensional array is to make a loop for each dimension:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0 1\n", + " 2 3\n", + " 4 5\n" + ] + } + ], + "source": [ + "a = np.arange(6).reshape(3,2)\n", + "for ligne in a:\n", + " for element in ligne:\n", + " print(\" \", element, end=\"\") # end=\"\" avoid the return after each print\n", + " print()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We saw in the manipulation of the form of an array that we can make it flatter, but rather than using `flatten()` which makes an array in 1 dimension, we prefer to use `flat` which gives an [iterator](https://en.wikipedia.org/wiki/Iterator) to iterate through all the elements of the array." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n" + ] + } + ], + "source": [ + "for v in a.flat:\n", + " print(v)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It is also possible to make a loop on the indices but it is clearly less powerful." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n" + ] + } + ], + "source": [ + "for i in range(len(a)):\n", + " for j in range(len(a[i])):\n", + " print(a[i,j])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Think vector\n", + "\n", + "Making loops is often our way of thinking but it is not effective. It is better to\n", + "to work directly on the whole array. So rather than making the loop\n", + "\n", + "```\n", + "for i in range (len (x)):\n", + "   z[i] = x[i] + y[i]\n", + "```\n", + "\n", + "we will do\n", + "\n", + "```\n", + "z = x + y\n", + "```\n", + "   \n", + "Not only is it more readable but it is also faster." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.5 ms ± 494 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", + "35.3 ms ± 139 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", + "36.9 µs ± 156 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "def double_loop(a):\n", + " for i in range(a.shape[0]):\n", + " for j in range(a.shape[1]):\n", + " a[i,j] = np.sqrt(a[i,j]) # change in-place\n", + "\n", + "def iterate(a):\n", + " for x in a.flat:\n", + " x = np.sqrt(x) # modification not saved in a, x is a local var\n", + "\n", + "b = np.random.random(size=(200,200))\n", + "a = b.copy() # we need a copy to be sure to use the same data each time\n", + "%timeit double_loop(a)\n", + "\n", + "a = b.copy() \n", + "%timeit iterate(a)\n", + "\n", + "a = b.copy()\n", + "%timeit np.sqrt(a) # vectorial operation, 1000 times faster" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma1 np02 Filtres.ipynb b/PVCM/cama/en/ma1 np02 Filtres.ipynb new file mode 100644 index 0000000..61d0454 --- /dev/null +++ b/PVCM/cama/en/ma1 np02 Filtres.ipynb @@ -0,0 +1,411 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 1, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Let's look at how to extract pieces from an array or modify only some of its parts. For this, we\n", + "have two tools:\n", + " \n", + "* the extraction according to the indices\n", + "* the extraction by applying a logical filter on the values" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Filter by indices\n", + "\n", + "We can extract values from an array according to its indices as we did for lists. For each dimension of the table, you can indicate\n", + "\n", + "* the value of the desired index (an integer)\n", + "* a list of `start:end:jump` indices. Thus `1:6:2` means the odd values between index 1 and index 6 excluded. The `start`, `end` and `jump` values are optional:\n", + " * `:5` gives the first 5 values (indices 0,1,2,3 and 4)\n", + " * `3:` gives 4th to last values\n", + " * `::3` returns a value every 3 from the beginning to the end of the array.\n", + "* an explicit list of indices like `[1,3,-2]` (negative values means start from the end, hence `-2` is the penultimate index)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3]\n", + " [ 4 5 6 7]\n", + " [ 8 9 10 11]] \n", + "\n", + "[4 5 6 7] \n", + "\n", + "[[0 1]\n", + " [4 5]] \n", + "\n", + "[ 3 11] \n", + "\n", + "[[ 0 3]\n", + " [ 4 7]\n", + " [ 8 11]]\n" + ] + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "print(a, '\\n')\n", + "print(a[1, :], '\\n') # 2nd line\n", + "print(a[0:2, 0:2], '\\n') # top left sub-matrix\n", + "print(a[::2, -1], '\\n') # even lines, last column\n", + "print(a[:, [0,-1]]) # first and last column" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It is thus possible to indicate that an operation only applies to an extract from the table by indicating\n", + "which cells of the table will be modified:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 101, 2, 103],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 109, 10, 111]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[::2, 1::2] += 100\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It also makes it possible to simply write calculations such as extracting a grayscale image from a color image:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "image = np.random.randint(256, size=(800, 600, 3)) # RGB 800x600 image\n", + "gray_image = 0.2126 * image[:,:,0] + 0.7152 * image[:,:,1] + 0.0722 * image[:,:,2]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "You can also use `...` to replace multiple indices like `image[...,0] == image[:,:,0]`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Logical filters\n", + "\n", + "### A filter = a logical condition\n", + "\n", + "Numpy allows you to simply extract the values ​​that meet a logical condition.\n", + "\n", + "To do this, we use a filter, namely a Boolean array that is placed on an array of the same size, imagining that the True boxes are windows and False are walls. The result is the set of values ​​seen through the windows ordered by their index.\n", + "\n", + "The result is always a 1-dimensional array unless you use `where`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The filter a > 5 is\n", + " [[False False False False]\n", + " [False False True True]\n", + " [ True True True True]]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([ 6, 7, 8, 9, 10, 11])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "fil = a > 5 # a > 5 means all VALUES greater than 5\n", + "print(\"The filter a > 5 is\\n\", fil)\n", + "a[fil] # apply the filter and show the result (1D array)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It is easier and more readable to write the logical condition where we normally put the indices, namely between the square brackets:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 6, 7, 8, 9, 10, 11])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a>5]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### When the goal is the filter\n", + "\n", + "The filter can be used for something other than selecting values ​​from our array. It can be the result on which we want to work, for example for a population `fil = (age == weight)`. It is an array of Boolean which gives true cases and other false cases i.e. 0s and 1s.\n", + "\n", + "Thus, with a `fil` filter, we can know\n", + "\n", + "| | | |\n", + "|:-|:-|:-|\n", + "| how many cases are true: |`fil.sum()` | |\n", + "| if there is at least one true case: |`fil.sum() > 0` | Numpy also offers `np.any(fil)` |\n", + "| if all cases are true: |`fil.prod() == 1` | Numpy also offers `np.all(fil)` |\n", + "| if at least one case is false: |`fil.prod() == 0` |\n", + "|if all cases are false:| `fil.sum() == 0` |" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### `where` to handle non-filter values\n", + "\n", + "To preserve the shape of the array, it is necessary to tell it what to do with the values that do not meet the condition. To do this, we use the [`where`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html) function:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 0, 0, 0],\n", + " [ 0, 0, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.where(a > 5, a, 0) # if a > 5 then a else 0" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We can make all imaginable filters that give a boolean array." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, -1, -1, 6],\n", + " [-1, -1, 12, -1],\n", + " [-1, 18, -1, -1]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.where(a%3 == 0, 2*a, -1) # if a modulo 3 is 0 then 2 times a else -1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Update a table with a filter\n", + "\n", + "Another way to maintain the shape of the array is to change only the values ​​that match the filter." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 200, 200],\n", + " [200, 200, 200, 200]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "a[a > 5] = 200\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Here's how to add 100 to all values ​​in the array that are perfect squares as well as to the value 5:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[100, 101, 2, 3],\n", + " [104, 105, 6, 7],\n", + " [ 8, 109, 10, 11]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "a[(np.round(np.sqrt(a)) - np.sqrt(a) == 0) | (a==5)] += 100 # | is OR (AND is &)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "variables": { + " PreviousNext(\"np01 Numpy Introduction.ipynb\", \"np03 Manipulations.ipynb\")": "                                                                                                                                                                                                                                                                                                                                                                                                               
np01 Numpy Introduction  ← △ →  np03 Manipulations

 " + } + }, + "source": [ + "{{ PreviousNext(\"np01 Numpy Introduction.ipynb\", \"np03 Manipulations.ipynb\")}}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma1 np03 Manipulations.ipynb b/PVCM/cama/en/ma1 np03 Manipulations.ipynb new file mode 100644 index 0000000..3d713e9 --- /dev/null +++ b/PVCM/cama/en/ma1 np03 Manipulations.ipynb @@ -0,0 +1,821 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "[Array manipulations](https://docs.scipy.org/doc/numpy-1.15.1/reference/routines.array-manipulation.html) include:\n", + "\n", + "* the reorganization of the table (reindexing)\n", + "* the aggregation of 2 or more arrays\n", + "* the division of a table in 2 or more\n", + "\n", + "Before looking at these points, let's look at how Numpy presents the\n", + "dimensions of a multidimensional array with the notion of axes." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2, 4, 3)" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "# An array of marks of 3 exams for 4 students in two subjects \n", + "# (therefore 6 marks per students or 12 per subjects)\n", + "\n", + "# stud.1 stud.2 stud.3 stud.4\n", + "marks = np.array([[[7,13,11], [7,7,13], [5,9,11], [7,17,15]], # subject 1\n", + " [[8,12,14], [8,12,12], [8,12,10], [12,16,12]]]) # subject 2\n", + "marks.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## The axes\n", + "\n", + "A table has axes which correspond to the axes of a coordinate system in space. The order of the axes\n", + "is that of the inclusion of square brackets. In 2D an array of array is an array of rows with\n", + "each row which is a 1D array of values. The order is therefore rows then columns (unlike the $(x,y)$ axis in\n", + "space). In 3D the order is line, column, depth if you want to have an image, otherwise it's 0, 1 and 2.\n", + "\n", + "Many operations on tables are done along one of the axes of the table so it is important to\n", + "understand what axes are.\n", + "\n", + "Let's look at the example notes above. The axes are\n", + "\n", + "0. materials\n", + "1. students\n", + "2. exams" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Making the average of the values along axis 1 means to take data along axis 1 and performing the calculations on it, so here outputting an average." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 6.5, 11.5, 12.5],\n", + " [ 9. , 13. , 12. ]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "marks.mean(axis=1) # give means for each exam in each subject" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Another way to look at axes is to think of them as __projection axes__. If I project a 3D object\n", + "along the $y$ axis, the result is a 2D object in $(x,z)$. There is thus a reduction in dimension.\n", + "\n", + "If I sum on the 0 axis an array of dimension (2,4,3) as is our marks array, this means that I lose the 0 dimension and therefore the dimension of the result is (4,3)." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(4, 3)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "marks.mean(axis=0).shape # mean along axis 0 (subjects) therefore this axis disapears" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Some functions that support axes\n", + "\n", + "All functions that apply a set of values to produce a result\n", + "should be able to use axis concept (I don't have them all\n", + "checked but do not hesitate to give me a counter-example). We have the following mathematical functions:\n", + "\n", + "* arithmetic: `sum`, `prod`, `cumsum`, `cumprod`\n", + "* statistics: `min`, `max`, `argmin`, `argmax`, `mean` (average), `average` (weighted average), `std` (standard deviation), `var`, `median `, `percentile`, `quantile`\n", + "* others: `gradient`, `diff`, `fft`\n", + "\n", + "Moreover, it is possible to sort the values of an array according to the axis of your choice with `sort`.\n", + "However, they can be mixed, with [`shuffle`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.random.shuffle.html#numpy.random.shuffle ), only along the 0 axis.\n", + "\n", + "#### Apply a function along an axis\n", + "\n", + "The function [`apply_along_axis`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.apply_along_axis.html)\n", + "allows to apply a 1D functionto a table along an axis. This is the axis that will disappear in the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-> [ 7 13 11] 6\n", + "-> [ 7 7 13] 6\n", + "-> [ 5 9 11] 6\n", + "-> [ 7 17 15] 10\n", + "-> [ 8 12 14] 6\n", + "-> [ 8 12 12] 4\n", + "-> [ 8 12 10] 4\n", + "-> [12 16 12] 4\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[ 6, 6, 6, 10],\n", + " [ 6, 4, 4, 4]])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def diff_min_max(a):\n", + " print('->', a, a.max() - a.min())\n", + " return a.max() - a.min()\n", + "\n", + "np.apply_along_axis(diff_min_max, axis=-1, arr=marks) # -1 is the last axis, marks in our case" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Question: this is the difference between the marks, but which ones?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Apply a function along several axes\n", + "\n", + "Some operations may take a list of axes and not a single axis." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a.max \n", + " [17 16] \n", + "\n", + "a.max keepdim \n", + " [[[17]]\n", + "\n", + " [[16]]] \n", + "\n" + ] + } + ], + "source": [ + "print('a.max \\n', marks.max(axis=(1,2)), '\\n') \n", + "print('a.max keepdim \\n', marks.max(axis=(1,2), keepdims=True), '\\n') " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Question: what do the 2 output values ​​correspond to?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "One can also use the function [`apply_over_axes`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.apply_over_axes.html#numpy.apply_over_axes) to apply a\n", + "function along the given axes.\n", + "\n", + "Beware, the function given in argument will receive the whole table and the axis on which it must\n", + "work, the axes being given one after the other and the table being modified at each stage." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Apply over axis 1\n", + "[[[ 7 13 11]\n", + " [ 7 7 13]\n", + " [ 5 9 11]\n", + " [ 7 17 15]]\n", + "\n", + " [[ 8 12 14]\n", + " [ 8 12 12]\n", + " [ 8 12 10]\n", + " [12 16 12]]] \n", + "\n", + "Apply over axis 2\n", + "[[[ 7 17 15]]\n", + "\n", + " [[12 16 14]]] \n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[[17]],\n", + "\n", + " [[16]]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def mymax(array, axis):\n", + " print('Apply over axis', axis)\n", + " print(array, '\\n')\n", + " return array.max(axis)\n", + "\n", + "np.apply_over_axes(mymax, marks, axes=(1,2))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Arranging a table\n", + "\n", + "We have already seen `reshape` to change the shape of an array, `flatten` to flatten it in 1 dimension, let's have a look at\n", + "other array manipulation functions.\n", + "\n", + "### Reorder axes\n", + "\n", + "#### `moveaxis` moves an axis\n", + "\n", + "In our marks example, the 3 axes are subjects, students and exams.\n", + "The `moveaxis` function is used to move an axis. If so I want the exams to become the first axis\n", + "in order to make the marks stand out, I move axis 2 to position 0 and the other axes slide to make room, axis 0 becomes axis 1 and axis 1 becomes axis 2:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "marks.shape = (2, 4, 3) \n", + "\n", + "b.shape = (3, 2, 4)\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[[ 7, 7, 5, 7],\n", + " [ 8, 8, 8, 12]],\n", + "\n", + " [[13, 7, 9, 17],\n", + " [12, 12, 12, 16]],\n", + "\n", + " [[11, 13, 11, 15],\n", + " [14, 12, 10, 12]]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print('marks.shape = ',marks.shape, '\\n')\n", + "b = np.moveaxis(marks, 2, 0) \n", + "print('b.shape = ', b.shape)\n", + "b" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It is easier to see that the first examination was difficult." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### `swapaxes` 2 axis swap\n", + "\n", + "Rather than inserting one axis at a new position and dragging the others, you may want to swap two of them.\n", + "Here is how to get the marks for each subject and for each exam:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[ 7, 7, 5, 7],\n", + " [13, 7, 9, 17],\n", + " [11, 13, 11, 15]],\n", + "\n", + " [[ 8, 8, 8, 12],\n", + " [12, 12, 12, 16],\n", + " [14, 12, 10, 12]]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "marks.swapaxes(1,2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### `transpose` to do everything\n", + "\n", + "Finally `transpose` allows you to reorder all the axes as you want, thus: `transpose((2,0,1))` puts\n", + "\n", + "* axis 2 in position 0,\n", + "* axis 0 in place 1\n", + "* axis 1 in place 2.\n", + "\n", + "#### A simpler and faster apply over axis\n", + "\n", + "Unfortunately the `apply_over_axis` function is not optimized, so in some cases it may\n", + "be preferable to make a loop on its table, which means to put the axes which will remain at the beginning and those on which we make our reduction at the end:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Means per students [10.833333333333334, 9.833333333333334, 9.166666666666666, 13.166666666666666]\n", + "24 µs ± 2.01 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n", + "29.6 µs ± 1.23 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "print(\"Means per students\", [m.mean() for m in marks.transpose((1,0,2))])\n", + "\n", + "%timeit [m.mean() for m in marks.transpose((1,0,2))]\n", + "%timeit np.apply_over_axes(np.mean, marks, axes=(0,2))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Changing the order of array elements\n", + "\n", + "You can flip the values ​​of an array along an axis with [`flip`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.flip.html#numpy.flip )\n", + "which can also be done by indicating it at the level of the indices. Thus `np.flip(a, n)` is equivalent to\n", + "`a[:,:,..,::-1,:,..,:]` with `::-1` in $n$-th position." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[12, 13, 14, 15],\n", + " [16, 17, 18, 19],\n", + " [20, 21, 22, 23]],\n", + "\n", + " [[ 0, 1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11]]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(24).reshape([2,3,4])\n", + "np.flip(a,0)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "You can roll values along an axis with `roll` by specifying how much to slide them:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11],\n", + " [ 0, 1, 2, 3]],\n", + "\n", + " [[16, 17, 18, 19],\n", + " [20, 21, 22, 23],\n", + " [12, 13, 14, 15]]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.roll(a, 2, axis=1) # roll elements by 2 along axis 1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The transpose also applies regardless of the dimension. By default it reverses the order of the axes but you can\n", + "specify the desired output order." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[ 0, 12],\n", + " [ 4, 16],\n", + " [ 8, 20]],\n", + "\n", + " [[ 1, 13],\n", + " [ 5, 17],\n", + " [ 9, 21]],\n", + "\n", + " [[ 2, 14],\n", + " [ 6, 18],\n", + " [10, 22]],\n", + "\n", + " [[ 3, 15],\n", + " [ 7, 19],\n", + " [11, 23]]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.T" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[ 0, 4, 8],\n", + " [ 1, 5, 9],\n", + " [ 2, 6, 10],\n", + " [ 3, 7, 11]],\n", + "\n", + " [[12, 16, 20],\n", + " [13, 17, 21],\n", + " [14, 18, 22],\n", + " [15, 19, 23]]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.transpose(a, (0,2,1))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Aggregation\n", + "\n", + "### Concatenation\n", + "\n", + "The basic function is [`concatenate`](https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.concatenate.html) indicating the axis chosen for concatenation. This is, in my opinion, the method\n", + "the safest and it works whatever the size.\n", + "\n", + "However, for 2D or 3D arrays, we can use:\n", + "\n", + "* `vstack` or `row_stack` for vertical concatenation\n", + "* `hstack` or `column_stack` for horizontal concatenation\n", + "* `dstack` for deep concatenation\n", + "\n", + "All of these functions take a list of arrays to concatenate as an argument. Of course the sizes of the tables must be compatible." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. 0.]\n", + " [0. 0. 0.]\n", + " [1. 1. 1.]\n", + " [1. 1. 1.]] \n", + "\n", + "[[0. 0. 0. 1. 1. 1.]\n", + " [0. 0. 0. 1. 1. 1.]]\n" + ] + } + ], + "source": [ + "a = np.zeros((2,3))\n", + "b = np.ones((2,3))\n", + "\n", + "print(np.concatenate((a,b), axis=0), '\\n') # same than vstack\n", + "print(np.hstack((a,b))) # same than concatenate with axis=1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Stacking\n", + "\n", + "Unlike concatenation, stacking adds dimension.\n", + "Stack is useful for storing a bunch of 2D arrays, images for example, in a 3D array.\n", + "We use the function [`stack`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.stack.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[0., 0., 0.],\n", + " [0., 0., 0.]],\n", + "\n", + " [[1., 1., 1.],\n", + " [1., 1., 1.]]])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = np.stack((a,b)) # c[0] is a\n", + "c" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Note that `stack` has an `axis` option to indicate the direction in which one wishes to store the given arrays." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Splitting\n", + "\n", + "The inverse function of concatenation is splitting with [`split`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.split.html#numpy.split) which asks as arguments:\n", + "\n", + "* the array to split\n", + "* in how many pieces or at what indices\n", + "* the direction (the axis)\n", + "\n", + "To find our two tables that generated the result of the previous cell, we cut in 2 along the 0 axis. We can also cut along another axis." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "split part 1\n", + " [[[0. 0. 0.]]\n", + "\n", + " [[1. 1. 1.]]] \n", + "\n", + "split part 2\n", + " [[[0. 0. 0.]]\n", + "\n", + " [[1. 1. 1.]]]\n" + ] + } + ], + "source": [ + "e,f = np.split(c, 2, 1) # splits in 2 along axis 1\n", + "print(\"split part 1\\n\", e, '\\n')\n", + "print(\"split part 2\\n\", f)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "There are also `hsplit`, `vsplit` and `dsplit` to split along axes 0, 1 and 2.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## From Python to Numpy\n", + "\n", + "If you want to dig and look at many examples, you can read N. Rougier's book [From Python to Numpy](https://www.labri.fr/perso/nrougier/from-python-to-numpy/)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Pandas too\n", + "\n", + "We will find these manipulations with Pandas which is the super spreadsheet of Python. It also works on\n", + "array-like structures but without the constraint that all values are of the same type." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "variables": { + " PreviousNext(\"np02 Filtres.ipynb\", \"np04 Xarray.ipynb\")": "                                                                                                                                                                                                                                                                                                                                                                                                               
np02 Filtres  ← △ →  np04 Xarray

 " + } + }, + "source": [ + "{{ PreviousNext(\"np02 Filtres.ipynb\", \"np04 Xarray.ipynb\")}}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma1 np05 Notation Einstein.ipynb b/PVCM/cama/en/ma1 np05 Notation Einstein.ipynb new file mode 100644 index 0000000..4882e5f --- /dev/null +++ b/PVCM/cama/en/ma1 np05 Notation Einstein.ipynb @@ -0,0 +1,318 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Introduction to Einstein Notation\n", + "\n", + "This notation allows for expressing an extraordinary number of operations concisely. This section is not\n", + "necessary for the following but it is an interesting intellectual exercise.\n", + "\n", + "The basic idea is to sum the terms of an equation when the same index appears twice and is not defined elsewhere. Thus:\n", + "\n", + "$$ A_{i,i} \\quad \\textrm{means} \\quad \\sum_{i=1}^N A_{i,i} \\; \\textrm{(the trace of the matrix)}$$\n", + "\n", + "If we look at the matrix multiplication $A\\, B$, for every index (i,j) of the result we have:\n", + "\n", + "$$ C_{i,j} = A_{i,k} \\, B_{k,j} \\quad \\textrm{i.e.} \\quad C_{i,j} = \\sum_{k=1}^N A_{i,k} \\, B_{k,j} $$ \n", + "\n", + "The full name of the Einstein notation being the Einstein summation convention, the Numpy function is [`einsum`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.einsum.html). Here is how it works for our first 2 examples:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Trace 'ii' : 12 \n", + "\n", + "Multiplication matricielle A A 'ij,jk->ik' :\n", + "[[ 15 18 21]\n", + " [ 42 54 66]\n", + " [ 69 90 111]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "A = np.arange(9).reshape(3,3)\n", + "\n", + "print(\"Trace 'ii' : \", np.einsum('ii', A), '\\n') # 0 + 4 + 8 = 12\n", + "\n", + "print(\"Multiplication matricielle A A 'ij,jk->ik' :\")\n", + "print(np.einsum('ij,jk->ik', A, A)) # notez que j'ai nommé différement les indices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 15, 18, 21],\n", + " [ 42, 54, 66],\n", + " [ 69, 90, 111]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.dot(A) # on vérifie" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It is noted that the arguments of `einsum` are:\n", + "\n", + "* the summation rule in a string with a comma to separate each component\n", + "* the components on which the rule applies\n", + "\n", + "We can go a little further with Numpy. Here are all the rules that `einsum` uses:\n", + "\n", + "#### Basic and additional rules\n", + "\n", + "1. a repeated index implies summation over that index unless that index is mentioned in the result
(see example of the diagonal of A below for the exception)\n", + "2. indices that repeat from one component to another imply that the referenced elements will be multiplied together
(see example of the matrix product)\n", + "3. a letter omitted in the result (after `->`) implies summation over that index
(see example of summing the elements of a vector below)\n", + "4. if you don't put the arrow, einsum will put it for you with on the right all the indices that are not doubled arranged in alphabetical order
(see example of the transpose below)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Here is a list of operations taken from the [blog of Dr. Goulu](https://www.drgoulu.com/2016/01/17/einsum):\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
einsum SignatureNumpy EquivalentDescription
('i->', v)sum(v)sum of values of vector v
('i,i->i', u, v)u \\* velement-wise multiplication of vectors u and v
('i,i', u, v)inner(u, v)dot product of u and v
('i,j', u, v)outer(u, v)dyadic product of u and v
('ij', A)Areturns matrix A
('ji', A)A.Ttranspose of A
('ii->i', A)diag(A)diagonal of A
('ii', A)trace(A)sum of the diagonal of A
('ij->', A)sum(A)sum of values of A
('ij->j', A)sum(A, axis=0)sum of columns of A
('ij->i', A)sum(A, axis=1)sum of rows of A
('ij,ij->ij', A, B)A \\* Belement-wise transposed matrix multiplication of A and B
('ij,jk', A, B)dot(A, B)dot product of A and B
('ij,jk->ij', A, B)inner(A, B)inner product of A and B
('ij,jk->ijk', A, B)A[:, None] \\* Beach row of A multiplied by B
('ij,kl->ijkl', A, B)A[:, :, None, None] \\* Beach value of A multiplied by B
\n", + "\n", + "The `None` in the last two lines is a way to reshape an array. So `np.arange(6)` is a 1-dimensional array, `np.arange(6)[:]` is the same 1-dimensional array, while `np.arange(6)[:,None]` is a 2-dimensional array namely `6 x 1` when `np.arange(6)[None,:,None]` has 3 dimensions: `1 x 6 x 1`." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Practical Application\n", + "\n", + "We will compare the performance of `einsum` and the corresponding Numpy functions. To do this, calculate\n", + "\n", + "* the cube of each element of a vector\n", + "* of a square matrix, $A^3$,\n", + "\n", + "with `einsum` and without. Compare the execution speed in all cases with 10000 elements." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# a vous de jouer\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solution :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "11.5 µs ± 112 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n", + "15.2 µs ± 131 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n" + ] + } + ], + "source": [ + "u = np.random.random(10000)\n", + "\n", + "%timeit u*u*u\n", + "%timeit np.einsum('i,i,i->i', u,u,u)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "138 µs ± 9.48 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n", + "134 ms ± 1.12 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "A = u.reshape(100,100)\n", + "\n", + "%timeit A.dot(A).dot(A)\n", + "%timeit np.einsum('ij,jk,kl->il', A, A, A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We observe that `einsum` is slower (\\*). But looking on the web, we see that this has not always been the case and that it is related to the version of the Numpy library. In conclusion, if we want performance, we should test our code beforehand to choose the fastest method.\n", + "\n", + "(\\*) slightly slower for vector calculation but 1000 times slower on my laptop for `A.dot(A)` (all my processors are running at 100% while the calculation by `einsum` is only done on 1 processor). The `A.dot(A)` version is much faster thanks to the MKL library used by Numpy on my machine." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma1 np06 Linalg pour le calcul matriciel.ipynb b/PVCM/cama/en/ma1 np06 Linalg pour le calcul matriciel.ipynb new file mode 100644 index 0000000..7edc3b1 --- /dev/null +++ b/PVCM/cama/en/ma1 np06 Linalg pour le calcul matriciel.ipynb @@ -0,0 +1,425 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 1, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Linalg (linear algebra)\n", + "\n", + "Numpy integrates matrix calculus (or linear algebra) in its sub-library [numpy.linalg](https://docs.scipy.org/doc/numpy/reference/routines.linalg.html). To be effective it is\n", + "important that Numpy is linked to the [Lapack](https://www.netlib.org/lapack/) and [BLAS](https://www.netlib.org/blas/) libraries (Intel's version is [ MKL](https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl.html)). These libraries are unbeatable, Numpy linked to these libraries will be much faster than a program in any other language that does not use them (you take up the challenge?).\n", + "\n", + "The [Scipy](https://scipy.org/) library also has a [linalg](https://docs.scipy.org/doc/scipy/reference/linalg.html) sub-library which is very similar. If you can't find\n", + "what you're looking for in Numpy's version, it might be worth looking to see if Scipy has it." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "blas_mkl_info:\n", + " NOT AVAILABLE\n", + "blis_info:\n", + " NOT AVAILABLE\n", + "openblas_info:\n", + " libraries = ['openblas', 'openblas']\n", + " library_dirs = ['/usr/local/lib']\n", + " language = c\n", + " define_macros = [('HAVE_CBLAS', None)]\n", + " runtime_library_dirs = ['/usr/local/lib']\n", + "blas_opt_info:\n", + " libraries = ['openblas', 'openblas']\n", + " library_dirs = ['/usr/local/lib']\n", + " language = c\n", + " define_macros = [('HAVE_CBLAS', None)]\n", + " runtime_library_dirs = ['/usr/local/lib']\n", + "lapack_mkl_info:\n", + " NOT AVAILABLE\n", + "openblas_lapack_info:\n", + " libraries = ['openblas', 'openblas']\n", + " library_dirs = ['/usr/local/lib']\n", + " language = c\n", + " define_macros = [('HAVE_CBLAS', None)]\n", + " runtime_library_dirs = ['/usr/local/lib']\n", + "lapack_opt_info:\n", + " libraries = ['openblas', 'openblas']\n", + " library_dirs = ['/usr/local/lib']\n", + " language = c\n", + " define_macros = [('HAVE_CBLAS', None)]\n", + " runtime_library_dirs = ['/usr/local/lib']\n", + "Supported SIMD extensions in this NumPy install:\n", + " baseline = SSE,SSE2,SSE3\n", + " found = SSSE3,SSE41,POPCNT,SSE42,AVX,F16C,FMA3,AVX2\n", + " not found = AVX512F,AVX512CD,AVX512_KNL,AVX512_KNM,AVX512_SKX,AVX512_CLX,AVX512_CNL,AVX512_ICL\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3)\n", + "np.show_config()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Basic operations\n", + "\n", + "We have seen that the operators +, -, \\*and / are applied term by term which is correct for + and - in the context of matrix calculation but not for \\* and /.\n", + "\n", + "* The __dot product__ uses the `dot` method or the `@` operator\n", + "* The division that we can imagine as\n", + " * the __resolution__ of a matrix system uses the `solve` function\n", + " * the calculation of the __inverse__ of the matrix uses the `inv` function" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "multiplication terme à terme : \n", + " [[ 1 4]\n", + " [ 9 16]]\n", + "produit matriciel : \n", + " [[ 7 10]\n", + " [15 22]]\n" + ] + } + ], + "source": [ + "A = np.array([[1,2],[3,4]])\n", + "print(\"multiplication terme à terme : \\n\",A * A) # tous les opérateurs sont appliqués terme à terme\n", + "print(\"produit matriciel : \\n\", A.dot(A)) # A @ A can be used too" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Matrix system resolution:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [3. 7.]\n", + "verification : [17. 37.]\n" + ] + } + ], + "source": [ + "b = np.array([17,37])\n", + "x = lin.solve(A, b) # bien mieux que de calculer la matrice inverse (plus rapide et plus stable)\n", + "print(\"x = \", x)\n", + "print(\"verification : \", A @ x)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "If you really want to, you can calculate the inverse matrix (but it takes longer):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A⁻¹ :\n", + " [[-2. 1. ]\n", + " [ 1.5 -0.5]]\n", + "x = [3. 7.]\n" + ] + } + ], + "source": [ + "print(\"A⁻¹ :\\n\", lin.inv(A)) # la matrice inverse\n", + "print(\"x = \", lin.inv(A).dot(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Finally __the transpose__ is simply `T`:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 3],\n", + " [2, 4]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.T" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Extraction\n", + "\n", + "We can extract\n", + "\n", + "* the diagonal of a matrix with the `diag` function (note the result is a vector if the argument is a matrix and a matrix if the argument is a vector)\n", + "* the lower triangular matrix with the function `tril` (l for lower) and upper with `triu` (u for upper). It is possible to shift the diagonal of the triangle, see the doc\n", + "\n", + "We can also construct a triangular matrix with 1s and 0s with `tri` and therefore also any triangular matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4., 0., 0.],\n", + " [8., 9., 0.],\n", + " [5., 5., 4.]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.tri(3,3) * np.random.randint(1, 10, size=(3,3))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "And here is how to extract a tridiagonal matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[3, 7, 0, 0, 0],\n", + " [6, 1, 8, 0, 0],\n", + " [0, 3, 5, 9, 0],\n", + " [0, 0, 4, 4, 7],\n", + " [0, 0, 0, 6, 3]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.random.randint(1, 10, size=(5,5))\n", + "np.tril(np.triu(A, k=-1), k=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Matrix operations\n", + "\n", + "The library provides functions for\n", + "\n", + "* decomposition (LU, Choleski, QR, SVD...)\n", + "* eigenvalues and eigenvectors\n", + "* norm, determinant, conditioning and rank" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-0.349 0.585 0.132 0.359 0.624]\n", + " [-0.697 -0.557 0.221 -0.298 0.257]\n", + " [-0.465 -0.061 -0.052 0.668 -0.576]\n", + " [-0.349 0.585 0.132 -0.564 -0.447]\n", + " [-0.232 0.036 -0.956 -0.134 0.115]] \n", + "\n", + " [[ -8.602 -7.44 -10.927 -13.252 -10.23 ]\n", + " [ 0. 7.527 -0.039 3.907 7.559]\n", + " [ 0. 0. 1.61 -3.513 -0.301]\n", + " [ 0. 0. 0. 4.333 0.656]\n", + " [ 0. 0. 0. 0. 1.302]]\n", + "\n", + "Vérification :\n", + " [[3. 7. 4. 8. 9.]\n", + " [6. 1. 8. 5. 3.]\n", + " [4. 3. 5. 9. 4.]\n", + " [3. 7. 4. 4. 7.]\n", + " [2. 2. 1. 6. 3.]]\n" + ] + } + ], + "source": [ + "Q,R = lin.qr(A) # Q est orthogonale, R est triangulaire supérieur\n", + "print(Q, '\\n\\n', R)\n", + "print(\"\\nVérification :\\n\", Q.dot(R))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Eigenvalues ​​and eigenvectors" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([23.099+0.j , -3.442+1.822j, -3.442-1.822j, -1.408+0.j ,\n", + " 1.192+0.j ]),\n", + " array([[-0.547+0.j , -0.191+0.047j, -0.191-0.047j, -0.51 +0.j ,\n", + " 0.487+0.j ],\n", + " [-0.457+0.j , -0.035-0.466j, -0.035+0.466j, -0.462+0.j ,\n", + " -0.423+0.j ],\n", + " [-0.476+0.j , 0.441+0.128j, 0.441-0.128j, 0.41 +0.j ,\n", + " -0.519+0.j ],\n", + " [-0.447+0.j , -0.536+0.j , -0.536-0.j , -0.167+0.j ,\n", + " -0.101+0.j ],\n", + " [-0.257+0.j , 0.435+0.233j, 0.435-0.233j, 0.575+0.j ,\n", + " 0.552+0.j ]]))" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lin.eig(A) # donne les valeurs propres et les vecteurs propres de A" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Determinant, norm etc." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Déterminant : -587.9999999999999\n", + "Norme 2 : 26.343879744638983 \n", + "Norme 1 : 32.0\n", + "Conditionnement : 35.929347867977604\n" + ] + } + ], + "source": [ + "print(\"Déterminant :\", lin.det(A))\n", + "print(\"Norme 2 :\", lin.norm(A), \"\\nNorme 1 :\", lin.norm(A, 1) )\n", + "print(\"Conditionnement :\", lin.cond(A,2)) # I choose norm 2 to compute the condition number" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma1 np90 petits exercices.ipynb b/PVCM/cama/en/ma1 np90 petits exercices.ipynb new file mode 100644 index 0000000..fd79b8d --- /dev/null +++ b/PVCM/cama/en/ma1 np90 petits exercices.ipynb @@ -0,0 +1,430 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Numpy - Exercises\n", + "\n", + "Here is a series of tests to check your knowledge in Numpy. The goal is for this library and the vectorized programming it implies to become natural. You should forget about classic programming with loops (do not use a `for` loop or anything else in this notebook except for list comprehension).\n", + "\n", + "Functions should never modify their arguments.\n", + "\n", + "The exercises indicate the number of lines in the answer. This includes the function header when there is one.\n", + "\n", + "Remember to test your results." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8c0a79d0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3]\n", + " [ 4 5 6 7]\n", + " [ 8 9 10 11]] \n", + "\n", + "[[ 3 -8 -8 -4 7]\n", + " [ 9 0 -9 -10 7]\n", + " [ 5 -1 -10 4 -10]\n", + " [ 5 9 4 -6 -10]\n", + " [ 6 -6 7 -7 -8]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "rand = np.random.RandomState(123)\n", + "\n", + "A = np.arange(12).reshape(3,4)\n", + "B = rand.randint(-10, 10, size=(5,5))\n", + "print(A, '\\n')\n", + "print(B)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Square Matrix\n", + "\n", + "Create the 5x5 square matrix containing the first 25 integers, from 1 to 25.\n", + "\n", + "1 line" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "14ccdaf5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1, 2, 3, 4, 5],\n", + " [ 6, 7, 8, 9, 10],\n", + " [11, 12, 13, 14, 15],\n", + " [16, 17, 18, 19, 20],\n", + " [21, 22, 23, 24, 25]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Vector Norm\n", + "\n", + "Return the Euclidean norm of a vector without using the `norm` function.\n", + "\n", + "2 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "079b9d00", + "metadata": {}, + "outputs": [], + "source": [ + "def norm(v):\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Sub-Matrix\n", + "\n", + "Extract the sub-matrix of size (n-2)x(m-2) that removes the borders of the nxm matrix A.\n", + "\n", + "2 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1c313908", + "metadata": {}, + "outputs": [], + "source": [ + "def submat(A):\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Random Vector\n", + "\n", + "Create a function that takes a size n and returns a random integer vector of size n between -a and +a and centered as close as possible to 0.\n", + "\n", + "3 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e93d8900", + "metadata": {}, + "outputs": [], + "source": [ + "def rand_vec(n, a):\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Trace\n", + "\n", + "Return the trace of a matrix without using the `trace` function (you have to find the missing elements yourself).\n", + "\n", + "2 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "8df7f55b", + "metadata": {}, + "outputs": [], + "source": [ + "def trace(A):\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Matrix of Multiples of 3\n", + "\n", + "Round the given matrix to the nearest multiple of 3 (for each value).\n", + "\n", + "2 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "55860b91", + "metadata": {}, + "outputs": [], + "source": [ + "def round3(A):\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Count of 9s\n", + "\n", + "Count the number of 9s in an integer matrix A given as a parameter.\n", + "\n", + "2 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "9296a705", + "metadata": {}, + "outputs": [], + "source": [ + "def nb9(A):\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Column with the Smallest Average\n", + "\n", + "Return the index of the column of a matrix with the smallest average.\n", + "\n", + "2 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c3c9d6a1", + "metadata": {}, + "outputs": [], + "source": [ + "def min_col_mean(A):\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### ChessSum\n", + "\n", + "We consider the matrix as a chessboard with alternating white and black squares. The square at [0,0] is black. \n", + "Calculate the sum of the values on the white squares.\n", + "\n", + "2 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "3921063c", + "metadata": {}, + "outputs": [], + "source": [ + "def chess_sum(A):\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### 2 Minimums\n", + "\n", + "Return the 2 smallest values of a matrix using a method with linear complexity. Note that if the matrix has its minimum value duplicated, the answer is twice this minimum value.\n", + "\n", + "6 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "b680cc53", + "metadata": {}, + "outputs": [], + "source": [ + "def mins(A):\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Rows in Order\n", + "\n", + "Sort the rows of a matrix in ascending order of their average.\n", + "\n", + "2 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "5784c5be", + "metadata": {}, + "outputs": [], + "source": [ + "def sort_lines(A):\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Unique Values\n", + "\n", + "Provide the list of unique values (appearing only once) in a numpy array (the `unique` function will be useful).\n", + "\n", + "3 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "c95ce1bb", + "metadata": {}, + "outputs": [], + "source": [ + "def val_unique(A):\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Magic Tensor\n", + "\n", + "Construct a 3D tensor of size nxnxn using n times the first n² integers and such that the sum of the elements of each plane (slice) is always the same.\n", + "\n", + "3 lines" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c1ca40c0", + "metadata": {}, + "outputs": [], + "source": [ + "def mk_magic_tensor(n):\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Tensor Slices\n", + "\n", + "Extract all the slices of a 3D tensor. We return a list of arrays.\n", + "\n", + "5 lines (2 lines with the `take` function)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "e4d39b2a", + "metadata": {}, + "outputs": [], + "source": [ + "def extract_planes(T):\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "761e6ee4", + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma20 Rappels sur les matrices.ipynb b/PVCM/cama/en/ma20 Rappels sur les matrices.ipynb new file mode 100644 index 0000000..fbd8389 --- /dev/null +++ b/PVCM/cama/en/ma20 Rappels sur les matrices.ipynb @@ -0,0 +1,530 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "**Note**: The Python code must be ignored until the first lab." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def arrow2D(a,b, color='k', text=\"\", **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " a,b = np.array(a), np.array(b)\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))\n", + " direction = (b - a) / np.sqrt(np.square(b - a).sum())\n", + " plt.text(*(b + 0.1 * direction), r\"$\\bf\" + text + r\"$\", horizontalalignment='center', size=14)\n", + " \n", + "def vector(v, color='k', text='', **kargs):\n", + " arrow2D([0,0], v, color, text)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Vector\n", + "\n", + "A vector is\n", + "\n", + "* an arrow that indicates a direction and whose length measures an intensity (physicist's vision)\n", + "* a table with 2 values in 2D or 3 in 3D (computer vision)\n", + "* a concept that verifies certain properties (mathematician's view)\n", + "\n", + "As part of this course we focus on the first 2 visions and we add\n", + "\n", + "* a vector at its origin at (0,0)\n", + "\n", + "From a typographical point of view, vectors are denoted with an arrow $\\vec v$ or in bold $\\bf v$. We will use this last notation in this course. A vector function (which returns a vector) is denoted as a $\\bf f(\\,)$." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 287, + "width": 572 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "vector([3,2], 'b', \"v\")\n", + "vector([-2,1], 'g', \"w\")\n", + "vector([-1,-1.5], 'r')\n", + "plt.gca().spines[:].set_position('zero')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The basic vector operations are\n", + "\n", + "* addition\n", + "$$ \\begin{bmatrix}\n", + " v_1 \\\\\n", + " v_2\n", + " \\end{bmatrix} \n", + " +\n", + " \\begin{bmatrix}\n", + " w_1 \\\\\n", + " w_2\n", + " \\end{bmatrix} \n", + " = \n", + " \\begin{bmatrix}\n", + " v_1 + w_1 \\\\\n", + " v_2 + w_2\n", + " \\end{bmatrix} \n", + "$$\n", + "* multiplication by a scalar:\n", + "$$\n", + " α \\,\n", + " \\begin{bmatrix}\n", + " w_1 \\\\\n", + " w_2\n", + " \\end{bmatrix} \n", + " =\n", + " \\begin{bmatrix}\n", + " α \\, w_1 \\\\\n", + " α \\, w_2\n", + " \\end{bmatrix} \n", + "$$\n", + "\n", + "Of course vectors exist in 3D and in any dimension." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Matrices and linear maps\n", + "\n", + "The matrices are\n", + "\n", + "* a representation of a linear map (mathematician's vision)\n", + "* a 2D table (vision of a computer scientist who didn't understand everything)\n", + "* a very practical tool to do many things\n", + "\n", + "A ${\\bf f}$ map or transformation is said to be linear if it satisfies:\n", + "\n", + "* ${\\bf f(v)} + {\\bf f(w)} = {\\bf f(v + w)}$\n", + "* ${\\bf f}(α \\, {\\bf v}) = α \\, {\\bf f(v)}$ with α a scalar.\n", + "\n", + "This offers 2 properties:\n", + "\n", + "* the origin (0,0) stays at (0,0)\n", + "* any line remains a line after its transformation by a linear map.\n", + "\n", + "To define a linear map, it suffices to indicate how the base is transformed:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 298, + "width": 572 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# base d'origine\n", + "vector([1,0], text='i')\n", + "vector([0,1], text='j')\n", + "# base transformée\n", + "vector([-2,1], 'r', 'f(i)')\n", + "vector([-1,-1], 'r', 'f(j)')\n", + "plt.gca().spines[:].set_position('zero')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "For any vector ${\\bf v}$ we have\n", + "\n", + "$$ {\\bf f(v)} = {\\bf f}( v_1 \\, {\\bf i} + v_2 \\, {\\bf j}) = v_1 \\, {\\bf f(i)} + v_2 \\, {\\bf f(j)} $$\n", + "\n", + "since $\\bf f$ is linear. This shows that it is enough to know the transformation of the base.\n", + "\n", + "Carrying out the calculations, we have in the case of the figure above\n", + "\n", + "$$ \n", + "v_1 \\, {\\bf f(i)} + v_2 \\, {\\bf f(j)} = \n", + "v_1 \\,\n", + "\\begin{bmatrix}\n", + " -2 \\\\\n", + " 1\n", + "\\end{bmatrix} \n", + "+\n", + "v_2 \\,\n", + "\\begin{bmatrix}\n", + " -1 \\\\\n", + " -1\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + " -2 \\, v_1 \\\\\n", + " 1 \\, v_1 \n", + "\\end{bmatrix} \n", + "+\n", + "\\begin{bmatrix}\n", + " -1 \\, v2\\\\\n", + " -1 \\, v2\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + " -2 \\, v_1 -1 \\, v2\\\\\n", + " 1 \\, v_1 -1 \\, v2\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + " -2 & -1 \\\\\n", + " 1 & -1\n", + "\\end{bmatrix} \n", + "\\,\n", + "\\begin{bmatrix}\n", + " v_1 \\\\\n", + " v_2\n", + "\\end{bmatrix} \n", + "$$\n", + "\n", + "The matrix and the matrix product are thus introduced.\n", + "\n", + "The linear map $\\bf f$ of our figure can therefore be represented by a matrix operation: ${\\bf f}({\\bf v}) = A \\, {\\bf v}$ where the matrix A is\n", + "\n", + "$$\n", + "A =\n", + "\\begin{bmatrix}\n", + " -2 & -1 \\\\\n", + " 1 & -1\n", + "\\end{bmatrix} \n", + "$$\n", + "\n", + "Note that we find $\\bf f(i)$ in the first column and $\\bf f(j)$ in the second column.\n", + "\n", + "One will be able to check in exercise that the application ${\\bf f} : {\\bf v} \\mapsto A \\, {\\bf v}$ is indeed linear." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Determinant of a matrix\n", + "\n", + "The determinant indicates the magnification of the surface of an object after transformation by $\\bf f$ or, what is the same, after multiplication by A." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 305, + "width": 572 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# base d'origine\n", + "vector([1,0], text='i')\n", + "vector([0,1], text='j')\n", + "plt.fill([0,1, 1, 0],[0,0,1,1], '#bbbbbb')\n", + "plt.text(0.5, 0.5, 'Surface = 1', horizontalalignment='center', size=16)\n", + "# base transformée\n", + "vector([-2,1], 'r', 'f(i)')\n", + "vector([-1,-1], 'r', 'f(j)')\n", + "plt.fill([0,-2, -3, -1],[0,1,0,-1], '#ffbbbb')\n", + "plt.text(-1.5, 0, 'Surface = det(A)', horizontalalignment='center', size=16)\n", + "plt.gca().spines[:].set_position('zero')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.0" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy.linalg as lin\n", + "\n", + "A = np.array([[-2, -1], [1, -1]])\n", + "lin.det(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "* if det(A) = 0 then that means that $\\bf f(i)$ and $\\bf f(j)$ are collinear, so that we have lost a dimension (we look at the slice of the plane).\n", + "* if det(A) < 0 then that means that $\\bf f(i)$ is after $\\bf f(j)$ counterclockwise (we flipped the plane)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "If you are not comfortable with linear algebra, I invite you to watch [the videos of 3 blues, 1 brown](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Standards\n", + "\n", + "### Norm of a vector\n", + "\n", + "There are different norms, the best known being the Euclidean norm or norm 2. Its definition is:\n", + "\n", + "$$\n", + "|| {\\bf v} ||_2 = \\sqrt{\\sum_{i=1}^n v_i^2} = \\sqrt{\\bf v . \\bf v}\n", + "$$\n", + "\n", + "We also have norm 1 (also known as Manhattan):\n", + "\n", + "$$\n", + "||{\\bf v}||_1 = \\sum_{i=1}^n |v_i|\n", + "$$\n", + "\n", + "Norm n:\n", + "\n", + "$$\n", + "|| {\\bf v} ||_n = \\left( {\\sum_{i=1}^n v_i^n} \\right)^{1/n}\n", + "$$\n", + "\n", + "and therefore the infinite norm is the max (one must use the limits to understand why)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v = [ 0.1 1. 4. 10. 50. ]\n", + "v¹⁰⁰ = [1.000e-100 1.000e+000 1.607e+060 1.000e+100 7.889e+169]\n", + "Σ v¹⁰⁰ = 7.888609052210118e+169\n", + "ǁvǁ₁₀₀ = 50.00000000000001\n" + ] + } + ], + "source": [ + "v = np.array([0.1, 1, 4, 10, 50])\n", + "print(\"v =\", v)\n", + "print(\"v¹⁰⁰ =\", v**100)\n", + "print(\"Σ v¹⁰⁰ =\", (v**100).sum())\n", + "print(\"ǁvǁ₁₀₀ =\", (v**100).sum()**0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Norm of a matrix\n", + "\n", + "The norm that derives from the scalar product is the **Frobenius norm**:\n", + "\n", + "$$\n", + "|| A ||_F = \\sqrt{\\textrm{trace}(A A^*)} = \\sqrt{ \\sum_{1 \\le i\\le m \\atop 1 \\le j\\le n}|A_{ij}|^2 }\n", + "$$\n", + "\n", + "with $A^*$ the adjoint matrix (or the transpose matrix if we are in R)." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 1]\n", + " [2 3]]\n", + "ǁAǁ = 3.872983346207417\n" + ] + } + ], + "source": [ + "A = np.array([[1, 1], [2, 3]])\n", + "print(A)\n", + "print(\"ǁAǁ = \", np.linalg.norm(A))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The **subordinate norm** is induced by the vector norm:\n", + "\n", + "$$\n", + "||B||_n = \\sup_{\\bf v} \\frac{||B\\, {\\bf v}||_n}{||\\textbf{v}||_n} = \\sup_{\\textbf{v} \\, t.q. ||\\textbf{v}||_n = 1} ||B\\, {\\bf v}||_n = \\sup_{\\textbf{v} \\, t.q. ||\\textbf{v}||_n \\le 1} ||B\\, {\\bf v}||_n\n", + "$$\n", + "\n", + "This is the default norm used in this course." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ǁAǁ₂ = 3.8643284505408246\n" + ] + } + ], + "source": [ + "print(\"ǁAǁ₂ = \", np.linalg.norm(A,2))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Properties\n", + "\n", + "In our case, where the arrival space and the departure space are $\\mathbb{R}^n$ or $\\mathbb{C}^n$, norms have the following properties:\n", + " \n", + "$$\n", + "\\begin{array}{l}\n", + "|| A B || \\le ||A|| \\; ||B|| \\\\\n", + "|| A {\\bf v} || \\le ||A|| \\; ||{\\bf v}||\n", + "\\end{array}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma21 Transformations isometriques.ipynb b/PVCM/cama/en/ma21 Transformations isometriques.ipynb new file mode 100644 index 0000000..b800edc --- /dev/null +++ b/PVCM/cama/en/ma21 Transformations isometriques.ipynb @@ -0,0 +1,458 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Isometric transformations\n", + "\n", + "In the world of vector (or matrix) calculus, we speak of orthogonal automophism rather than of isometric transformation as we\n", + "will see it at the end." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0. 0.5 0.866 1. 0.866 0.5 0. -0.5 -1. -1. -1. -0.5 0. ]\n", + " [-1. -0.866 -0.5 0. 0.5 0.866 1. 1. 1. 0.5 0. -0.5 -1. ]]\n" + ] + } + ], + "source": [ + "angle = np.array([θ for θ in np.linspace(-np.pi/2,np.pi/2,7)])\n", + "shape1 = np.concatenate([np.array([np.cos(angle), np.sin(angle)]), \\\n", + " np.array([[-0.5, -1, -1, -1], [1, 1, 0.5, 0]]), \\\n", + " np.array([[-0.5, 0], [-0.5, -1]])], axis=1)\n", + "print(shape1)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 300, + "width": 606 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(shape1[0], shape1[1], '-or')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Rotation matrix centered at (0,0)\n", + "\n", + "R=\n", + "$\n", + "\\begin{bmatrix}\n", + "cos(θ) & -sin(θ) \\\\\n", + "sin(θ) & cos(θ) \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "### Properties\n", + "\n", + "* Performs a rotation with center (0,0) and angle θ\n", + "* Determinant = 1\n", + "* orthogonal matrix $\\rightarrow$ no shape deformation or enlargement (orthogonal automorphism)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0.707 -0.707]\n", + " [ 0.707 0.707]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 300, + "width": 606 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "θ = np.pi / 4\n", + "\n", + "R = np.array([[np.cos(θ), -np.sin(θ)], [np.sin(θ), np.cos(θ)]])\n", + "print(R)\n", + "\n", + "shape2 = R @ shape1\n", + "\n", + "plt.plot(shape2[0], shape2[1], '-ob')\n", + "plt.axis('equal');\n", + "\n", + "np.save(\"mouse.npy\", shape2) # pour le prochain cours" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Orthogonal matrix so (by definition) $R.R^T = \\textrm{Id}$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 0.],\n", + " [0., 1.]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "R @ R.T" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "So the transpose is the rotation of angle -θ which is logical since sine is an odd function." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Axial Symmetry\n", + "\n", + "The horizontal symmetry, which transforms (a,b) into (a,-b), is\n", + "\n", + "Sx =\n", + "$\n", + "\\begin{bmatrix}\n", + "1 & 0 \\\\\n", + "0 & -1 \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "We therefore see that to have an axial symmetry with respect to a straight line which passes through (0,0) it suffices to\n", + "\n", + "* rotate to put the axis of symmetry horizontal\n", + "* apply horizontal symmetry\n", + "* do the reverse rotation\n", + "\n", + "Thus the axial symmetry with respect to the straight line which passes through (0,0) and which has an angle of alpha is:\n", + "\n", + "$S = R_{-α}^{-1}\\; Sx\\; R_{-α} = R_α\\;Sx\\; R_{-α}$\n", + "\n", + "Note that the order of the matrices is the reverse since we apply the points **x** to the right of $S$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-0.766 0.643]\n", + " [ 0.643 0.766]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 383 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def Rα(α):\n", + " return np.array([[np.cos(α), -np.sin(α)], [np.sin(α), np.cos(α)]])\n", + "\n", + "Sx = np.array([[1, 0],[0,-1]])\n", + "\n", + "θ = 70 * (2 * np.pi)/360 # 70 degrés\n", + "\n", + "shape2 = Rα(θ) @ Sx @ Rα(-θ) @ shape1\n", + "\n", + "print(Rα(θ) @ Sx @ Rα(-θ))\n", + "\n", + "plt.plot(shape1[0], shape1[1], \":\")\n", + "plt.plot(shape2[0], shape2[1])\n", + "plt.plot([-np.cos(θ),np.cos(θ)],[-np.sin(θ),np.sin(θ)],\"-.\") # axe de symétrie\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0., 1.],\n", + " [ 1., -0.]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "θ = np.pi / 4\n", + "Rα(θ) @ Sx @ Rα(-θ)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "I don't know if there is a simpler direct formula to have the axial symmetry with respect to any line that passes through (0,0)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Translation\n", + "\n", + "We cannot express the translation with a matrix product because it is not a linear map:\n", + "\n", + "$T(2\\;\\textbf{x}) \\ne 2\\; T(\\textbf{x})$\n", + "\n", + "It is also not an isometric transformation because the distance from a point to (0,0) changes after a translation.\n", + "\n", + "From a vector point of view a translation is an addition:\n", + "\n", + "$T(\\textbf{x}) = \\textbf{x} + \\textbf{v}_t$\n", + "\n", + "There is a trick to express the translations in the form of a matrix product: we change the representation of the points:\n", + "\n", + "$\\textbf{x} = (x_1, x_2)$ becomes $\\textbf{x} = (x_1, x_2, 1)$\n", + "\n", + "Thus the translation by the vector $(v_1, v_2)$ is\n", + "\n", + "$T(X) = \n", + "\\begin{bmatrix}\n", + "1 & 0 & v_1\\\\\n", + "0 & 1 & v_2 \\\\\n", + "0 & 0 & 1 \\\\\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "x_1 \\\\\n", + "x_2 \\\\\n", + "1 \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "We can verify that $T$ is indeed a linear application since $T(2\\;\\textbf{x}) = 2\\; T(\\textbf{x})$ but on arrival\n", + "the new point does not follow the $(x_1, x_2, 1)$ convention." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Translate matrix:\n", + " [[1. 0. 1.]\n", + " [0. 1. 2.]\n", + " [0. 0. 1.]]\n", + "Shape1 3d:\n", + " [[ 0. 0.5 0.866 1. 0.866 0.5 0. -0.5 -1. -1. -1. -0.5 0. ]\n", + " [-1. -0.866 -0.5 0. 0.5 0.866 1. 1. 1. 0.5 0. -0.5 -1. ]\n", + " [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. ]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "v = np.array([1,2])\n", + "\n", + "T = np.identity(3)\n", + "T[0:2,2] = v\n", + "print(\"Translate matrix:\\n\", T)\n", + "\n", + "shape1_3d = np.concatenate([shape1, np.ones((1, len(shape1[0])))], axis=0)\n", + "print(\"Shape1 3d:\\n\", shape1_3d)\n", + "\n", + "shape2 = T @ shape1_3d\n", + "\n", + "plt.plot(shape1[0], shape1[1], \":\")\n", + "plt.plot(shape2[0], shape2[1])\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The inverse matrix of our translation matrix is ​​the one that puts the orange shape back in its original place, so that applies the $-\\textbf{v} = (-1,-2)$ transaction.\n", + "\n", + "$T^{-1} = \n", + "\\begin{bmatrix}\n", + "1 & 0 & -1\\\\\n", + "0 & 1 & -2 \\\\\n", + "0 & 0 & 1 \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "which is not the transpose of T so T is not orthogonal.\n", + "\n", + "The catch is that there are 2 types of isometries:\n", + "\n", + "* vector isometry or orthogonal automorphism which requires that $\\forall\\, \\textbf{x}, \\;||\\textbf{f}(\\textbf{x})|| = ||\\textbf{x}||$ as well as the conservation of angles\n", + "* the geometric isometry that wants $\\forall\\, \\textbf{a}, \\textbf{b}, \\; ||\\textbf{f}(\\textbf{a}) - \\textbf{f}(\\textbf{b})|| = ||\\textbf{a} - \\textbf{b}||$.\n", + "\n", + "The translation is indeed a geometric isometry but not vectorial hence the fact that we prefer to speak\n", + "orthogonal automorphism rather than isometry to avoid confusion." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Exercise 1.1\n", + "\n", + "Write in the form of a matrix product the axial symmetry with respect to an axis which does not pass through (0,0).\n", + "We will take the axis which passes through (2,0) and which has an angle of π/3 with respect to the horizontal.\n", + "\n", + "Is it an orthogonal automorphism? Show it." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma22 Changement de repere.ipynb b/PVCM/cama/en/ma22 Changement de repere.ipynb new file mode 100644 index 0000000..f57bf47 --- /dev/null +++ b/PVCM/cama/en/ma22 Changement de repere.ipynb @@ -0,0 +1,697 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "hide_input": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt\n", + "from scipy import linalg as lin\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid']) #,'data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "hide_input": true + }, + "outputs": [], + "source": [ + "matplotlib.rcParams['figure.figsize'] = (12.0, 8.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Matrice de passage\n", + "\n", + "On a vu qu'une matrice représente une application linéaire qui déplace les points qu'on lui donne.\n", + "\n", + "On va voir qu'une matrice sert aussi à représenter un changement de repère à savoir quelle est la valeur\n", + "d'un point par rapport à un autre repère." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "hide_input": true + }, + "outputs": [], + "source": [ + "def arrow2D(a,b, color='k', **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "hide_input": true, + "tags": [ + "hide-input" + ] + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 462, + "width": 693 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# beaucoup de code pour un petit dessin\n", + "\n", + "δx = np.array((0.1, 0))\n", + "δy = np.array((0, 0.1))\n", + "\n", + "O = np.array((0,0))\n", + "I = np.array((1,0))\n", + "J = np.array((0,1))\n", + "plt.annotate(\"O\", O - δx -δy , size=20, color='k')\n", + "plt.annotate(\"I\", I + δx, size=20, color='k')\n", + "plt.annotate(\"J\", J - δx, size=20, color='k')\n", + "\n", + "A = np.array((0,0))\n", + "B = np.array((2,1))\n", + "C = np.array((-1.5,1))\n", + "plt.annotate(\"A\", A - 1.5* δy, size=20, color='r')\n", + "plt.annotate(\"B\", B + δy, size=20, color='r')\n", + "plt.annotate(\"C\", C + δy , size=20, color='r')\n", + "\n", + "arrow2D(O,I)\n", + "arrow2D(O,J)\n", + "arrow2D(A,B, 'r')\n", + "arrow2D(A,C, 'r')\n", + "\n", + "plt.xticks(np.arange(-3,3,1))\n", + "plt.yticks(np.arange(0,2,1))\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hide_input": true + }, + "source": [ + "La matrice de passage d'un repère à un autre l'ensemble des vecteurs de la seconde base exprimés dans la première base.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 2. , -1.5],\n", + " [ 1. , 1. ]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P = np.array([(B-A), (C-A)]).T # matrice de passage : déformation sans la translation\n", + "P" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Vecteurs dans le nouveau repère\n", + "\n", + "Cette déformation permet de passer d'une représentation de l'espace à une autre (d'un repère à un autre). \n", + "\n", + "Regardons ce que valent certains vecteur dans chacune des bases :\n", + "\n", + "| | base départ (O,I,J) | base d'arrivée (A,B,C) |\n", + "| --:| :-: | :-: |\n", + "AB | [2,1] | [1,0] |\n", + "AC | [-1.5, 1] | [0,1] |\n", + "OI | [1,0] | ? |" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-1.5, 1. ])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P @ [0,1] # donne AC, [0,1] de base d'arrivée, exprimé dans la base de départ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "C'est logique puisqu'il s'agit de la 2e colonne de la matrice de passage. On a donc\n", + "\n", + "$$ \\mathbf{v}_{(d)} = P \\; \\mathbf{v}_{(a)} $$\n", + "\n", + "avec :\n", + "\n", + "* $ \\mathbf{v}_{(d)}$ : le vecteur __v__ exprimé dans la base de départ\n", + "* $ \\mathbf{v}_{(a)}$ : le vecteur __v__ exprimé dans la base d'arrivée\n", + "\n", + "et on a aussi \n", + "\n", + "$$ \\mathbf{v}_{(a)} = P^{-1} \\; \\mathbf{v}_{(d)} $$\n", + "\n", + "Cela nous permet de calculer la case qui nous manque à savoir OI exprimé dans la base d'arrivée :" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.286, -0.286])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xa = lin.inv(P) @ [1,0]\n", + "xa" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "c.a.d. OI = 0.286 AB - 0.286 AC." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Matrice de passage vue comme une transformation\n", + "\n", + "En tant que matrice, une matrice de passage représente aussi une application linéaire. Elle prend un vecteur et le déforme.\n", + "\n", + "Ainsi le vecteur OI est déformé par P pour devenir AB. On peut donc écrire :\n", + "\n", + "$$ AB = P\\; OI $$\n", + "\n", + "Dans ce cas, tout est exprimé en fonction du repère de départ. On a \n", + "\n", + "$$ \\mathbf{w}_{(d)} = P \\; \\mathbf{v}_{(d)} $$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hide_input": true + }, + "source": [ + "### Points dans le nouveau repère\n", + "\n", + "Lorsqu'on pense en point, alors l'orgine des deux repères peut être différente.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "hide_input": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 462, + "width": 693 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.annotate(\"O\", O - 4*δx, size=20, color='k')\n", + "plt.annotate(\"I\", I + δx, size=20, color='k')\n", + "plt.annotate(\"J\", J - 3*δx, size=20, color='k')\n", + "\n", + "A = np.array((3,3))\n", + "B = np.array((5,4))\n", + "C = np.array((1.5,4))\n", + "plt.annotate(\"A\", A - 3*δy, size=20, color='r')\n", + "plt.annotate(\"B\", B + δx, size=20, color='r')\n", + "plt.annotate(\"C\", C - 4*δx , size=20, color='r')\n", + "\n", + "arrow2D(O,I)\n", + "arrow2D(O,J)\n", + "arrow2D(A,B, 'r')\n", + "arrow2D(A,C, 'r')\n", + "\n", + "arrow2D([1,1], [2.5,3], 'b')\n", + "plt.annotate(\"p\", (1.3,2), size=30, color='b')\n", + "plt.yticks(np.arange(0,5,1))\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Si on veut travailler sur les points il faut prendre en compte la translation d'un repère vers l'autre soit de O vers A.\n", + "\n", + "La bonne facon de faire en mathématique est de séparer la déformation de la translation ce qui permet de rester\n", + "dans l'espace 2D.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([5., 4.])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P2D = P\n", + "A + P2D @ I # passage de I en B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Mais on a vu qu'on peut intègrer la translation dans une matrice d'une dimension supérieure." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 2. , -1.5, 3. ],\n", + " [ 1. , 1. , 3. ],\n", + " [ 0. , 0. , 1. ]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P = np.identity(3) # defines the size and set the last line (others will be overwritten)\n", + "P[:2, :2] = P2D # deformation\n", + "P[:2, 2] = A # translation\n", + "P" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "hide_input": false + }, + "outputs": [], + "source": [ + "def to3D(x):\n", + " \"\"\" Transform 2D point(s) to 3D point(s) with 1 as third value \"\"\"\n", + " if type(x) == list:\n", + " x = np.array(x)\n", + " if len(x.shape) == 1:\n", + " return np.array([*x,1])\n", + " elif len(x.shape) == 2:\n", + " return np.array([*x,np.ones(len(x[0]))])\n", + " else:\n", + " raise Exception('Erreur de dimension')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notre matrice de passage P qui inclu la translation de l'origine permet de calculer la position d'un point\n", + "dans le nouveau repère." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1.5, 4. , 1. ])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P @ to3D([0,1]) # C expressed in start basis including translation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Notre souris dans le nouveau repère\n", + "\n", + "A quoi ressemble la souris exprimée dans le repère d'arrivée vue depuis le repère de départ." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 476, + "width": 707 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "mouse = np.load('data/mouse.npy')\n", + "\n", + "dmouse = P2D @ mouse\n", + "\n", + "plt.plot(mouse[0,:], mouse[1,:], color='r', label=\"repère d'arrivée\")\n", + "plt.plot(dmouse[0,:], dmouse[1,:], color='k', label='repère de départ')\n", + "plt.title('Déformation sans la translation')\n", + "plt.legend()\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On peut aussi voir la souris noire comme la transformée de la souris rouge par la matrice de passage.\n", + "\n", + "Si on ajoute la translation, alors on a :" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 476, + "width": 693 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "ε = 0.03 # pour voir les 2 repères qui sont supperposés\n", + "\n", + "pmouse = P @ to3D(mouse)\n", + "\n", + "arrow2D(O+ε,I+ε, 'k')\n", + "arrow2D(O+ε,J+ε, 'k')\n", + "arrow2D(O,I, 'r')\n", + "arrow2D(O,J, 'r')\n", + "arrow2D(A,B, 'g')\n", + "arrow2D(A,C, 'g')\n", + "\n", + "plt.plot(mouse[0,:], mouse[1,:], 'red')\n", + "plt.plot(pmouse[0,:], pmouse[1,:], 'black')\n", + "plt.axis(\"equal\")\n", + "plt.title('Changement de repère de la souris avec en vert affichage du repère ABC exprimé dans la base de départ (noire)');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercice -- Et l'inverse ?\n", + "\n", + "À quoi ressemble la souris du repère de départ vue depuis le repère d'arrivée ?" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 476, + "width": 698 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "pmouse = lin.inv(P) @ to3D(mouse)\n", + "\n", + "arrow2D(O+ε,I+ε, 'k')\n", + "arrow2D(O+ε,J+ε, 'k')\n", + "arrow2D(O,I, 'r')\n", + "arrow2D(O,J, 'r')\n", + "arrow2D(A,B, 'g')\n", + "arrow2D(A,C, 'g')\n", + "\n", + "plt.plot(mouse[0,:], mouse[1,:], 'k')\n", + "plt.plot(pmouse[0,:], pmouse[1,:], 'r')\n", + "plt.axis(\"equal\")\n", + "plt.title('Changement de repère de la souris avec en vert affichage du repère ABC exprimé dans la base de départ (noire)');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Une application linéaire transposée dans le nouveau repère\n", + "\n", + "Combinons les deux usages qu'on a vu de la multiplication matricielle.\n", + "\n", + "Choisissons une rotation comme exemple d'application linéaire. Elle prendre un point et le fait tourner dans le sens trigonométrique de θ autour de (0,0).\n", + "\n", + "Que fait cette rotation dans notre nouveau repère ?\n", + "\n", + "Pour le voir \n", + "\n", + "* on fait tourner point (1,0) autour du centre du repère de départ (le cercle noir),\n", + "* on déforme le cercle avec l'inverse de la matrice de passage P (la forme rouge) \n", + "* on applique plusieurs fois la rotation du depuis le repère d'arrivée au point $I$ vu depuis le repère d'arrivée (la forme violette pointillée)\n", + "\n", + "La rotation dans le repère de départ est $R_{(d)}$.\n", + "L'application qui correspond à cette rotation vue du repère d'arrivée est $Q_{(a)}$ : \n", + "\n", + "$$Q_{(a)} = P^{-1} \\, R_{(d)} \\, P$$\n", + "\n", + "En effet (de droite à gauche), \n", + "\n", + "* $P$ permet d'exprimer un point du repère d'arrivée dans le repère de départ,\n", + "* ce qui permet d'y effectuer la rotation $R_{(d)}$\n", + "* puis on repart dans le nouveau repère avec $P^{-1}$.\n", + "\n", + "On espère que la *rotation* $Q_{(a)}$ du point $I$ vu depuis le repère d'arrivé va donner la même chose que le changement de repère du cercle noir." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "def Rot(θ):\n", + " return np.array([[np.cos(θ), -np.sin(θ)], [np.sin(θ), np.cos(θ)]])\n", + "\n", + "def Rot3D(θ):\n", + " return np.array([[np.cos(θ), -np.sin(θ), 0], [np.sin(θ), np.cos(θ), 0], [0, 0, 1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1.145, -0.546, -0.157],\n", + " [ 0.84 , 0.473, 1.348],\n", + " [ 0. , 0. , 1. ]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 462, + "width": 707 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# plusieurs rotation qui donnent le cercle bleu :\n", + "cercle = np.array([Rot(α) @ I for α in np.linspace(0, 2*np.pi, 10)]).T\n", + "\n", + "# le cercle exprimé dans le nouveau repère (noir)\n", + "p_cercle = lin.inv(P) @ to3D(cercle)\n", + "\n", + "# construction de Q\n", + "Q = lambda θ: lin.inv(P) @ Rot3D(θ) @ P # définition de Q en fonction de θ (c'est une fonction)\n", + "display(Q(2*np.pi/10))\n", + "# calcul de inv(P) @ I puis on applique Q pour faire tourner B autour de A (orange)\n", + "Ia = lin.inv(P) @ to3D(I)\n", + "p_rot_A = np.array([Q(α) @ Ia for α in np.linspace(0, 2*np.pi, 10)]).T \n", + "\n", + "# on affiche les repères\n", + "ε = 0.01\n", + "arrow2D(O+ε,I+ε, 'k')\n", + "arrow2D(O+ε,J+ε, 'k')\n", + "arrow2D(O,I, 'r')\n", + "arrow2D(O,J, 'r')\n", + "plt.annotate(r\"$I$\", I+δx , size=20, color='black')\n", + "plt.annotate(r\"$I_{(a)}$\", Ia[:2]+δx , size=20, color='purple')\n", + "\n", + "# et voici nos rotations\n", + "plt.plot(cercle[0,:], cercle[1,:], 'o-k', \n", + " label=\"cercle dans le repère de départ\") \n", + "plt.plot(p_cercle[0,:], p_cercle[1,:], 'o-r', lw=2, \n", + " label=\"même cercle vu depuis le repère d'arrivée\")\n", + "plt.plot(p_rot_A[0,:], p_rot_A[1,:], 'o:', lw=3, color='purple', \n", + " label=r\"point $I_{(a)}$ transformé plusieurs fois par $Q_{(a)}$\")\n", + "plt.legend(fontsize=14)\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma24 Vectors propres.ipynb b/PVCM/cama/en/ma24 Vectors propres.ipynb new file mode 100644 index 0000000..fb29cb8 --- /dev/null +++ b/PVCM/cama/en/ma24 Vectors propres.ipynb @@ -0,0 +1,807 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# $A^n \\textbf{x}$\n", + "\n", + "Soit A une matrice qui représente une application linéraire quelconque. Que se passe-t-il si on l'applique $n$ fois ?" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def arrow2D(a,b, color='k', **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 300, + "width": 606 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "mouse = np.load('data/mouse.npy')\n", + "\n", + "plt.plot(mouse[0], mouse[1], ':ob')\n", + "plt.plot([0,mouse[0][0]], [0,mouse[1][0]], 'r') # le point 0\n", + "plt.plot([0,mouse[0][3]], [0,mouse[1][3]], 'g') # le point 3 pour voir comment ils évoluent\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.707, 0.966, 0.966, 0.707, 0.259, -0.259, -0.707, -1.061, -1.414, -1.061, -0.707, -0. , 0.707],\n", + " [-0.707, -0.259, 0.259, 0.707, 0.966, 0.966, 0.707, 0.354, 0. , -0.354, -0.707, -0.707, -0.707]])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mouse" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[3, 1],\n", + " [0, 2]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# on prend une matrice de transformation au hasard (donc probablement pas orthoganale)\n", + "A = np.array([[3,1], [0,2]])\n", + "A" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1.414, 2.639, 3.157, 2.828, 1.742, 0.189, -1.414, -2.828, -4.243, -3.536, -2.828, -0.707, 1.414],\n", + " [-1.414, -0.518, 0.518, 1.414, 1.932, 1.932, 1.414, 0.707, 0. , -0.707, -1.414, -1.414, -1.414]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "as1 = np.dot(A, mouse) # autre facon d'écrire le produit matrice vecteur\n", + "as1" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 599 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(as1[0], as1[1], ':ob')\n", + "plt.plot([0,as1[0][0]], [0,as1[1][0]], 'r')\n", + "plt.plot([0,as1[0][3]], [0,as1[1][3]], 'g')\n", + "plt.title(\"Transformation de la souris par A\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On constate que la transformation n'est pas une isométrie donc que la matrice n'est pas orthogonale.\n", + "\n", + "Appliquons plusieurs fois de suite la transformation pour voir." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 596 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "aas1 = A @ A @ mouse\n", + "aaas1 = A @ A @ A @ mouse\n", + "\n", + "plt.plot(mouse[0], mouse[1], 'k')\n", + "plt.plot(as1[0], as1[1], 'r')\n", + "plt.plot(aas1[0], aas1[1], 'g')\n", + "plt.plot(aaas1[0], aaas1[1], 'b')\n", + "plt.plot([-40,36], [0,0], ':b')\n", + "plt.title(\"Transformation de la souris (en noir) par A, A² et A³\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On note \n", + "\n", + "* que la souris est de plus en plus grosse (donc le det(A) > 1)\n", + "* que sa pointe (son point le plus à gauche) reste toujours sur l'axe horizontal\n", + "* qu'elle est de plus en plus écrasée" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Évolution du point 0 transformé par A et A³\n", + "[ 1.414 -1.414] et normé [ 0.707 -0.707]\n", + "[ 5.657 -5.657] et normé [ 0.707 -0.707]\n", + "\n", + "Évolution du point 3 transformé par A et A³\n", + "[2.828 1.414] et normé [0.894 0.447]\n", + "[32.527 5.657] et normé [0.985 0.171]\n" + ] + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAABJsAAAJ8CAYAAABZZqAdAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAABYlAAAWJQFJUiTwAACqGUlEQVR4nOzdd3hT9f/+8bsbOqBQmrI3LYUEFQRkuFAQFQEXbkVUlKG4cftxj6+KsgQEB4iDISAuQKYMGUUlYQ/Z0JSW0pYOaJvfH/312JKkdKRNKc/HdXFdPTmvnLxPehKaO+/h43A4HAIAAAAAAAA8wNfbDQAAAAAAAEDVQdgEAAAAAAAAjyFsAgAAAAAAgMcQNgEAAAAAAMBjCJsAAAAAAADgMYRNAAAAAAAA8BjCJgAAAAAAAHgMYRMAAAAAAAA8hrAJAAAAAAAAHkPYBAAAAAAAAI8hbAIAAAAAAIDHEDYBAAAAAADAYwibAAAAAAAA4DGETQBQAmlpaXr77bfVo0cPmc1mXXDBBXriiSe83awqZe3atYqJiVFMTIyee+45bzenQt1zzz3GuR88eNDbzakSxowZYzynP/zwg7ebg3NEZXkf4vr1rh9++MF4/seMGePt5gDAOcXf2w0AUL7Wrl2re++9t8zHadCggZYsWeKBFp3bhgwZonXr1hnbp0+f1rFjx7zYIgBV0V9//aWZM2cqLi5Odrtdubm5MplMuvjii3Xbbbfpwgsv9HYTy8Xy5cv1008/6Z9//pHdbldOTo5q1qypmJgYXXHFFbrxxhsVGhrq7WYCXvPBBx/os88+M7a//PJLdenSxYstqhgrVqzQQw89ZGwPGTJEjz/+eLHuu23bNk2ePFkbN26U3W5XcHCwLBaL7r//fnXv3r2cWgyAsAkAimnXrl1G0BQaGqoPPvhAF1xwgXJzc73csnPP+PHjlZOTo0cffdRp38UXX6yNGzdKkgICAiq6aahiHn74YQ0aNEiSFBQUVG6Ps337di1cuFCxsbG6+uqrS32c3Nxcvfbaa/ruu++c9u3fv1/79+/XDz/8oLvvvlsvvfSSfHx8ytLsMjty5IhmzZqlBg0a6Kabbir1cY4dO6YnnniiUJifLyEhQQkJCVq5cqUmTpyojz76SJ06dSpLs4Fi6du3r6655hpJleP/o1OnTmn27NmFbvv+++8rXdg0bdo0JScn67777lONGjU8csxvv/220Pbs2bM1fPhw+fsX/XF27dq1euihh5SVlaWWLVvqsssu0/79+7Vy5UqtWrVKo0aN0rXXXuuRNgIojLAJqOIKfnB3ZcSIEfrjjz8kSZMmTdLFF1/sss7Xl1G3+/btM37u3bu3rrzySi+25ty1a9cuffLJJ5LkMmzy8/NTSEhIRTcLVVRgYKACAwPL/XHmzZunKVOm6MYbbyxT2PTee+8ZQVObNm00bNgwWSwW+fn5yWazaezYsbJarfr6668VEhKiJ5980lOnUCpLlizR2LFj1alTp1KHTenp6br33nu1e/duSVKHDh00ePBgtWzZUsHBwdq5c6e++OILLV26VAkJCXrkkUc0e/ZsNWvWzJOnAjjx9/c/a5hRkRYsWKCkpCRJUvv27bVx40b9/vvvSkxMVEREhJdblyctLU3vvPOOcnJydOONN3okbDpy5IiWL18u6b/zttvtWrZs2Vnfb1955RVlZWXp0Ucf1fDhw43b33jjDX399deaMmUKYRNQTvj0CFRx+R/c3f3z8/MzaqtVq+a2rnr16l48i8ohJSXF+NlkMnmxJee29evXe7sJgMdt2LChzMfYvHmzpk6dKklq27atvvvuO1199dWKiopSnTp1dMUVV+ibb76RxWKRJE2ZMkXbt28v8+OWhSfOe+LEiUbQdP311+ubb77RFVdcoYYNG6p27drq3LmzJkyYoBtuuEGSdPLkSX366adlflzgXJMfRDds2FBPP/20pLzh/Gf2dvKmjRs3Kicnx6PHnDFjhnHMN9980/hCylUP0IJycnL04IMP6umnn9bAgQML7bvsssskSVlZWR5tK4D/EDYBQDE5HA7jZ3p6lZ4nPpwClUlGRoa2bNlS5uNMmzbNGJb7wgsvuBz2FxgYaExYnZ2dra+//rrMj1sWnng9z5o1S1LeMKXXXnvNbV3BxRiWLVtW5scFziU7d+40Xm/XX3+92rdvr/r160uSZs6cWehvFG+Ki4vz6PGys7M1c+ZMSdJFF12kFi1a6KqrrpIkrVq1qsjFNPz8/HTrrbfqoYceKjTXW1ZWljEsr2fPnh5tL4D/VJ5+oQDOCT/88IOef/55SdK4cePUuXNnjRkzRj///LOSk5M1YsQIDR48uNB90tLSNHPmTC1fvly7du1SSkqKcnNzFR4ertatW+uaa65R//793c6H0KNHDx06dEitW7fWvHnzlJWVpdmzZ2vOnDnatWuXTp06pZo1a6pt27a67bbbiuxSffjwYX3//fdas2aN9u3bp7S0NPn5+SkiIkIxMTHq2bOnbrjhhkLDbu655x6neUTGjh2rsWPHSpI6deqkadOmFdp/4sQJfffdd1q5cqX27NmjEydOKCgoSHXq1FH79u11ww03qGvXri7bWHBS9+eff1533nmnJk2apFmzZikhIUG33nqr/ve//0mSnnvuOc2ZM0eStGbNGtWoUUOzZ8/W999/r927d8vX11d169ZVr169dP/99ys8PFySlJSUpK+++kqLFy/WoUOHJEnNmjVT3759dc899xTq8XamAwcO6Pvvv9e6deuM5zAgIEB16tRRu3btdNNNN7mccNPV8xgTE2P8vHjxYjVs2LDQ+d9444169913XbbDk8/xwIEDtX//fk2dOlVLly5VfHy8/Pz8FBUVpS5duuiBBx5Q48aN3T4nxZGcnKwpU6Zo6dKlOnTokHx8fBQVFaXLLrtM99xzjxo2bFjsY23atEmzZs1SXFycjhw5ouzsbNWuXVutWrXSNddco379+hU5v0hSUpJmzJhhPHf5vfZq1aqlVq1a6YorrtBNN91UqomYDx48aHwQ6NOnjz788EP9+++/+uqrr7Rq1SpjQv369evryiuv1KBBg1S7du0ij7lnzx7jmjt8+LDS0tIUGhqq+vXrq1OnTrrtttvUvHlzl/cdM2aM8Vp95513Cg31OvP97Oqrr9a2bdv01VdfafXq1UpMTFRAQIAaNGigSy+9VA888IDq1Knj8lzzzZkzx3hNunpvcCcrK0sLFiyQJDVu3NjtkGYpb3h048aNtX//fv366696+eWXSz1U8OTJk/rhhx+0bNkybdu2TSdOnFBISIhMJpO6deumW265RS1btnS6X8HXriStW7fOuK0kC0qkpaWpY8eOOn78uOrWrauwsDC3tQ0aNFDt2rWVlJSkEydOGNdBaSxbtkzfffedrFarTpw4ofDwcEVHR6t///7q27dvsY9T2ufP05YvX64ff/xRNptNdrtdWVlZCgkJUePGjdWlSxfdeeedRjBRWqdPn9a8efP0+++/a9u2bTp+/Liys7MVGhqqJk2aqEuXLhowYIAaNGjg9hgOh0OLFi3Sr7/+qn/++cc4Rv7zf8UVV+iWW25x25s6/+8BSUX26jvb/yP51+pVV12l8ePH66efftLEiRP177//qkmTJvr5558lFX6PGD58uMuh33///bd++OEH/fXXXzp8+LAyMjIUFBSkqKgotWvXTn379vXIJNQFe/H069dPPj4+uvHGGzVu3Djt379fq1evVrdu3cr8OFLe3xNz5szR33//rYSEBOXm5ioiIkJms1nXXnutevfu7TRfXMG/R/IVfH+cOnWqOnfuXOK2LF68WAkJCZJkvDZvvvlm/fjjj8rNzdXMmTOLvSrwm2++qZ07dxpfDjz00EMaOnRoidsEoHgImwCUyRNPPGHM+SQ5d0fetGmThg4davyhUFD+pK9//PGHvvnmG02ePPmscw4kJSXp4Ycf1qZNmwrdnpiYqBUrVmjFihUaOnSoRowY4XTfX375Rc8995xTG7Ozs3X48GEdPnxYS5cu1ZdffqkpU6aUeqjc4sWL9eyzzyotLa3Q7adPn1ZaWpr27t2rH374QT169NCHH36o4ODgIo/31ltvFfojMzMz02Xd6dOnNXz4cC1durTQ7Xv27NGECRO0bNkyTZ8+XfHx8XrggQd05MiRQnWbN2/W5s2btW3bNrcBz4wZM/TGG2/o1KlThW7Pzs7WgQMHdODAAf3888/q16+f3nnnnSJDq7Lw9HO8bNkyPfHEE0pPTy90rH379mnfvn36+eefNXXqVLVp06ZU7d21a5fuu+8+p5UL9+zZoz179uiHH34wApGinDp1Sm+88YZmzJjhtO/IkSM6cuSIVqxYoS+//FJjx45V06ZNnerWrl2r4cOHFxoWms9ut8tut2vVqlX64osvNGnSJLVq1ar4J3qGzMxMrVixQiNGjCj03Ep5z8muXbs0e/Zsff7554qNjXV5jNGjR2vChAlOwzKSk5OVnJysLVu2aNq0aRo6dGih+ThKY+bMmfrf//6n7Oxs47bTp09r586d2rlzp3766SfNnDlTdevWLdPjuGK1Wo3nqGPHjmet79ixo/bv36/U1FRt2bKlVKvTxcXFacSIEU7vz/nP7Y4dOzRt2jQNGTKkzM+tO6Ghofr444+LXZ/f88vX17fUAdubb77pFALm/3+0atUq/f7777rjjjvOepzK8PxlZGToiSeecHrfl/KGfttsNtlsNk2fPl3vv/9+qXtxxMfH68EHH9SOHTuc9uWf7z///KMvv/xS77zzjq677jqnumPHjmnYsGH6+++/nfblv/fkTwI/fvx4tWvXrlRtLalffvlFTz31lLGdkZFR7Pu+/fbb+uqrr5xuT09P17///qt///1X8+bN03XXXaf/+7//K/X8T+np6Zo3b56k/3r3SHmhy6effqrc3Fx9//33ZQ6bUlNT9cwzz7i8ng4dOqRDhw5pwYIFat++vcaNG3fWLwo8Ib8HUrVq1dSnTx9JUufOndWkSRPt27dPs2fP1qOPPlqs53b9+vXatm2bJKlp06aqVq1apekRBlRFhE0ASm3FihVatWqVHn30Ud10002qXr16of+0k5OT9cgjjygxMVGSdMsttxjfevr6+mr79u0aO3asNmzYoC1btuipp57Sl19+6fbxHA6Hnn76ae3Zs0dPPfWUevbsqdq1aysxMVE//vijJkyYIIfDoU8//VR9+vQx/hiT8lZxGjlypE6dOqWwsDANHz5c3bt3V+3atXXq1Cnt3r1bM2bM0G+//aYdO3bomWeeMf6A/Oyzz5STk6P58+fr1VdflZS3wtXDDz8sSYUClXXr1mn48OHKzc1VQECAHnjgAfXu3Vv16tVTVlaWNm3apPHjx2vLli1asmSJnnzySU2YMMHtOe/Zs0czZszQ3XffrXvuuUe1atVyCnryTZgwQX/++aeeeeYZ9e7dW6Ghodq6daveeust7dy5U9u2bdPXX3+t+fPnKzAwUJ988ok6duyo3NxcrV69Wq+//rrS0tI0Z84c3XnnnU5/6G/YsEGvvPKKHA6HAgMDNXz4cF111VWKiIjQqVOntH79en3wwQc6cuSI5s2bp6ZNmxb6xjD/eezTp48OHz4sSYUmrz9bIFRez/HevXv18ccfq3nz5ho6dKguuOAC+fv7GxOZr1+/XqmpqXrttdf0/fffF6uNBZ06dUpDhgwxgqYrr7xSgwcPVrNmzZSZmam4uDiNHTtWTz31lGrVqlXksV566SXjA0dMTIweeeQRtW3bVjVq1ND+/fs1a9YszZgxQzt37tTAgQP1ww8/FPowkJKSoscee0wpKSkKCAjQkCFDdNVVVykyMlI5OTnav3+/fvzxR33//fc6fPiwhg8frp9//rnUH5COHTumJ598UpGRkXr00Ud18cUXKygoSHv27NGnn36qlStXKikpSUOGDNFvv/2matWqFbr/+PHjNW7cOElSZGSkhg4dqm7duik8PFzJyclatWqVxo4dq8TERI0ZM0bBwcHGynMltX79ek2dOlWdOnXS4MGDFRsbK4fDIZvNpg8++EA7duyQ3W7X+++/r48++khSXk+bjRs3asOGDUaPzhtuuMEYClaSsHXXrl3Gz8WZ+LpgkLhz584Sh03bt2/Xgw8+qPT0dPn7++vee+9V79691ahRI6Wnp2vdunUaP368Dhw4oDFjxigwMLBQr9WNGzfqyJEjuv766yXlTeqdvxx7eQ0z3r17t5KTkyXlTZ5emrBp5syZRtBUo0YNPf7447riiisUEhKigwcPau7cufr666+Vmppa5HHK+vx5yltvvWUEA9HR0Ro+fLjMZrNCQ0OVkJCguXPnasqUKUpPT9eTTz6pn376SU2aNCnx44wcOdIImvr3769bb71VDRs2VGBgoDFR88SJE5Wenq5nn31Wbdu2LfQ4WVlZGjhwoHbu3ClJ6tKliwYNGqTY2Fj5+/vrwIEDmj17tr777jslJCRo4MCBmjdvnho1auSBZ8m9nJwcvffee+rSpYuefPJJNWnSxCkYd2fevHnG3wmtWrXSI488IovFovDwcKWkpGjTpk2aMmWKNm/erF9++UUtWrQodej4888/G9fkLbfcYtzeoEEDdevWTX/88YfRAygyMrJUj5Gdna1hw4Zp7dq1kvIC7UGDBikmJkbVq1fXzp079fXXX2vhwoXauHGj7r//fs2cOdN4Hb7++ut6+eWX9dBDDxlD6X7++WfVq1dPkpze34tj7969+vPPPyVJ11xzjTHZuI+Pj2655RZ9+OGHSkhI0OLFi41VA4syb94842++UaNGacyYMdqyZYvGjx9f4rYBKAYHgPPa4MGDHdHR0Y7o6GjHn3/+edb62bNnG/UWi8UxZswYt7WTJ082ap955hmXNRkZGY4rr7zSqNuyZYtTTf7+mJgYh9lsdlitVpfHeuGFF4zjjBs3rtC+8ePHG/t++uknt21+8cUXjbodO3a4PffRo0c73TcnJ8dx9dVXGzULFy50+RgnT5509OnTx6hbtGhRof1//vlnoef4ueeec9vekSNHGrWtW7d2LF++3Klm27ZtRk1MTIyja9eujmPHjjnVTZ061agbNWqU0/6C18rMmTNdtmfHjh2OmJgYR3R0tKNTp06O7Oxsp5qCv29XCp7/yJEjC+0rj+c4JibGceeddzoyMzOdjpOamuro2LGjUXvkyBGXj1eUb775xrj/vffe68jJyXGqOX78uOOqq64y6qKjox0HDhwoVLN06VJj3x133OGyvQ6Hw/HFF18YdS+//HKhffPmzTP2TZw40W2bC75eli5dWqLzPXDgQKHz6NatmyMxMdGpLjs723HHHXcYdV9++WWh/fv27XO0adPGER0d7bj44osd+/fvd/l4u3btcrRr1854vSQkJBTaP3r0aOMxZs+eXWhfwdd0TEyM4/HHH3f5+zl48KAjNjbWeIzTp08X2l/UNVtco0aNMo4xf/78s9bPnz/fqP/4449L/Hg333yzcd6LFy92WXP8+HHj9Wo2m51+BwV/13fffXeJ21ASGRkZjrvvvtt4vN9++63Ex8jOznZ07979rP/nffnll4WuYVe/U088f8VR1PVrt9uN67JTp04u39cdDofj/fffN47x5ptvlrgNR48eNe4/aNAgt3UbNmww6t59991C+8aMGWPsGzZsmMvX2Zl1Q4cOddp/tv8/8p3tNVnw/9jevXs7srKyXB6nqP/3Bw4caFwDR48edXn/rKws4/+iLl26uD3vs7nxxhsd0dHRjosuushx8uTJQvsWLFhgtPHTTz8t1fEdDofj66+/No4zYsQIt2194403jLoJEyY47S/4Oj3z/7GSeuedd4xjrV+/vtC+hIQER9u2bR3R0dGO+++/v8THzsjIcFgsFkd0dHSpXpsAzo4ZbgGUmo+Pj9PqHgXVqFFD1157rTp16qTbb7/dZU21atUKLTn7119/uT2ew+HQ3XffLbPZ7HJ/r169jJ/P7OpfcMhYdHS028d48sknNX36dC1btqxQz6ji+OOPP7R//35JUvfu3d0OVwgODi40zC9/clxXsrKyNGTIkGI9fteuXY3VVQqKiYlRVFSUpLzn8P7773c5XLHgfffs2eO0v3nz5urZs6cxH5IrrVq1MlbKSk5O1t69e4vV9uIqj+fY4XDo1VdfdTkZc2hoqLp06WJsl2blr19++cX4efjw4S57fYSHh5/1G+8pU6ZIynvdvfnmmy7bK0n33nuv0etl3rx5hb6lL+7r4L777tO0adP0+++/l3mukaFDh7ocauHn56dhw4YZ24sWLSq0//vvvzeGsz344INuezi0aNFCt912m6S818uPP/5YqnYGBgbq5Zdfdvn7adCggTGEMisrS/v27SvVYxQlv8eOJGOlpaIU7Al44sSJEj3W2rVrZbVaJeVNNNyjRw+XdeHh4Xr88ccl5fXQO3M+lvKSk5OjkydPGkPRZs6cqRtvvFHr1q2Tv7+/nn766WL1YjjThg0bZLfbJeUNw3E3f8w999xTZO+fyvL8nThxQn379tWll16q22+/3e0w9ILzlLkawnY2+T1RpaLfNzp06KDp06frl19+0WOPPWbcnpOTYwwF9/X11UsvveS299vDDz9svF8sW7bMaeixp2VlZWnQoEGl6iWX/7yEh4cb/8eeKTAwUKNHj9asWbM0f/78UvX627RpkzZv3iwpbx68M3sBX3nllcZccjNmzDCGmpZU/v8xwcHB+t///ue2rU888YTRw6g0vX2LKysry3jNNG/e3Gkeuzp16ujKK6+UJK1evdr426Cg3bt365VXXjF6pRcUFBRk9D5NSkrydPMBiNXoAJTBBRdcUOTkrLfeeqs+/vhjTZs2Te3bt3dbV/BD5PHjx4t8zILB1JkKTkp65nw0BSf1/eabb9yO0a9du7Yuvvhi1atXr8R/FK5Zs8b4uXfv3kXWXnbZZcYEzuvXr3fbnoYNGxZ7YuorrrjC7b6Cc8y4CqTOrHE1hGTkyJEaO3asvv32W7dBh1Sy32dJlcdz3LJlyyI/QBV1XZ1Nbm6u/vnnH0l5AUJRr4Orr77a7TWXlpZmDDmMjY11Oxm2lPdhLj+Ey8zM1Pr16419BV8HM2bM0OnTp10eIzg4WJ06dVKjRo1KPYQuX1G/p44dOxof8mw2W6HfUcHfdVGve6nwJLRnTkJfXJdcckmR848UvA5KGu4UR8HhsUW9vlzVlHTp7hUrVhg/u5pbp6AePXoY10DB+5WnDRs2qH379urcubNuuOEGvfTSS0pLS9Odd96puXPn6qGHHirVcQt+mXHppZe6rfP19XWa+L2gyvL8tWzZUu+++64mT55c5ATJZX1PLvi+sXDhQpdzMOa7+OKL1aJFi0ITfO/atcu4z0UXXVTknGcBAQG6/PLLJeUN6yo41Lq8lHaeo/zhasePHy/0pcKZmjVrJovFctY5Kd3Jn7NIkgYMGOC0PyAgQDfeeKOkvHmVVq5cWeLH2L17tzHxev5QZXdCQkKMLyEOHTpUaAiwJ/36669GCH/rrbe6rMm/3eFwuJzLMDw8XLNmzdJ3332n33//3en46enpCggIKPL/VAClR9gEoNTKurJNvoLfKJ7tG7miehsVnA/gzA/RBVeY++abb9SvXz998cUX2r17d2ma7NLWrVuNn89cqelMgYGBRu+TtLS0Qt8cF1SS57ioUKrgB1N3PUQK1hScILmkCv4+z5zUuazK4zk+Ww+2gh+a3IUz7hw6dMgIAho3blzkHD75q6u5sm3bNuN3UrduXZ08ebLIfwXn/CnYy+/qq682PkQsXrxY1113ncaNG6ctW7aU+tvwokRFRRUZ4AQGBhrnnJGRYXwgzcnJMdodHBx81nlbCk5i7moC4+Ioz+ugOApeG2eu8uRKwZqSTsSf30tCygsSirqWfHx8jKBt165dXptM99ixY1qzZo3mzZtnzANYUgV7bJ5tXqyi3l/OteevJP/HutKoUSNdcsklkvJWYLzuuuv0+uuv688//3S7YEVBJXnfljzzei6u/BVbS6Pg3ElPPPGEHnzwQc2dO1fx8fGeap5SUlL066+/Ssqbp8xdz+5bb73VeE8oTW8jm81m/BwVFXXW/2MKhjPl9TvK7w0XEBCg/v37u6zp3r278X/IDz/84PTeHBERoUceeUSSNGzYMA0YMEBPPvmk7rrrLj355JOSpCFDhhS5CiaA0mOCcAClVtxVSP744w8tWLBAW7duVWJiohITE91Ocn02xRle4kqzZs00atQoPfPMM0pPT9f27dv17rvv6t1331Xt2rXVtWtX9ejRw5gotjQKfmNcnG8wC04GnZyc7HK56JKs9FLcyTfdLSldHFlZWfr555+1fPly/fvvv0pKSlJSUpLHQyV3yuM5Lu7E5KVRcGhUzZo1z1pfq1YtHTx40On2gue9ZMmSIntInSl/2FB+GyZMmKBhw4YpMTFR+/fv1+jRozV69GiFhYWpc+fOuuKKK9SzZ88iv9kuruL8jgo+L6mpqTKZTEpLSzM+NNSqVeus4Ut+jcPhKPScl0R5XgfFUfB9pzgf4AuumFXS96yCQ0Zc9ZQo6jFTU1ONITTlpXPnztq+fbuys7N1/Phx7d27V7/88otmzJihzz77TDNnztT48ePVoUOHEh23YI+0s13fRU3WX9mev4MHD+qHH35QXFycjh49qsTExLNOcF5SH3zwgYYMGSKr1aqUlBRNnz5d06dPV0BAgC666CJdeuml6t27t8svPQq+Jkvzvl2ewsPDSz2hff/+/fXvv/9q0qRJys3N1R9//GGsztu0aVN169ZNPXv2VKdOnUq9MuucOXOM13rBcOtMTZo0UadOnbR27VotW7ZMdru9RCvqFvw/5uuvv9bXX39d7PsW/D/GU7Zt22b0RLzqqqvc/i3k6+urm2++WWPGjFFiYqJ+//13p56wjz32mGJjY/Xtt99q8+bNstlsql69ujp27Kjbb7/dWOQAgOcRNgEotbOFFsePH9fjjz9urCTibVdffbWWLFmi6dOn64cffjC6jCclJemnn37STz/9pLCwMN1///0aMmRIif8ALfjhrzjBT8GeRO4+XJYlGPK0zZs367HHHnMZhlSU8niOy1PB4U3FmRPEXU1xV0dy5eTJk4W2L7roIv3++++aMWOGZsyYYfTuS01N1e+//67ff/9db7zxhm677TY99dRTpVpBKF9xrt/8oY7Sf0PJSvp79vHxUWBgoLKysko8pKyyKDgkOS0t7az1BcOEkn4rX5Kl3c908uTJcg+b8vn7+ysyMlKRkZHq2LGjrr/+eg0aNEjJyckaPny4Fi1aVORQ7jMVfA842+uxqP2V6fmbPHmyRo0aVabeqMURGRmpGTNmaNGiRZo2bZo2btyonJwcnT59WuvWrdO6dev04YcfqkePHnrppZcKBfsF37+KM0S04Gu+vN+3y/p/7BNPPKF+/fppypQpWrRokRFo7t27V3v37tX06dPVuHFjPfXUU2cd+u1Kfu8eKW+1t9dff/2s98nOztasWbMKrQZ7Np78P8YTvvnmG+Pn3377rVg94qS8Xl2uhl337NnT7RyPAMoPYROAcjNixAhjCd3IyEgNGDBAl156qaKiolSjRg2jt8L8+fNdTt5YHmrVqqXhw4dr+PDh2r17t/744w+tWbNG69atU3p6ulJTUzV69Gjt3r3bWN68uAr2jCjOh5GCf0SXtjdVRUlKStLgwYONyVpjY2N10003qXPnzgoPDy/0ge/VV1/V/Pnzy6Ud59pzXPADa3GGXrn7YFWw7QMGDNAbb7xRpnYFBwdr4MCBGjhwoA4ePKiVK1dq9erVWrNmjVJSUpSVlaWpU6dq8+bNmjZtWqm/lS/OOResyf8gWvD3XJwPm7m5uUZQ5e0eSqVVcKhgwYnc3SkY+uYPFy2ugtfTihUr3E5uXNlcfPHFuvXWW/X1118rKSlJP//8szE5fHEUDDrO1ru2qPeXyvL8zZ07V//3f/8nKa+HR58+fdSrVy9FR0erRo0ahd5/StIb0h1fX19dc801uuaaa3TixAmtWrVKq1ev1urVq40vb5YsWaJNmzZp5syZxvCmkr6eCz7358LruXnz5nrrrbf0+uuv6++//9bKlSu1Zs0abdq0STk5Odq/f79GjBih1157ze1iKa6sXbvW5WIdxTFr1iw98sgjxf7SrOA1/cQTTxhDz7whLS2t1H9D/Pnnn9q3b1+RE/wDqDiETQDKxV9//WUETbVr19bs2bPd/kFenPlJykOLFi3UokULDRw40FjF6r333lNqaqp+/vln3XzzzSWaOLRgN+/ExEQ1bNiwyPqCQzGKGrJRGcycOdMImjp16qQvvvjC7cTR5Tknybn2HBfscVKcSaXdDUcoOEFvaeercadhw4a6/fbbdfvttys7O1u///673n77bcXHxysuLk6zZ88u0VChgoozGXHB31H+0KbQ0FAFBATo9OnTSkpKUm5ubpEfmo4fP25cdyUZelqZtG7d2vi5OBPu7ty50/g5Nja2RI9VcChTUlLSORM2STJWu5QKzwVUHCV5PRY1CXZlef4+/fRT4+fXXnvN7eu0tMPWi1KzZk1dd911xgTp//zzj9555x399ddfOnbsmD788EN9+OGHkgq/JouzulzB94TSvp7Lo7fN2fj5+alDhw7q0KGDRowYocTERH3xxReaPHmyHA6H3n//ffXu3bvYQ5QLTgz+8ssvuxwGfqa5c+fqt99+06FDh/THH38Yk62fTXn+H1NSP/74o9HT6rbbbjNWnCvKli1bNHr0aDkcDn3//fd69tlny7uZAIqBsAlAuSg4gWqfPn2K/GN8y5YtFdGkIgUFBenWW29VcHCwMWnk8uXLSxQ2tWnTRqtXr5aUd04XXHCB29rMzExj+fSIiIhK/2Gv4O/zvvvuK3KFsvL8fZ5rz3HDhg2N0GT//v1FhiaJiYluP+DGxMTI399f2dnZ5fr8+vv7q3fv3qpbt67RY2T58uWlDpsOHTqkkydPuu1VlpWVpaNHj0rKCwLyP1j6+voqNjZWmzZtUkZGhv79998iJ/Devn278XPB0OZc0qJFC9WuXVtJSUlGUO9Obm6usepe3bp1S9yzqW3btsaKVTabrcRhlSf99ttv+vzzz3Xs2DHdcccdZ11prmBPuJKulFjwecp/b3CnqCCrMjx/J0+e1N69eyXlBT9FzedT0lCuNC644AJ9/vnnuvLKK5WcnFxo5b22bduWqC0FX89nPrcFf+dZWVluh+WVtkeQJ0VEROjpp59WSkqKvv/+e508eVIbNmzQ1Vdffdb7Hjt2zFg9rWnTprr77ruL/Zi//fabpLwheMUNm9q0aWP8XPD/e2/IHzro6+urIUOGqF69eme9T7du3TR16lQlJydrzpw5evzxx4s1dB1A+WI1OgDlouC3ikVNjGy32wt1ly6PFbHS09O1fPlyTZgwQZs2bSqytuAH1ZKuOJW/FLAk4489d5YsWWLMsdG1a9cSPY43FPf3uXTp0kJ/5J/t91nSXlDn2nMcEBBgXFNpaWmyWq1ua4s6n/zJTKW8IVZnmwdtzZo1mjt3bqHw6tSpU1q9erWmTJliTGLrTsEPeGVZeS03N1dLlixxu3/t2rXG8c8c5lMw6D3b73rBggXGzwWvEW8obc8+f39/Y6Lao0ePFvqwfqYlS5YYvT/69etX4t6hl112mfHzvHnziqzNycnRpEmTFBcXV+RCAKU975o1a+qff/7RoUOH9Ouvv571OBs3bjR+PtuKcmdq166d8XN+aO3KqVOntHjxYrf7y+P5K6mC78lhYWFF9vybMmWK8XNp/o+1Wq369ttvC/W0cSU4ONgYvlTwfaN58+bGkLpNmzYZQ+5cycrK0vLlyyXlve+d+b5QcL4rdyuMSoXfE8qD3W7XL7/8olGjRp11MvbSvJ/OmjXLqL3xxhuL3a527doZq/ktX7682CvjNWvWzPjd/fXXX9q/f3+R9QsWLNCvv/561h6CJX1f2LhxoxE2dunSpVhBk5Q3ZD2/l11SUpIWLVpUoscFUD4ImwCUi4J/IOSvKHKm48ePa9iwYYV6PZRH9+309HQNGTJEo0aN0jvvvFPkBMIFexQUd0LKfF26dFF0dLSkvHkD8r+VPFNqaqo++eQTY7u431h6U3F+n1u2bNHzzz9faAWcgsMh8hWc/LWkS0Sfi8/xNddcY/xccNhLQQkJCW735bv33nuNn998802lpKS4rDt8+LCef/55jRw5UjfeeKMxhMbHx0ePP/643n//fb355ptFfkgoGGaV9HVwprFjx7qc8DonJ0fjx483tgs+T5J0xx13GN9Mf/HFF24/oG7btk2zZ8+WlDcMr0+fPmVqb2kUnGS4LMue33fffUZPjXfffdflUKDU1FS99957kvLmWbnrrrtK/DgXX3yx0dtk/fr1mjFjhtvacePG6cMPP9Sdd96p6dOnF9pX8LxLuyJVp06djBXMNm/eXCgYOdOmTZuMLycCAgJ01VVXleixunTpYoQVK1eudPvlw6RJk4o8H089f2VRq1Yt4730yJEjbq+78ePHa9WqVcbcR8nJySUOvcaOHav//e9/evPNN4vsWZmUlGQM7yz4vuHj42O8BzscDr3zzjtuQ4jRo0cb7239+vVzmvy+ZcuWxs/uAoWZM2cWGex7wsaNG/XEE09owoQJhd7HXCnp3xW5ubnGNeXr66v+/fuXqG359Tk5OZo5c2ax73fPPfcYj//SSy+5HX65bds2Pf/883r88cd1//33O+0vy//xBSdEL0nIdmZ9weMA8B7CJgDlonv37sYHkZUrV+rtt9/W7t27lZycrJ07d2rKlCnq06ePjhw5otGjRxv3W7x4sbZs2eLR0KlOnTrGMKCNGzfqjjvu0Jw5c4z2HDt2TFarVaNGjdK7774rSYqKiirVh9a33nrLWF3riSee0JgxY7Rz506lpKTo8OHD+vnnn3X77bcbwx/uueceXXjhhR45z/JUcBWXTz/9VN9++60OHTqkxMRE/fXXX3rrrbd02223KTY2VsOHDzdqv/vuOx05cqTQ8tUF51l66623tG7dOq1evbpY89Tk3+dceo7vuOMOYz6MpUuXasSIEdq0aZOSk5N1+PBhzZ0715gvqail3Hv06GFckzt37tRNN92kOXPm6NChQzp+/Li2b9+uzz77TLfeeqsxwfQzzzxjBDYBAQHGEKW9e/dqwIABmj59unbu3KmkpCQlJSVp+/btmjRpkp5++mlJeT0VSjKh7Znatm2r9PR03XHHHVqwYIHi4+N1/PhxbdiwQYMHDzaCy2bNmqlv376F7hsVFaWnnnpKUl7Acvvtt2vmzJk6ePCgUlJStHv3bn355Ze69957jR4Ar7/+uldWcCx4Ta9bt05ff/21Nm7cqEWLFpVovpxGjRrp0UcflSTt3r1bt99+u37//XfZ7XbZ7Xb99ttvuvXWW41eB88++2yph4e+/fbbRrD1yiuv6OWXX9Y///yjpKQkY76XoUOHaty4cZLyPuSfeS1EREQYIca+ffs0ZswYxcXFaenSpcWar0vKm+fm9ddfN17T//d//6eRI0dq3bp1SkxM1IkTJ7R161Z98sknuueee4zf9SOPPKK6deuW6JwDAwM1ePBgSXmhx+DBgzVr1iwdPXpUycnJ2rRpk1555RWNGTPmrCtXeeL5K4uAgABjLpucnBwNHTpUa9euVVJSkg4fPqwFCxbonnvu0SeffKKXX37Z6GGZkZGhadOm6fjx48VegSx/ouns7GzdfffdGjNmjDZt2qT4+HglJydr3759mjVrlu6++27jmIMGDSp0jHvvvVdms1lSXkj00EMPac2aNcZ7T1xcnJ599llNnjxZklS/fn3j9V9QwZXGxo0bp+nTp+vQoUNKSUnRtm3b9Pbbb+uVV17RwIEDS/aEltDVV19tfPHx+eef67HHHtOyZct04MABpaSk6OjRo1qzZo2efvpp/frrr5KkK6+8Us2bNz/rsVesWGGE6127di3xdd6vXz9jUYeZM2cWO1y88847dfHFF0vKC8gGDBigBQsW6OjRo0pKStLmzZv18ccf684779TJkyfl5+enkSNHOh2n4Pvhxx9/rNWrV2vt2rVn7Vl+/PhxoxdrWFhYiVePK9ira926dZViKCVwvmPOJgDlonbt2nrhhRf0yiuvyOFw6KuvvtJXX31VqKZBgwb69NNPFR0drVatWmnnzp06duyY8e1UwXkbyuqFF15QUlKSFixYoM2bN+u5555zW9ugQQONHz++REtq52vXrp0mTJigJ598UidOnNDYsWM1duxYpzofHx/de++9Lv9Qq4wuv/xy9e3b15i483//+59TzSWXXKJPPvlEJ0+eNOYpWrduna644gp16tRJ06ZNkyTdcsstxjCJhQsXauHChZKk559/vtC31u6ca89xaGioxo4dqwcffFBpaWn67bffnIaFBQcHa/To0Wf9Fvrdd99VUFCQZs+erQMHDri9joOCgvTMM8+oX79+hW5/8MEHFR8fr2nTpmnv3r1FLqMdHh6uUaNGFWtSWndCQkL07LPP6tFHH9Vjjz3msqZu3boaP368ETYUlD95/yeffCK73a6XXnrJ5TGqV6+u119/3al3VEWpXbu2rrzySi1dulQ5OTmFVgtcv359ieYOeeihh5SZmanx48drx44dGjZsmFNNQECAnn766TKFF61bt9aXX36pxx57TAkJCZoxY4bbHjoXXHCBRo8e7fI8br75ZuO1XfC1OHfu3GJPyt+lSxd9+umneu6553Ts2DHNnTtXc+fOdVnr7++vIUOGFAq1S2LQoEHaunWrfv75Zx0/flwvvviiU83ll1+uoUOHFjkUx1PPX1k8++yziouLk91ul81mK9T7UcrrFfP888+rf//+SkhIMIYgvvPOO8a/m2666ayPc9FFF+ndd9/VK6+8opMnT7p9z5Xyrs3HH3/c6bUYEBCgzz77TI899pjWr1+vP/74w+1w3tatW2vcuHGFhszlu/zyy9WnTx/99NNPyszM1Ouvv+70Pta/f389/PDD+uKLL856bqXl7++vCRMm6JFHHtGOHTu0YMGCIofude7c2eiReDYFe+UU5/dzpsjISHXv3l3Lly/X0aNHtXz5cvXo0eOs9/Pz89PEiRP11FNPadmyZdq6davb9+2wsDC9+eab6ty5s9O+m266Sd9++60cDofWr19v9H669957Cw1lPdOcOXOMnufXXXddoR5SxdW/f39jhcYZM2YU+bcegPJH2ASg3AwYMEBNmjTRl19+qX/++UcnTpxQYGCgmjVrphtuuEE333yz8cfkqFGj9Nprr2nz5s3y9fUtNKGoJwQGBmr06NFas2aN5s+fL6vVqsOHDys9PV0BAQGKiIhQTEyMrrrqKvXt29ftpKPF0b17d/3+++/67rvvtGLFCu3evVupqamqVq2a6tWrp06dOmnAgAFlHp5U0d5//3116tRJc+bM0Y4dO5Senq6wsDC1adNGt956q3r16iV/f3/VqFFDo0aN0scff6z9+/crLCysUM+iXr166fXXX9dXX32lAwcOKCAgQA0aNCjRJMfn2nN80UUX6ZdfftGUKVO0YsUKHT16VD4+PjKZTOrWrZvuvfdeNW3aVD///HORxwkICNDbb7+t22+/XbNmzdKGDRsUHx+vzMxMhYaGqmnTpuratatuvfVWY46Ugnx8fPTSSy+pX79+mjNnjv766y9jEm9fX1+Fh4crOjpal156qW666SaXH/ZK6pJLLtGcOXM0bdo0/fHHH0avq/r16+vqq6/WoEGDipwH7OGHH1bv3r31zTff6M8//zRet2FhYWratKm6d++uO+64o9AKYd7w7rvv6r333tMff/yh5ORkhYWFqWXLli5DtLN59NFH1bNnT33zzTdau3at4uPj5ePjo3r16qlr16666667SjxfkSvt27fXokWLNHPmTC1btkw7duxQcnKy/Pz8VKdOHVksFl133XXq2bOn23mhnnrqKfn5+WnhwoVKSEhQSEiImjVrVuJr59JLL9WiRYs0d+5crVixQlu3btWJEyeUnZ1tXNudO3fWzTffbAy7Kw0/Pz999NFHuvrqqzV79mxt3rxZaWlpqlmzplq2bKk+ffrolltuKXJeoXyeeP7Kon79+pozZ44mTZqk5cuX6/Dhw3I4HDKZTOrevbvuvPNOo0fTvffeq6NHj2rBggU6ceKEGjZsqEaNGhX7sfr166fOnTtr5syZWrNmjfbt26cTJ07I4XAoNDRUzZo1U6dOnXTLLbe4/f3Url1b06ZN0+LFi/XTTz9p06ZNSkxMlMPhUO3atWWxWNSrVy9dd911Rs8cVz744ANdcsklmjt3rnbu3Km0tDSFhobKYrFowIABuuaaa9wOM/akBg0aaPbs2frll1+0ePFibd26VceOHVNWVpaqVaumunXrymKx6Prrry/2RN2HDx82voypUaNGsSYTd+Wmm24yjvP9998XK2yS8r4cmThxolavXq158+Zp48aNOnbsmE6fPq3Q0FC1atVKl156qW655Ra3KwVaLBYjkPz333/l6+urqKioIv8/zl9FrmD7S6Nfv3766KOPlJOTozlz5ujJJ59konDAi3wc5blGNQAAOK8cPHjQmEunYI82AAAAnD+YswkAAAAAAAAeQ9gEAAAAAAAAjyFsAgAAAAAAgMcQNgEAAAAAAMBjCJsAAAAAAADgMYRNAAAAAAAA8Bgfh8Ph8HYjAAAAAAAAUDXQswkAAAAAAAAeQ9gEAAAAAAAAjyFsAgAAAAAAgMf4e7sBZRUXF+ftJgAAAAAAAFRJHTp0KPF96NkEAAAAAAAAjznnezblK03SVtls3bpVkhQbG+vllqCq41pDReJ6Q0XiekNF4npDReJ6Q0XieoNUtpFk9GwCAAAAAACAxxA2AQAAAAAAwGMImwAAAAAAAOAxhE0AAAAAAADwGMImAAAAAAAAeAxhEwAAAAAAADyGsAkAAAAAAAAeQ9gEAAAAAAAAjyFsAgAAAAAAgMcQNgEAAAAAAMBjCJsAAAAAAADgMYRNAAAAAAAA8Bh/bzdgzZo1+vrrr/X3338rOTlZISEhiomJUb9+/XTTTTfJ15c8DAAAAAAA4Fzh1bBp3LhxGj16tHx8fNStWzc1btxYycnJWrZsmdatW6fffvtN48ePV2BgoDebCQAAAAAAgGLyWthktVo1ZswY+fj4aNKkSbrsssuMfYcPH9aAAQP0xx9/6JtvvtHAgQO91UwAAAAAAACUgNfGqC1cuFAOh0OXXHJJoaBJkurXr6877rhDkrRgwQJvNA8AAAAAAACl4LWwKTU1VZJUt25dl/vr168vSUpJSamwNgEAAAAAAKBsvBY2NW3aVJK0b98+l/uPHDkiSWrevHlFNQkAAAAAAABl5LWw6cYbb1TNmjW1ceNGLV++vNC+Y8eOaebMmZKku+66yxvNAwAAAAAAQCn4OBwOh7ce3Gq16sknn9SBAwfUtWtXNWnSRCdOnNCKFSvk4+OjZ599VrfeemuRx4iLi5MkBQcHV0STy1VGRoYkqXr16l5uCao6rjVUJK43VCSuN1QkrjdUJK43VCSuN0hSenq6JKlDhw4lvq/XVqOTpJYtW+q2227Tp59+qlWrVmnVqlWSJB8fHw0YMKBUJwQAAAAAAADv8VrYdOLECd19993asWOHbrrpJj3yyCOqX7++Tpw4oSVLluj999/X/PnzNX78eHXp0uWsx4uNja2AVpevrVu3Sqoa54LKjWsNFYnrDRWJ6w0ViesNFYnrDRWJ6w3SfyPJSsNrczaNGjVKO3bs0LXXXqt33nlHTZo0UUBAgOrUqaMBAwborbfeUnp6ul599VXl5uZ6q5kAAAAAAAAoAa+FTb/99pskqU+fPi73d+/eXVLeanW7du2qsHYBAAAAAACg9LwWNqWlpUmSqlWr5nK/v7+/fHx8JP03KRUAAAAAAAAqN6+FTQ0bNpQkbd682eX+PXv2yOFwyMfHR40aNarIpgEAAAAAAKCUvBY29e3bV5L0+eefa9++fYX2ZWVl6cMPP5QkdevWTRERERXePgAAAAAAAJSc11aje/DBBxUXF6eVK1eqT58+6t69u+rVq6fU1FStWbNGCQkJatCggd544w1vNREAAAAAAAAl5LWwKTAwUJ999pl+/PFH/fjjj/rrr7+0YsUKVatWTc2aNdNdd92lu+++W2FhYd5qIgAAAAAAAErIa2GTJPn6+qp///7q37+/N5sBAAAAAAAAD/HanE0AAAAAAACoegibAAAAAAAA4DGETQAAAAAAAPAYwiYAAAAAAAB4DGETAAAAAAAAPIawCQAAAAAAAB5D2AQAAAAAAACPIWwCAAAAAACAxxA2AQAAAAAAwGMImwAAAAAAAOAxhE0AAAAAAADwGMImAAAAAAAAeAxhEwAAAAAAADyGsAkAAAAAAAAeQ9gEAAAAAAAAjyFsAgAAAAAAgMcQNgEAAAAAAMBjCJsAAAAAAADgMYRNAAAAAAAA8BjCJgAAAAAAAHgMYRMAAAAAAAA8hrAJAAAAAAAAHkPYBAAAAAAAAI8hbAIAAAAAAIDHEDYBAAAAAADAYwibAAAAAAAA4DGETQAAAAAAAPAYwiYAAAAAAAB4DGETAAAAAAAAPIawCQAAAAAAAB5D2AQAAAAAAACPIWwCAAAAAACAxxA2AQAAAAAAwGMImwAAAAAAAOAxhE0AAAAAAADwGMImAAAAAAAAeAxhEwAAAAAAADyGsAkAAAAAAAAeQ9gEAAAAAAAAjyFsAgAAAAAAgMcQNgEAAAAAAMBjCJsAAAAAAADgMYRNAAAAAAAA8BjCJgAAAAAAAHgMYRMAAAAAAAA8xt/bDZCk5cuXa+rUqbLZbMrKylLdunXVq1cvDRw4ULVr1/Z28wAAAAAAAFBMXu/ZNHr0aA0ePFgbN25Uly5ddN111ykzM1MTJ07ULbfcosTERG83EQAAAAAAAMXk1Z5NS5cu1bhx49SoUSN99dVXatCggSQpKytLDz74oNatW6dRo0bpzTff9GYzAQAAAAAAUExeDZs++ugjSdIbb7xhBE2SFBQUpBdffFGLFy/WBRdc4K3mAQAAAAAAoIS8Fjbt2LFDO3bsUJMmTdSlSxen/a1bt1br1q290DIAAAAAAACUltfmbFq3bp0kqVOnTt5qAgAAAAAAADzMaz2bdu7cKUlq0qSJ9u3bp3Hjxmn16tVKTk6WyWTS5ZdfriFDhshkMnmriQAAAAAAACghH4fD4fDGAw8bNky///677rzzTs2dO1cmk0nt27dXTk6O/vjjDyUlJclkMunbb79Vw4YN3R4nLi5OkhQcHFxRTS83GRkZkqTq1at7uSWo6rjWUJG43lCRuN5QkbjeUJG43lCRuN4gSenp6ZKkDh06lPi+XuvZlN/ob7/9VsOHD9fQoUPl65s3qi8tLU0DBw6U1WrVq6++qilTpnirmQAAAAAAACgBr4VN+cFS8+bNNWzYMPn4+Bj7QkND9dxzz+muu+7SypUrdeTIEdWrV6/I48XGxpZreyvC1q1bJVWNc0HlxrWGisT1horE9YaKxPWGisT1horE9VZy2bnZWrR7kbYnblfaqTSFBoYqJiJGvVr0kp+vn7ebVyr5I8lKw2thU2hoqCTpwgsvLBQ05evQoYOCgoKUlZWlLVu2nDVsAgAAAAAAqEgJJxM0KW6SJsZN1IGUA077G9dsrIc7PKyH2j+kyJBIL7TQO7y2Gl3jxo0lSZmZmS73+/j4qE6dOpL+G3IHAAAAAABQGaw+sFqx42L10tKXXAZNkrT/xH69uORFxY6L1ZoDayq4hd7jtbDJbDZLkvbu3etyf25urux2uySpdu3aFdUsAAAAAACAIq0+sFpXTb1KiRmJxapPzEhUj6k9zpvAyWthU/fu3RUcHKzNmzdry5YtTvvXrl2r06dPKyAgQBaLxQstBAAAAAAAKCzhZIL6fttXmdmuR2q5k5mdqRu+vUEJJxPKqWWVh9fCppCQEN1///2SpNdee02pqanGPrvdrnfeeUeSdMMNN6hGjRpeaSMAAAAAAEBBk+ImFbtH05kSMxL12cbPPNyiysdrE4RL0pAhQ2S1WrVixQr17t1bl112mRwOh5YtW6bjx48rNjZWzz//vDebCAAAAAAAIClv1bmJcRPLdIwJGyZoZLeR5+wqdcXhtZ5NkhQQEKCJEyfqlVdeUb169fTbb7/p119/VWRkpEaMGKFvvvmGXk0AAAAAAKBSWLR7kdvJwIvrQMoBLdy90EMtqpy82rNJknx9fXXXXXfprrvu8nZTAAAAAAAAXMrMztTaQ2s9cqwdiTt0batrPXKsysjrYRMAAAAAAEBltDtpt55b/Jxsdpt2Ju5U/bD6Hjlu6qnUsxedwwibAAAAAADAecfhcOhI2hHZ7Da1i2qnuqF1nWoC/QI1a8ssY9t+0u6Rxw4LDPPIcSorr87ZBAAAAAAAUNFeWPyC6vxfHTX4qIGu+foaLdq9yGVdwxoNVTOoprGdlZPlkcePjoj2yHEqK8ImAAAAAABQJWRmZ+qvI39p2j/TNGbtmCJrkzKSjJ+tdqvLGh8fH5lNZmO7Sc0migqJKlMbG9dsrF4tepXpGJUdw+gAAAAAAMA572jaUTX8qKFyHDmSpNDAUA3rNEy+Ps79bAoGSJJks9vcHvfdq9+Vv6+/2kS2UY2gGnprxVt6aelLpW7nwx0elp+vX6nvfy6gZxMAAAAAAKi0Ek4maMGuBfpw9YcaOHegftn5i8u6qJAohQaGGttpp9K0/8R+l7UWk0WSFBwQrE4NOumCqAvcPn73xt11ScNLVCOohiRpcIfBiqgeUapziageoYfaP1Sq+55L6NkEAAAAAAAqrY///Fhvr3zb2DaFmHRdq+uc6nx8fGSJsmjl/pXGbdZ4q5qGN3WqjY2M1e7HdqtpeFOXPZ+KEhkSqfl3zFePqT2UmZ1Z7PtV86+m+XfMV2RIZIke71xE2AQAAAAAACpUTm6OvrF+I6vdKpvdpj3H92jLsC3FGvLmbn4lSWpnaqcDJw7IEmWRxWRR81rNXdb5+/q73VccXRp10eJ7F6vvt32VmJF41vqI6hGaf8d8dWnUpdSPeS4hbAIAAAAAAB6Xk5ujjOyMQkPb8vn6+Oqx3x5Tcmaycdu+5H1qVquZU60lylJo2xrvPmwac90YjfMZV/pGl0DXRl21ddhWfbbxM03YMEEHUg441TSu2ViPdHhED7Z/8Lzo0ZSPsAkAAAAAAHjEyv0rNXnjZNnsNm1J2KKhHYfqg14fONX5+PjIYrLoj/1/GLfZ7DaXYVN0RLQuaXiJ2tRpI0uURWaTWQ6HQz4+Pk61JR0SV1aRIZF64dIXNLLbSC3cvVA7Enco9VSqwgLDFB0RrV4telX5ycBdIWwCAAAAAADFkpyZLJvdpq6NuroMdg6mHNRX/3xlbBe1ypvZZC4UNlntVt0Qc4NTXaBfoNY8sKaMLS9ffr5+urbVtbq21bXebkqlQNgEAAAAAACKdNcPd2nFvhU6mHJQkrT7sd0u5zzKX+UtX1HzK90QfYNqBtU05leKqRPj2UbDawibAAAAAAA4T+Xk5mjP8T2y2q0KDQxVrxa9XNYdTDloBE1S3rxJrsKmVhGtFOAboNO5pyVJp3JOKe1Umst5m+gJVHURNgEAAAAAcB5asGuBbvz+RmVkZ0iSerXo5TZsMkeatWLfCmPbareqX+t+TnWBfoH67IbP1KBGA1lMFplCTC7nVkLVRtgEAAAAAEAVkj+vks1ukzXeque6P6dGNRs51TWq2cgImqSiV3nLXxHO39dfMRExCgsMc1t734X3laH1qAoImwAAAAAAqEL6fdevUC+kni16ugybWtUuPOTtSNoRJaYnujzmTbE3qWujroqJiFGQf1D5NBxVBmETAAAAAACVXEpWin7f83tebyW7VeFB4fqs72cuay0mS6GwyWa3qX/r/k51AX4Bal2ntY6kHZHFZJHZZDaCpzOZQkwyhZg8ci6o+gibAAAAAACoBBwOhxxyyNfH12nfwZSDunnGzcZ2vdB6bo9TkhXhVg1apdDA0ELzKh3X8ZI0G3BC2AQAAAAAgJfM3z5fC3YvkNVulTXeqs/7fe6yF1Kr2q0U6BeoUzmnJP035C0iOMKp9oK6F6hNZBujt1K3Rt3cPn5YkPu5l4DSImwCAAAAAKCcZGZn6lDKIbWo3cLl/oW7F2rc+nHGtjXeWuSQt03xm4zbbHabLm96uVPtJQ0v0eahm8veeKCUCJsAAAAAAPCgpIwkPfLTI7LardqZuFORIZE68tQRl7Vmk7nQdlFD3m5ve7uuaHKFzCazLFEWtYtq59F2A55C2AQAAAAAQDE5HA4dSTsia7xVzWs1V6uIVk41NYJqaN72ecaQt6NpR3Us/ZjqBNdxqrVEFZ5faVfSLreP/fylz5ex9UDFcJ51DAAAAAAAOPn4z48V8X6EGnzUQL2n99a3tm9d1vn7+iu2Tmyh22x2m8tai8miN698U3Nvm6vdj+3WhsEbPN5uoKLRswkAAAAAcF7LzM7U1oStstlt2n18t/53xf9c1gUHBOt45n8rtbkLkKS8Hkv/xP8jSWoa3lSpWaku68KCwvTiZS+WvvFAJUTYBAAAAAA4b+Xk5qjO+3V08vRJ47ZhHYcpMiTSqdZiKjzkraj5lZ7u8rSGdRymNpFtVCOohucaDJwDCJsAAAAAAFVOYnqiNhzeIJvdJqvdqu6Nu+vB9g861fn5+qlVRCv9ffRv4zab3aYrm13pVNvW1FaSFBIQoramtrow6kI5HA75+Pg41V5Q9wLPnQxwjiFsAgAAAABUOT9s/UGDfxpsbJ88fdJl2CTl9VgqTthUI6iG9o7Yq0Y1G8nXhymQAXcImwAAAAAA54zvbd8r7kicbHabbHabNgzeIFOIyanuzFXerPHuh7xZTBY1DW8qs8ksi8miTg06ua1tEt6k9I0HzhOETQAAAACASiMnN0epp1IVXi3c5f73Vr2nv47+ZWzb7Db1aNbDqa5tZNtC2zuTdirjdIaqB1R3qn2669N6ptszZWs4AANhEwAAAADAq6zxVn245kPZ7DZtSdii61pdp1kDZrmstURZihU2hQWFqV9MP0VUj5AlyiKzySw/Xz+Xx3Q15xKA0iNsAgAAAACUq+TMZG22b1a7qHYKCwpz2p9+Ol1f/fOVsV3UKm/mSHOh7aKGx829fW7JGwugzAibAAAAAADl4vHfHtfsrbN1MOWgJOn3e37XVc2vcqrLX+Ut366kXW6HvPVo1kPPd3/emF8pOiK6fBoPoNQImwAAAAAAJZKTm6M9x/fIarcqOzdbA9oOcFl3PPO4ETRJeUPeXIVNoYGhahbeTP8m/ytJql29tg6mHFSriFZOtR3qd1CH+h08dCYAygNhEwAAAACg2DbbN6vjZx2VkZ0hSYqOiHYbNllMZ6wIV8TwuFHXjFJIYIgsJotMISbmUQLOYYRNAAAAAACdyDwhm90mq90qm92mgRcO1MX1L3aqaxre1AiapKKHvJlNefMr+fv6KyYiRvXD6rt9/H6t+3ngLABUBoRNAAAAAACN+G1EoUm6W9Zu6TJsCgkMUfNazbXn+B5JUq4jV1sStrgc2ta9cXdtemSToiOiFeQfVH6NB1CpEDYBAAAAQBWVmZ2pX3b+YvRYSjuVpl/v+tVlrdOQtyJWeTObzErJSpHFZJHZZHa5wpyUNxeTJcrich+AqouwCQAAAADOYQ6HQzmOHPn7On+8y8nN0S0zbpFDDkmSj3yUfjpdwQHBTrVnhkK2BJvbx/zu5u9Uzb8a8yoBcImwCQAAAADOMcv2LtOsLbOM+ZVeuvQlPdHlCae6/CFvu4/vliQ55NCWhC0uh8dZTBa1jWwrs8kss8msDvXcr/jman4mAMhH2AQAAAAAlUxmdqZ2J+1WW1Nbl/s3HtmocevHGdtFrfJmNpmNsEmSbHaby7CpXlg92Ya6780EAMVF2AQAAAAAlUCuI1d3zr5T/8T/o52JO5XryFXq86kKCQxxqs1f5S2fze4+JOrfur8a12wsi8kiS5TF6b4A4GmETQAAAABQzhwOh46kHZE13qqI4AiXPYt8fXwVdyROu5J2GbdtSdiijg06OtWeOZn3vhP75HA4XM6hNPDCgRp44cCynwQAFBNhEwAAAACUo+9t32vIz0N0PPO4pLzw54t+X7isNZvMhcImm93mMmyqG1pX7139nmIiYmSJsqhpeFMm6wZQaRA2AQAAAEApZGZnamvCVtnsNlntVr16+asuh7zVrl7bCJokyRrvfn4li8miudvmSpKahjdVjiPHZZ2Pj4+e7fZs2U4AAMpJpQubli5dqkceeUSSNHXqVHXu3NnLLQIAAAAAZxdNvEjbjm0ztm9pc4s6NejkVGeJKjzkbUvCFuXk5sjP18+p9r4L7tO1La9VW1Nb1Qiq4flGA0AFqFRhU0pKil555RVvNwMAAADAeepE5gn9efBPo7dS81rN9crlrj+jxNaJLRQ22ew2l2FTVEiUIqpHKCM7Q2aTWeZIs06ePukyTGpRu4Va1G7huRMCAC+oVGHTW2+9Jbvdrlq1aun48eNnvwMAAAAAeND6w+vVe3pvY7tDvQ5uwyaLyaI52+YY2+5WhPPx8ZF1iFVRoVHy9fH1bIMBoBKqNGHT8uXLNXfuXPXq1UvJyclat26dt5sEAAAAoIqYv32+Vu5fKavdKqvdqlm3zlLnhs5Tdpy5ytvmhM1uh7xZoixqUrOJLFEWWUwWXd38arePXy+sXtlPAgDOEZUibEpNTdXLL7+sGjVq6KWXXtLTTz/t7SYBAAAAOIfk5OYoMSNRphCTy/1f/vOlftj6g7Fts9tchk2mEJPqBNfRsfRjkvImAd99fLeiI6Kdam+OvVm3tLnFQ2cAAFVHpQib3n77bcXHx+vtt99WVFSUt5sDAAAA4Bxw4MQBvbz0ZdnsNm1J2KLYyFjFDY5zWWuONDuFTa74+PhoQJsByszOlCXKIrPJrIY1GrqtBQA483rYtGLFCv3www/q3r27br75Zm83BwAAAEAlkZyZLJvdppa1W6puaF2n/YF+gfrqn6+M7aJWeTtzRbjNCZvdPu6468eVodUAAK+GTWlpaXrllVcUGhqqN998s0zH2rp1q4da5T0ZGRmSqsa5oHLjWkNF4npDReJ6Q0Xieis/E7dM1Pd7vtfR9KOSpNcvfl23NHc9XK12UG0lZSVJyhvytnDDQjUNa+pUVyu9lh5s/aCia0Yruma0moY1Pad+d1xvqEhcbygrr4ZN7777ro4cOaLXX39d9eoxYR4AAABQleXk5ujAyQPaeWKnEjMTdXvL213Wnc49bQRNkrTzxE63x2xVs5XW2tdKkmoF1VJCRoLLsKl+SH092e7Jsp0AAKBYvBY2rVq1SjNnzlSXLl102223lfl4sbGxHmiVd+WnxlXhXFC5ca2hInG9oSJxvaEicb2VTHJmsup/WF8Z2Xk9JoL8gvTK9a+4HPLWw9FD47eMN7YPZR9y+zy/W/1dZedmy2KyyBRiqrLzKHG9oSJxvUGS4uJcz4FXHF4Jm9LS0vTSSy8pJCSkzMPnAAAAAHhPSlaKrPFWWe1WWeOturbVteoT3cepLrxauMKCwoywKSsnS7uSdimmToxTrdlkliT5+/orJiJGMRHONfmuaHqFZ04EAOAxXgmbvvvuOx0+fFiNGjXS+++/77R/5868brJjxozR9OnT1blzZ911110V3UwAAAAAZzFqzSj9b/n/jG1/X3+XYZOUFyIt+XeJsW21W12GTS1rt9Q/j/yjmIgYBfkHebzNAIDy5ZWwKX+ysQMHDujAgQNu69avXy9JCg4OrpB2AQAAAJAcDofmbJsjm90mq92qHYk7FDc4Tv6+zh8fzlzlzWq3uj2uxWTRpvhNspgsspgsahbezGWdn6+f2kW1K9tJAAC8xith06OPPqpHH33U7f577rlH69at09SpU9W5c+cKbBkAAABwfnA4HDqVc8plzyEfHx8N+XmI7Cftxm27knapdZ3WTrX5Q97y2ew2t4/5fz3/Tx/3/rj0jQYAnBO8uhodAAAAgIqz4fAGffHXF7Il2GSNt+rudndr9LWjXdZaTBYt/nexsW2z21yGTS1qtVD7eu0VHREtc6RZZpNZuY5c+fr4OtUG+AV47mQAAJUWYRMAAABQRWRmZ2rbsW0ym8wuh7wdOHFA4zf8t8pbUb2QzgybrPFW3dLmFqc6P18/xQ0u/YpFAICqh7AJAAAAOMcN/Xmolvy7RDuTdirXkastQ7coNtJ5yfIzh7xZ7VY5HA75+Pg41V7T8hrlOnJlNpllibKobWTbcms/AKBqqZRh07Rp07zdBAAAAMDrHA6HjqQdkTXeKn9ff13V/CqXdbuSdml74nZj22a3uQybmtdqrur+1ZWRnbdgT/rpdB3PPK7a1Ws71fZu2Vu9W/b20JkAAM4nlTJsAgAAAM53K/atUP/v+ut45nFJ0hVNr3AbNplNZi3as8jYttqturXtrU51fr5+Gn3taJlCTDKbzGoa3tTl3EoAAJQFYRMAAABQgTKzM7U1YatsdptsdpuGdByipuFNnerqh9U3giYpb84kd0PeLCaL8XPT8Kaq5l/N7eM/2P7Bsp0AAABnQdgEAAAAVKD+3/XXgt0LjO0O9Tu4DJuahTcrNOQtMSNR8SfjVTe0rlPtda2u05oH1qhNZBvVCKpRbm0HAKA4CJsAAACAMjp56qRW7l8pm90mq92qav7VNKHPBJe1bSPbFgqbrPFWDWg7wKnOz9dPbU1ttTVhq9qa2socadbpnNMujxkVGqWo0CjPnAwAAGVE2AQAAAAUk7thbEfTjqr39P8m065dvbY+vf5T10PeoiyFtm0JNreP99tdv6lW9VrMqwQAOKcQNgEAAABuLN6zWAt2LzB6LH3Y60OXvZCa1Wqm4IBgpZ9OlyQlZSTpaNpR1Qur51RrMVnUNLypzCazLCaLujbq6vbxI4IjPHcyAABUEMImAAAAnLdycnN0JO2IGtZo6HL/r7t+1YdrPjS23Q158/XxVdvItlp/eL1xm81ucxk2dajfQf+O+NcDrQcAoHIibAIAAMB5JTUrVY/++qhsdpu2JGxRNf9qSnw20eWQN7PJXGjbare6PW7/1v1lMVlkibLIbDKrU4NOHm87AADnAsImAAAAVCnJmcnabN+sqNAotazd0ml/SGCIZm2ZpZOnT0qSMrIzdCTtiOqH1XeqtZgKz6+09dhWt4/7wqUvlLHlAABUDcw0CAAAgCph8sbJajSqkWq9V0vdv+iuL/76wmWdr4+v2praFrrNZnc9SXdsZKye7/68pt80Xf888o82PbLJ4+0GAKCqoWcTAAAAKrWc3BztOb5HVrtV245t0/Pdn3c55C3AN0AHUw4a20Wt8mYxWbTu0DpJUp3gOjqecdxlXXBAsN6+6u0yngEAAOcXwiYAAABUWg6HQ/U/qi/7Sbtx230X3KcGNRo41VqiCg95s8a7n19pWMdhut18uywmi0whJpfhFQAAKB3CJgAAAFS41KxUbYrfJKvdKpvdpgvrXqgH2z/oVOfj46Nm4c0KhU1Wu9Vl2BRbJ1a+Pr7ykY9i6sSoXVQ75Tpy5evjPHPERfUu8uwJAQAAA2ETAAAAKtycbXN039z7jO0bom9wGTZJeSvCrT201ti2xlvVu2Vvp7rqAdW1eehmNQtvpiD/IM83GgAAFAthEwAAADzm5x0/K+5InNFjadE9i9SwRkOnujNXebPa3Q95s5gsqhNcRxaTRRaTRR0bdHRb27pO69I3HgAAeARhEwAAAIrN4XAo/XS6QgJDXO5/Y8UbTr2QXIVNreu0lq+Pr3IduZKkvcl7lZqVqrCgMKfa4Z2G67HOjzGvEgAA5wjCJgAAABRpZ+JOffznx7Il2GSNt6pb426af8d8l7UWk6VQ2GSz23Rtq2ud6qoHVNd1ra5TSEBIXo+lKIsC/AJcHtPP188zJwIAACoEYRMAAMB5LjM7U1sTtqpl7ZYuexadPH1S4zeMN7aLWuXNaUW4IobHuQusAADAuY2wCQAA4Dz18pKXNXPLTO1M2qlcR65+vvNnXdfqOqe6M4e87TuxTylZKaoRVMOp9tLGl+rRTo8avZXaRLYp9/MAAACVC2ETAABAFeNwOHQk7Yis8VadPH1SN8Xe5LIu/mS8tiduN7ZtdpvLsKmafzW1qt3KqA0JCNG+5H1OvZgk6aJ6F+miehd56EwAAMC5iLAJAACgCtmVtEudJ3dWUkaSJKlJzSZuw6aSrAj3Vo+35O/rL0uURU3Dm8rXx9dzjQYAAFUKYRMAAMA5IH9eJZvdJqvdqlvb3KqODTo61TWs0VAnMk8Y20UNeTObzMbPTcObKqJ6hNvHv7nNzWU8AwAAcL4gbAIAADgHjPh1hCZtnGRsR1SPcBk2VfOvplYRrbTt2Dbjts32zerSqItTbccGHbV60Gq1NbV1GUYBAACUBmETAACAl5zOOa0l/y4xeisdSz+mn+78yWVtwV5IUtFD3iwmi/af2C+zySxzpFmhgaEu60IDQ12GUAAAAGVB2AQAAFDOHA6HfHx8nG7PdeTq+m+uV44jx7jtROYJ1axW06n2zMm4bXab28eb3HeyQgNDmVcJAAB4BWETAACAh/158E/N2TpHVrtVVrtVwzsO18juI53qgvyDFB0Rra3Hthq3bU7YrK6NujrVWkwWNanZRJYoi8yRZrWv197t4zMkDgAAeBNhEwAAQAnl5OZob/JetajdwuX+DYc36P3V7xvbRQ55i7IUCpus8VaXYVNEcIT2Pr639I0GAACoIIRNAAAAxeBwODR4/mD9dfQvbUnYoozsDB0feVzh1cKdai2mwkPeigqberfordCA0LweSyazOtTr4OmmAwAAVCjCJgAAAEnJmcmy2W0KCQjRRfUuctrv4+Oj1QdXa0vCFuO2zfbN6ta4m1PtmZN5707arZzcHPn5+jnV3n/R/br/ovs9cAYAAACVA2ETAAA4r/204ycN/XmoDqQckCTdablT02+a7rLWbDIXCptsdpvLsCkiOEKvX/G6WtRuIbPJrJiIGJdBEwAAQFVE2AQAAKqknNwc7Tm+R1a7VTa7TSM6j3C5yluNoBpG0CTlzZnkjsVk0YzNMyRJdYLrKDM7023ty5e/XIbWAwAAnLsImwAAQJXUeXJnxR2JM7Z7NOuh7o27O9WdOeRt27FtOp1zWgF+AU61t5tv1yUNL5HFZJEpxCQfHx/PNxwAAOAcR9gEAADOGemn0/XXkb9ktVtljbeqXlg9vXTZSy5rW9ZuWShsstltLsOm2tVrq35YfdlP2hUTESOzyayUrBRFBEe4PGbL2i09d0IAAABVEGETAAA4Z8QdjtNlX15mbJtNZrdhk8Vk0febvze2ixoet2rQKtUPq69Av0DPNRYAAOA8RdgEAAC8bsm/S/THvj9kS7DJZrdp8g2Ti7XK27Zj23Qq55TLkMhsMqtOcB1ZTBZZTBb1bNHT7eM3DW9a5nMAAABAHsImAABQ7hwOh1KyUlxO0C1JkzdO1re2b43tTfGbXIZNtarXUoOwBjqUekiSlJ2brR2JO5xCKEm6IeYGJbRO8NAZAAAAoLgImwAAQLmIT4vX68tfly3BJmu8VQ1qNJB1iOuhbGeGRVa7+yFvN0TfoOOZx2UxWWQ2mdW4ZmOXdb4+vqVvPAAAAEqNsAkAAJRKZnamth3bprqhdVU3tK7T/iD/II3fMN7YTj2V6nbIm8VkKbRdVNj0aZ9Py9BqAAAAlDfCJgAAUCKj147W+PXjtTNpp3IduRp33TgN7TjUqS68Wrga1miogykHJeUNedt+bLssURan2vb12uuxTo/JbDLLEmVRm8g25X4eAAAAKB+ETQAAQFLevEpH0o7IGm/VodRDGnTRIJd1J0+d1PbE7cZ2Uau8mU1mI2wKDgjWodRDLsOmBjUa6JNrPynjGQAAAKAyIGwCAABKP52uRqMaKSkjSZLk7+uvuyx3Kcg/yKn2zLDIlmBze9ynuzytRzo8IkuURU3DmzKPEgAAwHmAsAkAgCosMztTWxO2yma3yWa36dIml6pPdB+nuuCAYIUEhBhhU3ZutrYnble7qHZOtQUn824a3lRNajZx+/hXNb/KA2cBAACAcwlhEwAAVdjHf36s5xc/b2yfyDrhMmyS8kKkAykHjG2b3eYybGpSs4lWD1qttqa2qhFUw/ONBgAAwDmNsAkAgHPQwt0LZY23ymq3akvCFv1x/x8uh7wV7IUkFb3Km8Vk0Yp9K9TW1FbmSLMa12zsss7Hx0ddGnUp2wkAAACgyvJ62LR7925NmTJFf/75p+x2uwIDA9WsWTP17t1b9957r4KCnP9wBgDgfJCTmyM/Xz+X+x6a/5D2n9hvbG87tk0X1L3Aqc5iOmN+JbtNDodDPj4+TrWvXvGq3rn6HeZVAgAAQJl4NWxasGCBnn76aZ06dUqtW7dWly5ddOLECa1atUoffPCBfvvtN02dOlUhISHebCYAABXCZrdp6j9TjfmVrmt1nSb0meCy1mwyFwqbbHaby7Cpcc3GMpvMahreVOZIsyxRFuU4cuTv4/wnQHBAsOdOBgAAAOctr4VN8fHxeu6553Tq1CmNHDlSgwb9t7zy4cOHNWDAANlsNk2ePFkjRozwVjMBAPCYnNwc7Tm+R03DmyrAL8Bp/77kffq/1f9nbJ9tyNsvO38xtm121yvC+fj4yDrE/XEAAAAAT/NaP/m5c+cqPT1dF1xwQaGgSZLq16+vBx54QJK0cOFCbzQPAACPGblopC6edLHC3glT9NhobUnY4rLOEuV6yJsrVza9UoMuHKRR14zSonsW6amuT3m83QAAAEBpeK1nU/fu3VW7dm01bNjQ5f7mzZtLko4ePVqRzQIAoESSM5O12b5ZOY4cXdbkMpc1mxM2K+5InLFttVtdDnlrVKORagTVUEpWiiTp5KmTOpJ2RPXD6jvVXtPyGl3T8hoPnQUAAADgOV4Lm9q2bau2bdu63W+32yVJtWrVqqgmAQBQbOsPrddNM27SwZSDkqQuDbto9QOrXdZaTBb9vPNnY7uoIW/vXvWualarKbPJrJiIGJcrzAEAAACVmddXo3PF4XBo1qxZkqTevXt7uTUAgPNJ/rxKNrtNVrtVd7e7W81rNXeqiwqNMoImqehV3swms/FzneA68pFzTb4hHYeU8QwAAAAA7/JxuJsMwosmTZqkDz/8UOHh4Vq4cKFq1qzptjYuLm9YQnDwub+CTkZGhiSpevXqXm4JqjquNVSkc+16e3TVo1p8aLGx/W6nd9W3aV+nOofDoUvmXqLU06nGbYuuX6QGIQ2cao9lHtOOEzsUXTNaEUERLgMpeMa5dr3h3Mb1horE9YaKxPUGSUpPT5ckdejQocT3rXQ9mz7//HN99NFHCggI0CeffFJk0AQAQHGcyjkl23GbdiTv0K6UXXI4HHq5w8sua5uFNSu0vfPETpd1Pj4+alWzlTYlblLTsKZqVbOVsnOzXdbWqVZHdarVKdtJAAAAAOeIShM2ORwOvffee/riiy8UGBioDz/8UJdcckmx7x8bG1uOrasYW7dulVQ1zgWVG9caKlJluN4OnDigu2ffbWyHBoZq+l3TXfYwujL7Sk3eNtnYPpxz2G3b5zecr4jqEcyrVIlUhusN5w+uN1QkrjdUJK43SP+NJCuNShE2ZWVl6ZlnntGCBQtUo0YNjRkzpkRBEwDg/LTmwBot2rNIVrtV1nirXr7sZd3V7i6nuoY1GqpmUE2dyDohSUo7laZ9J/apaXhTp1qzyaw6wXVkMVlkMVnUtVFXt4/vapU4AAAA4Hzn9bDp1KlTevjhh7VmzRo1bNhQkyZNUosWLbzdLABAJeBwOJSYkag6wa6HoM3fMV/vrHzH2P4n/h/dJeewycfHR5Yoi1buX2ncZo23ugybLCaL7E/bmVcJAAAAKCWvhk25ubl65plntGbNGsXGxuqzzz5TZGSkN5sEAPCyzOxMPbXgKdkSbLLGW3U697ROPHdCvj6+TrUWk6XQttVudXvc3i16q0FYA1lMFplNZrc9lgiZAAAAgLLxatg0duxY/fbbb2rRooW++OIL1apVy5vNAQBUgMzsTG1N2KoaQTXUorZzT9YgvyB9Y/tGyZnJxm37kvepWa1mTrVmk7nQts1uc/u4L172YukbDQAAAKDYnL8mriC7d+/WxIkTFRAQoLFjxxI0AUAV9631W8WOi1Xo26FqP6m9JmyY4LLOx8fHKURy12Mppk6MHu30qCb1maQ1D6zR5qGbPd5uAAAAACXjtZ5NkyZNUnZ2tho1aqRvv/22yNphw4YpPDy8YhoGACgRh8OhI2lHZI23anPCZj1+yeMuh7z5+Pho27FtxnZRQ94spv/mVwoJCNGx9GMu6wL9AjX62tFlPAMAAAAAnuS1sOnw4cOSpAMHDmjq1KlF1t53332ETQBQScWMjdHOpJ3Gdv/W/dW8VnOnupIMeXvgogd0TYtrZImyqGl4U5fhFQAAAIDKyWth07Rp07z10ACAs8jKztLWY1tljbfKarcqJiJGD7R/wGVtvbB6hcImm93mMmyKjoiWv6+/snOz1TS8qcwms07lnFKgX6BTbYf6HdShfgfPnRAAAACACuPVCcKBipCdm61Fuxdpe+J2pZ1KU2hgqGIiYtSrRS/5+fp5u3lApTR321zdPvt2Y/uaFte4DZvMkWat2LfC2LbGW9U3pq9TXaBfoNY/tF7NazVXjaAanm80AAAAgEqBsAlVVsLJBE2Km6SJcRN1IOWA0/7GNRvr4Q4P66H2DykyJNILLQQq3vK9y7Xh8AZZ7Xk9lmbdOqtYq7wVOb9SlEXBAcEym8wyR5rVvl57t7UX1r2w1G0HAAAAcG4gbEKVtPrAavX9tq8SMxLd1uw/sV8vLnlRH635SPPvmK8ujbpUYAuB8nM657QC/AJc7nt12atavm+5sb0pfpPLsCk6IloBvgE6nXtaknQ49bCSMpJUu3ptp9pBFw3S4A6DmVcJAAAAgCTCJlRBqw+s1lVTr1Jmdmax6hMzEtVjag8tuXcJgRPOSfuS92n8+vFGb6U2kW204O4FLmvNJnOhsMlqt6pf635OdQF+Abq6+dXy8/WTOdIsS5TF5dxKktzeDgAAAOD8RNiEKiXhZIL6ftu32EFTvszsTN3w7Q3aOmwrQ+pQ6eTk5mjP8T2qG1pXYUFhTvtPnj6p91e/X6jenZKsCPfLXb+UorUAAAAAzneETahSJsVNKnLoXFESMxL12cbP9MKlL3i4VUDpvL/qfc3YPENbErYoIztDc26bo/6t+zvVtardSoF+gTqVc0qSdCTtiBLTExURHOFU26VhFw26cJAsURaZTWa1i2pX3qcBAAAA4DzDBBuoMrJzszUxbmKZjjFhw4Qie4UAnpKcmayV+1dq/vb5bmsOnDiguCNxysjOkOS+F1KAX4Ba12ltbPv7+mv38d0uay+oe4Gm9Juixy95XFc3v1qmEFMZzgIAAAAAnNGzCVXGot2LXK46VxIHUg5o4e6FurbVtR5qFVDYwZSD6jqlq3Gt1g2tqyMxR1zWlmRFuBe6v6AcR44sJoti6sQwjxIAAAAAryFsQpWxPXG7R46zI3EHYRNKLCc3R7uP75bNbpPNbtM1La5R54adneqiQqIUfzLe2D6adlTH0o+pTnAdp1pLlMX4uU5wHYUGhLp9/NvMt5XxDAAAAADAMwibUGWknUrzyHFST6V65Dg4vzy18Cl9svaTQre5CpsC/AIUWydW/8T/Y9y22b5Zlze93Kn2wroX6vd7fpfZZFZUaJTnGw0AAAAA5YCwCVVCxukMxR2O88ixwgKdV/vC+SknN0drDq6RzW6TNd6qQ6mHNPf2uS5r20S2KbRd1CpvliiLNidsVkxEjMwms0ICQ1zWBQcE66rmV5W6/QAAAADgDYRNOKdlnM7QxLiJem/VezqadtQjx4yOiPbIcXDuc8ihq6deraycLOO2hJMJigyJdKq1mCyFtouaX+njaz7WlL5TmFcJAAAAQJVE2IRzUnmETJLUuGZj9WrRy2PHQ+X0z9F/NG/7PFntVtnsNt1tuVsvXvaiU52/r79iI2P199G/jdtsdpuubHalU21bU1tFBkfKbDLLYrLogroXuH38iOAIj5wHAAAAAFRGhE04J/204yc9seAJjx/34Q4Py8/Xz+PHRcVyOBw6mnZU9cLqudy/7tA6vbrsVWP77/i/3R7LYrIUCpusdqvLsKlGUA3Zn7GXus0AAAAAUFUQNuGcdFPsTWoT2UZbErYYtwUHBGvQhYM03TpdxzOPl/iYEdUj9FD7hzzZTFSwpxY8pQ1HNsgab9XxzOOKfzpephCTU13BVd4kyRrvfshbj2Y9dCrnlCwmi8wms8tJvwEAAAAA/yFsQqXmcDjk4+PjdLufr59euewV3T77dgUHBGt4x+F6uuvTigyJ1J2WO9Vjag9lZmcW+3Gq+VfT/Dvmu5yLB5VDZnamth3bJl8fX7WLaueyZunepfrr6F/Gts1uU49mPZzq2ka2LbS9K2mXsrKzFOQf5FQ78MKBGnjhwLI1HgAAAADOI77ebgDgSsbpDH3858eKHRer4xmueynd0uYWvXvVu9o7Yq/e6/meERR1adRFi+9drIjqxZsXJ6J6hJbcu0RdGnXxWPvhOYv3LFbrsa0V8naILpp4kV5f/rrbWrPJXGjb3YpwYUFhevmylzWpzySteWCNkkYmuQyaAAAAAAAlR88mVCquJv7++M+P9dqVrznV+vn6aWT3kS6P07VRV20dtlWfbfxMEzZM0IGUA041jWs21iMdHtGD7R+kR5MXOBwOHUk7Imt83iTd9190v2pXr+1UFxoYqu2J241tdwGSVHhFuOCAYKVkpbitff1K96EVAAAAAKD0CJtQKRS1utzHaz/W45c8rlrVa5XomJEhkXrh0hc0sttILdy9UDsSdyj1VKrCAsMUHRGtXi16MRm4F/WY2kPL9i4zti+se6Guan6VU12byDaFtncm7VTG6QxVD6juVHtj7I2KjoiWJcqipuFN5etD500AAAAAqGiETfCqokKmfNm52Vp/eL16tehVqsfw8/XTta2u1bWtri1LU1EMp3JOaUvCFqO3Us1qNfXCpS+4rG1cs3GhbZvd5jJsCgsKU9PwptqbvFdNw5vKbDIrOTPZZdjUsnZLtazd0jMnAwAAAAAoFcImeEVxQqYzJ/5G5ff30b/VefJ/q7VFR0S7DZsKDnmTJKvd/Ypwv931m+qF1VONoBqeaSgAAAAAoNwQNqFCETKdm/48+KdW7V8lqz2vx9KHvT7U5U0vd6o7c8jbrqRdboe8mU1mBQcEy2wyyxxpVs/mPd0+fkydmLKfBAAAAACgQhA2VWHZudlatHuRtiduV9qpNIUGhiomIsZrcxX9se8PDZg1gJCpksrMzlQ1/2ou903YMEFf/fOVsf3X0b9chk2hgaFqFt5M/yb/K0nKdeRq67Gtal+vvVNtz+Y9lfp8KvMqAQAAAEAVQ9hUBSWcTNCkuEmaGDfR7SpsD3d4WA+1f6hCQ52YOjE6kXnC6XZCJu9IzkrWyEUjjd5K1fyracejO1zWmk3mQtvWePdD3nq16KVDqYdkjjTLEmVRk5pNXNYxOTsAAAAAVE2ETVXM6gOr1ffbvkrMSHRbs//Efr245EV9tOYjzb9jvro06lIhbTOFmDSs4zB9sOYDSYRM5S0nN0d7ju9RzWo1ZQoxOe0P9AvU+6vfN7Z95KP00+kKDgh2qj1zfiVbgs3t407oM6EMrQYAAAAAnOsYv1KFrD6wWldNvarIoKmgxIxE9ZjaQ2sOrPFYGzJOZ+irv7+Sw+Fwuf+Zbs8oMjhSz3Z9VntH7NV7Pd8jaPKwKRun6OJJFyvsnTBFj43W9E3TXdYF+werea3mxrZDDm1N2Oqy9sK6F2rQhYM06ppRWnTPIs27fV65tB0AAAAAcO6jZ1MVkXAyQX2/7avM7MwS3S8zO1M3fHuDtg7bWqbQ58yJv2tVr6W+MX2d6kwhJh144oCC/INK/Vjns+TMZG22b9be5L26q91dbmvijsQZ2za7+15IFpNFe47vkST5+fhp34l96lC/g1NdVGiUpvSbUsbWAwAAAADOB4RNVcSkuEnF7tF0psSMRH228TO3S9QXxd3qcv9b9j/dEH2DfHx8nO5D0FRyp3NOq9WYVtp3Yp+kvCFv/Vv3V0hgiFOtJarwkDer3f38SkM7DtWAtgNkNpkVExHD7wYAAAAAUGaETVVAdm62JsZNLNMxJmyYoJHdRhZ70mZ3IVO+v47+pfk75rvs3YT/5M+rlD9Jd4d6HXR99PVOdQF+AfL3/e/l6pBDW49t1cX1L3aqLTiZd53gOooKjXL7+L1a9CrjGQAAAAAAUBhhUxWwaPcil6vOlcSBlANauHuhrm11bZF1ZwuZpP8m/u7SsGImHj+XjVk3Rk8seMLYvv/C+12GTVJej6Xdx3cb2za7zWXYVC+0nhbfu1htI9sWGTQBAAAAAFAeCJuqgO2J2z1ynB2JO9yGTSUJmVhdLm+y9k3xm2SNt8qWYNMvd/7icshb28i2hbaLGvJmjjTrpx0/KSYiRmaTWQ1rNHRZ5+Pjox7NepTtBAAAAAAAKCXCpiog7VSaR46TeirV6TZCJvccDofLOakk6b6592lX0i5je0vCFnVs0NGp7sz5lTbbNysnN8flcMZnuj2jly57iXmVAAAAAACVGmFTFRAaGOqR44QFhjndtv7w+kLDvAo630KmnYk79a3tW1ntVlnjrbq08aX6rO9nLmvNJnOhsMlmt7kMm6JCotS6TmvVC60ns8ksi8mi7Nxsl2FTjaAanjsZAAAAAADKCWFTFRATEeOR40RHRDvddlmTy3RF0yu0bO8y47aqGjI5HA4dSTuiOsF1FOgX6LR/34l9enXZq8Z2USGfxWTR3G1zjW13w+N8fHy0ddjW0jcaAAAAAIBKhrCpCujZoqfqhdbTkbQjpT5GoxqN3K5M9urlr2rZ3mVVNmR6c8WbWrRnkazxVh3PPK61D65VpwadnOospsJD3rYkbHE75K174+66re1tspgsMpvM6lC/Q7m1HwAAAACAyoSwqQrYm7xXJ0+fLNMxUrJSdCDlgJqGN3Xad0XTKzT+uvG6pc0t51zIlJmdqa0JW5V+Ol3dGndzWfPX0b+0Yt8KY9tmt7kMm0whJtUJrqNj6cckSRnZGdp3Yp+a12ruVNurRS+34R0AAAAAAFUZYdM5blfSLl351ZVKyUop03FOZJ3Q23+8rUk3THK5f0jHIWU6fkWz2W26deat2pm4UzmOHHWo10EbBm9wWWuONOuHrT8Y29Z490PeXr7sZVX3ry6zyay2prbMowQAAAAAwBkIm85h+UHTwZSDHjneF39/oRcufcFl76bKIn9eJWu8VTa7Tf1a91PL2i2d6kwhJm07ts3Y3pzgfpW3givCBQcE63TuabeP/1jnx8p4BgAAAAAAVG2ETecod0HTtS2v1bpD65SYkVjiYwb6BSrucFylDpvum3ufpm2aZmyHVwt3GzZFBkcqIT1BUt5wut3Hd7udBH3ubXNlibKoaXhT+fr4lt8JAAAAAABQxRE2nYPcBU33XXCfpvSdoqSMJH228TNN2DBBB1IOnPV43p74Ozs3Wza7zeitlH46XWOuG+Oy9sz5kdyt8iZJZpNZS/cuVZOaTWSJsuh0juseS6YQk/q17lf6EwAAAAAAAAbCpnPM2YImP18/RYZE6olLnlA1/2p6c8WbOp553OWxvB0y5UvKSNJFEy8ytoP8gvRx749dD3k7Y0U4m93m9rhf9PtCtarXYl4lAAAAAAAqEGHTOaQ4QZMkbTyyUdd/c72Oph11eZyKCpn+Pvq3Fu9ZLKs9r8fSiM4jdM8F9zjVmUJMMoWYZD9plyRl5WRpV9IuxdSJcao1m8wKDgiW2WSWOdKsro26un38JuFNPHcyAAAAAACgWAibzhHFDZokqXWd1sp15DodozxCprRTaQoNDHW5b962efrf8v8Z2xsOb3AZNkl5IdKSf5cY2za7zWXYFB0RrdTnU5lXCQAAAACASoqw6RxQkqBJyguVRnYbqacWPmVseypkys7N1ouLXzR6K9lP2pX2Qpr8fZ0vJbPJXGi7qPmVejTtkddjKdIsS5TFbY8lHx8f+cinTOcAAAAAAADKD2FTJZCWdFTvPd1F+9MO65RPjqr5+KthcD29MCpOh3KSXAZNd1nuUsf6HZXjyJGfnOc2euTiRzRu/TjdEntLiUKmnNwc7Tm+RwF+AS5XpfP39ddX/3yl+JPxxm27knapdZ3WTrWWqOLPr/TiZS8Wq30AAAAAAKBy83rYtG/fPk2cOFFr1qxRQkKCQkJCdNFFF2ngwIG65JJLvN28crX2x081+pvHtKxBtg4Xml4oR9JeffF6hDodlAJMkur8t7dj/Y5a/O9iTbdOV4BfgAZ3GOx07OCAYG0fvt1ljyNX5m2bpzdWvKEtCVuUkZ2hRzs9qtHXjnZZazaZFf/vf2GTzW5zGTa1qNVCD7V/SG0i28hisshsMsvhcMjHh55JAAAAAABUVV4Nm+Li4vTggw8qPT1dHTt21GWXXab4+HitXLlSS5cu1csvv6y7777bm00sNx+N6KS3qq1XUqz7mkM1pDltpNrp0tW7pN9bStX9q2v94fVGzVt/vKWBFw5UoF+g0/3zg6bkzGTZ7DbZ7DY92P5BlwFUjiNHcUfijO2ieiFZTBYt/nex8RhHUo+4rPPz9dOkGya5P0EAAAAAAFDleC1sysjI0DPPPKP09HS999576t+/v7Fv48aNuu+++/Tuu++qc+fOatWqlbeaWS4+GtFJL4atV2ZA8eqTgqWVTaS28dLmqIxC+/af2K8v//7SZe8mSer4WUdtOLzB2L68yeWKjXROuCymwkPerHar215Id7W7S50adJLZZFZMnRiXQRcAAAAAADg/eW1Jr19//VWHDh1S9+7dCwVNktS+fXvdfvvtOn36tL766ivvNLCcrP3xU71VrfhBU77MAOlwmFT75H+3BfoFqlujbso8nen2fuHVwgttu+ux1LxWc1X3ry5JqhNcRxaTRemn013WXlz/Yt1huUOWKAtBEwAAAAAAKMRrYdPChQslSb1793a5/5prrpEkLVq0qMLaVBFGf/OYkoJLd9/jwZLFLiPgOZVzSqsOrNKc7XPc3ufMHkvuwiY/Xz8tvW+pjj51VAnPJGjJfUsUEhhSuoYCAAAAAIDzltfCpi1btkiS2rRp43J/27ZtJUnJyck6ePCgy5pzTVrSUS1rkF2mY+yMkBbeMr/Qbdb4vCFvrphNZvn7+qttZFvd1vY2tYtq5/bYnRt2VlRoVJnaBwAAAAAAzm9embPp1KlTio/PW82sXr16LmuqV6+u8PBwJScna9++fWrYsGFFNrFcvPd0lzNWnSu5wzWkhe8/rOotqisjO2/+psSMRMWfjFfd0LpO9XeY79Dd7e5muBsAAAAAAKgQXgmb0tLSjJ9DQtwP1QoODlZycrJOnjzptibf1q1bPdK28rQ/7bBHjnMo7bA61Omk07mn1bJGS0XXjNa+3ft0PPC4R46Pqi8jIy+oPBdeNzj3cb2hInG9oSJxvaEicb2hInG9oay8EjZlZWUZPwcEuJ8pOzAwrzdO/oV+rjvlk+OR42T55GjSZZM8ciwAAAAAAABP8krYVK1aNePn06dPKygoyGXdqVOnJOUNqTub2NhYzzSuHFXz8ZdU9sCpmvzPifNF5ZX/DQXXESoC1xsqEtcbKhLXGyoS1xsqEtcbJCkuLq7U9/XKBOEFh84VNUQuf7hdWFhYubepIjQMdj0/VYmPE+KZ4wAAAAAAAHiaV8KmwMBANWjQQJJ06NAhlzWpqalKSUmRJDVr1qzC2laeRn6wRvVTynaMBinSC6NKny4CAAAAAACUJ6+ETZJkNpslSZs2bXK5/++//5YkRUZGqm5d51XWzkWhtevqikNlG7l4+SF/Va9Z20MtAgAAAAAA8CyvhU29e/eWJP36668u9//000+SpOuvv77C2lQRHrtztGqnl+6+tdOlxy0Pe7ZBAAAAAAAAHuS1sKlnz55q1qyZ1q9fr++//77QvuXLl+vHH39UcHCw7r//fi+1sHx07jtEL2V1UrXTJbtftdPSxB+lji+Nk778slzaBgAAAAAAUFZeWY1OkgICAvTRRx/p/vvv1yuvvKL58+erZcuWOnjwoFavXi1fX1+98847VWYIXUFPfLxWjhGd9Fa19UoKPnt97fS8oOmWbf//hvwAbuDA8moiAAAAAABAqXitZ5MktWnTRvPmzdPtt9+uw4cPa9asWdqyZYt69uypWbNmGUPtqqInP1mnX7qN151b/d1OGt4gRbpri79WzKn5X9CU7/77pf8/1BAAAAAAAKCy8FrPpnx169bVa6+95u1meEXnvkM0ve8QZZxI0ttPdNCBtMPK8slRNfmrYUg9vTAqLm8y8KwsKTJSSk0tfICHH5aWLZNatfJK+wEAAAAAAM7k9bAJUvWatfXG5/9q69atkqTY2NjCBUFBUkKCc+B0+LB05ZXS0qUETgAAAAAAoFLw6jA6lEB+4BQTU/j2Q4fyAqedO73TLgAAAAAAgAIIm84lQUHSli3/TRCej8AJAAAAAABUEgyjO9f4+kqTJ+f9/MUX/91+6JB08cXSJ5/8t0pddra0aJG0fbuUliaFhub1jOrVS/Lzq/CmAwAAAACAqo+w6VzkLnBKScnr9ZSSkje308SJ0oEDzvdv3DhvcvGHHsqbBwoAAAAAAMBDCJvOVe4CJ0kaMaLo++7fL734ovTRR9L8+VKXLuXTRgAAAAAAcN5hzqZzWX7gFB5euvsnJko9ekhr1ni0WQAAAAAA4PxF2HSu8/WVjhzJm4+pNDIzpRtuyFvpDgAAAAAAoIwIm6qCatWkp54q/f0TE6XPPvNcewAAAAAAwHmLsKkqyM6WPv+8bMeYMEHKyfFMewAAAAAAwHmLsKkqWLTI9apzJXHggLRwoWfaAwAAAAAAzluETVXB9u2eOc6OHZ45DgAAAAAAOG8RNlUFaWmeOU5qqmeOAwAAAAAAzluETVVBaVeiO1NYmGeOAwAAAAAAzluETVVBTIxnjhMd7ZnjAAAAAACA8xZhU1XQs6fUqFHZjtG4sdSrl2faAwAAAAAAzluETVWBv7/08MNlO8bDD0t+fp5pDwAAAAAAOG8RNlUVgwdLERGlu29EhPTQQ55tDwAAAAAAOC8RNlUVkZHS/PlStWolu1+1ann3+/JLadGicmkaAAAAAAA4fxA2VSVdukiLFxe/h1NEhLRkibRsmfTss1Lv3gROAAAAAACgTAibqpquXaWtW6W33nI/aXjjxtLbb+fVLVsmvfBC3u25uQROAAAAAACgTPy93QCUg8jIvABp5Ehp4UJpxw4pNVUKC5Oio/NWncufDPzrrwvfNzdXGjBAWrdOatWq4tsOAAAAAADOaYRNVZmfn3TttXn/3PnnH6lNG2nnzv9uS06WrrxSWrqUwAkAAAAAAJQIw+jOd/7+0pYtzqHSoUN5gVPBEAoAAAAAAOAsCJuQFzht3Srdf3/h2wmcAAAAAABACTGMDnn8/KTJk/N+/uKL/27PD5wWLswbbidJ2dl5k4hv3y6lpUmhoVJMTOG5oAAAAAAAwHmJsAn/8fV1Hzi1ayd9+23eZOMTJ0oHDjjfv3Fj6eGHpYceypukHAAAAAAAnHcIm1CYu8ApJydvlbqi7N8vvfii9NFH0vz5Upcu5ddOAAAAAABQKTFnE5zlB079+pXu/omJUo8e0po1nm0XAAAAAACo9Aib4JqvrzRrltSsWenun5kp3XCDlJDg2XYBAAAAAIBKjbAJ7vn7SwMHlv7+iYnSZ595rDkAAAAAAKDyI2yCe9nZ/83fVFoTJuTN9wQAAAAAAM4LhE1wb9Ei16vOlcSBA9LChZ5pDwAAAAAAqPQIm+De9u2eOc6OHZ45DgAAAAAAqPQIm+BeWppnjpOa6pnjAAAAAACASo+wCe6FhnrmOGFhnjkOAAAAAACo9Aib4F5MjGeOEx3tmeMAAAAAAIBKj7AJ7vXsKTVqVLZjNG4s9erlmfYAAAAAAIBKj7AJ7vn7Sw8/XLZjPPyw5OfnmfYAAAAAAIBKj7AJRRs8WIqIKN19IyKkhx7ybHsAAAAAAEClRtiEokVGSvPnS9Wqlex+1arl3S8yUjp1qnzaBgAAAAAAKh3CJpxdly7S4sXF7+EUESEtWZJ3v59+kmJjpZ07y7eNAAAAAACgUiBsQvF07Spt3Sq99Zb7ScMbN5befjuvLj9ouvlmac8e6corCZwAAAAAADgP+Hu7ATiHREZKL7wgjRwpLVwo7dghpaZKYWFSdHTeqnP5k4H/9Vde0JQ/hO7QIalHj7wgKjTUe+cAAAAAAADKlVfDpt27d2vKlCn6888/ZbfbFRgYqGbNmql379669957FRQU5M3mwR0/P+naa/P+udOunXTnndKXX/5328svEzQBAAAAAFDFeW0Y3YIFC9S/f3/Nnj1bYWFh6tevn7p27ao9e/bogw8+0J133qmTJ096q3koKz8/afJkaeDAvO2JE/NWtgMAAAAAAFWaV3o2xcfH67nnntOpU6c0cuRIDRo0yNh3+PBhDRgwQDabTZMnT9aIESO80UR4Qn7gdO+9eXM2AQAAAACAKs8rPZvmzp2r9PR0XXDBBYWCJkmqX7++HnjgAUnSwoULvdE8eJKfH0ETAAAAAADnEa/0bOrevbtq166thg0butzfvHlzSdLRo0crslnwhl9/lVq2lFq18nZLAAAAAACAB3glbGrbtq3atm3rdr/dbpck1apVq6KaBG+YPz9vxTqTSVq6lMAJAAAAAIAqwGsThLvjcDg0a9YsSVLv3r293BqUm/yg6fRp6dChvKF2O3d6u1UAAAAAAKCMfBwOh8PbjSho0qRJ+vDDDxUeHq6FCxeqZs2aRdbHxcVJkoKDgyuieeUqIyNDklS9enUvt6T81X31VdWaObPQbYfefVcpfft6qUXnl/PpWoP3cb2hInG9oSJxvaEicb2hInG9QZLS09MlSR06dCjxfcs8jO6JJ57Q1q1bi1UbFRWlr776yu3+zz//XB999JECAgL0ySefnDVowrnr6Kuvyic7W+Fz5kiSjrz+OkETAAAAAABVQJnDpkOHDunff/8tVu2pU6dc3u5wOPTee+/piy++UGBgoD788ENdcsklJWpHbGxsieoro/zQriqcS7HMmiU99JDUpYvqPfig6nm7PeeR8+5ag1dxvaEicb2hInG9oSJxvaEicb1B+m8kWWmUOWyaMWNGme6flZWlZ555RgsWLFCNGjU0ZsyYEgdNOEf5+kqTJ0s+Pt5uCQAAAAAA8BCvrEaX79SpU3r44Ye1Zs0aNWzYUJMmTVKLFi282SRUtLMFTVlZUlBQxbQFAAAAAACUmddWo8vNzdUzzzyjNWvWKDY2Vt999x1BEwqbN0+KjWWVOgAA/l979x5lZVnoD/w7MwwC4jWVUNAoGyE08y7KItG8dbzltQIRvGTlqXNqne5axyzLVqaVlxCQQFTULI7aEjVvIOLlh1qmpphKOF4gDQOGq+zfH7MGRQcdZjb7nRk+n3/Yez/v3vPdq6dH+M77vg8AQAdSWNl0ySWXZOrUqfnIRz6S8ePHZ+utty4qCu3R//1fcsIJyfPPJ0OHKpwAAACggyikbPr73/+e0aNHp7a2Npdcckm22GKLImLQXs2a1Vg0rVjR+Ly+PjnooGTx4mJzAQAAAO+rkHs2XXHFFVm5cmX69u2ba6+99j2PPeuss7L55ptXJhjtw267JcOHJ+PHNz6vqkr+93+TjTcuNBYAAADw/gopm1566aUkydy5czNx4sT3PPaUU05RNm1omnapS5Lf/rbx8amnFhoJAAAAaJlCyqarrrqqiB9LR9JUOI0cmQwZUnQaAAAAoIUKu0E4vK/qakUTAAAAdDDKJjquW26xSx0AAAC0M8omOqYpU5LPfCYZOlThBAAAAO2IsomOZ8qU5IQTkpUrk/p6hRMAAAC0I8omOp5bb20smpq89FLy8MPF5QEAAABWUzbR8Vx+eTJqVOPjqqpk3Ljk858vNhMAAACQJOlSdABYZ9XVydixjX/uv/9bxRMAAABQOGUTHVNT4QQAAAC0Ky6jo/NatqzoBAAAALDBUTbROd14Y9K/f/Lss0UnAQAAgA2KsonO58Ybk89+NnnhheSAAxROAAAAUEHKJjqXhx5qLJpWrmx8Xl+fHHRQ0tBQbC4AAADYQCib6Fz22CMZPvyt51VVyXnnJT16FJcJAAAANiB2o6Nzqal5a5e6CROS3/42GTGi0EgAAACwIXFmE51PU+E0bZqiCQAAACpM2UTnVFOTDB5cdAoAAADY4Cib2DBNmZLMnl10CgAAAOh0lE1seG64ITn++GToUIUTAAAAlJmyiQ3LDTckn/tc8uabSX29wgkAAADKTNnEhuX22xuLpiYvv5w89lhhcQAAAKCzUTaxYfnNb5KRIxsfV1cnEyYkJ5xQaCQAAADoTLoUHQAqqqYmGTu28c8DDkiGDy86EQAAAHQqyiY2PE2FEwAAAFB2LqOD5ixdWnQCAAAA6JCUTfBO112X9O9vlzoAAABoBWUTvN111yXDhiVz5iRDhyqcAAAAYB0pm6DJAw80Fk1vvtn4vL4++dSnkiVLis0FAAAAHYiyCZrsvXcyYsRbz6urk5/8JOnevbhMAAAA0MHYjQ6aVFe/tUvdhAnJVVcln/98sZkAAACgg3FmE7xdU+E0fbqiCQAAAFpB2QTvVF2d7Ldf0SkAAACgQ1I2wbq68Ua71AEAAMBaKJtgXUyenJx4YjJ0qMIJAAAAmqFsgpaaPDkZNixZtSqpr1c4AQAAQDOUTdBSd97ZWDQ1efnl5C9/KS4PAAAAtEPKJmip0aOTUaMaH1dXJ1dfnRx3XLGZAAAAoJ3pUnQA6DCqq5OxY5OamuSgg5LPfrboRAAAANDuKJtgXVRXJ2PGFJ0CAAAA2i2X0UG5LVlSdAIAAAAojLIJyumaa5L+/e1SBwAAwAZL2QTlcs01ycknJ//4RzJ0qMIJAACADZKyCcrh/vsbi6ZVqxqf19cnBx+cLF1abC4AAACoMGUTlMO++yannPLW85qa5IILkm7dissEAAAABbAbHZRDdXUydmzj44kTk6uvTk46qdhMAAAAUIB2dWbT3XffnZ122ik77bRTHnzwwaLjwLppKpzuu0/RBAAAwAar3ZRN//73v/P973+/6BjQNtXVjZfUAQAAwAaq3ZRNP/7xjzNv3rxsscUWRUeB9ef665Nnny06BQAAAKw37aJsuvfeezNlypQccsgh+ehHP1p0HFg/Jk1KPvvZ5IADFE4AAAB0WoWXTQsXLsw555yTTTfdNGeffXbRcWD9mDQpGTEiKZWS+nqFEwAAAJ1W4WXT+eefn1dffTXf/va306tXr6LjwPpxzz2NRVOTV15J/vrXwuIAAADA+lJo2TRt2rT8/ve/z+DBg3PccccVGQXWr9Gjk5EjGx/X1CSTJyfHHFNkIgAAAFgvuhT1gxctWpTvf//76dmzZ370ox8VFQMqo6YmGTs26dIlOfTQ5Pjji04EAAAA60Wby6avfe1reeqpp1p0bK9evTJhwoQkyU9/+tO8/PLL+eEPf5jevXu3NUaLM7RnS5YsSdI5vgtr8fWvN/5Z8P/G5hqVZL5RSeYblWS+UUnmG5VkvtFWbS6b6uvr8/zzz7fo2OXLlydJZsyYkRtuuCGDBg3KSSed1NYI0GlULVmSUvfuRccAAACAVmtz2XT99dev0/GLFi3K2WefnY033risl88NGDCgbJ9VlKbWuDN8F1phwoTk+99P7rwz2XHH9fqjzDUqyXyjksw3Ksl8o5LMNyrJfCNJZs2a1er3VvyeTZMnT85LL72Uvn375mc/+9m7xmfPnp0k+fWvf52rr746++yzT4YNG1bpmFBZEyYko0Y17lh3wAGNu9et58IJAAAA1oeKl01N137OnTs3c+fOXetxDz/8cJKkR48eFckFhZk+/a2iKUnq65ODD07+9rdko42KzQYAAADrqOJl01e+8pV85StfWev4ySefnIceeigTJ07MPvvsU8FkUJD99ktOOSX57W8bn3fpkvz854omAAAAOqSKl03AO9TUJGPHNj6eNCmZPDk57rhiMwEAAEArVRcdAMhbhdOMGYomAAAAOjRlE7QXNTXJ3nsXnQIAAADapN1dRnfVVVcVHQHap2uuSfbaK/noR4tOAgAAAGvlzCboCMaPT4YPT4YOTWbPLjoNAAAArJWyCdq78eOT005LSqWkvl7hBAAAQLumbIL2bsaMxqKpyauvJk8/XVweAAAAeA/KJmjvrrgiGTWq8XGXLskNNyRHHFFsJgAAAFiLdneDcOAdqquTsWOT2trk8MOTY44pOhEAAACslbIJOoLq6mT06KJTAAAAwPtyGR10FosXF50AAAAAlE3QKVx5ZTJggF3qAAAAKJyyCTq6K69MTj89mTs3GTpU4QQAAEChlE3QkU2b1lg0lUqNz+vrk0MPTZYtKzYXAAAAGyxlE3RkgwcnI0e+9by2NrnoomSjjQqLBAAAwIbNbnTQkVVXJ2PHNj6eNCm54Ybk6KOLzQQAAMAGzZlN0NE1FU4zZyqaAAAAKJyyCTqD6upkjz2KTgEAAADKJtggTJpklzoAAAAqQtkEnd3YscnJJydDhyqcAAAAWO+UTdCZjR2bnHFG4+P6eoUTAAAA652yCTqrUqnxpuFvN29e8uyzxeQBAABgg6Bsgs6qqioZMyYZNarxeW1tcuONyeGHF5sLAACATq1L0QGA9ai6uvFSutra5IgjkiOPLDoRAAAAnZyyCTq76upk9OiiUwAAALCBcBkdkCxaVHQCAAAAOgllE2zoRo9OBgywSx0AAABloWyCDdno0ckXv5i8+GIydKjCCQAAgDZTNsEGqseDDzYWTU3q65PDDkuWLy8uFAAAAB2esgk2UA177pmMHPnWC127Jr/8ZeOfAAAA0Ep2o4MNVU1NMnZs4+NrrkluvDE54ohiMwEAANDhObMJNmRNhdMDDyiaAAAAKAtlE2zoamqS3XYrOgUAAACdhLIJeG/jxyfPPlt0CgAAADoIZROwdpddlpx6anLAAQonAAAAWkTZBDTvssuSs85qfFxfr3ACAACgRZRNwLuVSsn/+39rvjZ/fvLcc8XkAQAAoMPoUnQAoB2qqkrGjGksnX7726Rr12TKlOSQQ9597MqVyR13JE8/nSxalPTsmey0U+OxNTWVTg4AAEDBlE1A82pqkrFjk402So4+Ojn88DXH589PrrgiGT06mTv33e/ffvvkzDOTM85Itt66MpkBAAAonLIJWLuamuQ3v3n36/ffnxx1VPLaa2t/7z/+kXzve8kvfpHcfHMyaND6ywkAAEC74Z5NwLq5//7koIPeu2h6u9deSw48MJk5c/3mAgAAoF1QNgEtN39+4xlNS5eu2/uWLk2OPLLx/QAAAHRqyiag5a64ouVnNL3Ta6813nQcAACATk3ZBLTMypWNNwNvi9/8JnnzzfLkAQAAoF1SNgEtc8cdze86ty7mzk1uv708eQAAAGiXlE1Ayzz9dHk+55lnyvM5AAAAtEvKJqBlFi0qz+csXFiezwEAAKBdUjYBLdOzZ3k+Z5NNyvM5AAAAtEvKJqBldtqpPJ9TV1eezwEAAKBd6lJ0gHvvvTcTJ07MX//61yxbtiwf/OAHc8ghh2TkyJHZcssti44HNDn44KRv37bdJHz77ZNDDilfJgAAANqdQs9s+tWvfpUvfOELeeSRRzJo0KB8+tOfztKlSzN69Ogcf/zxee2114qMB7xdly7JmWe27TPOPDOpqSlPHgAAANqlwsqmu+++O5deemn69u2bW265JRdffHHOP//83Hbbbdl7771TX1+fiy66qKh4QHO+8IXkAx9o3Xs/8IHkjDPKmwcAAIB2p7DL6H7xi18kSc4777xst912q1/faKON8r3vfS933nlndt1116LiAc3Zeuvk5puTAw9Mli5t+fu6dWt839Zbr79sAAAAtAuFlE3PPPNMnnnmmeywww4ZNGjQu8b79++f/v37F5AMeF+DBiV33pkcdVTSkktdP/CBxqKpmf+vAwAA0PkUchndQw89lCTZe++9i/jxQFvtt1/y1FPJj3/ceNPw5my/fXL++Y3HKZoAAAA2GIWc2TR79uwkyQ477JA5c+bk0ksvzf33358FCxZkm222ySc/+cl86UtfyjbbbFNEPKAltt46+e53k299K7n99uSZZ5KFC5NNNknq6hp3nXMzcAAAgA1OValUKlX6h5511ln505/+lM9//vOZMmVKttlmm+y+++558803M3369Lz++uvZZpttcu2116ZPnz7v+VmzZs1KkvTo0aMS0derJUuWJEm6d+9ecBI6O3ONSjLfqCTzjUoy36gk841KMt9IkoaGhiTJHnvssc7vbfOZTV/72tfy1FNPtejYXr16ZcKECasDX3vttfnP//zPfPnLX051deMVfYsWLcrIkSPz+OOP5wc/+EHGjRvX1ogAAAAAVEiby6b6+vo8//zzLTp2+fLlSbK6WPrwhz+cs846K1VVVauP6dmzZ7797W9n2LBhue+++/Lyyy+nd+/e7/vZAwYMaEX69qWptOsM34X2zVyjksw3Ksl8o5LMNyrJfKOSzDeSt64ka402l03XX3/9Or+nZ8+eSZJPfOITaxRNTfbYY49stNFGWbZsWZ588skWlU0AAAAAFK+Q3ei23377JMnSpUubHa+qqspWW22V5K1rBAEAAABo/wopm3beeeckyQsvvNDs+KpVqzJv3rwkyZZbblmpWAAAAAC0USFl0+DBg9OjR4888cQTefLJJ981/uCDD2bFihWpra3NLrvsUkBCAAAAAFqjkLJp4403zqhRo5Ik5557bhYuXLh6bN68efnJT36SJDnyyCOz6aabFhERAAAAgFZo8w3CW+tLX/pSHn/88UybNi2HHXZYhgwZklKplHvuuSf/+te/MmDAgHznO98pKh4AAAAArVBY2VRbW5vRo0fn2muvzR/+8IdMnTo1q1atyvbbb58RI0Zk5MiR6dGjR1HxAAAAAGiFwsqmJKmurs6wYcMybNiwImMAAAAAUCaF3LMJAAAAgM5J2QQAAABA2SibAAAAACgbZRMAAAAAZaNsAgAAAKBslE0AAAAAlI2yCQAAAICyUTYBAAAAUDbKJgAAAADKRtkEAAAAQNkomwAAAAAoG2UTAAAAAGWjbAIAAACgbJRNAAAAAJSNsgkAAACAslE2AQAAAFA2yiYAAAAAykbZBAAAAEDZKJsAAAAAKBtlEwAAAABlo2wCAAAAoGyUTQAAAACUjbIJAAAAgLJRNgEAAABQNsomAAAAAMpG2QQAAABA2SibAAAAACgbZRMAAAAAZaNsAgAAAKBslE0AAAAAlI2yCQAAAICyUTYBAAAAUDbKJgAAAADKRtkEAAAAQNkomwAAAAAoG2UTAAAAAGWjbAIAAACgbJRNAAAAAJSNsgkAAACAslE2AQAAAFA2yiYAAAAAykbZBAAAAEDZKJsAAAAAKBtlEwAAAABl06XIHz5z5sxMmjQpjz32WBYsWJCNN944O+20U44++ugce+yxqa7WhQEAAAB0JIWVTZdeeml+9atfpaqqKvvvv3+23377LFiwIPfcc08eeuihTJ06NZdddlm6du1aVEQAAAAA1lEhZdPjjz+eX//616mqqsoVV1yRIUOGrB576aWXcuKJJ2b69Om55pprMnLkyCIiAgAAANAKhVyndvvtt6dUKmXfffddo2hKkm233Taf+9znkiS33XZbEfEAAAAAaKVCyqaFCxcmST74wQ82O77tttsmSf79739XLBMAAAAAbVdI2fShD30oSTJnzpxmx19++eUkyYc//OFKRQIAAACgDAopmz7zmc9ks802yyOPPJJ77713jbF//vOfueGGG5Ikw4YNKyIeAAAAAK1UVSqVSkX84Mcffzxf//rXM3fu3Oy3337ZYYcd8sYbb2TatGmpqqrKN7/5zZxwwgnv+zmzZs1KkvTo0WN9R17vlixZkiTp3r17wUno7Mw1Ksl8o5LMNyrJfKOSzDcqyXwjSRoaGpIke+yxxzq/t8270X3ta1/LU0891aJje/XqlQkTJiRJdtxxx5x00km5/PLLM2PGjMyYMSNJUlVVlRNPPLFVXwYAAACAYrW5bKqvr8/zzz/fomOXL1+eJHnjjTcyfPjwPPPMMzn22GPzxS9+Mdtuu23eeOON3HXXXfnZz36Wm2++OZdddlkGDRrUos8eMGBAq79De9FU2nWG70L7Zq5RSeYblWS+UUnmG5VkvlFJ5hvJW1eStUaby6brr79+nd9z0UUX5Zlnnsnhhx+en/zkJ6tf32qrrXLiiSdms802y1e/+tX84Ac/yNSpU1NdXcitpQAAAABYR4W0OFOnTk2SHHHEEc2ODx48OEnjbnXPPvtsxXIBAAAA0DaFlE2LFi1KknTr1q3Z8S5duqSqqirJWzekAgAAAKD9K6Rs6tOnT5LkiSeeaHb8ueeeS6lUSlVVVfr27VvJaAAAAAC0QSFl01FHHZUkufLKKzNnzpw1xpYtW5YLL7wwSbL//vvnAx/4QMXzAQAAANA6bb5BeGucfvrpmTVrVu67774cccQRGTx4cHr37p2FCxdm5syZmT9/frbbbrucd955RcQDAAAAoJUKKZu6du2aMWPG5KabbspNN92URx99NNOmTUu3bt3Sr1+/DBs2LMOHD88mm2xSRDwAAAAAWqmQsilJqqurc8wxx+SYY44pKgIAAAAAZVbIPZsAAAAA6JyUTQAAAACUjbIJAAAAgLJRNgEAAABQNsomAAAAAMpG2QQAAABA2SibAAAAACgbZRMAAAAAZaNsAgAAAKBslE0AAAAAlI2yCQAAAICyUTYBAAAAUDZVpVKpVHSItpg1a1bREQAAAAA6pT322GOd3+PMJgAAAADKpsOf2QQAAABA++HMJgAAAADKRtkEAAAAQNkomwAAAAAoG2UTAAAAAGWjbAIAAACgbLoUHYBkzpw5GT16dGbOnJn58+dn4403zm677ZaRI0dm3333LToencCDDz6YESNGvO9x//u//5vPfe5zFUhEZ1MqlXLVVVfl5z//eZYtW5aJEydmn332afbYZcuWZdKkSfnjH/+Y559/PqVSKf369csRRxyR4cOHZ6ONNqpwejqals63Aw88MPX19e/5Wbvuumuuv/769RWVDuzvf/97xo0blwceeCDz5s1L165d069fvxx22GEZMWLEu9YqaxttsS7zzdpGOUybNi2TJ0/On//85yxYsCA9evTIjjvumCOOOCInnXRSunRZsypYuHBhxo0blz/96U+ZO3duampqUldXl+OOOy7HHntsampqCvomtFfKpoLNmjUrp59+ehoaGrLXXntlyJAhefXVV3Pffffl7rvvzjnnnJPhw4cXHZNOolevXjn00EPXOr7TTjtVMA2dxT//+c985zvfybRp09732IaGhpx22ml55JFH0rt37xx22GFJkunTp+dnP/tZ7rrrrowbNy7dunVb37HpoNZlvjU59thj07Nnz2bHtttuu3JFoxO57bbb8j//8z9Zvnx5+vfvn0GDBuWNN97IjBkz8vOf/zxTp07NxIkTs/HGGyexttE26zrfmljbaK3zzz8/EyZMSHV1dQYNGpQ+ffrk5ZdfzsyZM/PII4/k9ttvz5gxY9K1a9ckjf/tPfnkk/Pcc8+lX79+Oeqoo9LQ0JDp06fn7LPPzn333ZeLL744VVVVBX8z2pUShWloaCgNHTq0VFdXV/rDH/6wxtisWbNKO++8c2ngwIGlZ555ppiAdBoPPPBAqa6urjR8+PCio9DJzJgxozRo0KBSXV1d6Yc//GFp8ODBpbq6utIDDzzQ7PEXXHBBqa6urnTGGWeUli5duvr1hQsXlk466aRSXV1d6cILL6xUfDqYdZ1vTf+NnTt3boWT0pG98sorpU984hOlurq60rhx49YYq6+vL+2///6lurq60sUXX7z6dWsbrdWa+WZtoy3uuOOOUl1dXWm33XYr/eUvf1lj7Kmnnlo9H8ePH7/69a9+9aulurq60tlnn11auXLl6tfnz59fOvjgg0t1dXWlyZMnV+or0EG4Z1OBbr311tTX12fw4ME55phj1hjbfffd89nPfjYrVqzIhAkTigkI8D5+//vfZ8WKFbnkkktyzjnnpLa2dq3HNjQ05Nprr02XLl1y7rnnrnFJQM+ePfODH/wgSTJp0qQsXbp0vWen41mX+QatNWXKlDQ0NGTXXXfNqaeeusbYtttum9NOOy1JcvvttyexttE26zrfoK1uuOGGJMmpp56aXXbZZY2x/v3758QTT0yS3HnnnUmSuXPnZurUqdlss83y3e9+d43L5bbaaqt885vfTJKMGzeuEvHpQFxGV6Cm/2g0nWr9ToceemgmTpyYO+64Iz/60Y8qGQ2gRXbdddf893//d/r06fO+x953331paGjI7rvvnt69e79rfMCAAenbt2/mzp2bGTNm5KCDDlofkenA1mW+QWsNHjw4W2655Vrn2Yc//OEkySuvvJLE2kbbrOt8g7b6yle+khNOOCE777xzs+M77LBDkmTx4sVJkj/96U9JkiFDhqR79+7vOn7IkCHp1q1b5syZk7/97W/p37//ekpOR+PMpgI9+eSTSZKPfexjzY4PHDgwSbJgwYK8+OKLFcsF0FInn3xyi//h/8QTTyR5a21rTtNY0/oIb7cu8w1aa+DAgTnhhBMyaNCgZsfnzZuXJNliiy2SWNtom3Wdb9BWO++8cz71qU/lgx/8YLPjc+fOTZJ85CMfSfL+a1zXrl3z0Y9+NIk1jjU5s6kgy5cvz6uvvpokzf4WLEm6d++ezTffPAsWLMicOXP8BZuyWLhwYe66664899xzWbVqVfr27ZtPfvKT6dWrV9HR6OSaSvO1/eUmeWs9fOGFFyoRiQ1EqVTKgw8+mEceeSQLFy7M5ptvnr333juf+MQnio5GB1MqlfK73/0uyVtnplvbWF+am2/vHLe2UU533313Jk2alK5du+aMM85I0vI17vHHH8+cOXMqkpOOQdlUkEWLFq1+/M6dJd6uR48eWbBgwerTGKEtZs+enU9+8pPvmk+1tbX5whe+kK9+9asFJWND0LTuvd+al8SaR1mNHDmy2TOE99prr1x44YXKdlpszJgxeeyxx7L55puv/oeYtY31pbn59nbWNtrq1VdfzdixY7N48eI89dRTefLJJzNw4MCce+65qaurS2KNo/VcRleQZcuWrX78Xjc4bdpucsmSJes9E53fokWLMnz48Nx22215/PHHc8899+T0009PqVTKpZdemjFjxhQdkU6s6ca4LVnz3ESXctp2220zceLEPProo5k1a1Yuvvji9O7dOw8//HDOOOOMrFixouiIdABXXnllfvGLX6S2tja//OUvs9lmmyWxtrF+rG2+vZ21jbZ6/fXXM3HixNx444158skn06dPn+y///7ZaqutVh+zLmucf7Pyds5sKki3bt1WP16xYsUaO5e83fLly5Ok2ZuxQUsNHDgwv/vd77L55punb9++q1/v3bt3vvGNb2STTTbJRRddlMsvvzzDhw8331gvmubVe/3lt2nNe/saCa11+eWXZ+XKlRkwYECqq9/6/drhhx+egQMH5sgjj8zTTz+dP/7xj+/aFRaalEqlXHDBBRk/fny6du2aCy+8MPvuu+/qcWsb5fR+8y2xtlE+AwYMyNNPP50lS5bkhRdeyE033ZQrr7wykyZNypgxY7Lnnnuu0xrn3xC8nTObCvL20xDf63TDptMWN9lkk/Weic6rZ8+e2WWXXdYomt7u1FNPTbdu3bJ48eI8+uijFU7HhqJp3bPmUSk77bRTBg4cuMY/xppsv/32+fSnP52kcTcxaM6yZcvyX//1Xxk/fnw23XTTjBkzJocccsgax1jbKJeWzLfE2kb5de/ePQMGDMi3vvWtfOc730lDQ0O++c1vZtWqVeu0xvXs2bMieekYlE0F6dq1a7bbbrskSX19fbPHLFy4MP/+97+TJP369atYNjY8Xbt2zdZbb50kee211wpOQ2fVtI699NJLaz2maT205lEJTRtvvP766wUnoT1avnx5zjzzzNx2223p06dPJk+e/K4zTBJrG+XR0vnWEtY22uLYY49N0rhuzZ492xpHqymbCrTzzjsnSf7yl780O/7YY48lSbbeeuv3vPs/tESpVEqpVFrr2IIFC5Kk2XsCQDm835qXJH/+85+TJB//+McrkonOb9WqVWsd+9e//pXEuse7rVq1Kt/4xjcyc+bMDBgwIJMnT169Dfg7Wdtoq3WZb29/z9pY21ibxYsX5/zzz8/Xv/71tf6CuaqqKlVVVUka79f0fmtcQ0NDZs+encQax5qUTQVq2sL01ltvbXb8lltuSZL8x3/8R8Uy0TmNHDkyH//4x9c616ZNm5aFCxemS5cu2XXXXSucjg3Ffvvtl0033TRPPPFE/vGPf7xr/IEHHsj8+fOz5ZZbtvq3udDkuuuuyz777JMzzzyz2fFly5blzjvvTJLsvvvulYxGB3DJJZdk6tSp+chHPpLx48evPvu3OdY22mpd5pu1jbbo0aNHbr755vzxj3/MXXfd1ewxTzzxREqlUqqqqtK3b9986lOfSnV1daZNm7bGjupNbr311qxcuTIf+9jHnNnEGpRNBTr44IPTr1+/PPzww7nuuuvWGLv33ntz0003pUePHhk1alRBCeks9txzzyxfvjw//elP88ILL6wx9uqrr+bHP/5xkuS4447zWzDWm65du2bkyJFZtWpVzjnnnDV2ZVqwYMHqeXjmmWemSxf7V9A2++23XxYtWpRp06blmmuuWWPszTffzAUXXJCXXnopW265pRvosoa///3vGT16dGpra3PJJZdkiy22eM/jrW20xbrON2sbbVFVVZWTTjopSXLhhRfm6aefXmN8/vz5q9esIUOGZMstt0yvXr3ymc98Jg0NDTn33HPz5ptvrj6+vr4+F110UZLkrLPOqtC3oKOoKq3tuhoq4sknn8yoUaOyYMGC7LXXXtlxxx3z4osv5v77709VVVUuvPDC1WdAQWstW7Ysp512Wh5++OHU1tbmgAMOyDbbbJP58+dn+vTpWbJkSfbee++MHj06PXr0KDouHcSCBQty6aWXrvHajTfemMWLF+fQQw9Nr169Vr8+fPjw7LDDDlm+fHm+/OUvZ/r06endu3f222+/vPnmm5k2bVpef/31HHroobnoootSU1NT6a9DO9ea+Xb11VfnvPPOS6lUysCBA7PLLrtkxYoVeeihhzJ37txsttlmueyyy7LnnntW+uvQjn3rW9/KlClT0rdv3wwdOvQ9jz3rrLOy+eabW9totdbMN2sbbfH29apLly7ZZ5990qdPn8yfPz8PPvhgFi9enO222y5XX311evfunSR54403MmrUqDzxxBPp169f9t577yxatCj33HNPFi9enBEjRuR73/tewd+M9kbZ1A688sorufzyyzN9+vTMmzcvm266afbaa6988YtfzIABA4qORyexcuXKXH/99bnlllsye/bsLF68OJtsskn69++fo48+OkcffbS/BLNOXnzxxRx00EEtOnbixInZZ599kjTOxcmTJ+cPf/hDnnvuuSRJXV1djj/++Bx33HHN7q4DrZ1vjz76aCZOnJhHHnkkr732Wmpra9OnT58MGTIkI0aMWKOkgiQ5+eST89BDD7Xo2DvvvHP1zZitbbRGa+ebtY22WLVqVW666aZMmTIlf/vb37Jw4cJstNFG+dCHPpQDDzwwp5xyyrt2z1yyZEnGjx+fW2+9NXPmzEltbW0GDhyYYcOG5dBDDy3om9CeKZsAAAAAKBu/YgEAAACgbJRNAAAAAJSNsgkAAACAslE2AQAAAFA2yiYAAAAAykbZBAAAAEDZKJsAAAAAKBtlEwAAAABlo2wCAAAAoGyUTQAAAACUjbIJAAAAgLJRNgEAAABQNsomAAAAAMpG2QQAAABA2SibAAAAACgbZRMAAAAAZaNsAgAAAKBslE0AAAAAlM3/BxiLll29EU99AAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 589 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "print('Évolution du point 0 transformé par A et A³')\n", + "print(as1[:,0], \" et normé \", as1[:,0] / lin.norm(as1[:,0]))\n", + "print(aaas1[:,0], \" et normé \", aaas1[:,0] / lin.norm(aaas1[:,0]))\n", + "print('\\nÉvolution du point 3 transformé par A et A³')\n", + "print(as1[:,3], \" et normé \", as1[:,3] / lin.norm(as1[:,3]))\n", + "print(aaas1[:,3], \" et normé \", aaas1[:,3] / lin.norm(aaas1[:,3]))\n", + "\n", + "plt.plot([0,mouse[0][0]], [0,mouse[1][0]], '-or') # vecteur (0,0) -- point 0 de la souris\n", + "plt.plot([0,mouse[0][3]], [0,mouse[1][3]], '-og') # vecteur (0,0) -- point 3 de la souris\n", + "plt.plot([0,as1[0][0]], [0,as1[1][0]], '--or')\n", + "plt.plot([0,as1[0][3]], [0,as1[1][3]], '--og')\n", + "plt.plot([0,aaas1[0][0]], [0,aaas1[1][0]], ':or')\n", + "plt.plot([0,aaas1[0][3]], [0,aaas1[1][3]], ':og')\n", + "plt.title(\"Transformation des point 0 et 3 de la souris A et A³\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Les transformations du point 0 de la souris par A et A³ sont sur la droite qui passe par (0,0) et le point 0 de la souris (en rouge) !" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Vecteurs propres et valeurs propres\n", + "\n", + "Calculons les valeurs propres et vecteurs propres de A.\n", + "\n", + "Par définition les valeurs propres et vecteurs propres respectent cette propriété :\n", + "\n", + "$$ A \\, {\\bf v_i} = \\lambda_i \\, {\\bf v_i} $$\n", + "\n", + "pour tout couple de valeur propre / vecteur propre $(\\lambda_i, {\\bf v_i})$. \n", + "\n", + "Cela veut dire que si un vecteur ${\\bf w}$ est sur la droite générée par ${\\bf v_i} $ alors appliquer $A \\, {\\bf w}$ le laisse sur la même droite. Ci-dessus on a déjà trouvé les vecteurs propres de A (avec pas mal de chance)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de A : [3.+0.j 2.+0.j] \n", + "\n", + "Vecteurs propres de A (chaque vecteur propre est écrit verticalement):\n", + " [[ 1. -0.707]\n", + " [ 0. 0.707]]\n" + ] + } + ], + "source": [ + "val_propre, vec_propre = lin.eig(A)\n", + "print(\"Valeurs propres de A :\", val_propre,\"\\n\")\n", + "print(\"Vecteurs propres de A (chaque vecteur propre est écrit verticalement):\\n\", vec_propre)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Le premier vecteur propre (1,0) correspond à la valeur propre 3\n", + "* Le second vecteur propre (-0.07, 0.707) correspond à la valeur propre 2\n", + "\n", + "Le point 0 de la souris est sur l'axe du second vecteur propre et on a donc\n", + "\n", + "$$A³ \\, s[0] = 2 \\times 2 \\times 2 \\times s[0]$$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " A³ s[0] = [ 5.657 -5.657] \n", + "8 A s[0] = [ 5.657 -5.657]\n" + ] + } + ], + "source": [ + "print(' A³ s[0] = ', aaas1[:,0], \"\\n8 s[0] = \", 2*2*2*mouse[:,0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Les vecteurs propres sont des sortes d'attracteurs qui vont capturer tous les points si on fait un nombre infini\n", + "de multiplication par A." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Les 12 points de la souris multipliés par A¹⁰ puis normés :\n", + "[[ 0.707 1. 1. 1. 1. 1. -0.707 -1. -1. -1. -1. -1. ]\n", + " [-0.707 -0.006 0.004 0.009 0.014 0.024 0.707 0.009 0. -0.004 -0.009 -0.018]]\n" + ] + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAABK8AAAKECAYAAADBvxkrAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAABYlAAAWJQFJUiTwAABa80lEQVR4nO3de5iVZb0//jcoB4eDqKEYamEKcXAb2hYtdgcLnVKLcFfurAALNQ+13WVamW1TA/0alubX0KxEykOZB/RHiulGETyEkgdI3WoIaKgoMRwHYX5/8GUadAbmsGbWM/h6XZfXtZjnXve61/N81r0e3+s5dKipqakJAAAAABRQx3IPAAAAAAAaIrwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGFtX+4BAAAAFM1zzz2X+++/P08++WSefPLJPPvss1m/fn1OOeWUnHrqqVt9/rRp0/Lb3/42f/3rX7Nu3brstddeOeqoozJmzJh06tSpDd4BwLZDeAUAAPAm1157bSZPntys555//vmZPHlytt9++xx88MGpqKjIAw88kIsuuij33HNPfvnLX6Zr164lHjHAtkt4BQAA8Cb9+/fPcccdl0GDBmXQoEGZNGlSbrnllq0+76677srkyZNTUVGRKVOmZPDgwUmS1157LaNHj86cOXPy05/+NGeccUZrvwWAbYbwCgAA4E0++9nPbvbvjh0bd7ngn//850mS448/vja4SpKdd945P/jBD3LsscdmypQpOemkk9KjR4/SDRhgG+aC7QAAACWwZMmSPP7440mSI4888i3L3//+92f33XdPdXV1ZsyY0dbDA2i3hFdAm6qpqcnkyZPzqU99Kvvvv3+GDBmSD33oQ+Ue1jbn0EMPzYABAzJgwIByD6VNLVq0qPZ9f+lLXyr3cLYZb9d6akiR6sy2KS/rv/h+8pOf1G6jAQMG5KqrrmrV15s3b16SpFevXtlzzz3rbTNkyJDN2rZ3Pgft21NPPZWhQ4dmwIABGTJkSO66665yDwnq5bRB2IoHH3wwX/7yl1vcT9++fXP33XeXYETt22WXXZZLL710s78tWbKkTKMBALZVCxcuzC9/+cvN/jZ//vxWfc1FixYlSXbfffcG2/Tp02eztlAu//jHP3LyySdn1apVecc73pGf/vSnef/731/uYUG9hFdAm/rNb35T+/iMM87IkUcemQ0bNpRxRO3TzTffnIULF+Yzn/lM9thjj7csv/32261XSqat6mlrdQ1FY64ttvHjx2ft2rXp0qVL1q5dmyT561//2qqvuXLlyiTJDjvs0GCbbt26bda2vfM5aJ82bNiQ//qv/8rChQuz//7759JLL81uu+1W7mFBg4RXsBXvf//788gjjzS4/Bvf+Ebuu+++JMkVV1zR4K8Vjb3I57ZsxYoVee2115Ike+21V4477rgyj6j9uvDCC7N06dIcdNBB9f5P/pZ2mqGp2qqetlbXUDTm2uK6//7786c//SlJcvLJJ+fKK69MVVVVnn/++dpAi9LwOWiffvzjH2fmzJn57Gc/m7PPPjudO3cu95Bgi4RXsBXbbbdd7S9kDS3fpGvXrlts+3b3j3/8o/bxrrvuWsaRtG/PPvtsli5dWu5hQEmpa6BU1q1bl/PPPz9J8s53vjNjxozJPffck0cffTRvvPFGnn766ey3336t8tqb9gNXr17dYJtNR1zZZ6RcVq5cmY4dO+bCCy/Mpz/96XIPBxrFoSBAm6mpqal97Ei05pszZ065hwAlp66BUpkyZUqeffbZJMl//dd/pUuXLunfv3/t8tY8dbBv375JkpdeeqnBNn//+983awttrVu3bvnmN78puKJdceQVlMGhhx6axYsX573vfW9uueWWzJw5M5deemnmz5+fjh07Zu7cuW95ziuvvJIbbrgh999/f55//vlUVVWlY8eO2XnnnTNo0KAcddRRqaysTIcOHRr1mmvXrs2NN96Ym266Kf/7v/+b6urq7Ljjjhk8eHA+//nP5+Mf/3i9/bz22mu54YYbMnPmzDz33HNZvnx5kmSnnXbKvvvum4985CMZNWpUunfvXvucSy+9ND/72c826+ehhx7a7K40Tz311GbL33jjjdxyyy3505/+lHnz5uX1119Phw4d0qtXrwwePDiHHnpoPv3pT2f77eufxpqyjje13XfffXPbbbfl9ddfz69//evcfvvt+fvf/55u3bplr732ymc+85kcc8wxtcHb008/nV/96lf585//nL///e/p2rVrBg8enDFjxuQjH/lIveNKmr8t61uPdW8mMH78+IwaNWqz91Tfum2tddzcmmqKRx55JNdcc03mzJmT1157LT179sy73/3uHHHEEfn85z/fqD42bNiQu+66K7fffnsef/zxvPrqq9luu+3yjne8IwcccECOOuqoDB8+fIt9NOdz0BSb1u2uu+6a++67L1VVVbn66qtz55135qWXXsqaNWvSu3fvDBs2LKNHj8573/veLfZXqm2dvLWeWloHTanr1l7vm5SizpLS1FoptPT7o7FKsX1aUquNmfeSzW/E8pnPfCYTJkyot5+mfH809Jrtba5oSa00Z9+mNSxdujSXXXZZkmT//ffPkUcemSTZd999a9u05l3+Bg0alCRZtmxZFi5cWO8dB5944okkyeDBg5v1GqXa7qX+zDTUT1t9Dkq1P1KKeaiI+59J+9gHgoYIr6DM/vznP+eEE07IG2+80WCbu+++O6effnpWrFjxlmUvvfRSXnrppfzpT3/KBz/4wVx22WVbvfbAa6+9lhNOOCGPPfbYZn9funRp7r333tx777056aST8o1vfGOz5Q8++GBOOeWU2i+pul5++eW8/PLLuf/++/OrX/0qV1xxxWY7ik3x/PPP52tf+1qef/75tyxbvXp1Xnrppdx111258sorM2nSpLzrXe/aYn+NWcebvPTSSxk9enQWLFhQ+7dly5Zl2bJleeyxx/L4449n/PjxueOOO/Ktb30r1dXVte2qq6sze/bszJ49Oz/60Y9y9NFHv6X/Um/L5ir1Om5uTTXFL37xi1x00UWbHcG3dOnSLF26NHPmzMntt9+e//7v/95iH0uWLMk3vvGNPProo29Z9sILL+SFF17IzTffnI997GP58Y9/XO/6b6vPQZKsWbMmCxcuzFe/+tX87W9/22zZ4sWL84c//CFTp07ND3/4w9qA581Kva23pDXroK3WeynqLClNrZVCW805pdg+bVmrjdWU7483a29zRSlrpSXrraUuuuiiVFVVJdl4Y5hNQVvdI69a846Dffr0yX777ZfHH388t912W772ta9ttvzPf/5zXnrppXTu3Dkf/vCHW/Rapdjura0tPwdJy7+HSjkPFWn/M2l/+0DwZh1q6u6dAU12wgkn5H/+53+SJJMnT86wYcO2+py6v8p07do1a9euzXe+850MGDAgK1as2OxCxQsWLMinPvWprFmzJh06dMhXvvKVHHnkkdltt92yfv36PPbYY/nJT36Sp59+Okny7//+77XXeajvNQcMGJB3vOMd+ctf/pITTjghI0aMyM4775ylS5fm1ltvzc9//vPU1NSkQ4cOuf322/Oe97wnSbJ8+fKMGDEiy5YtS6dOnfK1r30tH/vYx9K7d++sX78+L7zwQm699dZcf/31SZJ3v/vduf3227P99tunuro669aty0svvZQjjjgiSXLggQfmyiuvrB3fpus+vPbaa/nUpz6VV155JUnyiU98Iscee2z23nvvdOjQIc8991wmT56cO+64I8nGncSpU6emZ8+ezV7Hm9rus88+2XnnnbN48eJ861vfykEHHZSamprMmjUrP/zhD2t36H/84x/ne9/7Xg488MCcdNJJ2WeffVJVVZWbbrqp9tfeHXfcMTNnztzs4pct3Zab1uMPfvCDTJ06NcnmNwno0qVL7a+AW/oVtNTruLk11RSzZs3K2LFjkySdO3fOySefnMrKyvTq1StLlizJH//4x/ziF7/I+9///syaNStJctBBB+Waa66p7WPlypX53Oc+l//93/9Nknz84x/PF77wheyzzz7p2LFj5s2bl1/84hd56KGHkiQf+tCHNqvRpGWfg6bYtG67deuW/v3756mnnsqpp56aj3zkI9lll12yZMmS3HDDDZkyZUpqamqy/fbb53e/+13tL/6blHpbJw0fedXcOmhMXa9atapN1nsp6iwpTa011pa2Tam+P7amFJ+LUtRqaxx51djvjze/ZnubK0pRK01Zb63lsccey+c+97nU1NTk8MMPzyWXXFK77LXXXsshhxySJKmoqMgjjzzS5KMNzzzzzNx000055ZRTcuqppzbY7q677srJJ5+cioqKTJkypfYIq9dffz1f/vKX8/TTT+e4447LGWec0Yx3Wbrt3tpHXrX156Cl+yOlnIeKtP+Z1P+9dOyxx+Y973lP4faBoEE1QIscf/zxNf3796/p379/zQMPPNCo53z0ox+t6d+/f81+++1Xc/DBB9csXbq0wbbnnHNObf8/+clP6m3z6quv1gwdOrSmf//+Ne9973trXnvttQZfc8CAATVDhgypefzxx+vt67vf/W7t61122WW1f7/llltq/z5p0qQGx/t//+//rW13zz33bLZs4cKFtcu++MUv1vv8M888s7bNueee2+Dr1G13/vnnN/h+G7OO666bgw46qObvf//7W9pMnjy59vUGDBhQM2bMmJo33njjLe1OOeWU2nazZs3abFmptuUZZ5yx1Zrb9J769+//lmWlXsfNramm+OxnP1vbxx/+8Id620yfPr22TX01NmHChNplEyZMqLeP9evX15x00km17aZOnbrZ8lJ8Dhqj7vZ773vfW/Pwww/X2+7HP/5xbbuTTjrpLctLva3rq6dS1cGW6rqt1nsp6qympjS11lhb2jalmnO2phTbpxS1uqV1UdcDDzxQ2+6MM854y/LmfH+8+TXb21xRilppynprDRs2bKj9DA8ePLjmhRdeeEubD3zgA7Xv8/nnn99qn0888UTNZz/72dr/hg0bVtO/f/+af/u3f9vs70uWLHnLc88999zasXzlK1+pOfXUU2ve//731/Tv37/mmGOOqVm9enWz32uptnupPzPl/hy09HuolPNQkfY/a2ra1z4QNMQVk6GM1q5dm89//vPZeeedG2zTp0+fHH744TnwwAMbPAx4l112yYc+9KEkG89lf/Oh0nXV1NTki1/8YoYMGVLv8sMOO6z28aZfWJPNLzzav86h9282evToXHPNNbnrrruafC2Xf/zjH7n99tuTJD179sw3v/nNBtuefvrptb/k3HLLLVm3bl297RqzjjepqanJcccdl9122+0tyzat303tTjvttM3uNFlfu+eee26zZaXels3RGuu4uTXVWAsXLsxf/vKXJMlee+2VkSNH1tvu4x//eA4++OB6l61cuTLXXXddko0XyP2v//qvett17Ngx3/3ud2u37abnbNIWn4M3O/zww2uPQnqzcePGpWvXrkmS++67L2vWrKld1hrbektasw7aYr2Xos6S0tVaKbTVnNPS7dPWtdpYTfn+eLP2NFckpa2Vlqy3lrjppptqP8Nf+tKX6r3WVN1TmBpz6uCKFSvyl7/8pfa/119/PcnG06/q/r3uKVybnHXWWbn44ovzvve9L48++mhmzJiRPn365Jvf/Gauvvrq2u3RUi3Z7q2trT8HLfkeKvU8VKT9z/a8DwR1OYYPyuyDH/zgFpcff/zxjeqn7k7app2rhnziE59ocFndO9/UPZ/9He94R+3jG264IR/84AfTqVOntzy/oqIiBx10UKPG/GZz5szJ2rVrkyQf+chHtng9jZ133jkHHHBAHnrooSxbtixPP/10gxc+3do6rquhC1326dOn9nGvXr3yL//yL/W2q7vj8ebrAbTGtmyq1lrHzampxqp7cdMPfvCDWzzN47DDDssDDzzwlr//+c9/zqpVq5IkI0aMqLd26453yJAh+ctf/pI5c+Zk5cqVtae1tsXn4M0OP/zwBpf16NEj//Iv/5KHHnooa9euzVNPPZX9998/Sett6y1prTpoi/VeijpLSldrpdBWc05Lt085arWxmvL9UVd7miuS0tdKc9dbc61YsSITJ05MsvE7+s3Xmdqkf//+mT17dpKNdxzc0pyVJMOGDdvi6XRb88lPfjKf/OQnm/38xmjJdm9t5fgcNPd7qDXmoaLsf7bnfSCoy5FXUGa77757Sfqpe277hg0btth2S9ccqvtLYN1fkj7+8Y+nV69eSZI//elP+eQnP5nLLrss8+bN2+rrNVbdX0Hr3omwIXV/Qd3SkRxNWcd77bVXvX/v0qVL7eP6fs2tr11zL1TblG3ZVK21jptTU41V9xfEfv36bbFtQ78EPvnkk7WPd91116xcuXKL/216Pxs2bKi93XrSNp+DN3vzNUre7N3vfnft44ULF9Y+bq1tvSWtVQdtsd5LUWdJ6WqtLbV0zmnp9ilHrTZWc7+j29Nc0RSNrZVS7ds01s9+9rPa6xSdcsopb7lu3yZtdcfBttQW2725yvE5aO73UGvMQ0XZ/2zP+0BQlyOvoMx22WWXrbZZv359pk+fnj/96U/53//937z66qt5/fXXm326RHN+2d9xxx3z85//PCeffHKWLl2aF154IZdcckkuueSS9OjRI8OGDctHPvKRjBgxovaLranq/orbmPWy00471T5etmxZg+0a09cmjbnTVkvuClbqbdlUrbWOS3m0yJv94x//qH284447brFt3fHW9dprr9U+vvDCC3PhhRc2+vVffvnlzV6/tT8Hb7a17VR3ndT9tbW1tvWWtFYdtMV6L0WdJaWrtVJpizmnpdunHLXaWE35/qirPc0Vm5SyVpq73prj2WefzZQpU5JsDJ7/4z/+o8G2/dvojoNtqaXbvTWV43PQ3O+h1piHirL/2Z73gaAu4RWU2da+iBYuXJhTTz21EDtZQ4cOzV133ZUbbrghN9xwQ+2vMVVVVbnrrrty11135dxzz83nP//5fPOb32zy9RxWr15d+7juL0gNqdtmS9dxaK1b0DdVEbZla63j1lT3dd9895w3a2h53ffdVG++bXxrfw7ebGv1W/eQ/brXXWmP23pLWnu9l6LOktLWWku15ZzTku1T5FptyfdHe5krktLXSlt+7/7oRz+qDdgqKipy1llnNdi2br288sorWbp0aZsGba2hJdu9LbT156C5WmMeKsr+Z3veB4K6hFdQYNXV1Tn++ONrT2fZa6+98tnPfjYf/OAHs8suu6R79+6112WZNGlSJk2a1OpjqqioyJgxYzJmzJgsWrQoM2fOzKxZszJ79uwsX748a9euzeTJk/Pkk0/mmmuuqfeiklvqe5PG/A9J3TZ1n1tERdmW7XEd191B3NoRAA3toNX9Jfaiiy7KUUcd1aIxtebn4M3WrVu3xefXXSd1dxLb47bemtZc76Wos6T0tdZc5Zhzmrt9tsVa3aQ9zBVF+X5qjrvuuiszZ86s/feTTz652SlSWzN//vx2f0Hp5m73ttSWn4OWjHGTbW0eas/7QFCXa15Bgd155521O5N77713brrpphx//PEZPHhw+vTpk+7du6dbt26tesrWluyxxx455phjcskll2T27Nn56U9/WnvByDlz5uTGG29sUn9178jy6quvbrV93cOg2/quRk1VlG3ZHtdxjx49ah/XPbWrPpuuefJmdS8yunTp0tIM7P8p9efgzbZ2Ae2626juYfrtcVs3RanXeynqLGndWmuKcs85Tdk+bV2rK1eubPJzSqGoc0W5a6W5qqurM2HChBb1UYSj2luqudu9KUr5mWntz0Fzbcvfme15HwjqEl5BgdX99fDzn/98unfv3mDbcl94dPvtt09lZWUuueSS2r/NmDGjSX3UvehoY3Yo694BaODAgU16rbZWlG3ZHtdx3YvNLliwYIttG3pPdd93U36Vb6pSfA7ebGsXpK67Tt71rnfVPm6P27q5SrHeS1FnSdvV2tYUZc5Jtr59SlWrm25dn6T2rmH1efNt5MuhSHNFkWqlKa666qraC5AfeeSReeqppxr136mnnlrbx1//+tdyDb9kmrvdk/J/Zlrjc9Bc2/J3ZnveB4K6hFdQYHV/6drSr2V//etfc//999f+u9R3/Kiurs6sWbNy1VVX5b777tti27pf4E29yOuBBx5Ye+j1jBkzam/rW58lS5bU3tp+9913z957792k12prrbUta2pqmjSO9riO694WetasWVtse8cdd9T79wMOOKD2f8juvvvurV609sYbb8w999yz2fppq8/Bm911110NLlu+fHkef/zxJBuPHKp796P2uK03qVvXbbXeS1FnSWlqrRTa6vujFNunVLVa9w5zL774YoN9bGn7lUJ7myuKsq/RFH//+99zxRVXJNl4DbrTTjut0c+tWzNFCuOaq7nbPWndz0y5PgfN1Z6/M7emPe8DQV3CKyiwurfYfeSRR+pts3Dhwnz961/f7JDguocyl0KHDh3yn//5n7nwwgtz3nnnbfGUmgceeKD2cWNuNVxX9+7d85nPfCbJxp3piy++uN52NTU1mTBhQu2O8xe+8IV07Fjs6ayU27LuNSuWLFnSpHG0x3W8zz771N62+bnnnsu0adPqbXfzzTfX7qS/WUVFRT772c8m2Xjx0XPPPbfB4G/WrFn5/ve/nxNPPDHf/va3a//eVp+DN7vpppsaPDpg0qRJtb+Wf+xjH9vsV/T2tq0bquu2Wu+lqLOkNLVWCm31/VGK7VOqWt1nn31qH0+fPr3ePn73u99tcfuVQnubK4qyr9EUF154Ye3/WH/xi1/MHnvs0ejnbvqcJxuPSiriDSqaornbPWndz0y5PgfN1d6+M5uiKd9LM2fOLNQ+ENRV7E8avM19/OMfr71I6u9+97tMmjQpL7zwQl5//fU8+eST+elPf5qRI0emc+fOOeecc2qfd/PNN+f5558v2Y5lp06dMm7cuCTJ3/72t3zuc5/Lb37zmzzzzDN57bXX8tprr+Wpp57KFVdckW9961tJNn5RHnPMMU1+rf/8z//MO9/5ziTJ5MmT861vfSuPPvpoli1blldffTWzZ8/OCSeckP/v//v/kiSDBw/O2LFjS/I+W1Mpt2XdnfQrr7wyM2bMyJ///Oc8/PDDjRpLe1zHp5xySu3j7373u/n1r3+dhQsX5h//+Ef++te/5sc//nHOOuusjBgxosE+Tj311NpTw2699daMHj06M2bMyMsvv5xXXnklc+fOzXnnnZfjjz8+69evT0VFxWa/5rfl52CT7bbbLh/4wAcyevToTJkyJQsWLMg//vGPPP300znvvPPyi1/8IsnGi42fcMIJb3l+e9rWDdX13Llz22y9l6LOkpbXWim01fdHqT4XpajVT3ziE7WPL7vssvzmN7/J4sWLs3z58vz1r3/Nj370o5x99tkZM2ZME9Zk07W3uaIo+xqN9ec//zm33357kmTHHXfMiSee2KTn9+vXr/YC0uvXr9/s9K/2pqXfEa35mSnH56Cl2tN3ZlM19nvpxBNPLMw+ELyZuw1Cge2777458cQTc/nll2fDhg2ZOHFiJk6cuFmb9773vfn5z3+eHXfcMTvvvHNee+21PPvss6msrEzfvn1z9913l2QsX/3qV7NkyZJcc801+dvf/pYf/vCHDbbt1atXLr744vTt27fJr9OzZ89Mnjw5J510Up5++ulMnTo1U6dOrbftwQcfnJ/85Ceb3Qa6qEq5LY888shceumlWbNmTZ555pkcf/zxSTb+qvqv//qvWx1Le1zHn/zkJ/PEE0/kqquuyqpVqzJ+/PiMHz9+szb77bdfvv/97zf463G3bt1yzTXX5JRTTslf/vKXPPjgg3nwwQfrbdu7d+9cfPHFm/1Cn7Td52CT9evX59xzz83YsWNz7rnn1tumS5cu+T//5//Ue9pCe9rWW6rryy67rE3WeynqLClNrbVUW35/lOJzUYpa/fCHP5wjjzwyt912W9asWZMf/vCHbxnLyJEjc8IJJ+RXv/pVo95bc7WnuaJI+xpbs2HDhpx33nm1//7a176WHXfcsUl9dO7cOXvuuWf+9re/Jdl4faP999+/lMNsMy39jmjtz0xbfw5aqj19ZzZVe9wHgjcTXkHB/ed//mcGDx6c3/72t5k3b16qqqpSUVGRfffdN5/5zGfyqU99qvZ0m0svvTQ/+tGP8uyzz6ZLly6NCjIaq0OHDjnrrLPy6U9/OjfddFMeffTRLF68OCtXrkzHjh3Tq1ev9O/fP//2b/+WUaNGbXYdhabac889c9NNN+W2227LHXfckSeffDKvv/56tt9+++yyyy7Zf//9c9RRR+UjH/lIyd5fWyjVtuzTp0+uuuqqXHTRRXnqqadSU1OTXXbZJfvtt1+jx9Ie1/G3v/3tfOADH8i1116bv/zlL1m2bFm6d++ed7/73amsrKw9dH+77bbL+vXr6+1j1113zfXXX58777wz06ZNy2OPPZalS5dm/fr16dWrVwYMGJCPfvSj+cxnPlPvnbXa8nOwyW677Zbf//73mTJlSqZPn54XXnghq1atSu/evXPIIYfkuOOO22Lw0V629Zbqui3XeynqLGl5rZVCW31/lGr7lKJWL7roohx88MG5+eab88wzz2TFihXp3r179ttvv3zuc5/L4YcfvtXrvZRCe5srirKvsTXXXXdd7cW0+/btm2OPPbZZ/ey9996bhVftWUu/I1rzM1OOz0FLtZfvzOZoj/tAUFeHmqZe7RcAaFWHHnpoFi9enCTt+pQWoHWZK96ebHfg7cg1rwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYHWpqamrKPQgAAAAAqI8jrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABTW9uUeQNHMmTOn3EMAAAAA2CYdeOCBTX6OI68AAAAAKCxHXjWgOUlgKc2fPz9JMnDgwLKOA5pC3dJeqV3aK7VLe6Ruaa/ULu1VUWq3JWe6OfIKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIW1fbkHAEDreeONZPr05KmnkhUrku7dkwEDksMOS7bbrtyjAwAA2DrhFcA26JVXkiuuSCZNShYufOvyvfZKTjghGTcu6d277ccHAADQWE4bBNjGzJqVDByYnHVW/cFVkrzwQvK9721sN3t2244PAACgKYRXANuQWbOSj30sWbq0ce2XLk0OPVSABQAAFJfwCmAb8coryac+laxZ07TnrVmTHHXUxucDAAAUjfAKYBtxxRWNP+LqzZYuTa68srTjAQAAKAXhFcA24I03Nl6cvSV+/vNk/frSjAcAAKBUhFcA24Dp0xu+OHtjLVyY3HlnacYDAABQKsIrgG3AU0+Vpp+nny5NPwAAAKUivALYBqxYUZp+qqpK0w8AAECpCK8AtgHdu5emnx49StMPAABAqQivALYBAwaUpp/+/UvTDwAAQKkIrwC2ASNGJHvu2bI+9torOeyw0owHAACgVIRXANuA7bdPTjihZX2ccEKy3XalGQ8AAECpCK8AthHHH5/sskvznrvLLsm4caUdDwAAQCkIrwC2Eb17J1OnJl27Nu15XbtufF7v3q0zLgAAgJYQXgFsQw45JPnTnxp/BNYuuyR3373xeQAAAEUkvALYxnzgA8n8+cn55zd8Efe99kp+9KON7QRXAABAkW1f7gEAUHq9eyff/W5yxhnJnXcmTz+dVFUlPXok/ftvvKugi7MDAADtgfAKYBu23XbJJz6x8T8AAID2yGmDAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDC2r7cA1iwYEEmTZqU2bNn55VXXkm3bt0ydOjQjBkzJgcffHCT+5sxY0YmT56cJ554ImvXrk2fPn1y2GGHZcyYMdl5551b4R0AAAAA0FrKeuTVnDlzMnLkyNx4443p27dvjj766AwdOjQzZ87M6NGjM2XKlCb1d8kll+T444/PI488kkMOOSSf/OQns2bNmkyaNCn//u//nqVLl7bSOwEAAACgNZTtyKvVq1fn9NNPz6pVq3LBBRdk5MiRtcseeeSRjB49OhMmTMiwYcOy7777brW/e+65J5dddln23HPPXH311enbt2+SZO3atfnqV7+ahx56KBdffHHOO++81npLAAAAAJRY2Y68mjZtWhYvXpzhw4dvFlwlyQEHHJBjjjkm69aty9VXX92o/iZOnJgkOffcc2uDqyTp0qVLvve97+XrX/96KisrSzZ+AAAAAFpf2cKrO++8M0kaDJQOP/zwJMn06dO32tfTTz+dp59+Ou9617tyyCGHvGX5e9/73px88skZPnx4C0YMAAAAQFsrW3g1b968JMmgQYPqXT548OAkybJly7Jo0aIt9vXQQw8lSQ466KASjhAAAACAcitLeFVdXZ0lS5YkSXbfffd62+ywww7p1atXko13JNySZ555Jknyrne9KwsWLMi3v/3tDB8+PEOGDMmhhx6ac845Jy+//HLp3gAAAAAAbaIsF2xfsWJF7eNu3bo12K6ioiLLli3LypUrt9jfq6++miR58cUXM3LkyOy66675t3/7t6xfvz733Xdffvvb3+auu+7Ktddemz322KNRY5w/f36j2rWW1atXF2Ic0BTqlvZK7dJeqV3aI3VLe6V2aa+2hdotS3i1du3a2sedOnVqsF3nzp2T/HNFN2TVqlVJkmuvvTannHJKTjrppHTsuPGgshUrVmTMmDF5/PHH84Mf/CBXXXVVS4cPAAAAQBspS3jVtWvX2sfr1q1Lly5d6m1XXV2dZOMphFuyKajae++9c/LJJ6dDhw61y7p3754zzzwzxx57bGbOnJmXXnqpwVMV6xo4cOBW27SmTYlouccBTaFuaa/ULu2V2qU9Ure0V2qX9qootTtnzpxmP7cs17yqe6rglk4J3HR6YY8ePbbYX/fu3ZMk73vf+zYLrjY58MADawOyTReKBwAAAKD4yhJede7cOX379k2SLF68uN42VVVVWb58eZKkX79+W+xvr732SpKsWbOm3uUdOnTIO97xjiT/PMUQAAAAgOIrS3iVJEOGDEmSPPbYY/Uunzt3bpKkd+/e6dOnT6P6+tvf/lbv8g0bNtTebXDnnXduxmgBAAAAKIeyhVeVlZVJkmnTptW7/LbbbkuSHHHEEVvta/jw4amoqMiTTz5Z72mBDz74YNatW5dOnTplv/32a8GoAQAAAGhLZQuvRowYkX79+uXhhx/O9ddfv9myGTNm5NZbb01FRUXGjh1b+/fp06ensrIy48aN26x9t27datudc845qaqqql328ssvZ/z48UmSo446Kj179myttwQAAABAiZXlboNJ0qlTp0ycODFjx47N2WefnalTp2afffbJokWLMmvWrHTs2DHjx4/f7JTBqqqqPP/88/X297WvfS2PP/547r333lRWVuZDH/pQampq8j//8z95/fXXM3DgwHznO99pq7cHAAAAQAmULbxKkkGDBuWWW27J5Zdfnvvuuy9z585Nz549M2LEiJx44olNuo1jp06dMmnSpFx77bW56aab8sc//jEbNmzIXnvtlS9/+csZM2ZMKioqWvHdAAAAAFBqZQ2vkqRPnz4555xzGtV21KhRGTVqVIPLO3bsmGOPPTbHHntsqYYHAAAAQBmV7ZpXAAAAALA1wisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKKyyh1cLFizId7/73Xz0ox/NkCFDMmzYsJx44ol54IEHWtz3PffckwEDBmTAgAF58MEHSzBaAAAAANpSWcOrOXPmZOTIkbnxxhvTt2/fHH300Rk6dGhmzpyZ0aNHZ8qUKc3ue/ny5Tn77LNLOFoAAAAA2tr25Xrh1atX5/TTT8+qVatywQUXZOTIkbXLHnnkkYwePToTJkzIsGHDsu+++za5//PPPz8vv/xydtppp7z++uslHDkAAAAAbaVsR15NmzYtixcvzvDhwzcLrpLkgAMOyDHHHJN169bl6quvbnLfM2bMyM0335zDDjusWcEXAAAAAMVQtvDqzjvvTJJUVlbWu/zwww9PkkyfPr1J/VZVVeX73/9+evbsmbPOOqtlgwQAAACgrMoWXs2bNy9JMmjQoHqXDx48OEmybNmyLFq0qNH9/uhHP8qSJUty5plnZrfddmv5QAEAAAAom7KEV9XV1VmyZEmSZPfdd6+3zQ477JBevXol2XhHwsa4995784c//CHDhw/P0UcfXZKxAgAAAFA+Zblg+4oVK2ofd+vWrcF2FRUVWbZsWVauXNmoPs8+++x079495513XovHOH/+/Bb30RKrV68uxDigKdQt7ZXapb1Su7RH6pb2Su3SXm0LtVuWI6/Wrl1b+7hTp04NtuvcuXOSf67oLZkwYUJeeumlfPvb327waC4AAAAA2peyHHnVtWvX2sfr1q1Lly5d6m1XXV2dZOMphFty//3353e/+10OOeSQfP7zny/JGAcOHFiSfpprUyJa7nFAU6hb2iu1S3uldmmP1C3tldqlvSpK7c6ZM6fZzy3LkVd1TxXc0imBm04v7NGjxxbbnHXWWenWrVtJThcEAAAAoDjKcuRV586d07dv3yxevDiLFy/Ozjvv/JY2VVVVWb58eZKkX79+DfZ13XXX5cUXX8yee+6ZCy+88C3Ln3nmmSTJpZdemt/85jcZNmxYjj322BK9EwAAAABaU1nCqyQZMmRIFi9enMceeyz77bffW5bPnTs3SdK7d+/06dOnwX42XQ9r4cKFWbhwYYPtHn744SQbLwIPAAAAQPtQtvCqsrIyd9xxR6ZNm1bvkVC33XZbkuSII47YYj+nnnpqTj311AaXf+lLX8pDDz2UyZMnZ9iwYS0bNAAAAABtqizXvEqSESNGpF+/fnn44Ydz/fXXb7ZsxowZufXWW1NRUZGxY8fW/n369OmprKzMuHHj2nq4AAAAAJRB2Y686tSpUyZOnJixY8fm7LPPztSpU7PPPvtk0aJFmTVrVjp27Jjx48dvdspgVVVVnn/++XINGQAAAIA2VrbwKkkGDRqUW265JZdffnnuu+++zJ07Nz179syIESNy4oknlv02jgAAAACUV1nDqyTp06dPzjnnnEa1HTVqVEaNGtWk/q+55prmDAsAAACAAijbNa8AAAAAYGuEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWNuXewALFizIpEmTMnv27Lzyyivp1q1bhg4dmjFjxuTggw9uUl/PPvtsrrrqqjzwwAN5+eWX07lz5/Tr1y+VlZX58pe/nC5durTSuwAAAACgNZT1yKs5c+Zk5MiRufHGG9O3b98cffTRGTp0aGbOnJnRo0dnypQpje7rjjvuqO2rR48e+fSnP50PfOADee6553LRRRflC1/4QlauXNmK7wYAAACAUivbkVerV6/O6aefnlWrVuWCCy7IyJEja5c98sgjGT16dCZMmJBhw4Zl33333WJfS5YsyZlnnpnq6uqcccYZOe6442qXvfjii/nc5z6XJ554Ir/4xS/yjW98o7XeEgAAAAAlVrYjr6ZNm5bFixdn+PDhmwVXSXLAAQfkmGOOybp163L11Vdvta+bb745q1atyv77779ZcJUk73znO/OVr3wlSXLnnXeWbPwAAAAAtL6yhVebgqTKysp6lx9++OFJkunTp2+1r+HDh+e8887LaaedVu/yvffeO0ny97//vTlDBQAAAKBMynba4Lx585IkgwYNqnf54MGDkyTLli3LokWLssceezTY1+DBg2vb1+fll19Okuy0007NHS4AAAAAZVCWI6+qq6uzZMmSJMnuu+9eb5sddtghvXr1SrLxjoTNVVNTk9///vdJGj7KCwAAAIBiKsuRVytWrKh93K1btwbbVVRUZNmyZS26S+CVV16ZuXPnplevXhk3blyjnzd//vxmv2YprF69uhDjgKZQt7RXapf2Su3SHqlb2iu1S3u1LdRuWY68Wrt2be3jTp06Ndiuc+fOSf65opvql7/8ZSZOnJhOnTrlpz/9aXbcccdm9QMAAABAeZTlyKuuXbvWPl63bl26dOlSb7vq6uokG08hbIqamppccMEF+dWvfpXOnTvnxz/+cQ4++OAm9TFw4MAmtS+1TYlouccBTaFuaa/ULu2V2qU9Ure0V2qX9qootTtnzpxmP7cs4VXdUwVXrlzZYHi16fTCHj16NLrvtWvX5vTTT88dd9yRnj175tJLL21ycAUAAABAMZTltMHOnTunb9++SZLFixfX26aqqirLly9PkvTr169R/VZXV+eEE07IHXfckT322CPXXXed4AoAAACgHStLeJUkQ4YMSZI89thj9S6fO3dukqR3797p06fPVvvbsGFDTj/99MyePTsDBw7Mddddl/e85z0lGy8AAAAAba9s4VVlZWWSZNq0afUuv+2225IkRxxxRKP6+9nPfpY//vGPec973pNf/epX6d27d2kGCgAAAEDZlC28GjFiRPr165eHH344119//WbLZsyYkVtvvTUVFRUZO3Zs7d+nT5+eysrKjBs3brP2zz77bCZNmpROnTrlZz/7WXbaaac2eQ8AAAAAtK6yXLA9STp16pSJEydm7NixOfvsszN16tTss88+WbRoUWbNmpWOHTtm/Pjxm50yWFVVleeff/4tfV1xxRV54403sueee+baa6/d4uuefPLJ6dWrV6nfDgAAAACtoGzhVZIMGjQot9xySy6//PLcd999mTt3bnr27JkRI0bkxBNPbPRtHF988cUkycKFCzN58uQtth09erTwCgAAAKCdKGt4lSR9+vTJOeec06i2o0aNyqhRo97y92uuuabUwwIAAACgAMp2zSsAAAAA2BrhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIW1fbkHAAAAAEX1xhvJ9OnJvffulFWrOqZfv2TAgOSww5Lttiv36ODtQXgFAAAAb/LKK8kVVySTJiULFyZJn82W77VXcsIJybhxSe/eZRkivG04bRAAAADqmDUrGTgwOeusTcHVW73wQvK9721sN3t2244P3m6EVwAAAPD/zJqVfOxjydKljWu/dGly6KECLGhNwisAAADIxlMFP/WpZM2apj1vzZrkqKM2Ph8oPeEVAAAAZOM1rhp7xNWbLV2aXHllaccDbOSC7UCLuQMLAADt3RtvbLw4e0v8/OfJGWfYB4ZSE14BzeYOLAAAbCumT2/44uyNtXBhcuedySc+UZoxARs5bRBoFndgAQBgW/LUU6Xp5+mnS9MP8E9lP/JqwYIFmTRpUmbPnp1XXnkl3bp1y9ChQzNmzJgcfPDBZesLaNimO7A09kKWm+7AcvfdySGHtO7YAACgOVasKE0/VVWl6Qf4p7IeeTVnzpyMHDkyN954Y/r27Zujjz46Q4cOzcyZMzN69OhMmTKlLH0BDXMHFgAAtkU77FCafrp1K00/wD+V7cir1atX5/TTT8+qVatywQUXZOTIkbXLHnnkkYwePToTJkzIsGHDsu+++7ZZX8CWleIOLN/9bmnHBAAALbVyZWn6ceQVlF7ZjryaNm1aFi9enOHDh28WNiXJAQcckGOOOSbr1q3L1Vdf3aZ9AQ0r1R1Y1q8vzXgAAKBUunYtTT+OvILSK1t4deeddyZJKisr611++OGHJ0mmT5/epn0BDSvlHVgAAKBInniiNP385S+l6Qf4p7KFV/PmzUuSDBo0qN7lgwcPTpIsW7YsixYtarO+gIa5AwsAANuqf/yjNP04bRBKryzhVXV1dZYsWZIk2X333etts8MOO6RXr15JNt5FsC36ArasVF/opeoHAABKpVR3G1y+vDT9AP9UlvBqRZ1ZodsWTgiuqKhIkqzcwpXzStkXsGWlOnCxpaceAgBAqXXvXpp+evYsTT/AP5XlboNr166tfdypU6cG23Xu3DnJxrsJtkVfdc2fP79R7VrLpnGWexxQ11//ukeSHiXopyrz5zuFl+Iw59JeqV3aI3VLUdXU7J6kV4v7Wb9+WebPf6nF/UCpbAvzblmOvOpa5zYO69ata7BddXV1ko2n/bVFX8CW1dSUewQAANA6Oncuzc5uly52mqHUynLkVd3T+1auXJkuXbrU227TKYE9ejR8pEcp+6pr4MCBjWrXWjYlouUeB9RV50DHFlmzpofaplDMubRXapf2SN1SVLvsUpp+dt55pwwcuFNpOoMSKMq8O2fOnGY/tyxHXnXu3Dl9+/ZNkixevLjeNlVVVVn+/650169fvzbpC9iyLZyZW5Z+AACgVN75ztL08//+9xQoobKEV0kyZMiQJMljjz1W7/K5c+cmSXr37p0+ffq0WV9Aw0qV/cqQAQAomh13LFY/wD+VLbyqrKxMkkybNq3e5bfddluS5IgjjmjTvoCGleqScVu4MSgAAJTFgAGl6ad//9L0A/xT2cKrESNGpF+/fnn44Ydz/fXXb7ZsxowZufXWW1NRUZGxY8fW/n369OmprKzMuHHjWtwX0HTbbVeafjp0KE0/AABQKiNGJHvu2bI+9torOeyw0owH+KeyXLA9STp16pSJEydm7NixOfvsszN16tTss88+WbRoUWbNmpWOHTtm/Pjxm53mV1VVleeff74kfQFNV6rz910HAACAotl+++SEE5Kzzmp+HyecULoffIF/KtuRV0kyaNCg3HLLLTnmmGPy4osv5ve//33mzZuXESNG5Pe//33t6YBt3RdQv549S9OP6wAAAFBExx/f/LsO7rJL8qaThIASKduRV5v06dMn55xzTqPajho1KqNGjSpJX0DTuQ4AAADbst69k6lTk0MPTdasafzzunbd+LzevVtvbPB2VtYjr4D2xXUAAADY1h1ySPKnPzX+CKxddknuvnvj84DWIbwCGm3TdQBawnUAAAAoug98IJk/Pzn//IZ/vN1rr+RHP9rYTnAFravspw0C7cvxxycXX5wsXdr057oOAAAA7UXv3sl3v5uccUZy553Jfff9PStXdszee++a/v03nk3gR1loG8IroElcBwAAgLeT7bZLPvGJ5N3vfj1JMnDgrmUeEbz9OG0QaDLXAQAAAKCtCK+AZnEdAAAAANqC0waBZnMdAAAAAFqb8ApoMdcBAAAAoLU4bRAAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGFtX84XX7BgQSZNmpTZs2fnlVdeSbdu3TJ06NCMGTMmBx98cJP7e/bZZ3PVVVflgQceyMsvv5zOnTunX79+qayszJe//OV06dKlFd4FAAAAAK2lbEdezZkzJyNHjsyNN96Yvn375uijj87QoUMzc+bMjB49OlOmTGlSf3fccUdtfz169MinP/3pfOADH8hzzz2Xiy66KF/4wheycuXKVno3AAAAALSGshx5tXr16px++ulZtWpVLrjggowcObJ22SOPPJLRo0dnwoQJGTZsWPbdd9+t9rdkyZKceeaZqa6uzhlnnJHjjjuudtmLL76Yz33uc3niiSfyi1/8It/4xjda4y0BAAAA0ArKcuTVtGnTsnjx4gwfPnyz4CpJDjjggBxzzDFZt25drr766kb1d/PNN2fVqlXZf//9NwuukuSd73xnvvKVryRJ7rzzzpKMHwAAAIC2UZbwalOIVFlZWe/yww8/PEkyffr0RvU3fPjwnHfeeTnttNPqXb733nsnSf7+9783dagAAAAAlFFZThucN29ekmTQoEH1Lh88eHCSZNmyZVm0aFH22GOPLfY3ePDg2ufU5+WXX06S7LTTTs0ZLgAAAABl0uZHXlVXV2fJkiVJkt13373eNjvssEN69eqVZOMdCVuipqYmv//975M0fKQXAAAAAMXU5uHVihUrah9369atwXYVFRVJ0uI7BF555ZWZO3duevXqlXHjxrWoLwAAAADaVotPGzzttNMyf/78RrXdbbfdMmHChNp/d+rUqcG2nTt3TrLxzoTN9ctf/jITJ05Mp06d8tOf/jQ77rhjo5/b2PfUWja973KPA5pC3dJeqV3aK7VLe6Ruaa/ULu3VtlC7LQ6vFi9enOeff75Rbaurq9O1a9faf69bty5dunRpsG2y8RTCpqqpqckFF1yQX/3qV+ncuXN+/OMf5+CDD25yPwAAAACUV4vDqxtuuKFJ7TeFUsnGUwIbCq82nV7Yo0ePJvW/du3anH766bnjjjvSs2fPXHrppc0KrgYOHNjk55TSpkS03OOAplC3tFdql/ZK7dIeqVvaK7VLe1WU2p0zZ06zn9vm17zq3Llz+vbtm2TjUVv1qaqqyvLly5Mk/fr1a3Tf1dXVOeGEE3LHHXdkjz32yHXXXeeIKwAAAIB2rM3DqyQZMmRIkuSxxx6rd/ncuXOTJL17906fPn0a1eeGDRty+umnZ/bs2Rk4cGCuu+66vOc97ynJeAEAAAAoj7KEV5WVlUmSadOm1bv8tttuS5IcccQRje7zZz/7Wf74xz/mPe95T371q1+ld+/eLR8oAAAAAGVVlvBqxIgR6devXx5++OFcf/31my2bMWNGbr311lRUVGTs2LGbLZs+fXoqKyszbty4zf7+7LPPZtKkSenUqVN+9rOfZaeddmr19wAAAABA62vxBdubo1OnTpk4cWLGjh2bs88+O1OnTs0+++yTRYsWZdasWenYsWPGjx//llMGq6qq6r2z4RVXXJE33ngje+65Z6699totvvbJJ5+cXr16lfLtAAAAANBKyhJeJcmgQYNyyy235PLLL899992XuXPnpmfPnhkxYkROPPHEJl0F/8UXX0ySLFy4MJMnT95i29GjRwuvAAAAANqJsoVXSdKnT5+cc845jW4/atSojBo16i1/v+aaa0o5LAAAAAAKoizXvAIAAACAxhBeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhlTW8WrBgQb773e/mox/9aIYMGZJhw4blxBNPzAMPPFCS/u+5554MGDAgAwYMyIMPPliSPgEAAABoO2ULr+bMmZORI0fmxhtvTN++fXP00Udn6NChmTlzZkaPHp0pU6a0qP/ly5fn7LPPLtFoAQAAACiH7cvxoqtXr87pp5+eVatW5YILLsjIkSNrlz3yyCMZPXp0JkyYkGHDhmXfffdt1mucf/75efnll7PTTjvl9ddfL9HIAQAAAGhLZTnyatq0aVm8eHGGDx++WXCVJAcccECOOeaYrFu3LldffXWz+p8xY0ZuvvnmHHbYYc0OvwAAAAAov7KEV3feeWeSpLKyst7lhx9+eJJk+vTpTe67qqoq3//+99OzZ8+cddZZzR8kAAAAAGVXlvBq3rx5SZJBgwbVu3zw4MFJkmXLlmXRokVN6vtHP/pRlixZkjPPPDO77bZbywYKAAAAQFm1eXhVXV2dJUuWJEl23333etvssMMO6dWrV5KNdyRsrHvvvTd/+MMfMnz48Bx99NEtHisAAAAA5dXm4dWKFStqH3fr1q3BdhUVFUmSlStXNrrfs88+O927d895553XskECAAAAUAgtvtvgaaedlvnz5zeq7W677ZYJEybU/rtTp04Ntu3cuXOSjXcmbIwJEybkpZdeyg9/+MMGj+hqisa+p9ay6X2XexzQFOqW9krt0l6pXdojdUt7pXZpr7aF2m1xeLV48eI8//zzjWpbXV2drl271v573bp16dKlS4Ntk42nEG7N/fffn9/97nc55JBD8vnPf75RYwEAAACg+FocXt1www1Nar8plEo2nhLYUHi16fTCHj16bLG/FStW5Kyzzkq3bt1KerrgwIEDS9ZXc2xKRMs9DmgKdUt7pXZpr9Qu7ZG6pb1Su7RXRandOXPmNPu5LQ6vmqpz587p27dvFi9enMWLF2fnnXd+S5uqqqosX748SdKvX78t9nfdddflxRdfzJ577pkLL7zwLcufeeaZJMmll16a3/zmNxk2bFiOPfbYErwTAAAAAFpbm4dXSTJkyJAsXrw4jz32WPbbb7+3LJ87d26SpHfv3unTp88W+9p07ubChQuzcOHCBts9/PDDSf55IXgAAAAAiq8s4VVlZWXuuOOOTJs2rd6joG677bYkyRFHHLHVvk499dSceuqpDS7/0pe+lIceeiiTJ0/OsGHDmj9oAAAAANpcx3K86IgRI9KvX788/PDDuf766zdbNmPGjNx6662pqKjI2LFjN1s2ffr0VFZWZty4cW05XAAAAADKpCxHXnXq1CkTJ07M2LFjc/bZZ2fq1KnZZ599smjRosyaNSsdO3bM+PHj33LKYFVVVaPvbAgAAABA+1eW8CpJBg0alFtuuSWXX3557rvvvsydOzc9e/bMiBEjcuKJJ5b9KvgAAAAAlF/Zwqsk6dOnT84555xGtx81alRGjRrVpNe45pprmjosAAAAAAqiLNe8AgAAAIDGEF4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGFtX84XX7BgQSZNmpTZs2fnlVdeSbdu3TJ06NCMGTMmBx98cLP6nDFjRiZPnpwnnngia9euTZ8+fXLYYYdlzJgx2XnnnUv8DgAAAABoTWU78mrOnDkZOXJkbrzxxvTt2zdHH310hg4dmpkzZ2b06NGZMmVKk/u85JJLcvzxx+eRRx7JIYcckk9+8pNZs2ZNJk2alH//93/P0qVLW+GdAAAAANBaynLk1erVq3P66adn1apVueCCCzJy5MjaZY888khGjx6dCRMmZNiwYdl3330b1ec999yTyy67LHvuuWeuvvrq9O3bN0mydu3afPWrX81DDz2Uiy++OOedd15rvCUAAAAAWkFZjryaNm1aFi9enOHDh28WXCXJAQcckGOOOSbr1q3L1Vdf3eg+J06cmCQ599xza4OrJOnSpUu+973v5etf/3oqKytLMn4AAAAA2kZZwqs777wzSRoMkw4//PAkyfTp0xvV39NPP52nn34673rXu3LIIYe8Zfl73/venHzyyRk+fHgzRwwAAABAOZQlvJo3b16SZNCgQfUuHzx4cJJk2bJlWbRo0Vb7e+ihh5IkBx10UIlGCAAAAEARtHl4VV1dnSVLliRJdt9993rb7LDDDunVq1eSjXck3JpnnnkmSfKud70rCxYsyLe//e0MHz48Q4YMyaGHHppzzjknL7/8cmneAAAAAABtps0v2L5ixYrax926dWuwXUVFRZYtW5aVK1dutc9XX301SfLiiy9m5MiR2XXXXfNv//ZvWb9+fe6777789re/zV133ZVrr702e+yxR6PGOX/+/Ea1ay2rV68uxDigKdQt7ZXapb1Su7RH6pb2Su3SXm0Ltdvi8Oq0005r9ArYbbfdMmHChNp/d+rUqcG2nTt3TvLPlbwlq1atSpJce+21OeWUU3LSSSelY8eNB5WtWLEiY8aMyeOPP54f/OAHueqqqxo1VgAAAADKr8Xh1eLFi/P88883qm11dXW6du1a++9169alS5cuDbZNNp5CuDWbgqq99947J598cjp06FC7rHv37jnzzDNz7LHHZubMmXnppZcaPF2xroEDB261TWvaFAiWexzQFOqW9krt0l6pXdojdUt7pXZpr4pSu3PmzGn2c1scXt1www1Nar8plEqSlStXNhhebTq9sEePHlvts3v37kmS973vfZsFV5sceOCB6dKlS9auXZt58+Y1KrwCAAAAoPza/ILtnTt3Tt++fZNsPGqrPlVVVVm+fHmSpF+/flvtc6+99kqSrFmzpt7lHTp0yDve8Y4k/zzFEAAAAIDia/PwKkmGDBmSJHnsscfqXT537twkSe/evdOnT59G9/e3v/2t3uUbNmyovdvgzjvv3MTRAgAAAFAuZQmvKisrkyTTpk2rd/ltt92WJDniiCMa1d/w4cNTUVGRJ598MvPmzXvL8gcffDDr1q1Lp06dst9++zVz1AAAAAC0tbKEVyNGjEi/fv3y8MMP5/rrr99s2YwZM3LrrbemoqIiY8eO3WzZ9OnTU1lZmXHjxm32927dutW2Peecc1JVVVW77OWXX8748eOTJEcddVR69uzZGm8JAAAAgFbQ4gu2N0enTp0yceLEjB07NmeffXamTp2affbZJ4sWLcqsWbPSsWPHjB8//i2nDFZVVTV4Z8Ovfe1refzxx3PvvfemsrIyH/rQh1JTU5P/+Z//yeuvv56BAwfmO9/5Tlu8PQAAAABKpCzhVZIMGjQot9xySy6//PLcd999mTt3bnr27JkRI0bkxBNPbPItHDt16pRJkybl2muvzU033ZQ//vGP2bBhQ/baa698+ctfzpgxY1JRUdFK7wYAAACA1lC28CpJ+vTpk3POOafR7UeNGpVRo0Y1uLxjx4459thjc+yxx5ZieAAAAACUWVmueQUAAAAAjSG8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwhJeAQAAAFBYwisAAAAACkt4BQAAAEBhCa8AAAAAKCzhFQAAAACFJbwCAAAAoLCEVwAAAAAU1vblHgAAAADJmjXJhRcmjz6aVFUlPXokQ4cmZ56ZdO5c7tEBlI/wCgAAoIzmz0++/vXknnuS9es3X3bzzckPf5gcemjy058mAweWZYgAZeW0QQAAgDKZNCkZPDi56663BlebrF+fTJ++sd0VV7Tt+ACKwJFXAAAAZTBpUnLiiY1vX1OTnHDCxsfHH986YwIoIkdeAQAAtLH585Ovfa15zz3xxI3PB3i7EF4BAAC0sa9/feORVM1RU5N84xulHQ9AkQmvAAAA2tCaNRsvzt4Sd9+dVFeXZjwARSe8AgAAaEMXXtjwxdkba/36ZMKE0owHoOiEVwAAAG3o0UdL08/cuaXpB6DohFcAAABtqKqqNP0sX16afgCKTngFAADQhnr0KE0/PXuWph+AohNeAQAAtKGhQ0vTz/veV5p+AIpOeAUAANCGvv3tZLvtWtbHdtslZ55ZmvEAFJ3wCgAAoA117Zp89KMt6+PQQ5POnUszHoCiE14BAAC0sUsuSTp0aN5zO3RIfvrT0o4HoMiEVwAAAG1s4MDk5z9v3nN//vONzwd4uxBeAQAAlMHxx28Mohp7BFaHDsmkSRufB/B2IrwCAAAokxNOSJ58MhkxouGLuG+3XXLYYRvbCa6At6Ptyz0AAACAt7OBA5M770yqq5MJE5K5c5Ply5OePZP3vW/jXQVdnB14OxNeAQAAFEDnzsnZZ5d7FADF47RBAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsDrU1NTUlHsQRTJnzpxyDwEAAABgm3TggQc2+TmOvAIAAACgsBx5BQAAAEBhOfIKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACis7cs9gLe7mpqaXHPNNbnooouydu3aTJ48OcOGDWtSHw8++GC+/OUvb7Xdf//3f+c//uM/mjtU2EwpaneTBQsWZNKkSZk9e3ZeeeWVdOvWLUOHDs2YMWNy8MEHl3jkvJ2VqtbMu7SWUs6H5lbaUinqzdxKOZRqn9acS1trae22tzlXeFVGr776ar7zne/k3nvvLUl/u+22Ww4//PAGlw8YMKAkrwOlrN05c+bkq1/9alatWpV//dd/zYc+9KEsWbIkM2fOzD333JPvf//7+eIXv1iCUfN21xq1Zt6llEpZo+ZW2lKp683cSlsp1T6tOZe2Vsr/H2s3c24NZXH//ffXHHLIITX9+/ev+eEPf1gzfPjwmv79+9c88MADTe7rgQceqOnfv3/NF7/4xVYYKWyulLW7atWqmo9+9KM1/fv3r7nppps2WzZnzpyaIUOG1AwePLjm6aefLtHoebsqda2Zdym1UtaouZW2VMp6M7fSlkq1T2vOpa2Vqnbb25zrmldl8oc//CHr1q3Lz372s3z/+99Pp06dyj0kaJRS1u60adOyePHiDB8+PCNHjtxs2QEHHJBjjjkm69aty9VXX93CUfN2p9YoulLWqHqnLak32qtS7dP6DNDW3q5ZgvCqTPbff//cdNNNGTFiRLmHAk1Sytq98847kySVlZX1Lt90+Or06dNb/Fq8vak1iq6UNareaUvqjfaqVPu0PgO0tbdrliC8KpMvfelL2WOPPco9DGiyUtbuvHnzkiSDBg2qd/ngwYOTJMuWLcuiRYtK8pq8Pak1iq6UNareaUvqjfaqVPu0PgO0tbdrluCC7duYqqqq3H333XnuueeyYcOG7Lnnnvnwhz+c3XbbrdxDg81UV1dnyZIlSZLdd9+93jY77LBDevXqlWXLlmXBggVvy0malmvtWjPv0lKlrFFzK22pNevN3Ep7YM5lW9Ee5lzh1TbkmWeeyYc//OGsXLlys7936tQpxx9/fL7+9a+XaWTwVitWrKh93K1btwbbVVRUZNmyZW+pa2is1qw18y6lUMoaNbfSllqr3syttBfmXLYF7WXOFV610GmnnZb58+c3qu1uu+3WqhfqW7FiRY477riMGjUq73znO7N06dJMmTIlv/71r3PZZZdlhx12yLhx41rt9Wlfyl27a9eurX28pYsMdu7cOUmyevXqkr4+7VdTa3fChAm1/y51rZl3KYVSzofmVtpSa9WbuZX2wpzLtqC9zLnCqxZavHhxnn/++Ua1ra6ubpUxDB48OL///e/Tq1ev7LnnnrV/33333XP66aenR48eufjii3P55Zfni1/8YnbYYYdWGQftS7lrt2vXrrWP161bly5dumzxtdUtmzS1dluj1sy7lFIpa9TcSlsqdb2ZW2lvzLm0Z+1tzhVetdANN9xQ7iGke/fu2W+//Rpcftxxx+Xyyy/PypUr8+ijj+YDH/hAG46Ooip37dY9tHrlypUNftlvOhy7R48ebTIuiq+ptVs3fC1VrZl3KaVSzofmVtpSqevN3Ep7Y86lPWtvc667Db4NdO7cOb17906SLF26tMyjgY06d+6cvn37Jtl4JE19qqqqsnz58iRJv3792mxsbFvKUWvmXZqilDVqbqUttXW9mVspGnMu27KizbnCq21ETU1NampqGly2bNmyJMmOO+7YhqOCLRsyZEiS5LHHHqt3+dy5c5MkvXv3Tp8+fdpqWGyDWqPWzLuUUilr1NxKWyp1vZlbaW/MubRn7WnOFV5tA8aMGZN/+Zd/ybRp0+pdfu+996aqqirbb7999t9//zYeHTSssrIySRqs3dtuuy1JcsQRR7TZmNg2lbrWzLuUWilr1NxKWyplvZlbaY/MubRX7W3OFV61I9OnT09lZeVbrvT//ve/P9XV1ZkwYUL+9re/bbZsyZIlOf/885MkRx99dCESU95+GqrdESNGpF+/fnn44Ydz/fXXb7ZsxowZufXWW1NRUZGxY8e25XDZBjW31sy7tJXm1Ki5lSIoZe2aWykycy7t1bYy57pgexksW7Ysl1122Vv+liS/+c1vctddd9X+/Ytf/GLe9a53Jdl4vnR9d9gaN25cHnjggTz88MM58sgj85GPfCS77rprXnnlldx3331ZvXp1DjrooJx55pmt96Z4Wyh17Xbq1CkTJ07M2LFjc/bZZ2fq1KnZZ599smjRosyaNSsdO3bM+PHjHWJNizW31sy7tJXm1Ki5lSIoZe2aW2krzdmnNedSBKWs3fY25wqvymDFihWZPHlyvcvuuOOOzf798Y9/vDYAaEiXLl3y61//OjfccENuu+22PPjgg1m5cmV69OiR/fffP5/+9Kfz6U9/Otttt13J3gNvT6Wu3SQZNGhQbrnlllx++eW57777Mnfu3PTs2TMjRozIiSeemIEDB5Zk7FDKWjPv0hpKWaPmVtpSqerN3EpbKfU+rTmXtlLK2m1vc26HmoauzgUAAAAAZeaaVwAAAAAUlvAKAAAAgMISXgEAAABQWMIrAAAAAApLeAUAAABAYQmvAAAAACgs4RUAAAAAhSW8AgAAAKCwhFcAAAAAFJbwCgAAAIDCEl4BAAAAUFjCKwAAAAAKS3gFAAAAQGEJrwAAAAAoLOEVAAAAAIUlvAIAAACgsIRXAAAAABSW8AoAAACAwvr/AayhT/RlYBPIAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 322, + "width": 599 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "A10 = np.linalg.matrix_power(A,10)\n", + "a10s1 = np.array([x/lin.norm(x) for x in (A10 @ mouse).T]).T\n", + "print(\"Les 12 points de la souris multipliés par A¹⁰ puis normés :\")\n", + "print(a10s1[:,:-1])\n", + "\n", + "plt.plot(a10s1[0], a10s1[1], 'ob')\n", + "plt.title(r\"Transformation des points de la souris par $A^{10}$ puis normés\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Tous les points sont alignés sur le premier vecteur propre sauf ceux qui ont commencé alignés sur le second vecteur propre." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Nombre de points proche du 1er vecteur propre : 40\n", + "Nombre de points proche du 2e vecteur propre : 0\n" + ] + } + ], + "source": [ + "N = 100\n", + "cercle = np.array([[np.cos(i * 2*np.pi/N), np.sin(i * 2*np.pi/N)] for i in range(N)]).T\n", + "a10c = np.array([x for x in (A10 @ cercle).T]).T\n", + "a10cn = np.array([x/lin.norm(x) for x in a10c.T]).T # a10c normé\n", + "nb1 = np.sum([lin.norm(a10cn[:,i] - vec_propre[:,0]) < 0.01 for i in range(N)]) \\\n", + " + np.sum([lin.norm(a10cn[:,i] + vec_propre[:,0]) < 0.01 for i in range(N)])\n", + "nb2 = np.sum([lin.norm(a10cn[:,i] - vec_propre[:,1]) < 0.01 for i in range(N)]) \\\n", + " + np.sum([lin.norm(a10cn[:,i] + vec_propre[:,1]) < 0.01 for i in range(N)])\n", + "print(\"Nombre de points proche du 1er vecteur propre : \", nb1)\n", + "print(\"Nombre de points proche du 2e vecteur propre : \", nb2)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 572, + "width": 1164 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(2,2, figsize=(20,10))\n", + "ax[0,0].plot(cercle[0], cercle[1], '.', label='cercle' )\n", + "ax[0,1].plot((A @ cercle)[0], (A @ cercle)[1], '.', label='A cercle' )\n", + "ax[1,0].plot((A @ A @ A @ cercle)[0], (A @ A @ A @ cercle)[1], '.', label='A³ cercle' )\n", + "ax[1,1].plot(a10c[0], a10c[1], '.' , label=r'$A^{10}$ cercle')\n", + "for x in ax.flat:\n", + " x.axis(\"equal\")\n", + " x.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On voit que les points du cercles s'alignent dans l'axe du premier vecteur propre." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Le cas des matrices de rotation\n", + "\n", + "On sait bien que si on applique plusieurs fois une rotation tous les points ne vont pas s'aligner dans une direction.\n", + "On a donc un comportement totalement différent. Qu'en est-il des vecteurs propres d'une matrice de rotation ?" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de R : [0.809+0.588j 0.809-0.588j] \n", + "\n", + "Norme des valeurs propres de R : 1.0 et 1.0 \n", + "\n", + "Vecteurs propres de R :\n", + " [[0.707+0.j 0.707-0.j ]\n", + " [0. -0.707j 0. +0.707j]]\n" + ] + } + ], + "source": [ + "def Rot(θ):\n", + " return np.array([[np.cos(θ), -np.sin(θ)], [np.sin(θ), np.cos(θ)]])\n", + "\n", + "R = Rot(2*np.pi/10)\n", + "\n", + "R_valp, R_vecp = lin.eig(R)\n", + "print(\"Valeurs propres de R :\", R_valp,\"\\n\")\n", + "print(\"Norme des valeurs propres de R :\", lin.norm(R_valp[0]), \" et \", lin.norm(R_valp[1]), \"\\n\")\n", + "print(\"Vecteurs propres de R :\\n\", R_vecp)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de R : [0.+1.j 0.-1.j] \n", + "\n", + "Vecteurs propres de R :\n", + " [[0.707+0.j 0.707-0.j ]\n", + " [0. -0.707j 0. +0.707j]]\n" + ] + } + ], + "source": [ + "# regardons un autre angle\n", + "R = Rot(np.pi/2)\n", + "\n", + "R_valp, R_vecp = lin.eig(R)\n", + "print(\"Valeurs propres de R :\", R_valp,\"\\n\")\n", + "print(\"Vecteurs propres de R :\\n\", R_vecp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On constate que\n", + " \n", + "* les valeurs propres et vecteurs propres sont des complexes\n", + "* les valeurs propres sont de norme 1 (normal puisque c'est une isométrie)\n", + "* l'angle de rotation θ se retrouve dans les valeurs propres $ v_p = e^{\\pm \\,i\\, θ}$\n", + "\n", + "C'est le second point qui fait qu'aucun des vecteurs propre ne peut prendre l'ascendant et qu'on ne retrouve pas\n", + "l'alignement des points de notre figure le long du premier vecteur propre." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0.9510565162951535+0.3090169943749474j),\n", + " (0.9510565162951535+0.3090169943749474j),\n", + " (0.9510565162951535-0.3090169943749474j))" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "θ = np.pi / 10\n", + "R = Rot(θ)\n", + "R_valp, R_vecp = lin.eig(R)\n", + "np.e**(0+1j * θ), R_valp[0], R_valp[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Symétrie axiale horizontale\n", + "\n", + "Sx = \n", + "$\n", + "\\begin{bmatrix}\n", + "1 & 0 \\\\\n", + "0 & -1 \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "Là c'est simple puisque la matrice est diagonale, donc ses valeurs propres sont les valeurs de la diagonales.\n", + "Elles ont la même norme donc pas d'alignement des points dans la direction du premier vecteur propre." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de Sx : [ 1.+0.j -1.+0.j] \n", + "\n", + "Vecteurs propres de Sx :\n", + " [[1. 0.]\n", + " [0. 1.]]\n" + ] + } + ], + "source": [ + "Sx = np.array([[1, 0], [0, -1]])\n", + "\n", + "Sx_valp, Sx_vecp = lin.eig(Sx)\n", + "print(\"Valeurs propres de Sx :\", Sx_valp,\"\\n\")\n", + "print(\"Vecteurs propres de Sx :\\n\", Sx_vecp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Une matrice diagonale ne modifie que la i-ième coordonnée de **x** par la i-ème valeur de sa diagonale. Aussi ses vecteurs propres sont ceux de la base d'origine." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4, 0, 0, 0, 0],\n", + " [0, 7, 0, 0, 0],\n", + " [0, 0, 9, 0, 0],\n", + " [0, 0, 0, 8, 0],\n", + " [0, 0, 0, 0, 6]])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D = np.diag(np.random.randint(10,size=5))\n", + "D" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de D : [4.+0.j 7.+0.j 9.+0.j 8.+0.j 6.+0.j] \n", + "\n", + "Vecteurs propres de D :\n", + " [[1. 0. 0. 0. 0.]\n", + " [0. 1. 0. 0. 0.]\n", + " [0. 0. 1. 0. 0.]\n", + " [0. 0. 0. 1. 0.]\n", + " [0. 0. 0. 0. 1.]]\n" + ] + } + ], + "source": [ + "D_valp, D_vecp = lin.eig(D)\n", + "print(\"Valeurs propres de D :\", D_valp,\"\\n\")\n", + "print(\"Vecteurs propres de D :\\n\", D_vecp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Diagonalisation d'une matrice\n", + "\n", + "On voit l'importance des valeurs et vecteurs propres pour caractériser une application linéaire. En fait ils sont tellement\n", + "important qu'en appliquant le bon changement de repère, l'application est représentée par une matrice diagonale\n", + "contenant les valeurs propres. \n", + "\n", + "$$\n", + "\\exists P \\; / \\; A = P\\, \\Lambda \\, P^{-1} \\quad \\textrm{avec } \\Lambda \\textrm{ la matrice diagonale des valeurs propres } \\lambda_i\n", + "$$\n", + "\n", + "La matrice de passage $P$ représente la nouvelle base donc sans surprise il s'agit des vecteurs propres. \n", + "\n", + "Vérifions le avec A :" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A :\n", + " [[3 1]\n", + " [0 2]] \n", + "\n", + "𝑃 Λ inv(𝑃) :\n", + " [[3.+0.j 1.+0.j]\n", + " [0.+0.j 2.+0.j]]\n" + ] + } + ], + "source": [ + "print('A :\\n', A, '\\n')\n", + "print('𝑃 Λ inv(𝑃) :\\n', vec_propre @ np.diag(val_propre) @ lin.inv(vec_propre))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ainsi la formule pour obtenir la diagonalisation de A est $\\; \\Lambda = P^{-1} \\, A \\, P\\;$ lorsqu'on connait ses\n", + "vecteurs propres (en pratique si on a les vecteurs propres on a aussi les valeurs propres et donc la diagonalisation de A)." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P :\n", + " [[ 1. -0.707]\n", + " [ 0. 0.707]] \n", + "\n", + "inv(𝑃) A 𝑃 :\n", + " [[3. 0.]\n", + " [0. 2.]]\n" + ] + } + ], + "source": [ + "print('P :\\n', vec_propre, '\\n')\n", + "print('inv(𝑃) A 𝑃 :\\n', lin.inv(vec_propre) @ A @ vec_propre)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On retrouve nos 2 valeurs propres sur la diagonale." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Matrice inversible** Notons que si une des valeurs propres est nulle alors $\\Lambda$ n'est pas inversible et comme il s'agit de\n", + "la même application que A (dans un autre repère) alors A n'est pas inversible non plus.\n", + "\n", + "**Matrice non diagonalisable** Si l'ensemble des vecteurs propres ne génère pas un espace de la même dimension que d'origine (c.a.d. que 2 vecteurs propres sont colinéaires), alors on ne peut pas diagonaliser la matrice.\n", + "\n", + "**Matrice symétrique de réels** Dans ce cas il existe une matrice de passage orthogonale et la matrice diagonale des valeurs propres a toutes ses valeurs réelles.\n", + "\n", + "**Matrice symmétrique réelle définie positive** (c.a.d. $\\forall {\\bf x} \\in ℝ^n, \\; {\\bf x}^T\\, A \\, {\\bf x} > 0$) a toutes ses valeurs propres strictement positives." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma25 Drones -- Exercice.ipynb b/PVCM/cama/en/ma25 Drones -- Exercice.ipynb new file mode 100644 index 0000000..e6055c3 --- /dev/null +++ b/PVCM/cama/en/ma25 Drones -- Exercice.ipynb @@ -0,0 +1,294 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5, + "cells": [ + { + "cell_type": "markdown", + "id": "899494b3", + "metadata": { + "lang": "en" + }, + "source": [ + "# Drone show\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "ada5357c", + "metadata": { + "lang": "en" + }, + "source": [ + "The goal is to make a nice night show.\n", + "\n", + "We have a set of 100 drones that form the image of a boat in 3D. For us it is a set of 3D points (center of gravity of each drone) that we store in a Numpy 3 by 100 table. The boat fits in a 20x20x20 cube.\n", + "\n", + "Initially\n", + "\n", + "*all the drones are centered at (0,0,0) so if you want to position the boat at (10, 20, 200) you have to translate the same amount over all the drones.* the main axis of the boat is the axis of x i.e. the front of the boat is at x=10 and the back at x=-10." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "58dcf259", + "metadata": { + "ExecuteTime": { + "end_time": "2024-03-25T09:43:59.562566Z", + "start_time": "2024-03-25T09:43:59.487939Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-20., 20., 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 0., 0., 0., -10., 10.],\n", + " [ 0., 0., -5., 5., 0., 0., 0.]])" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "#boat = np.random.randint(-100, 100, size=(3,10)) / 10 # with a little luck...\n", + "\n", + "# A formation that allows for easier debugging\n", + "\n", + "boat = np.array([[-20., 0., 0.],\n", + " [ 20., 0., 0.],\n", + " [ 0., 0., -5.],\n", + " [ 0., 0., 5.],\n", + " [ 0., 0., 0.],\n", + " [ 0., -10., 0.],\n", + " [ 0., 10., 0.],\n", + " ])\n", + "boat = boat.T\n", + "boat" + ] + }, + { + "cell_type": "markdown", + "id": "1ab4a847", + "metadata": { + "lang": "en" + }, + "source": [ + "We want to move the boat in the sky by making it do figures (the units used are the meter and the second). All movements are broken down second by second i.e. we give the position of all the drones every second (another program manages to move the drones to their next position).\n", + "\n", + "### Figure 1\n", + "\n", + "Rotate the boat (therefore all the drones) horizontally around the point (0,0,80) at a distance of 100 m. It makes a full turn in 5 minutes.\n", + "\n", + "Care should be taken that the orientation of the boat follows the movement, i.e. that the front of the boat is always well oriented." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4818926d", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def circle(boat, t):\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "35cc29f4", + "metadata": {}, + "outputs": [], + "source": [ + "# Code to display\n", + "# Do not touch this unless you know what you are doing\n", + "import matplotlib.animation\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.patches import Circle\n", + "from matplotlib.transforms import Affine2D\n", + "import mpl_toolkits.mplot3d.art3d as art3d\n", + "matplotlib.rcParams['animation.embed_limit'] = 256 # 256mb max animation size\n", + "\n", + "plt.rcParams[\"animation.html\"] = \"jshtml\"\n", + "plt.rcParams['figure.dpi'] = 100 \n", + "plt.ioff()\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(projection='3d')\n", + "\n", + "# 5min -> 300 sec;\n", + "FRAMEPERSEC = 1.\n", + "\n", + "def animate(t):\n", + " boat_prime = circle(boat_start, t/FRAMEPERSEC)\n", + " plt.cla()\n", + " p = Circle((0, 0), 100, fill=False)\n", + " ax.add_patch(p)\n", + " art3d.pathpatch_2d_to_3d(p, z=80, zdir=\"z\")\n", + " plt.plot(boat_prime[0,:], boat_prime[1,:], boat_prime[2,:], '.b')\n", + " ax.set_xlim([-120, 120])\n", + " ax.set_ylim([-120, 120])\n", + " ax.set_zlim([0, 120]) # alternative\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_ylabel(\"y\")\n", + " ax.set_zlabel(\"z\")\n", + " ax.set_title(f\"t: {t} sec\")\n", + "\n", + "\n", + "matplotlib.animation.FuncAnimation(fig, animate, frames=int(300*FRAMEPERSEC))" + ] + }, + { + "cell_type": "markdown", + "id": "d9ca0600", + "metadata": { + "lang": "en" + }, + "source": [ + "### Figure 2\n", + "\n", + "We want to rotate the boat on its main axis (the x axis) until it returns to the original position. In aviation, this is called a barrel roll (rotation of 360 on the roll axis). Write the `barrel_roll(boat, T, t)` function that returns the position of each drone at time `t` given that a complete roll take `T` seconds." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3bbdb81d", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def barrel_rool(boat, T, t):\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3861ca65", + "metadata": {}, + "outputs": [], + "source": [ + "# Code to display\n", + "# You can change this\n", + "Tcomplete = 20\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(projection='3d')\n", + "\n", + "# Do not touch this unless you know what you are doing\n", + "def animate2(t):\n", + " boat_prime = barrel_roll(boat, Tcomplete, t)\n", + " plt.cla()\n", + " plt.plot(boat_prime[0,:], boat_prime[1,:], boat_prime[2,:], '.b')\n", + " ax.set_xlim([-60, 60])\n", + " ax.set_ylim([-60, 60])\n", + " ax.set_zlim([-60, 60])\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_ylabel(\"y\")\n", + " ax.set_zlabel(\"z\")\n", + " ax.set_title(f\"t: {t} sec\")\n", + "\n", + "# One frame per second for 2 complete rolls\n", + "matplotlib.animation.FuncAnimation(fig, animate2, frames=2*Tcomplete)" + ] + }, + { + "cell_type": "markdown", + "id": "51d00ff1", + "metadata": { + "lang": "en" + }, + "source": [ + "### Figure 3\n", + "\n", + "Combine figures 1 and 2 so that the boat rolls in 10 seconds every 30 seconds." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fc7aed8e", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def combined_move(boat, t):\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d2265fd3", + "metadata": {}, + "outputs": [], + "source": [ + "# Code to display\n", + "# Do not touch this unless you know what you are doing\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(projection='3d')\n", + "\n", + "def animate3(t):\n", + " boat_prime = combined_move(boat, t/FRAMEPERSEC)\n", + " plt.cla()\n", + " p = Circle((0, 0), 100, fill=False)\n", + " ax.add_patch(p)\n", + " art3d.pathpatch_2d_to_3d(p, z=80, zdir=\"z\")\n", + " plt.plot(boat_prime[0,:], boat_prime[1,:], boat_prime[2,:], '.b')\n", + " ax.set_xlim([-120, 120])\n", + " ax.set_ylim([-120, 120])\n", + " ax.set_zlim([0, 120])\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_ylabel(\"y\")\n", + " ax.set_zlabel(\"z\")\n", + " ax.set_title(f\"t: {t} sec\")\n", + "\n", + "# 5min -> 300 sec\n", + "matplotlib.animation.FuncAnimation(fig, animate3, frames=int(300*FRAMEPERSEC))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7c2da47f", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2f9122e6-899e-4afa-a49a-992e48e99647", + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma26 Vecteurs propres -- Exercices.ipynb b/PVCM/cama/en/ma26 Vecteurs propres -- Exercices.ipynb new file mode 100644 index 0000000..88d82df --- /dev/null +++ b/PVCM/cama/en/ma26 Vecteurs propres -- Exercices.ipynb @@ -0,0 +1,305 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Cas d'utilisation des valeurs et vecteurs propres" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fibonnacci\n", + "\n", + "La suite de Fibonnacci est $x_n = x_{n-2} + x_{n-1}$ avec $x_0 = 1, x_1 = 1$.\n", + "\n", + "Quelle est la complexité pour calculer $x_n$ ?\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Comme on a 2 termes à droite du signe égal, écrivons Fibonnacci sous forme d'un système matriciel $2\\times 2$ :\n", + "\n", + "$\n", + "\\begin{align}\n", + "x_{n-1} &= x_{n-1} \\\\\n", + "x_n &= x_{n-2} + x_{n-1} \\\\\n", + "\\end{align}\n", + "$\n", + "ce qui donne\n", + "$\n", + "\\begin{bmatrix}\n", + "x_{n-1}\\\\\n", + "x_n \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1 \\\\\n", + "1 & 1 \\\\\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "x_{n-2}\\\\\n", + "x_{n-1} \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "Écrire la matrice F ci-dessous et vérifier que le 6e élément de la suite de Fibonacci est 8 en n'utilisant que \n", + "la matrice F et les valeurs initiales de la suite. La fonction `numpy.linalg.matrix_power` pourra vous être utile." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calculer n produits matriciels n'est pas rentable, par contre sachant que\n", + "$F = P\\, D\\, P^{-1}$ avec\n", + "\n", + "* P la matrice des vecteurs propres\n", + "* D la matrice diagonale des valeurs propres\n", + "\n", + "on peut faire quelque chose car il va avoir des simplification lors du calcul de de $F^n$. \n", + "\n", + "* Ecrire la formule matriciel de la suite de Fibonnacci en fonction de P et D. \n", + "* Expliquer pourquoi le calcul du n-ème élément de la suite peut se faire en temps constant." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Écrire la fonction `fibo(n)` qui calcule le n-ème élément de la suite de Fibonnacci en temps constant." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vérifier que votre fonction est en temps constant en chronométrant `fibo(5)` et `fibo(1000)` avec la commande \n", + "`%timeit` de Jupyter." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Google page rank\n", + "\n", + "Soit N pages web numérotées qui font référence les unes aux autres. Disons que si la page 3 est référencée par les pages 8 9 et 13 j'écris $x_3 = x_8 + x_9 + x_{13}$. On voit qu'on peut écrire ces référencements dans une\n", + "matrice avec le i-ième ligne qui décrit par qui est référencée la i-ème page web. Cette matrice a un 1 dans\n", + "la j-ième colonne si la page j cite la page i et sinon un 0." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 1, 0, 0, 0, 1, 0, 0],\n", + " [0, 0, 0, 0, 0, 0, 1, 0],\n", + " [1, 1, 0, 0, 1, 0, 1, 1],\n", + " [1, 1, 1, 0, 1, 1, 0, 0],\n", + " [1, 1, 1, 0, 0, 0, 0, 0],\n", + " [0, 0, 1, 1, 1, 0, 1, 0],\n", + " [1, 1, 0, 1, 0, 1, 0, 1],\n", + " [1, 0, 0, 0, 0, 0, 0, 0]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.random.seed(42)\n", + "N = 8\n", + "A = np.random.randint(2,size=(N,N))\n", + "for i in range(len(A)):\n", + " A[i,i] = 0 # on ne compte pas les auto-référencements\n", + "A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Cet article](https://www.math.upenn.edu/~wilf/website/KendallWei.pdf) indique que Google à l'époque de l'écriture de l'article (2001) basait son classement des pages web \n", + "en utilisant les vecteurs propres de cette matrice (vous n'avez pas besoin de lire cet article pour faire l'exercice).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Approche itérative\n", + "Une bonne introduction qui va un peu plus loin peut-être trouvé [ici](https://pi.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html).\n", + "\n", + "Dans un premier temps on procède de la manière suivant pour trouver l'importance d'une page:\n", + "Étant donné N page à évaluer \n", + "* On initialise un vecteur __v__ de taille N avec 1 partout -> Correspond à une distribution uniforme de l'importance initialement\n", + "* On calcule le produit matrice vecteur A __v__\n", + "* On normalise le résultat pour que la norme 1 soit égale au nombre de pages (N)\n", + "* On répète ces étapes jusqu'à un point fixe\n", + "\n", + "De cette manière l'entrée i du vecteur __v__ correspond à l'importance de la page i -> Discutez pourquoi." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.774 0.387 1.419 1.419 1.032 1.29 1.548 0.129]]\n", + "[[0.542 0.5 1.25 1.583 0.833 1.75 1.292 0.25 ]]\n", + "[[0.742 0.426 1.127 1.608 0.756 1.636 1.526 0.179]]\n", + "[[0.672 0.497 1.183 1.527 0.748 1.635 1.496 0.242]]\n", + "[[0.694 0.487 1.19 1.542 0.766 1.613 1.489 0.219]]\n", + "[[0.683 0.484 1.189 1.545 0.771 1.622 1.481 0.226]]\n", + "[[0.686 0.482 1.187 1.546 0.767 1.624 1.485 0.222]]\n", + "[[0.686 0.484 1.186 1.546 0.767 1.624 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n" + ] + } + ], + "source": [ + "v = np.zeros((N,1))\n", + "vprime = np.ones((N,1))\n", + "\n", + "while (np.absolute(np.max(vprime - v)) > 1e-5): # which norm is used here?\n", + " v = vprime\n", + " vprime = \n", + " vprime *= \n", + " print(vprime.T)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Un autre approche\n", + "\n", + "Vous constatez que A.__v__ = α * __v__ pour une constante α. Est-ce que ça vous rappelle quelque chose ?\n", + "\n", + "* On considère que les composantes du premier vecteur propre représentent la valeur de chaque page. Calculez les valeurs des pages. Comparez avec le résultat obtenue auparavant.\n", + "* Calculez le nombre de citations pour chaque page." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma30 ACP.ipynb b/PVCM/cama/en/ma30 ACP.ipynb new file mode 100644 index 0000000..04f1e16 --- /dev/null +++ b/PVCM/cama/en/ma30 ACP.ipynb @@ -0,0 +1,460 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Principal component analysis (PCA)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import numpy.linalg as lin\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib\n", + "\n", + "def arrow2D(a,b, color='k', **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## A cloud of dots\n", + "\n", + "When we have a cloud of points we can study its shape by a **principal component analysis** (PCA). This comes back\n", + "to seek the eigenvectors of the covariance matrix (or correlation which is the covariance matrix normalized by the standard deviations). These eigenvectors describe the point cloud to us.\n", + "\n", + "To check it, let's make\n", + "a scatter plot with a strong correlation between $x$ and $y$:\n", + "\n", + "$$ y = 0.2 \\, x + 1.45 + U(-1,1) \\quad \\textrm{avec U la loi uniforme qui simule du bruit.}$$\n", + "\n", + "This linear relation between $x$ and $y$ allows us to know that we have:\n", + "\n", + "*a slope of 0.2* a vertical offset of 1.45 in x=0\n", + "\n", + "The goal is to\n", + "see if, with only the scatter plot, we can find the correlation between $x$ and $y$ despite the noise.\n", + "\n", + "$$ y = α x + β$$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "N = 50\n", + "x = 10 * np.random.rand(N) - 5\n", + "nuage = np.array([x, 0.2 * x + 1.45 + (2 * np.random.rand(N) - 1)])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 589 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.title('Un nuage de points')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Graphically, we are looking for the line that minimizes the distance between the points and their projection on the line.\n", + "\n", + "\n", + "We can also construct the **covariance matrix** (see below) and see that the slope of the first eigenvector is\n", + "equal to this coefficient 0.2 which connects x to y.\n", + "\n", + "Then the average of the point cloud in a point of the line that we are looking for, which means that with the direction vector that is the first eigenvector, we have our line." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[9.107, 1.925],\n", + " [1.925, 0.764]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov = np.cov(nuage.copy())\n", + "cov" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Let us take this opportunity to recall that if a matrix is ​​symmetric then\n", + "\n", + "* its eigenvalues are real\n", + "* its eigenvectors are orthogonal" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de la matrice de covariance : [9.53 0.341] \n", + "\n", + "Vecteurs propres de la matrice de covariance :\n", + " [[ 0.977 -0.215]\n", + " [ 0.215 0.977]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_26870/3419464211.py:2: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " val = val.astype('float') # on convertit puisqu'on sait que ce sont des réels\n" + ] + } + ], + "source": [ + "val, vec = lin.eig(cov)\n", + "val = val.astype('float') # on convertit puisqu'on sait que ce sont des réels\n", + "print(\"Valeurs propres de la matrice de covariance :\", val,\"\\n\")\n", + "print(\"Vecteurs propres de la matrice de covariance :\\n\", vec)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 595 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "arrow2D((0,0), val[0] * vec[:,0], 'r') # vecteur propre multiplié par sa valeur propre\n", + "arrow2D((0,0), val[1] * vec[:,1], 'g')\n", + "plt.title('Un nuage de points et les vecteurs propres de sa matrice de covariance')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Let's check that the slope of the first eigenvector is close to 0.2:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "La pente est de 0.21963615318288862 \n", + "\n", + "Le points moyen du nuage est [-0.152 1.327]\n" + ] + } + ], + "source": [ + "pente = vec[1,0] / vec[0,0] \n", + "print(\"La pente est de\", pente, '\\n')\n", + "moyenne = nuage.mean(axis=1)\n", + "print(\"Le points moyen du nuage est\", moyenne)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Le décalage verticale est de 1.360408912029785\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 589 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "eq_droite = lambda x: pente * (x - moyenne[0]) + moyenne[1]\n", + "\n", + "print(\"Le décalage verticale est de \", eq_droite(0))\n", + "\n", + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.plot([nuage[0].min(), nuage[0].max()], [eq_droite(nuage[0].min()), eq_droite(nuage[0].max())]) \n", + "plt.title(\"Un nuage de points et sa droite d'approximation\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "On a donc α = 0.220 et β = 1.360 sachant que le nuage a été généré avec 0.2 et 1.45\n" + ] + } + ], + "source": [ + "print(f'On a donc α = {pente:.3f} et β = {eq_droite(0):.3f} sachant que le nuage a été généré avec 0.2 et 1.45')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Covariance matrix\n", + "\n", + "The covariance between two datasets __x__ and __y__ indicates how closely they are related (i.e. if the i-th value of __y__ can be deduced from the i-th value of __x__ or not). If their covariance is large\n", + "in absolute value then they are strongly related, if it is close to 0, they are either independent\n", + "is linked by a more complicated relationship than a simple linear relationship.\n", + "\n", + "Covariance measures the linear relationship between 2 variables (see [this video](https://www.youtube.com/watch?v=UM-AOmT2RWk)\n", + "for a quick and complete presentation of covariance and its properties).\n", + "\n", + "$$\n", + "\\textrm{cov}(\\textbf{x},\\textbf{y}) = \\frac{1}{N} \\sum_{i=1}^N (x_i - \\overline{\\textbf{x}}) (y_i - \\overline{\\textbf{y}})\n", + "$$\n", + "\n", + "with $N$ the number of points of the cloud, $\\overline{\\textbf{x}}$ and $\\overline{\\textbf{y}}$ the averages of $\\textbf{x}$ and $\\textbf{y}$.\n", + "\n", + "If we place the origin of the axes at the mean $(\\overline{\\textbf{x}},\\overline{\\textbf{y}})$ then the formula indicates that to have correlation there must be more points in 2 diagonally opposite quadrans.\n", + "\n", + "If, conversely, we draw random points, so no relationship between x and y, then we will have points distributed evenly around the mean, so a\n", + "zero covariance.\n", + "Finally if all the values ​​of $\\textbf{y}$ have the same value, then they do not depend on x and $y_i - \\overline{\\textbf{y}} = 0 \\; \\forall i$ so the covariance is zero." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 708 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.plot([moyenne[0], moyenne[0]], [nuage[1].min(), nuage[1].max()],'k')\n", + "plt.plot([nuage[0].min(), nuage[0].max()], [moyenne[1], moyenne[1]],'k')\n", + "plt.title('La covariance indique une direction privilégiée et donc plus de points dans les quadrans traversés')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Here we can clearly see that the vast majority of points are in 2 opposite quadrans, of which our 2 variables are linked.\n", + "\n", + "The covariance matrix expresses all the possible covariances between the variables. In our case where\n", + "the cloud has 2 dimensions, we have:\n", + "\n", + "$$\n", + "\\textrm{Cov(nuage 2D)} = \n", + "\\begin{bmatrix}\n", + "\\textrm{cov}(\\textbf{x},\\textbf{x}) & \\textrm{cov}(\\textbf{x},\\textbf{y}) \\\\\n", + "\\textrm{cov}(\\textbf{y},\\textbf{x}) & \\textrm{cov}(\\textbf{y},\\textbf{y}) \\\\\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[8.925, 1.887],\n", + " [1.887, 0.749]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov = lambda x,y : np.dot((x - x.mean()), (y - y.mean())) / len(x)\n", + "\n", + "Cov = lambda x,y : np.array([[cov(x,x), cov(x,y)], [cov(y,x), cov(y,y)]])\n", + "\n", + "Cov(nuage[0], nuage[1]) # par défaut Numpy divise par (N-1), avec bias=True il divise par N et donne ce résultat" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "This result shows that x is very linked with itself, which is obvious. On the other hand, it seems that there is\n", + "less connected with himself. In fact the variations of y are smaller (between 0 and 3 while x varies between -5 and 5) which explains this smaller value. The fact that cov(x,y) is greater than cov(y,y) is already a\n", + "indicator that x and y are related.\n", + "\n", + "The calculation of the eigenvalues ​​and vectors of the covariance matrix is ​​even more interesting with\n", + "a large dimension because it highlights which are the most important. Thus the example of the article\n", + "from Wikipedia on ['principal component analysis](https://fr.wikipedia.org/wiki/Analyse_en_principales_components)\n", + "on the pollution of the Doubs water shows that the first clean vector is that of known pollutants: nitrates (nit), phosphates (pho), ammonia (amm)\n", + "and the second is that of PH. Note the anti-correlation between oxygen content and pollutants.\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "To fully understand this figure and see a use case, I invite you to watch this\n", + "[example of PCA with Excel](https://www.youtube.com/watch?v=GNBeWpkHFJw)." + ] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma31 Syst\303\250me d'\303\251quations.ipynb" "b/PVCM/cama/en/ma31 Syst\303\250me d'\303\251quations.ipynb" new file mode 100644 index 0000000..2d5453a --- /dev/null +++ "b/PVCM/cama/en/ma31 Syst\303\250me d'\303\251quations.ipynb" @@ -0,0 +1,799 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Systèmes matriciels\n", + "\n", + "Un système de plusieurs équations à autant d'inconnues peut s'écrire sous forme d'un système matriciel de la forme $A {\\bf x} = {\\bf b}$ c.a.d.\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "a_{11} a_{12} \\ldots a_{1n} \\\\\n", + "a_{21} a_{22} \\ldots a_{2n} \\\\\n", + " \\vdots \\\\\n", + "a_{n1} a_{n2} \\ldots a_{nn} \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "\\vdots \\\\\n", + "x_{n} \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "b_{1} \\\\\n", + "b_{2} \\\\\n", + "\\vdots \\\\\n", + "b_{n} \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Ainsi si votre épicier ne vous donne pas le prix des pommes, poires et bananes mais que vous en achetez 3 fois des quantités différentes, vous pouvez retrouver le prix de chaque fruit. Il suffit de résoudre les 3 équations\n", + "qui correspondent aux 3 achats ou le système matriciel 3x3 correpondant. Pour résourdre ce dernier la facon intuitive est d'inverser A et de calculer $A^{-1}\\, {\\bf b}$ :" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.8, 0.9, 0.6])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# A est la quantité de chaque fruit achetée\n", + "# x est le prix de chaque fruit\n", + "# b est la somme qu'on a payé pour chaque course\n", + "\n", + "A = np.array([[6,5,4], [5,3,2], [7,3,2]])\n", + "b = np.array([11.7, 7.9, 9.5])\n", + "\n", + "x = lin.inv(A) @ b\n", + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Les systèmes matriciels sont probablement l'application la plus importante des matrices car quoi de plus important que de connaitre le prix des bananes ?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Résolution d'un système matriciel\n", + "\n", + "On regardera les méthodes suivantes :\n", + "\n", + "* Méthode du pivot de Gauss (rendre la matrice triangulaire)\n", + "* Décomposition LU (effet de bord de la résolution par le pivot de Gauss)\n", + "* Méthode de Gauss-Jordan (rendre la matrice diagonale)\n", + "\n", + "**Note :** Si vous trouvez la suite difficile, faites une pause et regardez cette [explication sur une matrice 3x3](https://www.youtube.com/watch?v=VoMsTiJOUE4). Elle commence par triangulariser la matrice comme le fait\n", + "la méthode du pivot de Gauss, puis elle continue pour diagonaliser la matrice comme le fait Gauss-Jordan et\n", + "finalement elle arrive à l'inverse de la matrice. C'est très bien pour comprendre ou faire les calculs à la main\n", + "sur une petite matrice, c'est horrible à programmer. Ce que je vous montre c'est la transformation de l'intuition\n", + "qu'offre cette vidéo en un calcul matriciel rapide et simple à programmer." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Méthode du pivot de Gauss\n", + "\n", + "On transforme A en une matrice triangulaire qui permet ensuite de résoudre le système en O(n²) opérations.\n", + "\n", + "Pour cela on commence à mettre des 0 sur la première colonne en dessous de la diagonale. Pour cela il\n", + "suffit de multiplier A par la matrice $E_1$ suivante :\n", + "\n", + "\n", + "$$\n", + "E_1 = \n", + "\\begin{bmatrix}\n", + "\\;1 \\quad 0\\; 0 \\ldots 0 \\\\\n", + "\\frac{-a_{21}}{a_{11}} \\, 1\\; 0 \\ldots 0 \\\\\n", + "\\frac{-a_{31}}{a_{11}} \\, 0\\; 1 \\ldots 0 \\\\\n", + "\\vdots \\\\\n", + "\\frac{-a_{n1}}{a_{11}}\\; 0\\; 0 \\ldots 1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "$E_2$ sera la matrice équivalente avec des termes $\\frac{-a_{k2}}{a_{22}}$ sous la diagonales afin des 0 dans la 2e colonne de A sous la diagonale, etc.\n", + "\n", + "Si vous ne connaissez pas cette méthode, je vous conseille de vérifier à la main sur une matrice 4x4 que\n", + "$E_1 \\, A$ met bien des zéros là où il faut. Ensuite faites le travail sur la 2e colonne.\n", + "\n", + "Bien sur si on multiplie A par $E_1$, il faut aussi multiplier ${\\bf b}$ par $E_1$ pour que le système matriciel soit\n", + "équivalent. Cette multiplication $E_1 \\, \\bf b$ peut se calculer nettement plus rapidement qu'avec un \n", + "produit matrice vecteur. Donnez la bonne formule et vérifiez dans le code ci-dessous.\n", + "\n", + "#### Système matriciel avec matrice triangulaire\n", + "\n", + "Pour finir il faut résoudre U x = c avec U une matrice triangulaire supérieur. Cela se fait en partant\n", + "de la dernière ligne qui donne directement `x[-1] = c[-1] / U[-1,-1]`. Une fois `x[-1]` connu, on en\n", + "déduit la valeur de `x[-2]` avec l'avant dernière ligne, etc.\n", + "\n", + "On faisant les calculs on constate qu'il faut environ n²/2 additions et multiplications.\n", + "\n", + "Là encore, si vous ne vous rappelez pas comment on fait, faites le à la main avec une matrice 3x3. Vous pouvez aussi ajouter des `print` dans le code qui suit pour voir les matrices intermédiaires." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Cf analyse du code ci-dessous\n", + "\n", + "def solve_gauss(A, b):\n", + " A = A.astype(np.float64) # si A a des entiers, on va avoir des erreurs de calculs\n", + " for i in range(len(A)-1):\n", + " coefs = - A[i+1:,i] / A[i,i] # Normalement il faut tester que A[i,i] != 0\n", + " A[i+1:, i:] += np.outer(coefs, A[i, i:]) # ou np.einsum('i,j -> ij', coefs, A[i, i:])\n", + " b[i+1:] += coefs * b[i]\n", + " # A est maintenant triangulaire surpérieur\n", + " res = np.zeros(len(b), dtype=b.dtype)\n", + " res[-1] = b[-1] / A[-1,-1]\n", + " for i in range(len(A)-1)[::-1]:\n", + " res[i] = (b[i] - A[i,i+1:] @ res[i+1:]) / A[i,i]\n", + " return res\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Analyse du code\n", + "\n", + "Comme **E** = **Id** + **Coefs**, on a **E A** = **A** + **Coefs A** et donc **A** += **Coef A**. Ici **Coefs** est la matrice **E** ci-dessus sans les 1 sur la diagonale.\n", + "\n", + "Le problème est que `Coef @ A` fait n³ opérations ce qui est beaucoup trop et surtout inutile sachant que **Coef** est un vecteur dans une matrice de zéros. Si ce vecteur est dans la colonne $i$ alors seuls les termes de la ligne $i$ de A serviront pour générer ce produit matriciel (à faire sur un papier). De plus on a `res[j,k] = Coef[j,i] * A[i,k]` ce qui s'écrit en Numpy `res = np.outer(coefs, A[i,:])` si `coefs` est la colonne $i$ de `Coefs`.\n", + "\n", + "Comme la matrice **Coefs** n'a des valeurs non nulles qu'en dessous de la diagonale, cela veut dire que le résultat `res` de la multiplication n'a que des zéros au dessus de la ligne $i$. Donc autant ne faire que le calcul pour ce qui est en\n", + "dessus de la ligne $i$ : `A[i+1:, i:] += np.outer(coefs, A[i, i:])` avec `coefs` un vecteur de taille $n-i$. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A\n", + " [[2.878 0.086 7.04 4.388 7.731]\n", + " [1.997 0.405 9.546 0.681 3.954]\n", + " [9.664 5.849 3.799 5.096 8.049]\n", + " [7.136 3.182 6.452 1.741 3.594]\n", + " [1.064 3.951 8.733 7.093 9.787]] \n", + "b\n", + " [22.122 16.584 32.457 22.105 30.627]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1., 1.])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = 10 * np.random.random(size=(5,5))\n", + "b = A.sum(axis=1)\n", + "print(f\"A\\n {A} \\nb\\n {b}\")\n", + "solve_gauss(A, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Complexité du pivot de Gauss\n", + "\n", + "#### Exercice 10.1\n", + "\n", + "Calculer la complexité de `solve_gauss`. Vous devez trouver n³/3 multiplications et autant d'additions\n", + "plus des termes de degrés inférieurs. Pour compter les opérations je vous suggère de faire un dessin \n", + " et d'imaginer votre dessin en 3 dimensions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Décomposition LU (Lower, Upper)\n", + "\n", + "Si on a besoin de résoudre plusieurs systèmes matriciels avec A, alors il est préférable de décomposer\n", + "A en un produit d'une matriciel triangulaire inférieur et d'une matrice triangulaire supérieure.\n", + "\n", + "$A = L\\, U$\n", + "\n", + "Pour cela il suffit de relancer le pivot de Gauss mais au lieu de modifier **b** à chaque itération, on\n", + "fabrique à la volée l'inverse de la matrices $E_n \\ldots E_2\\, E_1$ : \n", + "\n", + "$$\n", + "E_n \\ldots E_2\\, E_1 \\, A\\, x = E_n \\ldots E_2\\, E_1 \\, b \\quad \\textrm{donc} \\\\\n", + "(E_n \\ldots E_2\\, E_1)^{-1} \\, E_n \\ldots E_2\\, E_1 \\, A\\, x = b \\\\\n", + "E_1^{-1} \\, E_2^{-1} \\ldots E_n^{-1} \\; E_n \\ldots E_2\\, E_1 \\, A\\, x = b \\\\\n", + "$$\n", + "\n", + "Ce calcul est très simple car ces matrices inverses ont la\n", + "même forme que les $E_k$ avec simplement le valeurs opposées sous la diagonale :\n", + "\n", + "$$\n", + "E_1^{-1} = \n", + "\\begin{bmatrix}\n", + "\\;1 \\quad 0\\; 0 \\ldots 0 \\\\\n", + "\\frac{a_{21}}{a_{11}} \\, 1\\; 0 \\ldots 0 \\\\\n", + "\\frac{a_{31}}{a_{11}} \\, 0\\; 1 \\ldots 0 \\\\\n", + "\\vdots \\\\\n", + "\\frac{a_{n1}}{a_{11}}\\; 0\\; 0 \\ldots 1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "et le produit $E^{-1} = E_1^{-1} \\,E_1^{-1} \\,E_2^{-1} \\,E_3^{-1} \\, \\ldots \\,E_n^{-1}$ est simplement la concaténation\n", + "des colonnes (je vous laisse vérifier) :\n", + "\n", + "$$\n", + "E^{-1} = \n", + "\\begin{bmatrix}\n", + "\\;1 \\quad 0\\; \\; 0 \\ldots 0 \\\\\n", + "\\frac{a_{21}}{a_{11}} \\; \\; 1\\; \\; 0 \\ldots 0 \\\\\n", + "\\frac{a_{31}}{a_{11}} \\, \\frac{a_{32}}{a_{22}} \\; 1 \\ldots 0 \\\\\n", + "\\vdots \\\\\n", + "\\frac{a_{n1}}{a_{11}}\\; \\frac{a_{n2}}{a_{22}}\\; \\frac{a_{n3}}{a_{33}} \\ldots 1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "et ainsi on a $L = E^{-1}$ et $U = E_n \\ldots E_2\\, E_1 \\, A$ puisque tout le travail fait sur A est\n", + "justement pour mettre des 0 sous la diagonale et donc en faire une matrice triangulaire supérieure.\n", + "\n", + "Une fois la décomposition LU faites, résoudre $L\\, U \\, {\\bf x} = {\\bf b}$ se fait en 2 étapes :\n", + "\n", + "* on résoud $L\\, {\\bf y} = {\\bf b}$ ce qui donne ${\\bf y}$ \n", + "* puis on résoud $U\\, {\\bf x} = {\\bf y}$ et on a notre solution ${\\bf x}$\n", + "\n", + "en O(n²) opérations à chaque fois puisqu'il s'agit de matrices triangulaires." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def LU(A):\n", + " L = np.diag([1.,] * len(A))\n", + " for i in range(len(A)-1):\n", + " E = np.diag([1.,] * len(A))\n", + " E[i+1:,i] = - A[i+1:,i] / A[i,i]\n", + " L[i+1:,i] = -E[i+1:,i]\n", + " A[i:, i:] = E[i:,i:] @ A[i:,i:]\n", + " return L, A" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A\n", + " [[7.512 7.513 5.909 4.879 0.641]\n", + " [8.468 6.44 4.16 1.435 4.431]\n", + " [6.661 4.823 2.936 3.073 4.768]\n", + " [5.927 6.654 1.168 9.273 0.706]\n", + " [0.631 1.075 2.517 6.229 7.547]]\n", + "L\n", + "[[ 1. 0. 0. 0. 0. ]\n", + " [ 1.127 1. 0. 0. 0. ]\n", + " [ 0.887 0.906 1. 0. 0. ]\n", + " [ 0.789 -0.358 122.023 1. 0. ]\n", + " [ 0.084 -0.219 -40.943 -0.357 1. ]]\n", + "U\n", + "[[ 7.512 7.513 5.909 4.879 0.641]\n", + " [ 0. -2.029 -2.502 -4.066 3.708]\n", + " [ 0. 0. -0.036 2.432 0.838]\n", + " [ 0. 0. 0. -292.814 -100.761]\n", + " [ 0. 0. 0. 0. 6.662]]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[ 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 0., -0., 0.],\n", + " [ 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 0., -0., -0.],\n", + " [ 0., 0., 0., -0., -0.]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = 10 * np.random.random(size=(5,5))\n", + "print(\"A\\n\",A)\n", + "L,U = LU(A.copy()) # Attention, notre fonction modifie A donc si on veut le réutiliser il faut une copie\n", + "print(f\"L\\n{L}\\nU\\n{U}\")\n", + "A - (L @ U)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Gauss Jordan\n", + "\n", + "L'idée est de diagonaliser A par des multiplications matricielles similaires à celles de Gauss mais qui\n", + "annulent aussi les termes au dessus de la diagonale :\n", + "\n", + "$$\n", + "E_3 = \n", + "\\begin{bmatrix}\n", + "1 \\; 0\\; \\frac{-a_{13}}{a_{33}} \\; 0 \\ldots 0 \\\\\n", + "0 \\; 1\\; \\frac{-a_{23}}{a_{33}} \\; 0 \\ldots 0 \\\\\n", + "0 \\; 0\\quad 1 \\quad 0 \\ldots 0 \\\\\n", + "0 \\; 0\\; \\frac{-a_{43}}{a_{33}} 1 \\ldots 0 \\\\\n", + "\\vdots \\\\\n", + "0 \\; 0\\; \\frac{-a_{n3}}{a_{33}} 0 \\ldots 1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "\n", + "Cette méthode est plus compacte à écrire que Gauss car il n'y a pas remonté finale, mais elle est plus lente car on modifie tout A et b à\n", + "chaque itération." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def solve_gauss_jordan(A,b):\n", + " for i in range(len(A)):\n", + " d1 = np.diag([1.,] * len(A))\n", + " d1[:,i] = - A[:,i] / A[i,i]\n", + " A = d1 @ A\n", + " b = d1 @ b\n", + " return b / np.diag(A)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1., 1.])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = 10 * np.random.random(size=(5,5))\n", + "b = A.sum(axis=1)\n", + "solve_gauss_jordan(A, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparaison de la vitesse de méthodes" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "n = 500\n", + "A = 10 * np.random.random(size=(n,n))\n", + "b = A.sum(axis=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.63 s ± 218 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" + ] + } + ], + "source": [ + "%timeit solve_gauss_jordan(A, b)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "101 ms ± 3.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" + ] + } + ], + "source": [ + "%timeit solve_gauss(A, b) # 2.5 fois plus rapide que Gauss-Jordan" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "16.4 ms ± 227 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%timeit B = lin.inv(A) # 6 fois plus rapide que mon pivot de Gauss" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "14.2 ms ± 277 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%timeit lin.solve(A, b) # un peu plus rapide" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pour n=5000, `lin.solve` est 3 fois plus rapide que `lin.inv` sur ma machine. Et plus on augmente $n$ et plus\n", + "l'écart se creuse \n", + "\n", + "**Note**: Les calculs utilisent tous les processeurs de ma machine, Numpy sait paralléliser et utilise\n", + "les bonnes bibliothèques (BLAS et Lapack) s'il est bien installé.\n", + "\n", + "#### Morale\n", + "\n", + "* Une bonne méthode est mieux qu'une mauvaise (et oui !).\n", + "* Une bonne bibliothèque fait toute la différence (vous ne ferez pas mieux que BLAS et Lapack)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Erreurs d'arrondi" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "finfo(resolution=1e-06, min=-3.4028235e+38, max=3.4028235e+38, dtype=float32)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.set_printoptions(precision=20, linewidth=150, suppress=True)\n", + "\n", + "np.finfo(np.float32)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A\n", + " [[0.000001 1. ]\n", + " [1. 2. ]] \n", + "b\n", + " [1. 3.]\n" + ] + } + ], + "source": [ + "e = 1E-6\n", + "A = np.array([[e, 1], [1, 2]], dtype='float32')\n", + "b = np.array([1., 3.], dtype='float32')\n", + "print(f\"A\\n {A} \\nb\\n {b}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [1.013279 0.999999]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([1. , 3.013277], dtype=float32)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = solve_gauss(A.copy(),b)\n", + "print(\"x =\", x)\n", + "A @ x # on ne retrouve pas exactement b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Il y a un problème d'arrondi évident sachant que la solution est [1 + 2*e, 1 - e] :" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "La solution est : [1.000002 0.999999]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([1., 3.], dtype=float32)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([1 + 2*e, 1 - e], dtype='float32')\n", + "print(\"La solution est :\", x)\n", + "A @ x # on retrouve b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Le problème est qu'on divise les valeurs de la première colonne de A par le premier pivot : 1E-6.\n", + "\n", + "Aussi on multiplie par 1E6 ce qui va faire des grandes valeurs or la précision est au niveau du 6e chiffre,\n", + "on pert les suivants comme le montre la simple addition qui suit :" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1000000.], dtype=float32)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([1E6], dtype='float32') # 1 million\n", + "y = np.array([1E-2], dtype='float32') # 0.01\n", + "x+y # résultat : 1 million sans rien après la virgule" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**À mélanger des grands nombres avec des petits, on fait des erreurs d'arrondi.**\n", + "\n", + "C'est vrai pour les calculs matriciels qu'on fait, c'est toujours vrai et c'est pour cela qu'on aime normaliser\n", + "les données sur lesquelles on travaille lorsqu'on le peut." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution au problème d'arrondi dans le cas du pivot de Gauss\n", + "\n", + "Il suffit d'échanger les lignes (ou colonnes mais c'est plus compliqué) pour avoir la plus grande valeur,\n", + "en valeur absolue, comme pivot. C'est la méthode du pivot partiel.\n", + "\n", + "La méthode du pivot total consiste à prendre comme pivot la plus grande valeur parmis la ligne et la colonne concernées.\n", + "\n", + "#### Exercice pour le TP\n", + "\n", + "Programmer la méthode du pivot partiel et vérifier ce que cela donne sur l'exemple ci-dessus qui pose\n", + "des problèmes d'arrondi." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "A = np.array([1,2,3])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "np.isin?" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(False)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.isin(5,A)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "B = np.array([1,5,6])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ True, False, False])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.isin(B,A)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma32 Conditionnement d'une matrice.ipynb b/PVCM/cama/en/ma32 Conditionnement d'une matrice.ipynb new file mode 100644 index 0000000..9ff805a --- /dev/null +++ b/PVCM/cama/en/ma32 Conditionnement d'une matrice.ipynb @@ -0,0 +1,589 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conditionnement d'une matrice\n", + "\n", + "Soit la matrice A suivante :" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[10, 7, 8, 7],\n", + " [ 7, 5, 6, 5],\n", + " [ 8, 6, 10, 9],\n", + " [ 7, 5, 9, 10]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.array([[10, 7, 8, 7], [7, 5, 6, 5], [8, 6, 10, 9], [7, 5, 9, 10]])\n", + "A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Une matrice symétrique qui n'a rien de méchant a priori. Son déterminant est 1." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9999999999999869" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lin.det(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Construisons **b** de telle sorte que la solution du système matriciel A **x** = **b** soit [1,1,1,1] :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[32 23 33 31]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1.])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b = A.sum(axis=1)\n", + "print(b)\n", + "x = lin.solve(A, b)\n", + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Perturbons légèrement **b**. Dans le cas d'une expérience cela s'appelle une erreur de mesure. En informatique\n", + "cela peut être le résultat d'erreurs d'arrondi." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0033319453118976702" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bp = [32.1, 22.9, 33.1, 30.9]\n", + "eb = lin.norm(b - bp) / lin.norm(b) # une erreur se mesure par rapport à la valeur de la donnée\n", + "eb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On a une erreur sur **b** de l'ordre de 0,3 %. On la note $ ||{\\bf \\delta b}|| \\, / \\,||{\\bf b}||$.\n", + "\n", + "On pourrait espérer une erreur sur le résultat du même ordre de\n", + "grandeur.\n", + "Regardons la solution **x** de notre système matriciel perturbé :" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 9.2, -12.6, 4.5, -1.1])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xp = lin.solve(A, bp)\n", + "xp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Cette solution n'a rien à voir avec [1, 1, 1, 1]." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8.19847546803699" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ex = lin.norm(x - xp) / lin.norm(x)\n", + "ex" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "L'erreur est de l'ordre de 8 pour 1.\n", + "\n", + "L'erreur est 2460 fois plus grande que l'erreur sur **b**." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2460.567236431514" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ex / eb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Pourquoi ?\n", + "\n", + "On a \n", + "\n", + "$$\n", + "\\begin{align}\n", + "& A ({\\bf x} + {\\bf \\delta x}) = {\\bf b} + {\\bf \\delta b} \\quad \\textrm{et donc} \\\\\n", + "& A \\, {\\bf \\delta x} = {\\bf \\delta b} \\; \\textrm{ puisque } A {\\bf x} = {\\bf b} \\quad \\textrm{et finalement}\\\\\n", + "& {\\bf \\delta x} = A^{-1} \\, {\\bf \\delta b}\n", + "\\end{align}\n", + "$$\n", + "\n", + "Comme A et son inverse sont des applications linéaires on a\n", + "\n", + "$$\n", + "\\begin{align}\n", + "& ||{\\bf b}|| \\le ||A|| \\, ||{\\bf x}||\n", + "\\quad \\textrm{et} \\quad ||{\\bf \\delta x}|| \\le ||A^{-1}|| \\, ||{\\bf \\delta b}||\n", + "\\end{align}\n", + "$$\n", + "\n", + "donc \n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{||{\\bf \\delta x}||}{||{\\bf x}||} \\le ||A^{-1}|| \\, \\frac{||{\\bf \\delta b}||}{||{\\bf x}||}\n", + "\\le ||A^{-1}|| \\, ||A|| \\, \\frac{||{\\bf \\delta b}||}{||{\\bf b}||}\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3009.5787080586942" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lin.norm(lin.inv(A)) * lin.norm(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Le problème est là.\n", + "\n", + "On appelle cela le conditionnement de A :\n", + " \n", + "cond(A) = $||A^{-1}|| \\, ||A||$\n", + "\n", + "**Une matrice mal conditionnée va générer des erreurs de calcul lors de la résolution du système matriciel.**" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2984.0927016757555" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.linalg.cond(A) # scipy n'a pas le conditionnement mais numpy l'a. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Bizarre cette différence avec le calul ci-dessus qui a donné 3009." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Perturbons la matrice\n", + "\n", + "Que ce passe-t-il si on perturbe A et non b ?" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.098, 0.43 , 0.206, 0.09 ],\n", + " [-0.153, 0.292, -0.125, 0.784],\n", + " [ 0.927, -0.233, 0.583, 0.058],\n", + " [ 0.136, 0.851, -0.858, -0.826]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Erreur relative sur A : 0.06868857112100454\n" + ] + } + ], + "source": [ + "np.random.seed(0)\n", + "\n", + "dA = 2 * np.random.random(size = A.shape) - 1\n", + "display(dA)\n", + "ea = lin.norm(dA) / lin.norm(A)\n", + "print('Erreur relative sur A :', ea)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[10.098, 7.43 , 8.206, 7.09 ],\n", + " [ 6.847, 5.292, 5.875, 5.784],\n", + " [ 8.927, 5.767, 10.583, 9.058],\n", + " [ 7.136, 5.851, 8.142, 9.174]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Ap = A + dA\n", + "Ap" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-12.365, 15.574, 10.146, -5.94 ])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xp = lin.solve(Ap, b)\n", + "xp" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "11.432687335993894" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ex = lin.norm(xp - x) / lin.norm(x)\n", + "ex" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "166.44235204505293" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ex / ea" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On note que l'erreur est nettement moins grande. La raison est qu'on n'a pas trouvé l'erreur sur A qui\n", + "perturbera le plus possible le résultat. En fait ce n'est pas que le conditionnement de A qui compte,\n", + "l'erreur est aussi importante. Deux erreurs de même norme pertuberont différemment le résultat.\n", + "\n", + "\n", + "Notons aussi que dans ce cas les maths sont un peu différente mais on retrouve le conditionnement de A :\n", + "\n", + "$$\n", + "\\begin{align}\n", + "& (A + \\Delta A) \\, ({\\bf x} + {\\bf \\delta x}) = {\\bf b} \\quad \\textrm{et donc} \\\\\n", + "& A \\, {\\bf \\delta x} + \\Delta A \\, ({\\bf x} + {\\bf \\delta x}) = 0 \\; \\textrm{ puisque } A {\\bf x} = {\\bf b} \\quad \\textrm{et finalement}\\\\\n", + "& {\\bf \\delta x} = -A^{-1} \\,\\Delta A \\, ({\\bf x} + {\\bf \\delta x}) \\quad \\textrm{et} \\\\\n", + "& ||{\\bf \\delta x}|| \\le ||A^{-1}|| \\, ||\\Delta A|| \\, ||{\\bf x} + {\\bf \\delta x}||\n", + "\\end{align}\n", + "$$\n", + "\n", + "Ainsi\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{||{\\bf \\delta x}||}{||{\\bf x} + {\\bf \\delta x}||} \n", + "\\le ||A^{-1}|| \\, ||\\Delta A|| = ||A^{-1}|| \\, ||A|| \\, \\frac{||\\Delta A||}{||A||}\n", + "\\end{align}\n", + "$$\n", + "\n", + "ou\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{||{\\bf \\delta x}||}{||{\\bf x} + {\\bf \\delta x}||} \n", + "\\le cond(A) \\, \\frac{||\\Delta A||}{||A||}\n", + "\\end{align}\n", + "$$\n", + "\n", + "L'erreur ne se mesure pas par rapport à **x** mais par rapport à ${\\bf x} + {\\bf \\delta x}$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Propriétés\n", + "\n", + "* $cond(A) \\ge 1$ car $Id = A\\, A^{-1}$ et donc $1 \\le ||A||\\, ||A^{-1}||$ (pour les normes subordonnées car $||Id||_F = \\sqrt{n}$)\n", + "* $cond(A) = cond(A^{-1})$ par définition du conditionnement\n", + "* $\\displaystyle cond_2(A) = \\frac{\\max_i |\\lambda_i|}{\\min_i |\\lambda_i|}$ si la matrice est normale \n", + " où le 2 indique qu'on utilise la norme 2 et $\\lambda_i$ sont les valeurs propres de A" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2984.092701676269+0j)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vp = lin.eigvals(A)\n", + "vp.max() / vp.min() # et voici la différence avec le calcul ||A|| ||inv(A)|| ci-dessus\n", + " # ca sent l'erreur numérique" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* si A est unitaire ou orthogonale alors $cond_2(A) = 1$ (une rotation ou symétrie ne va pas agrandir l'erreur)\n", + "* le conditionnement n'est pas modifié par transformation unitaire " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Préconditionnement\n", + "\n", + "Si le conditionnement n'est pas modifié par une transformation unitaire, il l'est par d'autres transformations.\n", + "Ainsi\n", + "\n", + "$$\n", + "\\forall A, \\exists B \\; \\textrm{appelée matrice de préconditionnement t.q.} \\quad cond(B\\, A) \\le cond(A)\n", + "$$\n", + "\n", + "aussi on lieu de résoudre $A {\\bf x} = {\\bf b}$ on résoud $B\\, A {\\bf x} = B\\, {\\bf b}$\n", + "\n", + "Toute la difficulté consiste à trouver une matrice de préconditionnement B qui soit simple à calculer.\n", + "\n", + "#### Exercice 11.1\n", + "\n", + "Quelle est la meilleure matrice de préconditionnement de A ? Pourquoi ?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma34 ACP -- Exercice.ipynb b/PVCM/cama/en/ma34 ACP -- Exercice.ipynb new file mode 100644 index 0000000..7890e42 --- /dev/null +++ b/PVCM/cama/en/ma34 ACP -- Exercice.ipynb @@ -0,0 +1,295 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "import plotly.graph_objects as go\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.random.seed(0)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Exercise: 3D point cloud\n", + "\n", + "We have measurement results and we know that we must have a relationship\n", + "quadratic between x and z:\n", + "\n", + "$$ z = \\alpha \\, x^2 + \\beta \\, x + \\gamma $$\n", + "\n", + "How to find these 3 coefficients?\n", + "\n", + "Of course we will do a principal component analysis but beware, this\n", + "only works for linear relations (it gives us a vector). Therefore\n", + "we must introduce a new variable so that our equation is linear.\n", + "\n", + "How to write our equation so that it is linear according to 2 variables?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### réponse :\n", + "\n", + "..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Experience Data\n", + "\n", + "Make a 2D point cloud with the equation\n", + "\n", + "$$ z = -1.3 \\, x^2 + 0.2 \\, x + 1.45 + U(-1,1)$$\n", + "\n", + "where U is the uniform law that simulates noise." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "N = 50\n", + "x = ... # x varie entre -3 et 3\n", + "z = ...\n", + "nuage = np.array([x,z])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.title('Un nuage de points')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Calculations to find the characteristics of our cloud\n", + "\n", + "Manufacture from our 2D point cloud a 3D point cloud by introducing the new\n", + "variable that we have chosen.\n", + "\n", + "The new cloud is called `nuage3D`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=nuage3D[0], y=nuage3D[1], z=nuage3D[2], mode='markers')])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Calculate the covariance matrix of our cloud and its eigenvectors (we will store the eigenvectors in the `vec` variable)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=nuage3D[0], y=nuage3D[1], z=nuage3D[2], mode='markers'),\n", + " go.Scatter3d(x=[0,-5*vec[0,0]], y=[0,-5*vec[1,0]], z=[0,-5*vec[2,0]]),\n", + " go.Scatter3d(x=[0,vec[0,1]], y=[0,vec[1,1]], z=[0,vec[2,1]])])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "What can we deduce from our first eigenvector?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### réponse\n", + "\n", + "..." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Create a 2D point cloud that no longer takes into account the impact of the coefficient\n", + "that we just found.\n", + "\n", + "We call this new cloud `nuage2D` (it is not the same as our initial `cloud`)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.plot(nuage2D[0], nuage2D[1], 'x')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "What can we deduce from this?\n", + "\n", + "#### response\n", + "\n", + "...." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(\"Les coefficients de z fonction polynomiale de degré 2 en x sont :\\n\")\n", + "print(f\"alpha = {alpha}\")\n", + "print(f\"beta = {beta}\")\n", + "print(f\"gamma = {gamma}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "You can rerun everything with changing the value of the randomness seed. You will see that sometimes the\n", + "noise disturbs the results much more." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma35 Syst\303\250me matriciel -- Exercices.ipynb" "b/PVCM/cama/en/ma35 Syst\303\250me matriciel -- Exercices.ipynb" new file mode 100644 index 0000000..5d74dcb --- /dev/null +++ "b/PVCM/cama/en/ma35 Syst\303\250me matriciel -- Exercices.ipynb" @@ -0,0 +1,190 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Vector Programming\n", + "\n", + "The aim of the exercises is\n", + "\n", + "* to have a program that gives the correct answer\n", + "* which is as fast as possible (and for this we use massively Numpy)\n", + "\n", + "Generally if you have nested `for` it's a bad sign." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "np.set_printoptions(precision=10, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Partial Gaussian pivot method\n", + "\n", + "The announcement is in the course. We will check on the case which generates\n", + "rounding errors." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Choleski factorization\n", + "\n", + "This is to decompose A into $A = B\\, B^T$ with B a lower triangular matrix. This is not possible\n", + "that if the matrix A is symmetric and positive definite (this is moreover a way of verifying that a\n", + "matrix is ​​positive definite).\n", + "\n", + "Write Choleski's algorithm that takes A and returns B (to guess the algorithm, try to find the\n", + "coefficients of B from the coefficients of A on a 4x4 matrix A)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Reminder: no nested `for` loops but vector and matrix operations (on sub-matrices).\n", + "\n", + "Create a positive definite symmetric matrix and verify that its program works." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Improve Jacobi\n", + "\n", + "When we write an iteration of the Jacobi method with all the coefficients, we find that\n", + "if we calculate the new value of **x** element by element then when we want to update `x[1]`,\n", + "we already know `x[0]`. Ditto when we update `x[2]` we already know `x[0]` and `x[1]`, etc.\n", + "\n", + "The idea of ​​the improved version of Jacobi is to use the new value of `x[0]` and not the old one\n", + "as is the case in the algorithm of the course. So by using updated values ​​we can expect\n", + "converge faster.\n", + "\n", + "In this case, each iteration requires a line-by-line calculation and therefore a `for` loop within the `for` loop on\n", + "the iterations." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Test stop\n", + "\n", + "We will add an `error` argument to the function which indicates the desired precision of the result. Unfortunately, to know the accuracy of our calculation, it is necessary to know the solution. We could also calculate\n", + "${\\bf A \\, x}^t - {\\bf b}$ but it's also not the gap between ${\\bf x}^t$ and the solution (besides\n", + "it is a calculation in n² therefore cumbersome).\n", + "\n", + "Also we will look when the\n", + "convergence slows down and therefore we stop when\n", + "$||{\\bf x}^{t+1} - {\\bf x}^t|| < \\texttt{error}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Bonuses\n", + "\n", + "Rewrite the method without the `for` loop but taking the new values ​​of `x`. For this we will cut the matrix **A** into two triangular matrices." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# les méthodes de Numpy triu et tril seront utiles\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma40 M\303\251thodes it\303\251ratives.ipynb" "b/PVCM/cama/en/ma40 M\303\251thodes it\303\251ratives.ipynb" new file mode 100644 index 0000000..c1d93e0 --- /dev/null +++ "b/PVCM/cama/en/ma40 M\303\251thodes it\303\251ratives.ipynb" @@ -0,0 +1,416 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "np.random.seed(123)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Numerical simulation\n", + "\n", + "If the price of bananas is important, the sector with the greatest system resolution needs\n", + "matrices is numerical simulation.\n", + "This includes this\n", + "\n", + "
\"simulation
\n", + "\n", + "and everything that is digitally simulated, namely everything related to transport, energy, construction, everything\n", + "what we manufacture, which is expensive and which must have a very specific physical behavior. But that's not all,\n", + "understanding our environment (weather, global warming, chemistry, etc.) also means solving\n", + "matrix systems as well as other areas. However, there are numerical simulation methods\n", + "that do not go through matrix systems.\n", + "\n", + "To make the image above, we transform physical equations like [Navier-Stokes](https://fr.wikipedia.org/wiki/%C3%89quations_de_Navier-Stokes) into a matrix system where the unknowns are defined at each point\n", + "of a mesh to be defined. In our case the unknown is the pressure and the mesh is the interior of a\n", + "imaginary box that includes the plane and the air that circulates around it.\n", + "\n", + "If the box is a cube with 1000 points in each direction, we have 1 billion points in the box (minus\n", + "what is inside the plane but let's stay on 1 billion). Then the matrix has 1 quadrillion elements (one billion squared).\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "a_{11} \\; a_{12} \\ldots a_{1,10^9} \\\\\n", + "a_{21} \\; a_{22} \\ldots a_{2,10^9} \\\\\n", + " \\vdots \\\\\n", + "a_{10^9,1} a_{n2} \\ldots a_{10^9,10^9} \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "p_{1} \\\\\n", + "p_{2} \\\\\n", + "\\vdots \\\\\n", + "p_{10^9} \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "f_{1} \\\\\n", + "f_{2} \\\\\n", + "\\vdots \\\\\n", + "f_{10^9} \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Inverting a matrix is ​​done in $O(n³)$ operations or $O(10^{27})$ in our case.\n", + "\n", + "If you have [the most powerful computer in the world](https://www.top500.org/) in 2024\n", + "you can do 1 Eflops or $10^{18}$ operations per second. Also you will need $10^{9}$ seconds or a little over 30 years. It's too much.\n", + "\n", + "**Inverting a matrix or solving by a direct method is not the right solution to solve a large matrix system.**\n", + "\n", + "#### Exercise 12.1\n", + "For such a simulation it is also necessary to calculate the speed of the air in each of the 1 billion points of our grid. A speed is 3 variables that must be added to the pressure. How long does it take to reverse\n", + "the matrix which also integrates the speed of the air?" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# ceci est une calculatrice, vous pouvez donc écrire la réponse ici\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It is a good idea to estimate the time of a large calculation before launching it.\n", + "\n", + "Besides, with such long times, he\n", + "should not stay with orders of magnitude but specify with the exact formula. So with Choleski it's $n^3/3$\n", + "operations therefore it runs 3 times faster, but it is still too much." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Iterative Methods\n", + "\n", + "Iterative methods are methods that approach the desired solution step by step. They allow\n", + "to find an approximation of ${\\bf x}$, the solution of $A\\, {\\bf x} = b$.\n", + "\n", + "In general we\n", + "stops the calculation when we estimate that we are at a chosen distance from the solution (which we call the error) rather\n", + "than waiting to be at the exact solution.\n", + "Anyway the exact solution on a computer which is limited in number of decimal places can\n", + "be unattainable. So **we will never seek to have an error smaller than our maximum precision**.\n", + "\n", + "The fundamental idea of ​​the iterative algorithm is to have a formula like $\\; {\\bf x}^{t+1} = B \\, {\\bf x}^t + {\\bf c}\\;$ or in Python:\n", + "\n", + "```\n", + "x = np.random(size = c.size)\n", + "while np.square(x - old_x) > threshold:\n", + " old_x = x\n", + " x = B @ x + c\n", + "```\n", + "\n", + "The magic is if **x** converges. In this case we have reached a fixed point i.e. that ${\\bf x}^{t+1} = {\\bf x}^t$\n", + "and so\n", + "\n", + "$${\\bf x}^t = B \\, {\\bf x}^t + {\\bf c} \\quad \\textrm{c.a.d.} \\quad (Id -B) \\, {\\bf x}^t = {\\bf c}$$\n", + "\n", + "We find our $A \\; {\\bf x} = {\\bf b}$ that being in practice we do not cut A into Id and B because\n", + "ca does not converge (except particular cases). Let's see how the Jacobi method does it." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Jacobi method\n", + "\n", + "The Jacobi method cuts the matrix A into M and N with\n", + "\n", + "*M the diagonal matrix that includes the elements of the diagonal of A* N = M - A (so 0 on the diagonal and the opposite of the elements of A elsewhere)\n", + "\n", + "So the system to solve is $\\; (M - N) \\, {\\bf x} = {\\bf b}$.\n", + "\n", + "The iterative formula is therefore for iteration k+1 expressed as a function of iteration k:\n", + "\n", + "$$\n", + "M \\; {\\bf x}^{k+1} = N\\; {\\bf x}^k + {\\bf b}\n", + "$$\n", + "\n", + "and since M is a diagonal matrix, we have:\n", + "\n", + "$$\n", + "\\begin{array}{l}\n", + "a_{11} x_1^{k+1} = \\qquad -a_{12} \\, x_2^k - a_{13} \\, x_3^k \\ldots - a_{1n} \\, x_n^k + b_1 \\\\\n", + "a_{22} x_2^{k+1} = -a_{21} \\, x_1^k \\qquad - a_{23} \\, x_3^k \\ldots - a_{2n} \\, x_n^k + b_2 \\\\\n", + "a_{33} x_3^{k+1} = -a_{31} \\, x_1^k - a_{32} \\, x_3^k \\qquad \\ldots - a_{3n} \\, x_n^k + b_3 \\\\\n", + " \\vdots \\\\\n", + "a_{nn} x_n^{k+1} = -a_{n1} \\, x_1^k - a_{n2} \\, x_3^k \\ldots - a_{n-1,n-1} \\, x_{n-1}^k \\qquad + b_n \\\\\n", + "\\end{array}\n", + "$$\n", + "\n", + "We see in watermark $A \\; {\\bf x} = {\\bf b}$.\n", + "\n", + "To calculate $x_1^{k+1}$ it is necessary to divide the right term of the first line by $a_{11}$ it is thus necessary that $a_{11} \\ne 0$.\n", + "\n", + "To calculate the following terms $x_i^{k+1}$ it is also necessary that $a_{ii}$ be non-zero so **it\n", + "A must not have zero on its diagonal**.\n", + "\n", + "This can be found in the following writing, which takes up the initial formula:\n", + "$ {\\bf x}^{k+1} = M^{-1} \\;(N\\; {\\bf x}^k + {\\bf b})$\n", + "\n", + "> We see that in order to be effective, M must be easily invertible, otherwise we might as well invert A directly.\n", + "Here it is indeed the case since M is diagonal." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Let's program Jacobi" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A:\n", + " [[2 2 6 1]\n", + " [3 9 6 1]\n", + " [0 1 9 0]\n", + " [0 9 3 4]] \n", + "b:\n", + " [11 19 10 16] \n", + "\n", + "M:\n", + " [[2 0 0 0]\n", + " [0 9 0 0]\n", + " [0 0 9 0]\n", + " [0 0 0 4]]\n", + "N:\n", + " [[ 0 -2 -6 -1]\n", + " [-3 0 -6 -1]\n", + " [ 0 -1 0 0]\n", + " [ 0 -9 -3 0]]\n", + "\n", + "x_0 = [0.398 0.738 0.182 0.175]\n", + "x_1 = [4.127 1.837 1.029 2.203]\n", + "x_2 = [-0.526 -0.195 0.907 -0.906]\n", + "x_3 = [3.427 1.782 1.133 3.759]\n", + "x_4 = [-1.56 -0.204 0.913 -0.86 ]\n", + "x_5 = [3.395 2.118 1.134 3.775]\n", + "x_6 = [-1.907 -0.196 0.876 -1.616]\n", + "x_7 = [3.877 2.342 1.133 3.784]\n", + "x_8 = [-2.133 -0.357 0.851 -2.12 ]\n", + "x_9 = [4.364 2.49 1.151 4.165]\n", + "x_10 = [-2.525 -0.574 0.834 -2.467]\n", + "x_11 = [4.804 2.671 1.175 4.665]\n", + "x_12 = [-3.027 -0.792 0.814 -2.89 ]\n", + "x_13 = [5.293 2.898 1.199 5.17 ]\n", + "x_14 = [-3.581 -1.027 0.789 -3.421]\n", + "x_15 = [5.87 3.159 1.225 5.719]\n", + "x_16 = [-4.194 -1.298 0.76 -4.026]\n", + "x_17 = [6.531 3.45 1.255 6.35 ]\n", + "x_18 = [-4.891 -1.608 0.728 -4.704]\n", + "x_19 = [7.277 3.779 1.29 7.073]\n" + ] + } + ], + "source": [ + "A = np.random.randint(10, size=(4,4))\n", + "b = A.sum(axis=1) # ainsi la solution est [1,1,1,1]\n", + "print('A:\\n', A, \"\\nb:\\n\", b, \"\\n\")\n", + "\n", + "M = np.diag(A) # attention, c'est un vecteur\n", + "N = np.diag(M) - A # np.diag d'une matrice donne un vecteur, np.diag d'un vecteur donne une matrice\n", + "print(f\"M:\\n {np.diag(M)}\\nN:\\n {N}\\n\")\n", + "\n", + "x = np.random.random(4)\n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = (N @ x + b) / M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It doesn't really converge... (if you rerun and see `NaN` it means there is a zero on the diagonal)\n", + "\n", + "2nd try:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A:\n", + " [[24 2 4 8]\n", + " [ 0 24 9 3]\n", + " [ 4 6 16 5]\n", + " [ 6 2 1 32]] \n", + "b:\n", + " [38 36 31 41] \n", + "\n", + "M:\n", + " [[24 0 0 0]\n", + " [ 0 24 0 0]\n", + " [ 0 0 16 0]\n", + " [ 0 0 0 32]]\n", + "N:\n", + " [[ 0 -2 -4 -8]\n", + " [ 0 0 -9 -3]\n", + " [-4 -6 0 -5]\n", + " [-6 -2 -1 0]]\n", + "\n", + "x_0 = [0.766 0.777 0.028 0.174]\n", + "x_1 = [1.456 1.468 1.4 1.088]\n", + "x_2 = [0.865 0.839 0.683 0.873]\n", + "x_3 = [1.109 1.135 1.134 1.045]\n", + "x_4 = [0.951 0.944 0.908 0.967]\n", + "x_5 = [1.031 1.039 1.043 1.015]\n", + "x_6 = [0.984 0.982 0.973 0.99 ]\n", + "x_7 = [1.009 1.011 1.014 1.005]\n", + "x_8 = [0.995 0.994 0.992 0.997]\n", + "x_9 = [1.003 1.003 1.004 1.002]\n", + "x_10 = [0.998 0.998 0.998 0.999]\n", + "x_11 = [1.001 1.001 1.001 1. ]\n", + "x_12 = [1. 0.999 0.999 1. ]\n", + "x_13 = [1. 1. 1. 1.]\n", + "x_14 = [1. 1. 1. 1.]\n", + "x_15 = [1. 1. 1. 1.]\n", + "x_16 = [1. 1. 1. 1.]\n", + "x_17 = [1. 1. 1. 1.]\n", + "x_18 = [1. 1. 1. 1.]\n", + "x_19 = [1. 1. 1. 1.]\n" + ] + } + ], + "source": [ + "A = np.random.randint(10, size=(4,4))\n", + "A = A + np.diag(A.sum(axis=0))\n", + "b = A.sum(axis=1) # ainsi la solution est [1,1,1,1]\n", + "print('A:\\n', A, \"\\nb:\\n\", b, \"\\n\")\n", + "\n", + "\n", + "M = np.diag(A) # attention, c'est un vecteur\n", + "N = np.diag(M) - A # np.diag d'une matrice donne un vecteur, np.diag d'un vecteur donne une matrice\n", + "print(f\"M:\\n {np.diag(M)}\\nN:\\n {N}\\n\")\n", + "\n", + "x = np.random.random(4)\n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = (N @ x + b) / M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Magic!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Why does the 2nd case work?\n", + "\n", + "For an iterative method of the ${\\bf x} = B\\; {\\bf x} + {\\bf c}$ type to converge, it is necessary to choose\n", + "\n", + "* $\\rho(B) < 1\\quad$ with $\\rho$ the spectral radius (which is the largest eigenvalue in absolute value)\n", + "* $||B|| < 1\\quad$ with a matrix norm is subordinate to a vector norm.\n", + " \n", + "\n", + "#### Case of the Jacobi method\n", + "\n", + "For the Jacobi matrix B, these conditions are met if A is at **dominant diagonal**, namely that each\n", + "diagonal element is greater in modulus than the sum of all other modulus elements in its row or column ($|a_{i,i}| \\ge \\sum_{j \\ne i} |a_{i,j}|$).\n", + "\n", + "Jacobi also converges if A is symmetric, real and positive definite\n", + "(i.e. $\\forall {\\bf x}, \\; {\\bf x}^T \\, A \\, {\\bf x} > 0$)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Calculation time\n", + "\n", + "If we converge in 10 iterations then\n", + "10 matrix multiplications, 10 vector additions and 10 vector divisions are used, i.e. 180 operations\n", + "to be compared to the $4^3 / 3 = 22$ operations of a direct method. Damn !\n", + "\n", + "Some reasons why we lose are\n", + "\n", + "* Matrix A is too small, iterative methods are interesting for large matrices\n", + "* Jacobi's method is not the best (but it is very easily parallelizable)\n", + "* The spectral radius of the matrix is too large. The greater the spectral radius\n", + " smaller and the faster we converge." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma41 Convergence de Jacobi avec inertie.ipynb b/PVCM/cama/en/ma41 Convergence de Jacobi avec inertie.ipynb new file mode 100644 index 0000000..3861220 --- /dev/null +++ b/PVCM/cama/en/ma41 Convergence de Jacobi avec inertie.ipynb @@ -0,0 +1,1144 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "In this course we look at 2 points:\n", + " \n", + "* how to improve Jacobi\n", + "* the convergence of iterative algorithms (how to understand it and exploit it well)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Add inertia to Jacobi\n", + "\n", + "Jacobi's method leads to the following iterative system\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = M^{-1} \\, ( N\\; {\\bf x}^k + {\\bf b})\n", + "$$\n", + "\n", + "We have seen that this method only converges if the matrix B has its spectral radius less than 1, $\\rho(M^{-1}\\,N) < 1$.\n", + "\n", + "We can modify this method so that it has a greater radius of convergence\n", + "and therefore converges for more matrices. For this we add inertia:\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = w \\, M^{-1} \\, (N\\; {\\bf x}^k + {\\bf b}) + (1-w) \\, {\\bf x}^k\n", + "$$\n", + "\n", + "with $0 < w \\le 1$.\n", + "\n", + "If $w = 1$ then we have classic Jacobi and if $w = 0$ then we don't move, ${\\bf x}^{k+1} = {\\bf x}^k$.\n", + "\n", + "We talk about inertia because we see that we are moving more slowly since the new value of ${\\bf x}^{k+1}$\n", + "is between the old value of ${\\bf x}^{k+1}$ and ${\\bf x}^k$.\n", + "\n", + "\n", + "Note: $w \\, {\\bf a} + (1-w) \\, {\\bf b}$ represents segment $[{\\bf b}, {\\bf a}]$ when $w$ varies between 0 and 1.\n", + "\n", + "The idea is that with inertia we may enter the convergence zone whereas without it we would have jumped\n", + "Above.\n", + "\n", + "This method is called *over-relaxation*, I don't know why." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Let's program inertia for Jacobi\n", + "\n", + "We start with a simple Jacobi to check that we diverge." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A:\n", + " [[5 7 6 0]\n", + " [1 7 2 5]\n", + " [5 6 5 1]\n", + " [0 6 3 7]] \n", + "b:\n", + " [18 15 17 16] \n", + "\n", + "M:\n", + " [[5 0 0 0]\n", + " [0 7 0 0]\n", + " [0 0 5 0]\n", + " [0 0 0 7]]\n", + "N:\n", + " [[ 0 -7 -6 0]\n", + " [-1 0 -2 -5]\n", + " [-5 -6 0 -1]\n", + " [ 0 -6 -3 0]]\n", + "\n", + "x_0 = [0.062 0.652 0.185 0.852]\n", + "x_1 = [2.465 1.472 2.384 1.647]\n", + "x_2 = [-1.322 -0.067 -1.161 0.002]\n", + "x_3 = [5.088 2.662 4.803 2.841]\n", + "x_4 = [-5.89 -1.986 -5.451 -2.055]\n", + "x_5 = [12.921 6.009 12.084 6.324]\n", + "x_6 = [-19.314 -7.672 -17.997 -8.044]\n", + "x_7 = [35.937 15.79 33.53 16.575]\n", + "x_8 = [-58.741 -24.41 -54.8 -25.618]\n", + "x_9 = [103.534 44.49 96.557 46.694]\n", + "x_10 = [-174.554 -73.588 -162.861 -77.23 ]\n", + "x_11 = [302.056 128.775 281.706 135.159]\n", + "x_12 = [-514.732 -218.038 -480.218 -228.824]\n", + "x_13 = [885.114 376.327 825.542 394.983]\n", + "x_14 = [-1513.908 -642.302 -1412.303 -674.084]\n", + "x_15 = [2597.587 1103.419 2422.887 1158.103]\n", + "x_16 = [-4448.651 -1888.411 -4149.91 -1981.882]\n", + "x_17 = [7627.267 3238.983 7114.521 3399.456]\n", + "x_18 = [-13068.402 -5548.37 -12190.539 -5823.066]\n", + "x_19 = [22399.965 9511.401 20894.459 9982.548]\n" + ] + } + ], + "source": [ + "np.random.seed(799)\n", + "\n", + "A = np.random.randint(10, size=(4,4))\n", + "b = A.sum(axis=1) # ainsi la solution est [1,1,1,1]\n", + "print('A:\\n', A, \"\\nb:\\n\", b, \"\\n\")\n", + "\n", + "M = np.diag(A) # attention, c'est un vecteur\n", + "N = np.diag(M) - A # np.diag d'une matrice donne un vecteur, np.diag d'un vecteur donne une matrice\n", + "print(f\"M:\\n {np.diag(M)}\\nN:\\n {N}\\n\")\n", + "\n", + "x0 = np.random.random(4)\n", + "x = x0\n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = (N @ x + b) / M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Now let's add inertia to Jacobi:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x_0 = [0.062 0.652 0.185 0.852]\n", + "x_1 = [1.264 1.062 1.284 1.25 ]\n", + "x_2 = [0.918 0.882 0.948 1.037]\n", + "x_3 = [1.072 0.941 1.082 1.08 ]\n", + "x_4 = [1.028 0.925 1.032 1.048]\n", + "x_5 = [1.047 0.939 1.042 1.049]\n", + "x_6 = [1.041 0.943 1.029 1.042]\n", + "x_7 = [1.043 0.949 1.024 1.039]\n", + "x_8 = [1.042 0.954 1.017 1.036]\n", + "x_9 = [1.043 0.959 1.011 1.034]\n", + "x_10 = [1.044 0.962 1.005 1.032]\n", + "x_11 = [1.045 0.966 1. 1.031]\n", + "x_12 = [1.046 0.969 0.995 1.03 ]\n", + "x_13 = [1.048 0.971 0.99 1.03 ]\n", + "x_14 = [1.05 0.973 0.986 1.029]\n", + "x_15 = [1.053 0.974 0.981 1.029]\n", + "x_16 = [1.056 0.976 0.977 1.03 ]\n", + "x_17 = [1.059 0.977 0.972 1.03 ]\n", + "x_18 = [1.063 0.977 0.968 1.031]\n", + "x_19 = [1.067 0.978 0.963 1.032]\n" + ] + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = w * (N @ x + b) / M + (1-w) * x" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The sought solution being [1,1,1,1] it seems to work well!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Let's study convergence\n", + "\n", + "To fully understand an iterative method, it is necessary to study its convergence and therefore draw a curve\n", + "absolute error (when the solution is known), or relative error (between 2 successive ${\\bf x}^i$)\n", + "or the residual ($||A \\, {\\bf x}^i - {\\bf b}||$) or any other measure that makes sense.\n", + "\n", + "Let's look:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 248, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "error = [np.square(x - np.ones(4)).sum()]\n", + "for i in range(20):\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error.append(np.square(x - np.ones(4)).sum())\n", + "plt.plot(range(len(error)), error);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "A priori it seems good, except that in fact you can't see anything because the scale prevents you from seeing what is happening at\n", + "the end.\n", + "\n", + "Let's look at a logarithmic scale:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(range(len(error)), error)\n", + "plt.semilogy();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Wow, the ending is scary...\n", + "\n", + "Morality: **Always look at an error in logarithmic scale.**\n", + "\n", + "Since we measure something\n", + "which must tend towards 0, with a normal scale we are quickly crushed and therefore we do not see if we are at\n", + "$10^{-3}$ or $10^{-6}$ while it is very very different.\n", + "\n", + "Similarly if we diverge we will not see the beginning because a linear scale will adjust to the last values ​​which\n", + "can be very large." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Let us resume our calculation on more iterations." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 375 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "error = [np.square(x - np.ones(4)).sum()]\n", + "for i in range(200):\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error.append(np.square(x - np.ones(4)).sum())\n", + "plt.plot(range(len(error)), error)\n", + "plt.title('Erreur absolue')\n", + "plt.semilogy();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "So we approached the solution and then we diverged, which is better than diverging directly.\n", + "\n", + "#### Relative error\n", + "\n", + "Could we have seen it if we had not known the solution? Let's look at the gap between 2 successive ${\\bf x}^k$s." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "It seems that there is a strong relationship between the gap between two successive **x** and the absolute error.\n", + "Let's check:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération présentant le minimum : 12 14\n", + "Erreur absolue minimum : 0.004062676542953207\n", + "Erreur absolue minimum devinée à partir du minimum de l'écart : 0.004333899458825818\n" + ] + } + ], + "source": [ + "k_min = np.argmin(error)\n", + "k2_min = np.argmin(error2)\n", + "print('Itération présentant le minimum : ', k_min, k2_min)\n", + "print('Erreur absolue minimum : ', min(error))\n", + "print(\"Erreur absolue minimum devinée à partir du minimum de l'écart : \", error[k2_min])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The gap between 2 successive **x** is a simple and relatively efficient way to know when to stop an algorithm\n", + "iterative." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### Residue\n", + "\n", + "Finally we can calculate the residue namely $||A \\, {\\bf x} - {\\bf b}||$ but it is $n^2$ operations:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "residu = []\n", + "for i in range(200):\n", + " old_x = x\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " residu.append(np.square(A @ x - b).sum())\n", + "plt.plot(range(len(residu)), residu)\n", + "plt.title('Résidu')\n", + "plt.semilogy();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Let's test other matrices with this algorithm" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def mk_A(seed):\n", + " np.random.seed(seed)\n", + " return np.random.randint(10, size=(4,4))\n", + "\n", + "A = mk_A(234)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_error(M, N, b, x0, w, n=200):\n", + " x = x0 \n", + " error = [np.square(x - np.ones(4)).sum()]\n", + " error2 = []\n", + " for i in range(n):\n", + " old_x = x\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error.append(np.square(x - np.ones(4)).sum())\n", + " error2.append(np.square(x - old_x).sum())\n", + " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n", + " ax1.plot(range(len(error)), error)\n", + " ax1.set_title('Erreur absolue')\n", + " ax1.semilogy();\n", + " ax2.plot(range(len(error2)), error2)\n", + " ax2.set_title('Erreur relative')\n", + " ax2.semilogy()\n", + " print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 17 40\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 822 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_error(M, N, b, x0, w=0.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We find the same behavior (convergence then divergence) but much more chaotic.\n", + "\n", + "We can reduce the oscillations by increasing the inertia, i.e. by decreasing $w$:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 81 209\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 822 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "error2 = plot_error(M, N, b, x0, w=0.1, n=1000) \n", + "# w 5 fois plus petit donc je fais 5 fois plus d'itération pour \"avancer\" d'autant (grosso modo)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The oscillations are gone! But we paid a high price since we had to do 5 times more iterations.\n", + "\n", + "It can be seen that in both cases the relative error (between 2 successive x) does not give the correct minimum.\n", + "So stopping an iterative algorithm based on relative error is not always the most efficient.\n", + "\n", + "Let's see what the residue gives:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 218\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 \n", + "w = 0.1\n", + "residu = []\n", + "for i in range(1000):\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " residu.append(np.square(A @ x - b).sum())\n", + "plt.plot(range(len(residu)), residu)\n", + "plt.title('Résidu')\n", + "plt.semilogy();\n", + "print(\"Itération du minimum :\", np.argmin(residu))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Exercise 20.1\n", + "\n", + "How is it that the curve of the residual has the same shape as that of the relative error?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Réponse**\n", + "\n", + "..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### New Matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 153 153\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 827 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "A = mk_A(123)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)\n", + "\n", + "plot_error(M, N, b, x0, w=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Here is a case with perfect convergence. Note that we stopped at iteration 150 when we passed\n", + "below machine precision (following values ​​must be 0 and as log(0) = $-\\infty$,\n", + "matplolib does not display them).\n", + "\n", + "Let us nevertheless verify that the basic Jacobi method would not have\n", + "it does not work :" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x_0 = [0.398 0.738 0.182 0.175]\n", + "x_1 = [4.127 1.837 1.029 2.203]\n", + "x_2 = [-0.526 -0.195 0.907 -0.906]\n", + "x_3 = [3.427 1.782 1.133 3.759]\n", + "x_4 = [-1.56 -0.204 0.913 -0.86 ]\n", + "x_5 = [3.395 2.118 1.134 3.775]\n", + "x_6 = [-1.907 -0.196 0.876 -1.616]\n", + "x_7 = [3.877 2.342 1.133 3.784]\n", + "x_8 = [-2.133 -0.357 0.851 -2.12 ]\n", + "x_9 = [4.364 2.49 1.151 4.165]\n", + "x_10 = [-2.525 -0.574 0.834 -2.467]\n", + "x_11 = [4.804 2.671 1.175 4.665]\n", + "x_12 = [-3.027 -0.792 0.814 -2.89 ]\n", + "x_13 = [5.293 2.898 1.199 5.17 ]\n", + "x_14 = [-3.581 -1.027 0.789 -3.421]\n", + "x_15 = [5.87 3.159 1.225 5.719]\n", + "x_16 = [-4.194 -1.298 0.76 -4.026]\n", + "x_17 = [6.531 3.45 1.255 6.35 ]\n", + "x_18 = [-4.891 -1.608 0.728 -4.704]\n", + "x_19 = [7.277 3.779 1.29 7.073]\n" + ] + } + ], + "source": [ + "x = x0\n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = (N @ x + b) / M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The basic Jacobi diverges, so it is indeed inertia that made it possible to converge." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### New Matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 0 0\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 827 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "A = mk_A(16)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)\n", + "\n", + "plot_error(M, N, b, x0, w=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Direct divergence but if we reduce $w$ we see that we are in the 1st case:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 32 38\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 817 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_error(M, N, b, x0, w=0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "But it's still not good. At best we are not even at $10^{-1}$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Normalize\n", + "\n", + "This last remark only makes sense if we know what we are comparing to.\n", + "\n", + "* If the solution is a billion, having an error of 0.1 is fine.\n", + "* If the solution is 0.01, an error of 0.1 is huge.\n", + "\n", + "We can therefore only judge an error according to a reference. If we know the exact solution, then\n", + "it is the right reference.\n", + "\n", + "$$\n", + "\\frac{||{\\bf x}^k - {\\bf x}||}{||{\\bf x}||}\n", + "$$\n", + "\n", + "Similarly, the error between 2 successive iterations only makes sense when normalized.\n", + "If $||{\\bf x}^k|| = 1 000 000$ then $||{\\bf x}^k - {\\bf x}^{k-1}|| = 1$ is fine but it is not\n", + "if $||{\\bf x}^k|| = 1$.\n", + "\n", + "Also we compare the difference between 2 iterations with the current **x** or the previous one:\n", + "\n", + "$$\n", + "\\frac{||{\\bf x}^{k+1} - {\\bf x}^k||}{||{\\bf x}^k||}\n", + "$$\n", + "\n", + "Let's do that and look at our previous results." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_error_normalized(M, N, b, x0, w, n=200):\n", + " x = x0 \n", + " error = [np.square(x - np.ones(4)).sum()]\n", + " error2 = []\n", + " for i in range(n):\n", + " old_x = x\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error.append((np.square(x - np.ones(4)).sum())/4) # normalisé par rapport à la solution\n", + " error2.append((np.square(x - old_x).sum())/np.square(x).sum()) # normalisé par rapport à x\n", + " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n", + " ax1.plot(range(len(error)), error)\n", + " ax1.set_title('Erreur absolue normalisée')\n", + " ax1.semilogy();\n", + " ax2.plot(range(len(error2)), error2)\n", + " ax2.set_title('Erreur relative normalisée')\n", + " ax2.semilogy()\n", + " print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 60 70\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 821 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "A = mk_A(799)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)\n", + "plot_error(M, N, b, x0, w=0.1, n=1000) " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 60 70\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 822 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_error_normalized(M, N, b, x0, w=0.1, n=1000) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The normalized relative error stabilizes in this case whereas unnormalized it always increased.\n", + "\n", + "However, to converge the gap between 2 iterations must tend to 0.\n", + "\n", + "Sometimes we can have a surprise:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 500 499\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 821 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "A = mk_A(308)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)\n", + "plot_error_normalized(M, N, b, x0, w=0.1, n=500) " + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.004062676542953207" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "min(error)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We converge but near the desired value. It is rare and it is due to the very bad conditioning\n", + "of the matrix A. This bad conditioning generates calculation errors which make it impossible to arrive\n", + "to the exact solution." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.1405202107473442e+17" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.linalg.cond(A)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma42 Surrelaxation pour Gauss-Seidel -- Exercice.ipynb b/PVCM/cama/en/ma42 Surrelaxation pour Gauss-Seidel -- Exercice.ipynb new file mode 100644 index 0000000..3798257 --- /dev/null +++ b/PVCM/cama/en/ma42 Surrelaxation pour Gauss-Seidel -- Exercice.ipynb @@ -0,0 +1,335 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Exercise ma21" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "\n", + "%matplotlib inline\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We will increase the radius of convergence the improved Jacobi method made in TD, namely the Gauss-Seidel method.\n", + "\n", + "We will study its convergence in different cases." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Gauss-Seidel\n", + "\n", + "When we calculate the following **x** with Jacobi we do not take advantage of the fact that N is triangular\n", + "and therefore we know the new value of $x_n$ when we calculate $x_{n-1}$. With Gauss-Seidel\n", + "the last computed value is always used, which accelerates convergence.\n", + "\n", + "To summarize Gauss-Seidel from a matrix point of view, we have:\n", + "\n", + "* D = the diagonal matrix extracted from A: `D = np.diag(np.diag(A))`* L = the lower strictly triangular matrix of A: `L = np.tril(A, -1)`\n", + "* U = the upper strictly triangular matrix of A: `U = np.triu(A, 1)`\n", + "\n", + "and an iteration is given by the following formula:\n", + "\n", + "$$\n", + "(D + L)\\, {\\bf x}^{k+1} = -U\\; {\\bf x}^k + {\\bf b}\n", + "$$\n", + "Where\n", + "$$\n", + "{\\bf x}^{k+1} = D^{-1} \\, ( -L\\, {\\bf x}^{k+1} - U\\; {\\bf x}^k + {\\bf b})\n", + "$$\n", + "i.e.\n", + "$$\n", + "\\begin{bmatrix}\n", + "x_{1}^{k+1} \\\\\n", + "x_{2}^{k+1} \\\\\n", + "\\vdots \\\\\n", + "x_{n}^{k+1} \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "1/a_{11} \\quad 0 \\quad \\ldots \\quad 0 \\\\\n", + "0 \\quad 1/a_{22} \\quad \\ldots \\quad 0 \\\\\n", + " \\vdots \\\\\n", + "0 \\quad 0 \\quad \\ldots \\quad 1/a_{nn} \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\left(\n", + "\\;\n", + "-\n", + "\\begin{bmatrix}\n", + "0 \\quad 0 \\quad \\ldots \\quad 0 \\\\\n", + "a_{21} \\; 0 \\quad \\ldots \\quad 0 \\\\\n", + " \\vdots \\\\\n", + "a_{n1} \\, a_{n2} \\; \\ldots \\quad 0 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_{1}^{k+1} \\\\\n", + "x_{2}^{k+1} \\\\\n", + "\\vdots \\\\\n", + "x_{n}^{k+1} \\\\\n", + "\\end{bmatrix}\n", + "-\n", + "\\begin{bmatrix}\n", + "0 \\; a_{12} \\; \\ldots \\; a_{1n} \\\\\n", + "0 \\quad 0 \\; \\ldots \\; a_{2n} \\\\\n", + " \\vdots \\\\\n", + "0 \\quad 0 \\; \\ldots \\; 0 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_{1}^k \\\\\n", + "x_{2}^k \\\\\n", + "\\vdots \\\\\n", + "x_{n}^k \\\\\n", + "\\end{bmatrix}\n", + "+\n", + "\\begin{bmatrix}\n", + "b_{1} \\\\\n", + "b_{2} \\\\\n", + "\\vdots \\\\\n", + "b_{n} \\\\\n", + "\\end{bmatrix}\n", + "\\; \\right)\n", + "$$\n", + "\n", + "Note that I can put $L\\, {\\bf x}^{k+1}$ to the right of the equal sign\n", + "if I solve my system line by line starting from the top since in\n", + "in this case the ${\\bf x}^{k+1}$ used are known. This is what we did during the last lab.\n", + "\n", + "### Gauss-Seidel overrelaxation\n", + "\n", + "As we did with Jacobi, we introduce inertia with $w$:\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = w \\, D^{-1} \\, ( -L\\, {\\bf x}^{k+1} - U\\; {\\bf x}^k + {\\bf b}) + (1-w) \\; {\\bf x}^k\n", + "$$\n", + "\n", + "Check that you arrive at the following matrix entry:\n", + "\n", + "$$\n", + "\\left(\\frac{D}{w} + L\\right)\\, {\\bf x}^{k+1} = \\left(\\frac{1-w}{w} \\, D - U\\right)\\; {\\bf x}^k + {\\bf b}\n", + "$$\n", + "\n", + "Written thus we see that this method consists in splitting elements of the diagonal on both sides of the equality.\n", + "This can be interpreted as an advantage linked to a better repartition of the information included in our matrix (it needs to be tested)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Let's program overrelaxed Gauss-Seidel\n", + "\n", + "We will write two functions:\n", + "\n", + "* `solve_triangular(L,b)` which returns the solution of L**x** = **b** when L is lower triangular\n", + "* `gauss_seidel_r(A, b, x0, w, n)` which does `n` Gauss-Seidel iteration starting at `x0` with `w` the given relaxation coefficient in argument.\n", + " This function returns an array of calculated **x** values ​​(thus an array in 2D).\n", + " \n", + "As always, be careful to limit `for` and do as many vector and matrix operations as possible." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(123)\n", + "A = np.random.randint(10, size=(4,4))\n", + "b = A.sum(axis=1)\n", + "x0 = np.random.random(4)\n", + "\n", + "res = gauss_seidel_r(A, b, x0, w=0.2, n=100)\n", + "print(res[-1])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_convergences(values, result):\n", + " error = np.square(values - result).sum(axis = -1) / np.square(result).sum(axis=-1)\n", + " error2 = np.square(np.diff(values)).sum(axis = -1) / np.square(values).sum(axis=-1)\n", + " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n", + " ax1.plot(range(len(error)), error)\n", + " ax1.set_title('Erreur absolue normalisée')\n", + " ax1.semilogy();\n", + " ax2.plot(range(len(error2)), error2)\n", + " ax2.set_title('Erreur relative normalisée')\n", + " ax2.semilogy()\n", + " print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot_convergences(res, np.ones(4))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Does the unrelaxed Gauss-Seidel method converge in this case?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### The good case\n", + "\n", + "Find a `seed` which allows to generate a case which does not converge with the basic Gauss-Seidel but which\n", + "converges with relaxation ($w=0.2$)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Plot the convergence curves for the selected case with and without relaxation." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Study by $w$\n", + "\n", + "Still in our chosen case,\n", + "indicate what is the interval of\n", + "values ​​of $w$ which guarantees convergence for our matrix system A **x** = **b** with always the same `x0`\n", + "and a number of iterations to be determined.\n", + "\n", + "Find the optimal value of $w$ to converge fastest for this case.\n", + "\n", + "The requested precision for the interval and the optimal value is $10^{-2}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma50 Optimisation - M\303\251thode du gradient.ipynb" "b/PVCM/cama/en/ma50 Optimisation - M\303\251thode du gradient.ipynb" new file mode 100644 index 0000000..97bd3a4 --- /dev/null +++ "b/PVCM/cama/en/ma50 Optimisation - M\303\251thode du gradient.ipynb" @@ -0,0 +1,36389 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "import plotly.offline as py\n", + "import plotly.graph_objects as go\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Optimization problem\n", + "\n", + "An optimization problem looks like this:\n", + "\n", + "Given a function $J : ℝ^n \\rightarrow ℝ$, find the minimum of $J$ i.e. find ${\\bf u}$ such that\n", + "\n", + "$$J({\\bf u}) = \\inf_{{\\bf v} \\in ℝ^n} J({\\bf v})$$\n", + "\n", + "### Optimization problem with constraint\n", + "\n", + "It is possible to search for **u** not in $ℝ^n$ but in a part of $ℝ^n$, then it is a\n", + "constrained optimization problem.\n", + "\n", + "**Example** We are in 2D and we are looking for the minimum of $J(x,y)$ but with the constraint that $y > x$. This is equivalent to looking in the part of $ℝ^2$ that matches $y > x$.\n", + "\n", + "We will not look at optimization problems with constraints in this course but they are problems\n", + "important that you will see in your schooling.\n", + "\n", + "## The gradient method\n", + "\n", + "One way to solve a 2D optimization problem is to imagine it as terrain with relief. The\n", + "function $J(x,y)$ represents the altitude at any point $(x,y)$.\n", + "\n", + "To find the minimum of $J$ just start from a random point and go down in the direction that\n", + "goes down the most. A drop of water follows this path.\n", + "\n", + "This is the gradient method.\n", + "\n", + "To fully understand the method, it is necessary to fully understand the partial derivatives as well as the\n", + "notations which are summarized in this [memo on partial derivatives](https://www.lrde.epita.fr/~ricou/notations.pdf).\n", + "\n", + "The gradient algorithm is therefore:\n", + "\n", + "* take a random starting point ${\\bf p^0} = (x_0, y_0)$\n", + "* calculate the gradient of J at this point\n", + "\n", + "$$\n", + "\\nabla J(x_0, y_0) = \n", + "\\begin{bmatrix} \n", + "\\frac{\\partial J}{\\partial x} \\\\\n", + "\\frac{\\partial J}{\\partial y}\n", + "\\end{bmatrix} (x_0, y_0)\n", + "$$\n", + "* move in the opposite direction (the grandiant goes up): ${\\bf p}^{k+1} = {\\bf p}^k - \\mu \\, \\nabla J({\\bf p}^k)$\n", + "\n", + "and we repeat this last step until we arrive at a fixed point, i.e. that\n", + "$|| {\\bf p}^{k+1} - {\\bf p}^k|| < \\varepsilon$ with $\\varepsilon$ a very small value." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def J(x, y):\n", + " return x**2 + 0.5 * y**2 - 2 * x + 3" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "linkText": "Export to plot.ly", + "plotlyServerURL": "https://plot.ly", + "showLink": false + }, + "data": [ + { + "type": "surface", + "x": [ + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ] + ], + "y": [ + [ + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3 + ], + [ + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394 + ], + [ + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879 + ], + [ + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183 + ], + [ + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758 + ], + [ + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697 + ], + [ + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362 + ], + [ + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757 + ], + [ + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515 + ], + [ + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546 + ], + [ + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394 + ], + [ + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333 + ], + [ + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725 + ], + [ + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212 + ], + [ + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514 + ], + [ + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091 + ], + [ + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303 + ], + [ + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697 + ], + [ + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092 + ], + [ + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484 + ], + [ + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878 + ], + [ + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273 + ], + [ + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665 + ], + [ + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606 + ], + [ + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454 + ], + [ + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849 + ], + [ + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243 + ], + [ + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635 + ], + [ + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303 + ], + [ + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424 + ], + [ + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817 + ], + [ + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121 + ], + [ + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606 + ], + [ + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1 + ], + [ + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394 + ], + [ + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789 + ], + [ + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183 + ], + [ + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573 + ], + [ + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968 + ], + [ + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362 + ], + [ + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757 + ], + [ + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151 + ], + [ + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546 + ], + [ + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403 + ], + [ + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304 + ], + [ + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725 + ], + [ + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193 + ], + [ + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138 + ], + [ + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083 + ], + [ + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276 + ], + [ + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276 + ], + [ + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083 + ], + [ + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138 + ], + [ + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238 + ], + [ + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293 + ], + [ + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335 + ], + [ + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403 + ], + [ + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546 + ], + [ + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151 + ], + [ + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757 + ], + [ + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367 + ], + [ + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972 + ], + [ + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578 + ], + [ + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183 + ], + [ + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789 + ], + [ + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394 + ], + [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + [ + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606 + ], + [ + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121 + ], + [ + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817 + ], + [ + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422 + ], + [ + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028 + ], + [ + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633 + ], + [ + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248 + ], + [ + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853 + ], + [ + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459 + ], + [ + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064 + ], + [ + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667 + ], + [ + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275 + ], + [ + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788 + ], + [ + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486 + ], + [ + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092 + ], + [ + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697 + ], + [ + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303 + ], + [ + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091 + ], + [ + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514 + ], + [ + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212 + ], + [ + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725 + ], + [ + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334 + ], + [ + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945 + ], + [ + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455 + ], + [ + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156 + ], + [ + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576 + ], + [ + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367 + ], + [ + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972 + ], + [ + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758 + ], + [ + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183 + ], + [ + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879 + ], + [ + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394 + ], + [ + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ] + ], + "z": [ + [ + 22.5, + 22.0188246097337, + 21.544995408631774, + 21.078512396694215, + 20.61937557392103, + 20.167584940312214, + 19.723140495867767, + 19.286042240587694, + 18.856290174471994, + 18.433884297520663, + 18.018824609733702, + 17.611111111111107, + 17.21074380165289, + 16.817722681359044, + 16.432047750229565, + 16.053719008264462, + 15.682736455463727, + 15.319100091827364, + 14.962809917355372, + 14.61386593204775, + 14.272268135904499, + 13.93801652892562, + 13.61111111111111, + 13.291551882460972, + 12.979338842975206, + 12.67447199265381, + 12.376951331496787, + 12.086776859504132, + 11.803948576675849, + 11.528466483011938, + 11.260330578512395, + 10.999540863177227, + 10.746097337006429, + 10.5, + 10.261248852157944, + 10.029843893480258, + 9.805785123966942, + 9.589072543617998, + 9.379706152433425, + 9.177685950413224, + 8.983011937557393, + 8.795684113865931, + 8.615702479338843, + 8.443067033976124, + 8.277777777777777, + 8.1198347107438, + 7.969237832874196, + 7.825987144168962, + 7.690082644628099, + 7.561524334251607, + 7.440312213039486, + 7.3264462809917354, + 7.219926538108356, + 7.120752984389347, + 7.028925619834711, + 6.944444444444445, + 6.867309458218549, + 6.797520661157025, + 6.735078053259872, + 6.679981634527089, + 6.632231404958677, + 6.5918273645546375, + 6.558769513314967, + 6.533057851239669, + 6.514692378328742, + 6.503673094582186, + 6.5, + 6.503673094582186, + 6.514692378328742, + 6.533057851239669, + 6.558769513314967, + 6.5918273645546375, + 6.632231404958677, + 6.67998163452709, + 6.735078053259872, + 6.797520661157025, + 6.86730945821855, + 6.944444444444445, + 7.028925619834711, + 7.120752984389348, + 7.219926538108357, + 7.3264462809917354, + 7.440312213039485, + 7.561524334251606, + 7.690082644628099, + 7.825987144168961, + 7.969237832874196, + 8.1198347107438, + 8.277777777777779, + 8.443067033976126, + 8.615702479338845, + 8.795684113865933, + 8.983011937557393, + 9.177685950413224, + 9.379706152433426, + 9.589072543617998, + 9.805785123966942, + 10.029843893480258, + 10.261248852157943, + 10.5 + ], + [ + 22.32001836547291, + 21.83884297520661, + 21.365013774104685, + 20.898530762167127, + 20.43939393939394, + 19.98760330578512, + 19.54315886134068, + 19.106060606060606, + 18.676308539944905, + 18.25390266299357, + 17.838842975206614, + 17.43112947658402, + 17.0307621671258, + 16.637741046831955, + 16.252066115702476, + 15.873737373737372, + 15.502754820936639, + 15.139118457300276, + 14.782828282828284, + 14.433884297520661, + 14.09228650137741, + 13.75803489439853, + 13.431129476584022, + 13.111570247933884, + 12.799357208448118, + 12.494490358126722, + 12.196969696969697, + 11.906795224977042, + 11.62396694214876, + 11.348484848484848, + 11.080348943985307, + 10.819559228650137, + 10.566115702479339, + 10.320018365472912, + 10.081267217630854, + 9.849862258953168, + 9.625803489439853, + 9.409090909090908, + 9.199724517906336, + 8.997704315886134, + 8.803030303030303, + 8.615702479338843, + 8.435720844811755, + 8.263085399449036, + 8.097796143250687, + 7.939853076216711, + 7.789256198347107, + 7.646005509641872, + 7.5101010101010095, + 7.381542699724518, + 7.260330578512397, + 7.146464646464646, + 7.039944903581267, + 6.940771349862258, + 6.8489439853076215, + 6.764462809917355, + 6.68732782369146, + 6.617539026629935, + 6.5550964187327825, + 6.5, + 6.452249770431588, + 6.411845730027548, + 6.378787878787879, + 6.35307621671258, + 6.3347107438016526, + 6.323691460055096, + 6.320018365472911, + 6.323691460055096, + 6.3347107438016526, + 6.35307621671258, + 6.378787878787879, + 6.411845730027547, + 6.452249770431588, + 6.5, + 6.5550964187327825, + 6.617539026629936, + 6.68732782369146, + 6.764462809917355, + 6.848943985307622, + 6.940771349862259, + 7.039944903581267, + 7.146464646464647, + 7.260330578512397, + 7.381542699724518, + 7.510101010101009, + 7.646005509641872, + 7.789256198347106, + 7.939853076216712, + 8.09779614325069, + 8.263085399449036, + 8.435720844811755, + 8.615702479338843, + 8.803030303030305, + 8.997704315886136, + 9.199724517906336, + 9.40909090909091, + 9.625803489439853, + 9.84986225895317, + 10.081267217630852, + 10.320018365472912 + ], + [ + 22.143709825528006, + 21.66253443526171, + 21.188705234159784, + 20.722222222222225, + 20.26308539944904, + 19.81129476584022, + 19.366850321395777, + 18.929752066115704, + 18.5, + 18.07759412304867, + 17.66253443526171, + 17.254820936639117, + 16.8544536271809, + 16.46143250688705, + 16.075757575757578, + 15.69742883379247, + 15.326446280991737, + 14.962809917355372, + 14.60651974288338, + 14.257575757575758, + 13.915977961432507, + 13.581726354453629, + 13.254820936639117, + 12.935261707988982, + 12.623048668503214, + 12.31818181818182, + 12.020661157024794, + 11.73048668503214, + 11.447658402203857, + 11.172176308539946, + 10.904040404040405, + 10.643250688705233, + 10.389807162534435, + 10.143709825528008, + 9.90495867768595, + 9.673553719008265, + 9.449494949494952, + 9.232782369146005, + 9.023415977961433, + 8.82139577594123, + 8.6267217630854, + 8.439393939393941, + 8.259412304866851, + 8.086776859504134, + 7.921487603305785, + 7.763544536271809, + 7.612947658402204, + 7.46969696969697, + 7.333792470156107, + 7.205234159779615, + 7.084022038567494, + 6.9701561065197435, + 6.863636363636364, + 6.764462809917355, + 6.672635445362719, + 6.588154269972453, + 6.511019283746557, + 6.441230486685033, + 6.37878787878788, + 6.323691460055097, + 6.275941230486685, + 6.2355371900826455, + 6.202479338842975, + 6.176767676767677, + 6.15840220385675, + 6.147382920110194, + 6.143709825528008, + 6.147382920110194, + 6.15840220385675, + 6.176767676767677, + 6.202479338842975, + 6.2355371900826455, + 6.275941230486685, + 6.323691460055098, + 6.37878787878788, + 6.441230486685033, + 6.511019283746558, + 6.588154269972453, + 6.672635445362719, + 6.764462809917356, + 6.863636363636365, + 6.9701561065197435, + 7.084022038567493, + 7.205234159779616, + 7.333792470156107, + 7.469696969696971, + 7.612947658402204, + 7.763544536271809, + 7.921487603305788, + 8.086776859504134, + 8.259412304866853, + 8.439393939393941, + 8.626721763085401, + 8.821395775941232, + 9.023415977961434, + 9.232782369146008, + 9.449494949494952, + 9.673553719008266, + 9.90495867768595, + 10.143709825528008 + ], + [ + 21.97107438016529, + 21.48989898989899, + 21.01606978879706, + 20.549586776859506, + 20.09044995408632, + 19.6386593204775, + 19.194214876033058, + 18.757116620752985, + 18.32736455463728, + 17.90495867768595, + 17.48989898989899, + 17.082185491276398, + 16.68181818181818, + 16.288797061524335, + 15.903122130394857, + 15.524793388429751, + 15.153810835629018, + 14.790174471992653, + 14.433884297520663, + 14.084940312213039, + 13.74334251606979, + 13.40909090909091, + 13.0821854912764, + 12.762626262626263, + 12.450413223140497, + 12.145546372819101, + 11.848025711662075, + 11.557851239669422, + 11.27502295684114, + 10.999540863177227, + 10.731404958677686, + 10.470615243342516, + 10.217171717171716, + 9.97107438016529, + 9.732323232323232, + 9.500918273645548, + 9.276859504132233, + 9.060146923783286, + 8.850780532598714, + 8.648760330578511, + 8.45408631772268, + 8.266758494031222, + 8.086776859504134, + 7.914141414141415, + 7.748852157943067, + 7.590909090909091, + 7.440312213039486, + 7.297061524334252, + 7.161157024793389, + 7.032598714416896, + 6.911386593204775, + 6.797520661157026, + 6.691000918273646, + 6.5918273645546375, + 6.5, + 6.415518824609734, + 6.338383838383839, + 6.268595041322315, + 6.206152433425161, + 6.1510560146923785, + 6.103305785123967, + 6.062901744719927, + 6.029843893480257, + 6.004132231404959, + 5.985766758494032, + 5.974747474747475, + 5.971074380165289, + 5.974747474747475, + 5.985766758494032, + 6.004132231404959, + 6.029843893480257, + 6.062901744719927, + 6.103305785123967, + 6.151056014692379, + 6.206152433425162, + 6.268595041322315, + 6.338383838383839, + 6.415518824609734, + 6.500000000000001, + 6.5918273645546375, + 6.691000918273646, + 6.797520661157026, + 6.911386593204775, + 7.032598714416897, + 7.161157024793388, + 7.297061524334252, + 7.440312213039485, + 7.59090909090909, + 7.74885215794307, + 7.914141414141415, + 8.086776859504134, + 8.266758494031222, + 8.454086317722682, + 8.648760330578513, + 8.850780532598716, + 9.06014692378329, + 9.276859504132233, + 9.500918273645548, + 9.732323232323232, + 9.97107438016529 + ], + [ + 21.80211202938476, + 21.320936639118457, + 20.84710743801653, + 20.380624426078974, + 19.92148760330579, + 19.46969696969697, + 19.025252525252526, + 18.588154269972453, + 18.15840220385675, + 17.73599632690542, + 17.320936639118457, + 16.913223140495866, + 16.512855831037648, + 16.119834710743802, + 15.734159779614325, + 15.355831037649219, + 14.984848484848486, + 14.621212121212121, + 14.264921946740131, + 13.915977961432507, + 13.574380165289258, + 13.240128558310378, + 12.913223140495868, + 12.59366391184573, + 12.281450872359965, + 11.976584022038569, + 11.679063360881543, + 11.38888888888889, + 11.106060606060607, + 10.830578512396695, + 10.562442607897154, + 10.301652892561984, + 10.048209366391184, + 9.802112029384757, + 9.5633608815427, + 9.331955922865015, + 9.1078971533517, + 8.891184573002754, + 8.681818181818182, + 8.47979797979798, + 8.285123966942148, + 8.09779614325069, + 7.917814508723601, + 7.745179063360883, + 7.579889807162534, + 7.421946740128559, + 7.271349862258953, + 7.12809917355372, + 6.992194674012857, + 6.863636363636364, + 6.742424242424243, + 6.628558310376493, + 6.522038567493114, + 6.422865013774105, + 6.331037649219468, + 6.246556473829202, + 6.169421487603307, + 6.099632690541783, + 6.037190082644629, + 5.982093663911846, + 5.934343434343435, + 5.8939393939393945, + 5.860881542699725, + 5.835169880624427, + 5.8168044077135, + 5.805785123966943, + 5.802112029384757, + 5.805785123966943, + 5.8168044077135, + 5.835169880624427, + 5.860881542699725, + 5.8939393939393945, + 5.934343434343435, + 5.982093663911847, + 6.03719008264463, + 6.099632690541783, + 6.169421487603307, + 6.246556473829202, + 6.331037649219469, + 6.422865013774105, + 6.522038567493114, + 6.628558310376493, + 6.742424242424243, + 6.863636363636365, + 6.992194674012856, + 7.12809917355372, + 7.271349862258953, + 7.421946740128558, + 7.579889807162537, + 7.745179063360883, + 7.917814508723602, + 8.09779614325069, + 8.28512396694215, + 8.479797979797981, + 8.681818181818183, + 8.891184573002757, + 9.1078971533517, + 9.331955922865015, + 9.5633608815427, + 9.802112029384757 + ], + [ + 21.63682277318641, + 21.155647382920108, + 20.681818181818183, + 20.215335169880625, + 19.75619834710744, + 19.30440771349862, + 18.859963269054177, + 18.422865013774103, + 17.993112947658403, + 17.57070707070707, + 17.15564738292011, + 16.747933884297517, + 16.3475665748393, + 15.954545454545453, + 15.568870523415976, + 15.190541781450872, + 14.819559228650137, + 14.455922865013774, + 14.099632690541782, + 13.75068870523416, + 13.409090909090908, + 13.074839302112029, + 12.74793388429752, + 12.428374655647382, + 12.116161616161616, + 11.81129476584022, + 11.513774104683197, + 11.22359963269054, + 10.940771349862258, + 10.665289256198347, + 10.397153351698805, + 10.136363636363637, + 9.882920110192837, + 9.63682277318641, + 9.398071625344352, + 9.166666666666668, + 8.942607897153351, + 8.725895316804406, + 8.516528925619834, + 8.314508723599632, + 8.1198347107438, + 7.932506887052341, + 7.752525252525253, + 7.579889807162534, + 7.414600550964186, + 7.25665748393021, + 7.1060606060606055, + 6.962809917355371, + 6.826905417814508, + 6.698347107438016, + 6.577134986225895, + 6.463269054178145, + 6.356749311294766, + 6.257575757575757, + 6.165748393021119, + 6.081267217630853, + 6.004132231404958, + 5.934343434343434, + 5.87190082644628, + 5.816804407713498, + 5.769054178145087, + 5.728650137741046, + 5.695592286501377, + 5.669880624426078, + 5.651515151515151, + 5.640495867768594, + 5.63682277318641, + 5.640495867768594, + 5.651515151515151, + 5.669880624426078, + 5.695592286501377, + 5.728650137741046, + 5.769054178145087, + 5.816804407713499, + 5.87190082644628, + 5.934343434343434, + 6.0041322314049586, + 6.081267217630854, + 6.16574839302112, + 6.257575757575758, + 6.356749311294766, + 6.463269054178145, + 6.577134986225895, + 6.698347107438016, + 6.826905417814508, + 6.96280991735537, + 7.1060606060606055, + 7.25665748393021, + 7.414600550964188, + 7.579889807162536, + 7.752525252525254, + 7.932506887052343, + 8.119834710743802, + 8.314508723599634, + 8.516528925619836, + 8.725895316804408, + 8.942607897153351, + 9.166666666666668, + 9.398071625344352, + 9.63682277318641 + ], + [ + 21.475206611570247, + 20.99403122130395, + 20.52020202020202, + 20.053719008264466, + 19.594582185491277, + 19.14279155188246, + 18.698347107438018, + 18.261248852157944, + 17.83149678604224, + 17.40909090909091, + 16.99403122130395, + 16.586317722681358, + 16.18595041322314, + 15.792929292929292, + 15.407254361799815, + 15.028925619834709, + 14.657943067033976, + 14.294306703397613, + 13.93801652892562, + 13.589072543617998, + 13.247474747474747, + 12.913223140495868, + 12.586317722681358, + 12.26675849403122, + 11.954545454545453, + 11.649678604224057, + 11.352157943067034, + 11.06198347107438, + 10.779155188246097, + 10.503673094582185, + 10.235537190082644, + 9.974747474747474, + 9.721303948576676, + 9.475206611570247, + 9.236455463728191, + 9.005050505050505, + 8.78099173553719, + 8.564279155188245, + 8.354912764003672, + 8.152892561983471, + 7.95821854912764, + 7.77089072543618, + 7.590909090909091, + 7.418273645546373, + 7.252984389348025, + 7.095041322314049, + 6.944444444444444, + 6.8011937557392095, + 6.6652892561983474, + 6.536730945821855, + 6.415518824609734, + 6.301652892561984, + 6.195133149678604, + 6.095959595959595, + 6.004132231404958, + 5.9196510560146915, + 5.842516069788797, + 5.7727272727272725, + 5.7102846648301195, + 5.655188246097337, + 5.607438016528925, + 5.567033976124884, + 5.533976124885216, + 5.508264462809917, + 5.48989898989899, + 5.4788797061524335, + 5.475206611570248, + 5.4788797061524335, + 5.48989898989899, + 5.508264462809917, + 5.533976124885216, + 5.567033976124884, + 5.607438016528925, + 5.655188246097337, + 5.7102846648301195, + 5.772727272727273, + 5.842516069788797, + 5.919651056014692, + 6.004132231404959, + 6.095959595959596, + 6.195133149678604, + 6.301652892561984, + 6.415518824609734, + 6.536730945821855, + 6.665289256198347, + 6.8011937557392095, + 6.944444444444445, + 7.095041322314048, + 7.252984389348027, + 7.418273645546375, + 7.5909090909090935, + 7.770890725436182, + 7.95821854912764, + 8.152892561983471, + 8.354912764003675, + 8.564279155188247, + 8.78099173553719, + 9.005050505050505, + 9.236455463728191, + 9.475206611570247 + ], + [ + 21.31726354453627, + 20.836088154269973, + 20.362258953168045, + 19.89577594123049, + 19.4366391184573, + 18.984848484848484, + 18.54040404040404, + 18.10330578512397, + 17.673553719008265, + 17.251147842056934, + 16.836088154269973, + 16.42837465564738, + 16.028007346189163, + 15.634986225895316, + 15.249311294765839, + 14.870982552800733, + 14.5, + 14.136363636363637, + 13.780073461891645, + 13.431129476584022, + 13.089531680440771, + 12.755280073461892, + 12.428374655647382, + 12.108815426997245, + 11.796602387511477, + 11.491735537190081, + 11.194214876033058, + 10.904040404040403, + 10.621212121212121, + 10.345730027548209, + 10.077594123048668, + 9.816804407713498, + 9.5633608815427, + 9.31726354453627, + 9.078512396694215, + 8.847107438016529, + 8.623048668503214, + 8.40633608815427, + 8.196969696969695, + 7.994949494949495, + 7.800275482093664, + 7.612947658402204, + 7.432966023875115, + 7.260330578512397, + 7.0950413223140485, + 6.937098255280073, + 6.786501377410468, + 6.643250688705233, + 6.507346189164371, + 6.378787878787879, + 6.257575757575758, + 6.143709825528008, + 6.037190082644628, + 5.938016528925619, + 5.846189164370982, + 5.7617079889807155, + 5.684573002754821, + 5.614784205693296, + 5.5523415977961434, + 5.497245179063361, + 5.449494949494949, + 5.409090909090908, + 5.37603305785124, + 5.350321395775941, + 5.3319559228650135, + 5.320936639118457, + 5.317263544536272, + 5.320936639118457, + 5.3319559228650135, + 5.350321395775941, + 5.37603305785124, + 5.409090909090908, + 5.449494949494949, + 5.497245179063361, + 5.5523415977961434, + 5.614784205693297, + 5.684573002754821, + 5.761707988980716, + 5.846189164370983, + 5.93801652892562, + 6.037190082644628, + 6.143709825528008, + 6.257575757575758, + 6.378787878787879, + 6.5073461891643705, + 6.643250688705233, + 6.7865013774104685, + 6.9370982552800715, + 7.095041322314051, + 7.260330578512399, + 7.432966023875117, + 7.612947658402206, + 7.800275482093664, + 7.994949494949495, + 8.196969696969699, + 8.406336088154271, + 8.623048668503214, + 8.847107438016529, + 9.078512396694215, + 9.31726354453627 + ], + [ + 21.16299357208448, + 20.68181818181818, + 20.207988980716255, + 19.741505968778696, + 19.28236914600551, + 18.830578512396695, + 18.38613406795225, + 17.949035812672175, + 17.519283746556475, + 17.096877869605144, + 16.681818181818183, + 16.27410468319559, + 15.873737373737372, + 15.480716253443525, + 15.09504132231405, + 14.716712580348943, + 14.34573002754821, + 13.982093663911845, + 13.625803489439853, + 13.276859504132231, + 12.93526170798898, + 12.601010101010102, + 12.274104683195592, + 11.954545454545453, + 11.642332415059688, + 11.337465564738292, + 11.039944903581269, + 10.749770431588614, + 10.46694214876033, + 10.19146005509642, + 9.923324150596876, + 9.662534435261708, + 9.40909090909091, + 9.162993572084481, + 8.924242424242426, + 8.69283746556474, + 8.468778696051423, + 8.25206611570248, + 8.042699724517906, + 7.8406795224977035, + 7.646005509641873, + 7.458677685950413, + 7.278696051423324, + 7.106060606060606, + 6.940771349862258, + 6.782828282828282, + 6.632231404958677, + 6.488980716253444, + 6.35307621671258, + 6.224517906336088, + 6.1033057851239665, + 5.989439853076217, + 5.882920110192838, + 5.7837465564738295, + 5.691919191919192, + 5.607438016528926, + 5.53030303030303, + 5.460514233241506, + 5.398071625344352, + 5.3429752066115705, + 5.2952249770431585, + 5.254820936639119, + 5.221763085399449, + 5.196051423324151, + 5.177685950413223, + 5.166666666666667, + 5.162993572084481, + 5.166666666666667, + 5.177685950413223, + 5.196051423324151, + 5.221763085399449, + 5.254820936639119, + 5.2952249770431585, + 5.342975206611571, + 5.398071625344353, + 5.460514233241506, + 5.530303030303031, + 5.607438016528926, + 5.691919191919192, + 5.7837465564738295, + 5.882920110192838, + 5.989439853076217, + 6.1033057851239665, + 6.2245179063360885, + 6.35307621671258, + 6.488980716253443, + 6.632231404958677, + 6.782828282828282, + 6.94077134986226, + 7.106060606060607, + 7.278696051423326, + 7.4586776859504145, + 7.646005509641874, + 7.840679522497705, + 8.042699724517908, + 8.25206611570248, + 8.468778696051423, + 8.69283746556474, + 8.924242424242424, + 9.162993572084481 + ], + [ + 21.01239669421488, + 20.531221303948577, + 20.05739210284665, + 19.590909090909093, + 19.131772268135904, + 18.67998163452709, + 18.235537190082646, + 17.798438934802572, + 17.36868686868687, + 16.946280991735538, + 16.531221303948577, + 16.123507805325985, + 15.723140495867767, + 15.33011937557392, + 14.944444444444443, + 14.566115702479339, + 14.195133149678604, + 13.83149678604224, + 13.475206611570249, + 13.126262626262626, + 12.784664830119375, + 12.450413223140496, + 12.123507805325985, + 11.80394857667585, + 11.491735537190081, + 11.186868686868687, + 10.889348025711662, + 10.599173553719007, + 10.316345270890725, + 10.040863177226814, + 9.772727272727272, + 9.511937557392102, + 9.258494031221304, + 9.012396694214877, + 8.77364554637282, + 8.542240587695133, + 8.318181818181818, + 8.101469237832873, + 7.892102846648301, + 7.690082644628099, + 7.495408631772268, + 7.308080808080808, + 7.12809917355372, + 6.955463728191001, + 6.790174471992653, + 6.632231404958677, + 6.4816345270890725, + 6.338383838383838, + 6.202479338842975, + 6.073921028466483, + 5.952708907254362, + 5.838842975206612, + 5.732323232323233, + 5.633149678604224, + 5.541322314049586, + 5.45684113865932, + 5.379706152433425, + 5.309917355371901, + 5.247474747474747, + 5.192378328741965, + 5.144628099173554, + 5.104224058769513, + 5.071166207529844, + 5.045454545454545, + 5.0270890725436175, + 5.016069788797061, + 5.0123966942148765, + 5.016069788797061, + 5.027089072543618, + 5.045454545454545, + 5.071166207529844, + 5.104224058769513, + 5.144628099173554, + 5.192378328741966, + 5.247474747474747, + 5.309917355371901, + 5.3797061524334255, + 5.456841138659321, + 5.541322314049587, + 5.633149678604225, + 5.732323232323233, + 5.838842975206612, + 5.952708907254362, + 6.073921028466483, + 6.202479338842975, + 6.338383838383837, + 6.4816345270890725, + 6.632231404958677, + 6.790174471992655, + 6.955463728191003, + 7.128099173553721, + 7.30808080808081, + 7.4954086317722695, + 7.6900826446281005, + 7.892102846648303, + 8.101469237832875, + 8.318181818181818, + 8.542240587695135, + 8.77364554637282, + 9.012396694214877 + ], + [ + 20.86547291092746, + 20.384297520661157, + 19.91046831955923, + 19.443985307621674, + 18.984848484848488, + 18.53305785123967, + 18.088613406795226, + 17.651515151515152, + 17.22176308539945, + 16.799357208448118, + 16.384297520661157, + 15.976584022038566, + 15.576216712580347, + 15.1831955922865, + 14.797520661157023, + 14.419191919191919, + 14.048209366391184, + 13.68457300275482, + 13.328282828282829, + 12.979338842975206, + 12.637741046831955, + 12.303489439853077, + 11.976584022038566, + 11.65702479338843, + 11.344811753902663, + 11.039944903581269, + 10.742424242424242, + 10.452249770431589, + 10.169421487603305, + 9.893939393939394, + 9.625803489439853, + 9.365013774104682, + 9.111570247933884, + 8.865472910927457, + 8.6267217630854, + 8.395316804407713, + 8.1712580348944, + 7.954545454545454, + 7.745179063360881, + 7.543158861340679, + 7.348484848484849, + 7.161157024793388, + 6.9811753902663, + 6.808539944903582, + 6.643250688705233, + 6.485307621671257, + 6.3347107438016526, + 6.191460055096419, + 6.055555555555555, + 5.926997245179063, + 5.805785123966942, + 5.691919191919192, + 5.585399449035814, + 5.486225895316805, + 5.394398530762167, + 5.309917355371901, + 5.232782369146006, + 5.162993572084481, + 5.1005509641873275, + 5.045454545454546, + 4.997704315886134, + 4.957300275482094, + 4.924242424242424, + 4.898530762167126, + 4.880165289256198, + 4.869146005509642, + 4.865472910927457, + 4.869146005509642, + 4.880165289256198, + 4.898530762167126, + 4.924242424242424, + 4.957300275482094, + 4.997704315886134, + 5.045454545454547, + 5.100550964187328, + 5.162993572084481, + 5.2327823691460065, + 5.309917355371901, + 5.394398530762167, + 5.486225895316805, + 5.585399449035814, + 5.691919191919192, + 5.805785123966942, + 5.926997245179064, + 6.055555555555555, + 6.191460055096418, + 6.3347107438016526, + 6.485307621671257, + 6.643250688705237, + 6.808539944903583, + 6.981175390266301, + 7.16115702479339, + 7.3484848484848495, + 7.543158861340681, + 7.745179063360883, + 7.954545454545457, + 8.1712580348944, + 8.395316804407715, + 8.6267217630854, + 8.865472910927457 + ], + [ + 20.72222222222222, + 20.24104683195592, + 19.767217630853995, + 19.300734618916437, + 18.84159779614325, + 18.389807162534435, + 17.94536271808999, + 17.508264462809915, + 17.078512396694215, + 16.656106519742885, + 16.241046831955924, + 15.83333333333333, + 15.432966023875112, + 15.039944903581265, + 14.65426997245179, + 14.275941230486684, + 13.90495867768595, + 13.541322314049586, + 13.185032139577594, + 12.836088154269971, + 12.49449035812672, + 12.160238751147842, + 11.833333333333332, + 11.513774104683193, + 11.201561065197428, + 10.896694214876032, + 10.599173553719009, + 10.308999081726354, + 10.02617079889807, + 9.75068870523416, + 9.482552800734616, + 9.221763085399449, + 8.96831955922865, + 8.722222222222221, + 8.483471074380166, + 8.25206611570248, + 8.028007346189163, + 7.811294765840219, + 7.601928374655646, + 7.399908172635444, + 7.2052341597796135, + 7.017906336088153, + 6.8379247015610645, + 6.665289256198347, + 6.499999999999998, + 6.342056932966022, + 6.191460055096417, + 6.048209366391184, + 5.91230486685032, + 5.783746556473828, + 5.662534435261707, + 5.548668503213957, + 5.4421487603305785, + 5.34297520661157, + 5.251147842056932, + 5.166666666666666, + 5.08953168044077, + 5.019742883379246, + 4.957300275482092, + 4.902203856749311, + 4.854453627180899, + 4.814049586776859, + 4.780991735537189, + 4.755280073461891, + 4.736914600550963, + 4.725895316804407, + 4.722222222222221, + 4.725895316804407, + 4.736914600550963, + 4.755280073461891, + 4.780991735537189, + 4.814049586776859, + 4.854453627180899, + 4.902203856749312, + 4.957300275482093, + 5.019742883379246, + 5.089531680440771, + 5.166666666666666, + 5.251147842056932, + 5.34297520661157, + 5.4421487603305785, + 5.548668503213957, + 5.662534435261707, + 5.783746556473829, + 5.91230486685032, + 6.048209366391183, + 6.191460055096417, + 6.342056932966022, + 6.5, + 6.6652892561983474, + 6.837924701561066, + 7.017906336088155, + 7.205234159779614, + 7.399908172635445, + 7.601928374655648, + 7.81129476584022, + 8.028007346189163, + 8.25206611570248, + 8.483471074380164, + 8.722222222222221 + ], + [ + 20.582644628099175, + 20.101469237832873, + 19.627640036730945, + 19.16115702479339, + 18.702020202020204, + 18.250229568411385, + 17.805785123966942, + 17.36868686868687, + 16.938934802571165, + 16.516528925619834, + 16.101469237832873, + 15.693755739210282, + 15.293388429752063, + 14.900367309458217, + 14.51469237832874, + 14.136363636363635, + 13.7653810835629, + 13.401744719926537, + 13.045454545454545, + 12.696510560146923, + 12.354912764003672, + 12.020661157024794, + 11.693755739210282, + 11.374196510560147, + 11.06198347107438, + 10.757116620752985, + 10.459595959595958, + 10.169421487603305, + 9.886593204775021, + 9.61111111111111, + 9.34297520661157, + 9.082185491276398, + 8.8287419651056, + 8.582644628099173, + 8.343893480257115, + 8.11248852157943, + 7.8884297520661155, + 7.67171717171717, + 7.4623507805325975, + 7.260330578512395, + 7.065656565656565, + 6.878328741965104, + 6.698347107438016, + 6.525711662075298, + 6.36042240587695, + 6.2024793388429735, + 6.051882460973369, + 5.908631772268135, + 5.772727272727272, + 5.644168962350779, + 5.522956841138658, + 5.409090909090908, + 5.30257116620753, + 5.203397612488521, + 5.111570247933884, + 5.0270890725436175, + 4.949954086317722, + 4.8801652892561975, + 4.817722681359044, + 4.762626262626262, + 4.71487603305785, + 4.67447199265381, + 4.64141414141414, + 4.615702479338842, + 4.597337006427915, + 4.5863177226813585, + 4.582644628099173, + 4.5863177226813585, + 4.597337006427915, + 4.615702479338842, + 4.64141414141414, + 4.67447199265381, + 4.71487603305785, + 4.762626262626263, + 4.817722681359045, + 4.8801652892561975, + 4.949954086317723, + 5.0270890725436175, + 5.111570247933884, + 5.203397612488521, + 5.30257116620753, + 5.409090909090908, + 5.522956841138658, + 5.64416896235078, + 5.772727272727272, + 5.9086317722681345, + 6.051882460973369, + 6.2024793388429735, + 6.360422405876953, + 6.525711662075299, + 6.698347107438018, + 6.878328741965106, + 7.065656565656566, + 7.260330578512397, + 7.462350780532599, + 7.671717171717173, + 7.888429752066116, + 8.112488521579431, + 8.343893480257115, + 8.582644628099173 + ], + [ + 20.44674012855831, + 19.96556473829201, + 19.491735537190085, + 19.025252525252526, + 18.56611570247934, + 18.11432506887052, + 17.669880624426078, + 17.232782369146005, + 16.803030303030305, + 16.38062442607897, + 15.965564738292013, + 15.557851239669418, + 15.1574839302112, + 14.764462809917354, + 14.378787878787877, + 14.000459136822773, + 13.629476584022038, + 13.265840220385675, + 12.909550045913683, + 12.56060606060606, + 12.21900826446281, + 11.88475665748393, + 11.557851239669422, + 11.238292011019283, + 10.926078971533517, + 10.621212121212121, + 10.323691460055096, + 10.033516988062441, + 9.75068870523416, + 9.475206611570247, + 9.207070707070706, + 8.946280991735536, + 8.692837465564738, + 8.44674012855831, + 8.207988980716253, + 7.976584022038567, + 7.752525252525253, + 7.5358126721763075, + 7.326446280991735, + 7.124426078971533, + 6.929752066115702, + 6.742424242424242, + 6.562442607897153, + 6.389807162534435, + 6.224517906336087, + 6.0665748393021115, + 5.915977961432506, + 5.772727272727272, + 5.63682277318641, + 5.508264462809917, + 5.387052341597796, + 5.273186409550046, + 5.166666666666666, + 5.067493112947657, + 4.97566574839302, + 4.891184573002754, + 4.814049586776859, + 4.744260789715335, + 4.681818181818182, + 4.626721763085399, + 4.578971533516987, + 4.5385674931129465, + 4.505509641873278, + 4.479797979797979, + 4.461432506887052, + 4.450413223140496, + 4.44674012855831, + 4.450413223140496, + 4.461432506887052, + 4.479797979797979, + 4.505509641873278, + 4.5385674931129465, + 4.578971533516987, + 4.626721763085399, + 4.681818181818182, + 4.7442607897153355, + 4.814049586776859, + 4.8911845730027546, + 4.975665748393022, + 5.067493112947658, + 5.166666666666666, + 5.273186409550046, + 5.387052341597796, + 5.508264462809917, + 5.636822773186409, + 5.772727272727272, + 5.915977961432506, + 6.066574839302111, + 6.224517906336089, + 6.389807162534435, + 6.562442607897154, + 6.742424242424242, + 6.929752066115704, + 7.124426078971535, + 7.3264462809917354, + 7.535812672176309, + 7.752525252525253, + 7.976584022038569, + 8.207988980716252, + 8.44674012855831 + ], + [ + 20.31450872359963, + 19.833333333333332, + 19.359504132231407, + 18.89302112029385, + 18.433884297520663, + 17.982093663911844, + 17.5376492194674, + 17.100550964187327, + 16.670798898071624, + 16.248393021120293, + 15.833333333333332, + 15.42561983471074, + 15.025252525252522, + 14.632231404958675, + 14.2465564738292, + 13.868227731864094, + 13.497245179063361, + 13.133608815426996, + 12.777318640955006, + 12.428374655647382, + 12.086776859504132, + 11.752525252525253, + 11.425619834710742, + 11.106060606060606, + 10.79384756657484, + 10.488980716253444, + 10.191460055096417, + 9.901285583103764, + 9.618457300275482, + 9.34297520661157, + 9.074839302112029, + 8.814049586776859, + 8.560606060606059, + 8.314508723599632, + 8.075757575757574, + 7.84435261707989, + 7.620293847566575, + 7.403581267217629, + 7.194214876033056, + 6.992194674012855, + 6.797520661157025, + 6.610192837465564, + 6.430211202938475, + 6.257575757575758, + 6.092286501377409, + 5.934343434343433, + 5.783746556473828, + 5.640495867768594, + 5.504591368227731, + 5.376033057851239, + 5.254820936639118, + 5.140955004591368, + 5.034435261707989, + 4.93526170798898, + 4.8434343434343425, + 4.758953168044076, + 4.681818181818182, + 4.6120293847566565, + 4.5495867768595035, + 4.494490358126722, + 4.44674012855831, + 4.406336088154269, + 4.3732782369146, + 4.347566574839302, + 4.3292011019283745, + 4.3181818181818175, + 4.314508723599632, + 4.3181818181818175, + 4.3292011019283745, + 4.347566574839302, + 4.3732782369146, + 4.406336088154269, + 4.44674012855831, + 4.494490358126722, + 4.549586776859504, + 4.612029384756657, + 4.681818181818182, + 4.758953168044076, + 4.843434343434343, + 4.93526170798898, + 5.034435261707989, + 5.140955004591368, + 5.254820936639118, + 5.37603305785124, + 5.5045913682277305, + 5.640495867768594, + 5.783746556473828, + 5.9343434343434325, + 6.092286501377412, + 6.257575757575758, + 6.430211202938477, + 6.610192837465565, + 6.797520661157025, + 6.992194674012856, + 7.194214876033058, + 7.403581267217632, + 7.620293847566575, + 7.84435261707989, + 8.075757575757574, + 8.314508723599632 + ], + [ + 20.18595041322314, + 19.70477502295684, + 19.230945821854913, + 18.764462809917354, + 18.305325987144172, + 17.853535353535353, + 17.40909090909091, + 16.971992653810837, + 16.542240587695133, + 16.119834710743802, + 15.704775022956841, + 15.29706152433425, + 14.896694214876032, + 14.503673094582183, + 14.117998163452707, + 13.739669421487601, + 13.368686868686869, + 13.005050505050505, + 12.648760330578513, + 12.29981634527089, + 11.95821854912764, + 11.62396694214876, + 11.29706152433425, + 10.977502295684113, + 10.665289256198346, + 10.36042240587695, + 10.062901744719927, + 9.772727272727272, + 9.48989898989899, + 9.214416896235077, + 8.946280991735536, + 8.685491276400366, + 8.432047750229568, + 8.18595041322314, + 7.947199265381084, + 7.715794306703398, + 7.491735537190083, + 7.275022956841138, + 7.065656565656565, + 6.863636363636363, + 6.668962350780532, + 6.4816345270890725, + 6.301652892561983, + 6.129017447199265, + 5.963728191000917, + 5.805785123966942, + 5.655188246097336, + 5.511937557392102, + 5.37603305785124, + 5.247474747474747, + 5.126262626262626, + 5.0123966942148765, + 4.905876951331496, + 4.8067033976124875, + 4.71487603305785, + 4.630394857667584, + 4.553259871441689, + 4.483471074380165, + 4.421028466483012, + 4.3659320477502295, + 4.3181818181818175, + 4.277777777777777, + 4.244719926538108, + 4.2190082644628095, + 4.200642791551882, + 4.189623507805326, + 4.18595041322314, + 4.189623507805326, + 4.200642791551882, + 4.2190082644628095, + 4.244719926538108, + 4.277777777777777, + 4.3181818181818175, + 4.3659320477502295, + 4.421028466483012, + 4.483471074380166, + 4.553259871441689, + 4.630394857667585, + 4.714876033057852, + 4.806703397612488, + 4.905876951331496, + 5.0123966942148765, + 5.126262626262626, + 5.247474747474747, + 5.376033057851239, + 5.511937557392102, + 5.655188246097336, + 5.805785123966941, + 5.96372819100092, + 6.129017447199266, + 6.301652892561986, + 6.481634527089074, + 6.668962350780532, + 6.863636363636363, + 7.0656565656565675, + 7.2750229568411395, + 7.491735537190083, + 7.715794306703398, + 7.947199265381084, + 8.18595041322314 + ], + [ + 20.06106519742883, + 19.579889807162534, + 19.10606060606061, + 18.63957759412305, + 18.180440771349865, + 17.728650137741045, + 17.284205693296602, + 16.84710743801653, + 16.417355371900825, + 15.994949494949495, + 15.579889807162534, + 15.172176308539942, + 14.771808999081724, + 14.378787878787877, + 13.993112947658402, + 13.614784205693296, + 13.243801652892563, + 12.880165289256198, + 12.523875114784207, + 12.174931129476583, + 11.833333333333334, + 11.499081726354454, + 11.172176308539944, + 10.852617079889807, + 10.540404040404042, + 10.235537190082646, + 9.938016528925619, + 9.647842056932966, + 9.365013774104684, + 9.089531680440771, + 8.82139577594123, + 8.56060606060606, + 8.30716253443526, + 8.061065197428833, + 7.822314049586777, + 7.590909090909092, + 7.366850321395777, + 7.150137741046831, + 6.940771349862258, + 6.7387511478420565, + 6.544077134986226, + 6.356749311294766, + 6.1767676767676765, + 6.004132231404959, + 5.83884297520661, + 5.680899908172635, + 5.530303030303029, + 5.387052341597796, + 5.251147842056933, + 5.122589531680441, + 5.0013774104683195, + 4.88751147842057, + 4.7809917355371905, + 4.681818181818182, + 4.589990817263544, + 4.505509641873278, + 4.428374655647383, + 4.358585858585858, + 4.296143250688705, + 4.241046831955924, + 4.193296602387512, + 4.152892561983471, + 4.119834710743802, + 4.094123048668504, + 4.075757575757576, + 4.064738292011019, + 4.061065197428833, + 4.064738292011019, + 4.075757575757576, + 4.094123048668504, + 4.119834710743802, + 4.152892561983471, + 4.193296602387512, + 4.241046831955924, + 4.296143250688706, + 4.358585858585859, + 4.428374655647383, + 4.505509641873278, + 4.589990817263545, + 4.681818181818182, + 4.7809917355371905, + 4.88751147842057, + 5.0013774104683195, + 5.1225895316804415, + 5.251147842056932, + 5.387052341597796, + 5.530303030303029, + 5.680899908172634, + 5.838842975206614, + 6.004132231404959, + 6.176767676767678, + 6.356749311294767, + 6.544077134986226, + 6.738751147842057, + 6.94077134986226, + 7.150137741046834, + 7.366850321395777, + 7.590909090909092, + 7.822314049586776, + 8.061065197428833 + ], + [ + 19.939853076216714, + 19.458677685950413, + 18.984848484848484, + 18.51836547291093, + 18.059228650137744, + 17.607438016528924, + 17.16299357208448, + 16.725895316804408, + 16.296143250688704, + 15.873737373737374, + 15.458677685950413, + 15.050964187327821, + 14.650596877869603, + 14.257575757575756, + 13.871900826446279, + 13.493572084481174, + 13.12258953168044, + 12.758953168044076, + 12.402662993572086, + 12.053719008264462, + 11.712121212121211, + 11.377869605142333, + 11.050964187327823, + 10.731404958677686, + 10.419191919191919, + 10.114325068870524, + 9.816804407713498, + 9.526629935720845, + 9.24380165289256, + 8.96831955922865, + 8.70018365472911, + 8.43939393939394, + 8.18595041322314, + 7.939853076216712, + 7.701101928374656, + 7.469696969696971, + 7.245638200183655, + 7.02892561983471, + 6.819559228650137, + 6.617539026629935, + 6.422865013774104, + 6.235537190082645, + 6.055555555555555, + 5.882920110192838, + 5.717630853994489, + 5.559687786960513, + 5.409090909090908, + 5.265840220385675, + 5.129935720844811, + 5.0013774104683195, + 4.880165289256198, + 4.766299357208448, + 4.659779614325069, + 4.5606060606060606, + 4.468778696051423, + 4.384297520661157, + 4.307162534435262, + 4.237373737373737, + 4.174931129476584, + 4.119834710743802, + 4.07208448117539, + 4.03168044077135, + 3.9986225895316805, + 3.9729109274563816, + 3.9545454545454546, + 3.943526170798898, + 3.9398530762167123, + 3.943526170798898, + 3.9545454545454546, + 3.9729109274563816, + 3.9986225895316805, + 4.03168044077135, + 4.07208448117539, + 4.1198347107438025, + 4.174931129476584, + 4.237373737373738, + 4.307162534435262, + 4.384297520661157, + 4.468778696051424, + 4.5606060606060606, + 4.659779614325069, + 4.766299357208449, + 4.880165289256198, + 5.0013774104683195, + 5.129935720844811, + 5.265840220385674, + 5.409090909090908, + 5.559687786960513, + 5.717630853994492, + 5.882920110192838, + 6.055555555555557, + 6.2355371900826455, + 6.422865013774105, + 6.617539026629936, + 6.819559228650139, + 7.0289256198347125, + 7.245638200183656, + 7.469696969696971, + 7.701101928374655, + 7.939853076216712 + ], + [ + 19.82231404958678, + 19.341138659320478, + 18.86730945821855, + 18.400826446280995, + 17.941689623507806, + 17.48989898989899, + 17.045454545454547, + 16.608356290174473, + 16.17860422405877, + 15.75619834710744, + 15.341138659320478, + 14.933425160697887, + 14.533057851239668, + 14.14003673094582, + 13.754361799816344, + 13.376033057851238, + 13.005050505050505, + 12.641414141414142, + 12.28512396694215, + 11.936179981634528, + 11.594582185491277, + 11.260330578512397, + 10.933425160697887, + 10.61386593204775, + 10.301652892561982, + 9.996786042240588, + 9.699265381083563, + 9.409090909090908, + 9.126262626262626, + 8.850780532598716, + 8.582644628099173, + 8.321854912764003, + 8.068411386593205, + 7.822314049586777, + 7.58356290174472, + 7.352157943067034, + 7.12809917355372, + 6.911386593204774, + 6.7020202020202015, + 6.5, + 6.305325987144169, + 6.117998163452709, + 5.938016528925621, + 5.765381083562902, + 5.600091827364555, + 5.4421487603305785, + 5.291551882460973, + 5.1483011937557395, + 5.0123966942148765, + 4.883838383838384, + 4.762626262626263, + 4.648760330578513, + 4.542240587695134, + 4.443067033976124, + 4.351239669421488, + 4.2667584940312215, + 4.189623507805326, + 4.1198347107438025, + 4.057392102846649, + 4.002295684113866, + 3.9545454545454546, + 3.9141414141414144, + 3.881083562901745, + 3.855371900826446, + 3.837006427915519, + 3.8259871441689626, + 3.822314049586777, + 3.8259871441689626, + 3.837006427915519, + 3.855371900826446, + 3.881083562901745, + 3.9141414141414144, + 3.9545454545454546, + 4.002295684113867, + 4.057392102846649, + 4.1198347107438025, + 4.189623507805327, + 4.2667584940312215, + 4.3512396694214885, + 4.443067033976125, + 4.542240587695134, + 4.648760330578513, + 4.762626262626263, + 4.883838383838384, + 5.012396694214876, + 5.148301193755739, + 5.291551882460973, + 5.442148760330578, + 5.600091827364556, + 5.765381083562903, + 5.938016528925622, + 6.117998163452711, + 6.305325987144171, + 6.500000000000002, + 6.702020202020204, + 6.911386593204776, + 7.12809917355372, + 7.352157943067036, + 7.58356290174472, + 7.822314049586778 + ], + [ + 19.708448117539028, + 19.227272727272727, + 18.7534435261708, + 18.286960514233243, + 17.827823691460058, + 17.376033057851238, + 16.931588613406795, + 16.494490358126722, + 16.064738292011018, + 15.642332415059688, + 15.227272727272727, + 14.819559228650135, + 14.419191919191917, + 14.02617079889807, + 13.640495867768593, + 13.262167125803488, + 12.891184573002754, + 12.52754820936639, + 12.1712580348944, + 11.822314049586776, + 11.480716253443525, + 11.146464646464647, + 10.819559228650137, + 10.5, + 10.187786960514233, + 9.882920110192838, + 9.585399449035812, + 9.295224977043159, + 9.012396694214875, + 8.736914600550964, + 8.468778696051423, + 8.207988980716253, + 7.954545454545454, + 7.708448117539026, + 7.46969696969697, + 7.2382920110192845, + 7.014233241505969, + 6.797520661157024, + 6.588154269972451, + 6.386134067952249, + 6.191460055096418, + 6.0041322314049586, + 5.824150596877869, + 5.651515151515151, + 5.486225895316803, + 5.328282828282827, + 5.177685950413222, + 5.034435261707989, + 4.898530762167125, + 4.7699724517906334, + 4.648760330578512, + 4.534894398530762, + 4.428374655647383, + 4.3292011019283745, + 4.237373737373737, + 4.152892561983471, + 4.075757575757575, + 4.005968778696051, + 3.943526170798898, + 3.8884297520661155, + 3.840679522497704, + 3.8002754820936637, + 3.7672176308539944, + 3.7415059687786956, + 3.7231404958677685, + 3.712121212121212, + 3.7084481175390263, + 3.712121212121212, + 3.7231404958677685, + 3.7415059687786956, + 3.7672176308539944, + 3.8002754820936637, + 3.840679522497704, + 3.8884297520661164, + 3.943526170798898, + 4.005968778696052, + 4.075757575757576, + 4.152892561983471, + 4.237373737373738, + 4.3292011019283745, + 4.428374655647383, + 4.534894398530763, + 4.648760330578512, + 4.7699724517906334, + 4.898530762167125, + 5.034435261707988, + 5.177685950413222, + 5.328282828282827, + 5.486225895316806, + 5.651515151515152, + 5.824150596877871, + 6.004132231404959, + 6.191460055096419, + 6.38613406795225, + 6.588154269972453, + 6.7975206611570265, + 7.01423324150597, + 7.2382920110192845, + 7.469696969696969, + 7.708448117539026 + ], + [ + 19.59825528007346, + 19.11707988980716, + 18.643250688705237, + 18.17676767676768, + 17.717630853994493, + 17.265840220385673, + 16.82139577594123, + 16.384297520661157, + 15.954545454545453, + 15.532139577594123, + 15.117079889807162, + 14.70936639118457, + 14.308999081726352, + 13.915977961432505, + 13.53030303030303, + 13.151974288337923, + 12.78099173553719, + 12.417355371900825, + 12.061065197428835, + 11.712121212121211, + 11.370523415977962, + 11.036271808999082, + 10.709366391184572, + 10.389807162534435, + 10.077594123048668, + 9.772727272727273, + 9.475206611570249, + 9.185032139577594, + 8.902203856749312, + 8.6267217630854, + 8.358585858585858, + 8.097796143250688, + 7.844352617079889, + 7.598255280073461, + 7.359504132231405, + 7.12809917355372, + 6.904040404040405, + 6.687327823691459, + 6.477961432506886, + 6.275941230486684, + 6.081267217630854, + 5.893939393939394, + 5.713957759412304, + 5.541322314049587, + 5.376033057851239, + 5.218089990817263, + 5.067493112947657, + 4.924242424242424, + 4.788337924701561, + 4.6597796143250685, + 4.538567493112947, + 4.424701561065198, + 4.318181818181818, + 4.2190082644628095, + 4.127180899908172, + 4.042699724517906, + 3.9655647382920107, + 3.8957759412304864, + 3.833333333333333, + 3.778236914600551, + 3.7304866850321394, + 3.6900826446280988, + 3.6570247933884295, + 3.631313131313131, + 3.6129476584022036, + 3.601928374655647, + 3.5982552800734617, + 3.601928374655647, + 3.612947658402204, + 3.631313131313131, + 3.6570247933884295, + 3.6900826446280988, + 3.7304866850321394, + 3.7782369146005514, + 3.8333333333333335, + 3.895775941230487, + 3.965564738292011, + 4.042699724517906, + 4.127180899908173, + 4.2190082644628095, + 4.318181818181818, + 4.424701561065198, + 4.538567493112947, + 4.659779614325069, + 4.78833792470156, + 4.924242424242424, + 5.067493112947657, + 5.218089990817262, + 5.376033057851242, + 5.541322314049587, + 5.713957759412306, + 5.8939393939393945, + 6.081267217630854, + 6.275941230486685, + 6.477961432506888, + 6.6873278236914615, + 6.904040404040405, + 7.12809917355372, + 7.359504132231404, + 7.598255280073461 + ], + [ + 19.49173553719008, + 19.010560146923783, + 18.53673094582186, + 18.070247933884296, + 17.611111111111114, + 17.159320477502295, + 16.714876033057852, + 16.27777777777778, + 15.848025711662075, + 15.425619834710744, + 15.010560146923783, + 14.602846648301192, + 14.202479338842974, + 13.809458218549127, + 13.42378328741965, + 13.045454545454545, + 12.67447199265381, + 12.310835629017447, + 11.954545454545455, + 11.605601469237833, + 11.264003673094582, + 10.929752066115702, + 10.602846648301192, + 10.283287419651057, + 9.97107438016529, + 9.666207529843893, + 9.368686868686869, + 9.078512396694215, + 8.795684113865931, + 8.52020202020202, + 8.25206611570248, + 7.991276400367309, + 7.73783287419651, + 7.491735537190083, + 7.2529843893480255, + 7.02157943067034, + 6.797520661157026, + 6.5808080808080796, + 6.3714416896235075, + 6.169421487603305, + 5.974747474747474, + 5.787419651056014, + 5.607438016528926, + 5.434802571166208, + 5.26951331496786, + 5.111570247933884, + 4.960973370064279, + 4.817722681359045, + 4.681818181818182, + 4.553259871441689, + 4.432047750229568, + 4.318181818181818, + 4.211662075298439, + 4.11248852157943, + 4.020661157024794, + 3.9361799816345266, + 3.859044995408632, + 3.7892561983471076, + 3.726813590449954, + 3.6717171717171717, + 3.62396694214876, + 3.58356290174472, + 3.55050505050505, + 3.524793388429752, + 3.5064279155188247, + 3.495408631772268, + 3.491735537190083, + 3.495408631772268, + 3.5064279155188247, + 3.524793388429752, + 3.55050505050505, + 3.5835629017447195, + 3.62396694214876, + 3.671717171717172, + 3.7268135904499546, + 3.7892561983471076, + 3.859044995408632, + 3.9361799816345275, + 4.020661157024794, + 4.112488521579431, + 4.211662075298439, + 4.318181818181818, + 4.432047750229568, + 4.55325987144169, + 4.681818181818182, + 4.817722681359045, + 4.960973370064279, + 5.111570247933884, + 5.269513314967862, + 5.434802571166209, + 5.607438016528928, + 5.787419651056016, + 5.974747474747476, + 6.169421487603307, + 6.371441689623509, + 6.580808080808081, + 6.797520661157025, + 7.021579430670341, + 7.2529843893480255, + 7.491735537190083 + ], + [ + 19.38888888888889, + 18.90771349862259, + 18.433884297520663, + 17.967401285583104, + 17.50826446280992, + 17.0564738292011, + 16.612029384756656, + 16.174931129476583, + 15.745179063360881, + 15.322773186409549, + 14.90771349862259, + 14.499999999999996, + 14.099632690541778, + 13.706611570247933, + 13.320936639118456, + 12.942607897153351, + 12.571625344352617, + 12.207988980716253, + 11.851698806244261, + 11.502754820936639, + 11.161157024793388, + 10.826905417814508, + 10.5, + 10.180440771349861, + 9.868227731864096, + 9.5633608815427, + 9.265840220385675, + 8.97566574839302, + 8.692837465564738, + 8.417355371900825, + 8.149219467401284, + 7.888429752066115, + 7.634986225895316, + 7.388888888888888, + 7.150137741046832, + 6.918732782369146, + 6.694674012855831, + 6.477961432506886, + 6.268595041322313, + 6.0665748393021115, + 5.87190082644628, + 5.684573002754821, + 5.504591368227731, + 5.3319559228650135, + 5.166666666666666, + 5.00872359963269, + 4.858126721763084, + 4.714876033057851, + 4.578971533516988, + 4.450413223140496, + 4.3292011019283745, + 4.215335169880625, + 4.1088154269972454, + 4.009641873278236, + 3.917814508723599, + 3.833333333333333, + 3.7561983471074374, + 3.686409550045913, + 3.62396694214876, + 3.5688705234159777, + 3.521120293847566, + 3.480716253443526, + 3.4476584022038566, + 3.4219467401285577, + 3.4035812672176307, + 3.392561983471074, + 3.3888888888888884, + 3.392561983471074, + 3.4035812672176307, + 3.4219467401285577, + 3.4476584022038566, + 3.480716253443526, + 3.521120293847566, + 3.5688705234159785, + 3.62396694214876, + 3.686409550045914, + 3.7561983471074383, + 3.833333333333333, + 3.9178145087236, + 4.009641873278237, + 4.1088154269972454, + 4.215335169880625, + 4.3292011019283745, + 4.450413223140496, + 4.578971533516987, + 4.71487603305785, + 4.858126721763084, + 5.008723599632689, + 5.166666666666668, + 5.331955922865014, + 5.504591368227733, + 5.684573002754822, + 5.871900826446282, + 6.066574839302113, + 6.268595041322316, + 6.477961432506888, + 6.694674012855831, + 6.918732782369148, + 7.150137741046832, + 7.388888888888889 + ], + [ + 19.28971533516988, + 18.80853994490358, + 18.334710743801654, + 17.868227731864096, + 17.40909090909091, + 16.957300275482094, + 16.512855831037648, + 16.075757575757574, + 15.646005509641874, + 15.223599632690542, + 14.808539944903583, + 14.40082644628099, + 14.000459136822771, + 13.607438016528924, + 13.221763085399449, + 12.843434343434343, + 12.47245179063361, + 12.108815426997245, + 11.752525252525253, + 11.40358126721763, + 11.06198347107438, + 10.727731864095501, + 10.400826446280991, + 10.081267217630852, + 9.769054178145087, + 9.46418732782369, + 9.166666666666668, + 8.876492194674013, + 8.593663911845729, + 8.318181818181818, + 8.050045913682276, + 7.789256198347107, + 7.535812672176308, + 7.2897153351698805, + 7.050964187327824, + 6.819559228650138, + 6.595500459136823, + 6.378787878787878, + 6.169421487603305, + 5.967401285583103, + 5.7727272727272725, + 5.585399449035813, + 5.4054178145087235, + 5.232782369146006, + 5.067493112947657, + 4.909550045913681, + 4.758953168044076, + 4.615702479338843, + 4.479797979797979, + 4.351239669421488, + 4.2300275482093666, + 4.116161616161616, + 4.0096418732782375, + 3.910468319559228, + 3.818640955004591, + 3.7341597796143247, + 3.6570247933884295, + 3.587235996326905, + 3.524793388429752, + 3.4696969696969697, + 3.4219467401285577, + 3.3815426997245175, + 3.348484848484848, + 3.3227731864095498, + 3.3044077134986223, + 3.293388429752066, + 3.2897153351698805, + 3.293388429752066, + 3.3044077134986223, + 3.3227731864095498, + 3.348484848484848, + 3.3815426997245175, + 3.4219467401285577, + 3.46969696969697, + 3.524793388429752, + 3.5872359963269056, + 3.65702479338843, + 3.734159779614325, + 3.818640955004591, + 3.9104683195592287, + 4.0096418732782375, + 4.116161616161616, + 4.230027548209366, + 4.351239669421488, + 4.479797979797979, + 4.615702479338842, + 4.758953168044076, + 4.909550045913681, + 5.06749311294766, + 5.2327823691460065, + 5.405417814508725, + 5.585399449035814, + 5.772727272727273, + 5.9674012855831045, + 6.169421487603307, + 6.378787878787879, + 6.595500459136822, + 6.819559228650139, + 7.050964187327823, + 7.2897153351698805 + ], + [ + 19.194214876033058, + 18.713039485766757, + 18.239210284664832, + 17.772727272727273, + 17.313590449954088, + 16.86179981634527, + 16.417355371900825, + 15.980257116620752, + 15.550505050505052, + 15.128099173553718, + 14.71303948576676, + 14.305325987144167, + 13.904958677685949, + 13.511937557392102, + 13.126262626262625, + 12.74793388429752, + 12.376951331496786, + 12.013314967860422, + 11.65702479338843, + 11.308080808080808, + 10.966483011937557, + 10.632231404958677, + 10.305325987144169, + 9.98576675849403, + 9.673553719008265, + 9.368686868686869, + 9.071166207529844, + 8.780991735537189, + 8.498163452708907, + 8.222681359044996, + 7.954545454545453, + 7.693755739210284, + 7.440312213039485, + 7.194214876033058, + 6.955463728191001, + 6.724058769513315, + 6.5, + 6.283287419651055, + 6.073921028466483, + 5.87190082644628, + 5.677226813590449, + 5.48989898989899, + 5.309917355371901, + 5.137281910009182, + 4.971992653810835, + 4.814049586776859, + 4.663452708907254, + 4.52020202020202, + 4.384297520661157, + 4.2557392102846645, + 4.134527089072543, + 4.020661157024794, + 3.9141414141414144, + 3.8149678604224055, + 3.723140495867768, + 3.638659320477502, + 3.5615243342516067, + 3.4917355371900825, + 3.429292929292929, + 3.374196510560147, + 3.3264462809917354, + 3.286042240587695, + 3.2529843893480255, + 3.227272727272727, + 3.2089072543617996, + 3.197887970615243, + 3.1942148760330578, + 3.197887970615243, + 3.2089072543618, + 3.227272727272727, + 3.2529843893480255, + 3.286042240587695, + 3.3264462809917354, + 3.3741965105601475, + 3.4292929292929295, + 3.491735537190083, + 3.561524334251607, + 3.6386593204775024, + 3.723140495867769, + 3.8149678604224064, + 3.9141414141414144, + 4.020661157024794, + 4.134527089072543, + 4.2557392102846645, + 4.384297520661157, + 4.520202020202019, + 4.663452708907254, + 4.814049586776859, + 4.971992653810837, + 5.137281910009184, + 5.309917355371903, + 5.489898989898991, + 5.677226813590451, + 5.871900826446282, + 6.073921028466485, + 6.283287419651057, + 6.5, + 6.7240587695133165, + 6.955463728191001, + 7.194214876033058 + ], + [ + 19.10238751147842, + 18.62121212121212, + 18.147382920110196, + 17.680899908172634, + 17.221763085399452, + 16.769972451790633, + 16.32552800734619, + 15.888429752066116, + 15.458677685950413, + 15.036271808999082, + 14.621212121212121, + 14.21349862258953, + 13.813131313131311, + 13.420110192837464, + 13.034435261707987, + 12.656106519742883, + 12.285123966942148, + 11.921487603305785, + 11.565197428833793, + 11.21625344352617, + 10.87465564738292, + 10.54040404040404, + 10.21349862258953, + 9.893939393939394, + 9.581726354453627, + 9.276859504132231, + 8.979338842975206, + 8.689164370982553, + 8.40633608815427, + 8.130853994490359, + 7.862718089990817, + 7.601928374655647, + 7.348484848484848, + 7.102387511478421, + 6.863636363636363, + 6.632231404958678, + 6.408172635445363, + 6.191460055096417, + 5.982093663911845, + 5.780073461891643, + 5.585399449035812, + 5.398071625344352, + 5.218089990817264, + 5.045454545454546, + 4.8801652892561975, + 4.722222222222221, + 4.571625344352617, + 4.428374655647382, + 4.2924701561065195, + 4.163911845730027, + 4.042699724517906, + 3.928833792470156, + 3.822314049586777, + 3.723140495867768, + 3.631313131313131, + 3.5468319559228645, + 3.4696969696969697, + 3.3999081726354454, + 3.337465564738292, + 3.2823691460055096, + 3.234618916437098, + 3.1942148760330578, + 3.161157024793388, + 3.13544536271809, + 3.1170798898071626, + 3.106060606060606, + 3.1023875114784207, + 3.106060606060606, + 3.1170798898071626, + 3.13544536271809, + 3.161157024793388, + 3.1942148760330573, + 3.234618916437098, + 3.28236914600551, + 3.3374655647382925, + 3.3999081726354454, + 3.4696969696969697, + 3.5468319559228654, + 3.6313131313131315, + 3.723140495867769, + 3.822314049586777, + 3.928833792470156, + 4.042699724517906, + 4.163911845730028, + 4.2924701561065195, + 4.428374655647382, + 4.571625344352617, + 4.722222222222221, + 4.8801652892562, + 5.045454545454547, + 5.2180899908172655, + 5.398071625344354, + 5.585399449035814, + 5.780073461891645, + 5.982093663911847, + 6.191460055096419, + 6.4081726354453625, + 6.632231404958679, + 6.863636363636363, + 7.102387511478421 + ], + [ + 19.01423324150597, + 18.53305785123967, + 18.059228650137744, + 17.592745638200185, + 17.133608815427, + 16.68181818181818, + 16.237373737373737, + 15.800275482093664, + 15.370523415977962, + 14.94811753902663, + 14.53305785123967, + 14.125344352617077, + 13.724977043158859, + 13.331955922865014, + 12.946280991735536, + 12.567952249770432, + 12.196969696969697, + 11.833333333333334, + 11.477043158861342, + 11.12809917355372, + 10.786501377410469, + 10.452249770431589, + 10.125344352617079, + 9.805785123966942, + 9.493572084481176, + 9.18870523415978, + 8.891184573002755, + 8.6010101010101, + 8.318181818181818, + 8.042699724517906, + 7.774563820018365, + 7.513774104683195, + 7.260330578512397, + 7.014233241505969, + 6.775482093663912, + 6.544077134986226, + 6.320018365472912, + 6.1033057851239665, + 5.893939393939394, + 5.691919191919192, + 5.497245179063361, + 5.309917355371901, + 5.129935720844812, + 4.957300275482094, + 4.792011019283746, + 4.6340679522497705, + 4.483471074380165, + 4.340220385674931, + 4.204315886134068, + 4.075757575757576, + 3.954545454545455, + 3.8406795224977044, + 3.7341597796143255, + 3.6349862258953163, + 3.5431588613406797, + 3.458677685950413, + 3.381542699724518, + 3.3117539026629936, + 3.2493112947658407, + 3.194214876033058, + 3.146464646464646, + 3.106060606060606, + 3.0730027548209367, + 3.0472910927456383, + 3.0289256198347108, + 3.0179063360881546, + 3.014233241505969, + 3.0179063360881546, + 3.0289256198347108, + 3.0472910927456383, + 3.0730027548209367, + 3.106060606060606, + 3.146464646464646, + 3.1942148760330586, + 3.2493112947658407, + 3.311753902662994, + 3.3815426997245184, + 3.4586776859504136, + 3.54315886134068, + 3.634986225895317, + 3.734159779614325, + 3.8406795224977053, + 3.954545454545455, + 4.075757575757576, + 4.204315886134068, + 4.340220385674931, + 4.483471074380165, + 4.63406795224977, + 4.792011019283748, + 4.957300275482095, + 5.129935720844814, + 5.309917355371902, + 5.497245179063362, + 5.691919191919193, + 5.8939393939393945, + 6.103305785123968, + 6.320018365472912, + 6.544077134986228, + 6.775482093663911, + 7.01423324150597 + ], + [ + 18.929752066115704, + 18.448576675849402, + 17.974747474747474, + 17.50826446280992, + 17.049127640036733, + 16.597337006427914, + 16.15289256198347, + 15.715794306703398, + 15.286042240587694, + 14.863636363636363, + 14.448576675849402, + 14.04086317722681, + 13.640495867768593, + 13.247474747474746, + 12.86179981634527, + 12.483471074380164, + 12.112488521579431, + 11.748852157943066, + 11.392561983471076, + 11.043617998163452, + 10.702020202020202, + 10.367768595041323, + 10.040863177226813, + 9.721303948576676, + 9.409090909090908, + 9.104224058769514, + 8.80670339761249, + 8.516528925619834, + 8.233700642791552, + 7.95821854912764, + 7.690082644628099, + 7.429292929292929, + 7.17584940312213, + 6.929752066115702, + 6.691000918273645, + 6.45959595959596, + 6.2355371900826455, + 6.0188246097336995, + 5.809458218549127, + 5.607438016528925, + 5.412764003673095, + 5.225436179981634, + 5.045454545454545, + 4.872819100091828, + 4.70752984389348, + 4.5495867768595035, + 4.398989898989898, + 4.2557392102846645, + 4.119834710743802, + 3.991276400367309, + 3.870064279155188, + 3.7561983471074383, + 3.649678604224059, + 3.55050505050505, + 3.4586776859504127, + 3.3741965105601466, + 3.2970615243342514, + 3.227272727272727, + 3.1648301193755737, + 3.1097337006427916, + 3.06198347107438, + 3.0215794306703394, + 2.98852157943067, + 2.9628099173553717, + 2.944444444444444, + 2.9334251606978876, + 2.9297520661157024, + 2.9334251606978876, + 2.9444444444444446, + 2.9628099173553717, + 2.98852157943067, + 3.0215794306703394, + 3.06198347107438, + 3.109733700642792, + 3.164830119375574, + 3.2272727272727275, + 3.297061524334252, + 3.374196510560147, + 3.4586776859504136, + 3.55050505050505, + 3.649678604224059, + 3.7561983471074383, + 3.870064279155188, + 3.99127640036731, + 4.119834710743801, + 4.2557392102846645, + 4.398989898989898, + 4.549586776859503, + 4.707529843893482, + 4.872819100091828, + 5.045454545454547, + 5.225436179981635, + 5.412764003673095, + 5.607438016528926, + 5.809458218549128, + 6.018824609733702, + 6.2355371900826455, + 6.45959595959596, + 6.6910009182736445, + 6.929752066115702 + ], + [ + 18.84894398530762, + 18.367768595041323, + 17.893939393939398, + 17.427456382001836, + 16.968319559228654, + 16.516528925619834, + 16.072084481175388, + 15.634986225895316, + 15.205234159779614, + 14.782828282828284, + 14.367768595041323, + 13.960055096418731, + 13.559687786960513, + 13.166666666666664, + 12.780991735537189, + 12.402662993572083, + 12.03168044077135, + 11.668044077134986, + 11.311753902662995, + 10.962809917355372, + 10.621212121212121, + 10.286960514233241, + 9.960055096418731, + 9.640495867768594, + 9.328282828282827, + 9.023415977961433, + 8.725895316804408, + 8.435720844811753, + 8.152892561983471, + 7.877410468319559, + 7.609274563820017, + 7.348484848484848, + 7.095041322314049, + 6.8489439853076215, + 6.610192837465565, + 6.378787878787879, + 6.154729109274564, + 5.938016528925619, + 5.728650137741046, + 5.526629935720845, + 5.3319559228650135, + 5.144628099173554, + 4.9646464646464645, + 4.792011019283747, + 4.626721763085399, + 4.468778696051423, + 4.3181818181818175, + 4.174931129476583, + 4.039026629935721, + 3.9104683195592287, + 3.7892561983471076, + 3.6753902662993574, + 3.568870523415978, + 3.4696969696969693, + 3.3778696051423323, + 3.293388429752066, + 3.2162534435261705, + 3.146464646464646, + 3.0840220385674932, + 3.0289256198347108, + 2.981175390266299, + 2.940771349862259, + 2.907713498622589, + 2.882001836547291, + 2.8636363636363633, + 2.852617079889807, + 2.8489439853076215, + 2.852617079889807, + 2.8636363636363638, + 2.882001836547291, + 2.907713498622589, + 2.9407713498622585, + 2.981175390266299, + 3.028925619834711, + 3.0840220385674932, + 3.1464646464646466, + 3.216253443526171, + 3.293388429752066, + 3.3778696051423327, + 3.4696969696969697, + 3.5688705234159785, + 3.675390266299358, + 3.7892561983471076, + 3.9104683195592287, + 4.03902662993572, + 4.174931129476583, + 4.3181818181818175, + 4.468778696051422, + 4.626721763085401, + 4.7920110192837475, + 4.964646464646466, + 5.144628099173555, + 5.331955922865014, + 5.5266299357208455, + 5.728650137741049, + 5.938016528925621, + 6.154729109274564, + 6.378787878787881, + 6.610192837465565, + 6.848943985307622 + ], + [ + 18.771808999081728, + 18.290633608815426, + 17.816804407713498, + 17.350321395775943, + 16.891184573002757, + 16.439393939393938, + 15.994949494949495, + 15.557851239669422, + 15.12809917355372, + 14.705693296602387, + 14.290633608815428, + 13.882920110192835, + 13.482552800734616, + 13.089531680440771, + 12.703856749311294, + 12.32552800734619, + 11.954545454545455, + 11.59090909090909, + 11.2346189164371, + 10.885674931129476, + 10.544077134986225, + 10.209825528007347, + 9.882920110192837, + 9.5633608815427, + 9.251147842056932, + 8.946280991735538, + 8.648760330578513, + 8.358585858585858, + 8.075757575757576, + 7.800275482093664, + 7.532139577594123, + 7.271349862258953, + 7.017906336088155, + 6.771808999081726, + 6.53305785123967, + 6.301652892561984, + 6.077594123048669, + 5.860881542699724, + 5.6515151515151505, + 5.449494949494949, + 5.254820936639119, + 5.067493112947658, + 4.88751147842057, + 4.714876033057852, + 4.5495867768595035, + 4.391643709825527, + 4.241046831955923, + 4.097796143250688, + 3.9618916437098255, + 3.8333333333333335, + 3.7121212121212124, + 3.598255280073462, + 3.491735537190083, + 3.392561983471074, + 3.3007346189164366, + 3.2162534435261705, + 3.1391184573002753, + 3.0693296602387514, + 3.0068870523415976, + 2.9517906336088156, + 2.904040404040404, + 2.8636363636363633, + 2.830578512396694, + 2.8048668503213956, + 2.7865013774104685, + 2.775482093663912, + 2.7718089990817263, + 2.775482093663912, + 2.7865013774104685, + 2.8048668503213956, + 2.830578512396694, + 2.8636363636363633, + 2.904040404040404, + 2.951790633608816, + 3.006887052341598, + 3.0693296602387514, + 3.1391184573002757, + 3.216253443526171, + 3.3007346189164375, + 3.3925619834710745, + 3.491735537190083, + 3.598255280073462, + 3.712121212121212, + 3.833333333333334, + 3.9618916437098255, + 4.097796143250688, + 4.241046831955923, + 4.391643709825527, + 4.549586776859506, + 4.714876033057853, + 4.8875114784205715, + 5.06749311294766, + 5.25482093663912, + 5.449494949494951, + 5.651515151515152, + 5.860881542699726, + 6.077594123048669, + 6.301652892561984, + 6.533057851239668, + 6.771808999081726 + ], + [ + 18.698347107438018, + 18.217171717171716, + 17.743342516069788, + 17.276859504132233, + 16.817722681359047, + 16.365932047750228, + 15.921487603305785, + 15.484389348025712, + 15.054637281910008, + 14.632231404958677, + 14.217171717171716, + 13.809458218549125, + 13.409090909090907, + 13.01606978879706, + 12.630394857667584, + 12.252066115702478, + 11.881083562901745, + 11.51744719926538, + 11.16115702479339, + 10.812213039485766, + 10.470615243342515, + 10.136363636363637, + 9.809458218549127, + 9.48989898989899, + 9.177685950413222, + 8.872819100091828, + 8.575298438934803, + 8.285123966942148, + 8.002295684113866, + 7.726813590449954, + 7.458677685950413, + 7.197887970615243, + 6.944444444444444, + 6.698347107438016, + 6.459595959595959, + 6.228191000918274, + 6.004132231404959, + 5.787419651056013, + 5.5780532598714405, + 5.376033057851239, + 5.181359044995409, + 4.994031221303948, + 4.814049586776859, + 4.641414141414142, + 4.4761248852157935, + 4.3181818181818175, + 4.167584940312212, + 4.024334251606978, + 3.8884297520661155, + 3.759871441689623, + 3.638659320477502, + 3.524793388429752, + 3.418273645546373, + 3.319100091827364, + 3.2272727272727266, + 3.1427915518824605, + 3.0656565656565653, + 2.995867768595041, + 2.9334251606978876, + 2.8783287419651056, + 2.830578512396694, + 2.7901744719926533, + 2.757116620752984, + 2.7314049586776856, + 2.713039485766758, + 2.7020202020202015, + 2.6983471074380163, + 2.7020202020202015, + 2.7130394857667586, + 2.7314049586776856, + 2.757116620752984, + 2.7901744719926533, + 2.830578512396694, + 2.878328741965106, + 2.933425160697888, + 2.9958677685950414, + 3.0656565656565657, + 3.142791551882461, + 3.2272727272727275, + 3.3191000918273645, + 3.418273645546373, + 3.524793388429752, + 3.638659320477502, + 3.759871441689624, + 3.8884297520661146, + 4.024334251606978, + 4.167584940312212, + 4.318181818181817, + 4.476124885215796, + 4.641414141414142, + 4.814049586776861, + 4.994031221303949, + 5.181359044995409, + 5.37603305785124, + 5.578053259871442, + 5.787419651056016, + 6.004132231404959, + 6.228191000918274, + 6.4595959595959584, + 6.698347107438016 + ], + [ + 18.62855831037649, + 18.147382920110193, + 17.673553719008268, + 17.207070707070706, + 16.747933884297524, + 16.296143250688704, + 15.851698806244261, + 15.414600550964188, + 14.984848484848484, + 14.562442607897154, + 14.147382920110193, + 13.739669421487601, + 13.339302112029383, + 12.946280991735536, + 12.560606060606059, + 12.182277318640955, + 11.81129476584022, + 11.447658402203857, + 11.091368227731865, + 10.742424242424242, + 10.400826446280991, + 10.066574839302111, + 9.739669421487601, + 9.420110192837464, + 9.107897153351699, + 8.803030303030303, + 8.505509641873278, + 8.215335169880625, + 7.932506887052341, + 7.65702479338843, + 7.3888888888888875, + 7.128099173553719, + 6.8746556473829195, + 6.6285583103764925, + 6.389807162534435, + 6.15840220385675, + 5.934343434343434, + 5.717630853994489, + 5.508264462809917, + 5.306244260789715, + 5.111570247933884, + 4.924242424242424, + 4.7442607897153355, + 4.571625344352617, + 4.406336088154269, + 4.248393021120293, + 4.097796143250688, + 3.954545454545454, + 3.818640955004591, + 3.690082644628099, + 3.568870523415978, + 3.455004591368228, + 3.3484848484848486, + 3.24931129476584, + 3.1574839302112023, + 3.073002754820936, + 2.995867768595041, + 2.926078971533517, + 2.8636363636363633, + 2.8085399449035813, + 2.7607897153351697, + 2.720385674931129, + 2.6873278236914597, + 2.6616161616161613, + 2.6432506887052343, + 2.6322314049586777, + 2.628558310376492, + 2.6322314049586777, + 2.6432506887052343, + 2.6616161616161613, + 2.6873278236914597, + 2.720385674931129, + 2.7607897153351697, + 2.8085399449035817, + 2.8636363636363638, + 2.926078971533517, + 2.9958677685950414, + 3.0730027548209367, + 3.157483930211203, + 3.2493112947658402, + 3.3484848484848486, + 3.455004591368228, + 3.5688705234159777, + 3.6900826446280997, + 3.818640955004591, + 3.954545454545454, + 4.097796143250688, + 4.248393021120293, + 4.406336088154272, + 4.5716253443526185, + 4.744260789715337, + 4.924242424242426, + 5.111570247933885, + 5.3062442607897164, + 5.508264462809919, + 5.717630853994491, + 5.934343434343434, + 6.158402203856751, + 6.389807162534435, + 6.6285583103764925 + ], + [ + 18.562442607897154, + 18.081267217630852, + 17.607438016528928, + 17.14095500459137, + 16.681818181818183, + 16.230027548209364, + 15.785583103764921, + 15.348484848484848, + 14.918732782369146, + 14.496326905417813, + 14.081267217630854, + 13.673553719008261, + 13.273186409550043, + 12.880165289256198, + 12.49449035812672, + 12.116161616161616, + 11.745179063360881, + 11.381542699724518, + 11.025252525252526, + 10.676308539944904, + 10.334710743801653, + 10.000459136822773, + 9.673553719008265, + 9.353994490358126, + 9.04178145087236, + 8.736914600550964, + 8.43939393939394, + 8.149219467401284, + 7.866391184573002, + 7.590909090909091, + 7.322773186409549, + 7.061983471074379, + 6.808539944903581, + 6.562442607897154, + 6.323691460055096, + 6.09228650137741, + 5.868227731864096, + 5.6515151515151505, + 5.442148760330578, + 5.240128558310376, + 5.045454545454545, + 4.858126721763085, + 4.678145087235997, + 4.505509641873278, + 4.340220385674931, + 4.1822773186409545, + 4.03168044077135, + 3.8884297520661155, + 3.752525252525252, + 3.62396694214876, + 3.502754820936639, + 3.388888888888889, + 3.28236914600551, + 3.183195592286501, + 3.0913682277318637, + 3.0068870523415976, + 2.9297520661157024, + 2.859963269054178, + 2.7975206611570247, + 2.742424242424242, + 2.6946740128558306, + 2.6542699724517904, + 2.621212121212121, + 2.5955004591368227, + 2.577134986225895, + 2.5661157024793386, + 2.5624426078971534, + 2.5661157024793386, + 2.577134986225895, + 2.5955004591368227, + 2.621212121212121, + 2.6542699724517904, + 2.6946740128558306, + 2.742424242424243, + 2.797520661157025, + 2.8599632690541785, + 2.929752066115703, + 3.006887052341598, + 3.0913682277318646, + 3.1831955922865016, + 3.28236914600551, + 3.3888888888888893, + 3.502754820936639, + 3.62396694214876, + 3.7525252525252517, + 3.8884297520661146, + 4.031680440771349, + 4.182277318640954, + 4.340220385674932, + 4.505509641873279, + 4.678145087235998, + 4.858126721763086, + 5.045454545454546, + 5.240128558310377, + 5.442148760330579, + 5.651515151515152, + 5.868227731864096, + 6.092286501377412, + 6.323691460055096, + 6.562442607897154 + ], + [ + 18.5, + 18.0188246097337, + 17.544995408631774, + 17.078512396694215, + 16.61937557392103, + 16.16758494031221, + 15.723140495867767, + 15.286042240587694, + 14.856290174471994, + 14.433884297520661, + 14.018824609733702, + 13.611111111111109, + 13.21074380165289, + 12.817722681359044, + 12.432047750229568, + 12.053719008264462, + 11.68273645546373, + 11.319100091827364, + 10.962809917355372, + 10.61386593204775, + 10.272268135904499, + 9.938016528925619, + 9.61111111111111, + 9.291551882460972, + 8.979338842975206, + 8.67447199265381, + 8.376951331496787, + 8.086776859504132, + 7.8039485766758485, + 7.528466483011938, + 7.260330578512396, + 6.999540863177226, + 6.746097337006428, + 6.5, + 6.2612488521579435, + 6.029843893480257, + 5.805785123966943, + 5.5890725436179975, + 5.379706152433425, + 5.177685950413222, + 4.983011937557392, + 4.795684113865932, + 4.615702479338843, + 4.443067033976125, + 4.277777777777777, + 4.119834710743801, + 3.969237832874196, + 3.825987144168962, + 3.6900826446280988, + 3.561524334251607, + 3.440312213039486, + 3.3264462809917354, + 3.2199265381083566, + 3.120752984389348, + 3.0289256198347103, + 2.944444444444444, + 2.867309458218549, + 2.7975206611570247, + 2.7350780532598717, + 2.6799816345270893, + 2.6322314049586772, + 2.591827364554637, + 2.5587695133149677, + 2.5330578512396693, + 2.514692378328742, + 2.5036730945821857, + 2.5, + 2.5036730945821857, + 2.514692378328742, + 2.5330578512396693, + 2.5587695133149677, + 2.591827364554637, + 2.6322314049586772, + 2.6799816345270897, + 2.7350780532598717, + 2.797520661157025, + 2.8673094582185494, + 2.9444444444444446, + 3.028925619834711, + 3.1207529843893482, + 3.2199265381083566, + 3.3264462809917354, + 3.440312213039485, + 3.561524334251607, + 3.6900826446280988, + 3.8259871441689617, + 3.969237832874196, + 4.119834710743801, + 4.2777777777777795, + 4.443067033976126, + 4.615702479338845, + 4.795684113865933, + 4.983011937557393, + 5.177685950413224, + 5.379706152433426, + 5.589072543617998, + 5.805785123966942, + 6.029843893480258, + 6.261248852157943, + 6.5 + ], + [ + 18.441230486685033, + 17.960055096418735, + 17.486225895316807, + 17.019742883379248, + 16.560606060606062, + 16.108815426997243, + 15.6643709825528, + 15.227272727272727, + 14.797520661157025, + 14.375114784205692, + 13.960055096418733, + 13.55234159779614, + 13.151974288337922, + 12.758953168044076, + 12.373278236914599, + 11.994949494949495, + 11.62396694214876, + 11.260330578512397, + 10.904040404040405, + 10.555096418732782, + 10.213498622589531, + 9.879247015610652, + 9.552341597796143, + 9.232782369146005, + 8.920569329660239, + 8.615702479338843, + 8.318181818181818, + 8.028007346189163, + 7.745179063360881, + 7.46969696969697, + 7.201561065197428, + 6.940771349862258, + 6.68732782369146, + 6.441230486685033, + 6.202479338842975, + 5.971074380165289, + 5.7470156106519745, + 5.530303030303029, + 5.3209366391184565, + 5.118916437098255, + 4.924242424242424, + 4.736914600550964, + 4.556932966023876, + 4.384297520661157, + 4.2190082644628095, + 4.061065197428833, + 3.9104683195592282, + 3.7672176308539944, + 3.631313131313131, + 3.502754820936639, + 3.381542699724518, + 3.2676767676767677, + 3.161157024793389, + 3.0619834710743796, + 2.9701561065197426, + 2.8856749311294765, + 2.8085399449035813, + 2.738751147842057, + 2.6763085399449036, + 2.621212121212121, + 2.5734618916437095, + 2.5330578512396693, + 2.5, + 2.4742883379247016, + 2.455922865013774, + 2.4449035812672175, + 2.4412304866850323, + 2.4449035812672175, + 2.455922865013774, + 2.4742883379247016, + 2.5, + 2.5330578512396693, + 2.5734618916437095, + 2.621212121212122, + 2.676308539944904, + 2.7387511478420574, + 2.8085399449035817, + 2.885674931129477, + 2.9701561065197435, + 3.0619834710743805, + 3.161157024793389, + 3.267676767676768, + 3.381542699724518, + 3.502754820936639, + 3.6313131313131306, + 3.7672176308539935, + 3.910468319559228, + 4.0610651974288325, + 4.219008264462811, + 4.384297520661158, + 4.556932966023877, + 4.736914600550965, + 4.924242424242425, + 5.118916437098256, + 5.320936639118458, + 5.530303030303031, + 5.7470156106519745, + 5.971074380165291, + 6.202479338842975, + 6.441230486685033 + ], + [ + 18.38613406795225, + 17.90495867768595, + 17.431129476584026, + 16.964646464646464, + 16.50550964187328, + 16.053719008264462, + 15.60927456382002, + 15.172176308539946, + 14.742424242424242, + 14.320018365472912, + 13.90495867768595, + 13.49724517906336, + 13.09687786960514, + 12.703856749311294, + 12.318181818181817, + 11.939853076216712, + 11.568870523415978, + 11.205234159779614, + 10.848943985307622, + 10.5, + 10.158402203856749, + 9.82415059687787, + 9.49724517906336, + 9.177685950413222, + 8.865472910927457, + 8.56060606060606, + 8.263085399449036, + 7.972910927456382, + 7.690082644628099, + 7.414600550964187, + 7.146464646464645, + 6.8856749311294765, + 6.632231404958677, + 6.38613406795225, + 6.147382920110193, + 5.915977961432508, + 5.691919191919192, + 5.475206611570247, + 5.265840220385675, + 5.0638200183654725, + 4.869146005509641, + 4.681818181818182, + 4.501836547291093, + 4.3292011019283745, + 4.163911845730027, + 4.005968778696051, + 3.855371900826446, + 3.712121212121212, + 3.576216712580349, + 3.4476584022038566, + 3.3264462809917354, + 3.2125803489439857, + 3.1060606060606064, + 3.0068870523415976, + 2.91505968778696, + 2.830578512396694, + 2.753443526170799, + 2.6836547291092745, + 2.621212121212121, + 2.566115702479339, + 2.5183654729109275, + 2.477961432506887, + 2.4449035812672175, + 2.419191919191919, + 2.400826446280992, + 2.389807162534435, + 2.38613406795225, + 2.389807162534435, + 2.400826446280992, + 2.419191919191919, + 2.4449035812672175, + 2.477961432506887, + 2.5183654729109275, + 2.5661157024793395, + 2.6212121212121215, + 2.683654729109275, + 2.7534435261707992, + 2.8305785123966944, + 2.915059687786961, + 3.006887052341598, + 3.1060606060606064, + 3.2125803489439857, + 3.3264462809917354, + 3.4476584022038574, + 3.576216712580349, + 3.712121212121212, + 3.855371900826446, + 4.005968778696051, + 4.16391184573003, + 4.329201101928376, + 4.501836547291095, + 4.681818181818183, + 4.869146005509643, + 5.063820018365474, + 5.265840220385677, + 5.47520661157025, + 5.691919191919192, + 5.9159779614325085, + 6.147382920110193, + 6.38613406795225 + ], + [ + 18.33471074380165, + 17.853535353535353, + 17.379706152433428, + 16.91322314049587, + 16.454086317722684, + 16.002295684113864, + 15.557851239669422, + 15.120752984389348, + 14.691000918273645, + 14.268595041322314, + 13.853535353535353, + 13.445821854912761, + 13.045454545454543, + 12.652433425160696, + 12.26675849403122, + 11.888429752066115, + 11.517447199265382, + 11.153810835629017, + 10.797520661157026, + 10.448576675849402, + 10.106978879706151, + 9.772727272727273, + 9.445821854912763, + 9.126262626262626, + 8.814049586776859, + 8.509182736455465, + 8.21166207529844, + 7.921487603305785, + 7.638659320477503, + 7.36317722681359, + 7.095041322314049, + 6.83425160697888, + 6.58080808080808, + 6.3347107438016526, + 6.095959595959596, + 5.864554637281911, + 5.640495867768596, + 5.42378328741965, + 5.214416896235077, + 5.012396694214876, + 4.8177226813590455, + 4.630394857667585, + 4.450413223140496, + 4.277777777777779, + 4.11248852157943, + 3.954545454545454, + 3.803948576675849, + 3.660697887970615, + 3.524793388429752, + 3.3962350780532597, + 3.2750229568411386, + 3.161157024793389, + 3.0546372819100096, + 2.955463728191001, + 2.8636363636363633, + 2.779155188246097, + 2.702020202020202, + 2.6322314049586777, + 2.5697887970615243, + 2.5146923783287423, + 2.4669421487603307, + 2.42653810835629, + 2.3934802571166207, + 2.3677685950413223, + 2.349403122130395, + 2.3383838383838382, + 2.334710743801653, + 2.3383838383838382, + 2.3494031221303953, + 2.3677685950413223, + 2.3934802571166207, + 2.42653810835629, + 2.4669421487603307, + 2.5146923783287427, + 2.5697887970615247, + 2.632231404958678, + 2.7020202020202024, + 2.7791551882460976, + 2.863636363636364, + 2.9554637281910012, + 3.0546372819100096, + 3.161157024793389, + 3.2750229568411386, + 3.3962350780532606, + 3.5247933884297513, + 3.660697887970615, + 3.8039485766758485, + 3.9545454545454533, + 4.112488521579433, + 4.277777777777779, + 4.450413223140497, + 4.630394857667586, + 4.8177226813590455, + 5.0123966942148765, + 5.214416896235079, + 5.423783287419653, + 5.640495867768596, + 5.864554637281911, + 6.095959595959595, + 6.3347107438016526 + ], + [ + 18.286960514233243, + 17.805785123966942, + 17.331955922865014, + 16.86547291092746, + 16.406336088154273, + 15.954545454545453, + 15.51010101010101, + 15.073002754820937, + 14.643250688705233, + 14.220844811753903, + 13.805785123966942, + 13.39807162534435, + 12.997704315886132, + 12.604683195592285, + 12.219008264462808, + 11.840679522497704, + 11.469696969696969, + 11.106060606060606, + 10.749770431588614, + 10.400826446280991, + 10.05922865013774, + 9.724977043158862, + 9.398071625344352, + 9.078512396694215, + 8.766299357208448, + 8.461432506887052, + 8.163911845730027, + 7.873737373737374, + 7.59090909090909, + 7.315426997245179, + 7.047291092745637, + 6.786501377410468, + 6.533057851239668, + 6.286960514233241, + 6.048209366391184, + 5.816804407713499, + 5.592745638200184, + 5.376033057851238, + 5.166666666666666, + 4.964646464646464, + 4.7699724517906334, + 4.582644628099173, + 4.4026629935720845, + 4.2300275482093666, + 4.064738292011018, + 3.906795224977042, + 3.7561983471074374, + 3.612947658402203, + 3.47704315886134, + 3.348484848484848, + 3.227272727272727, + 3.113406795224977, + 3.0068870523415976, + 2.9077134986225888, + 2.8158861340679517, + 2.7314049586776856, + 2.6542699724517904, + 2.584481175390266, + 2.5220385674931127, + 2.4669421487603307, + 2.4191919191919187, + 2.3787878787878785, + 2.345730027548209, + 2.3200183654729107, + 2.3016528925619832, + 2.2906336088154267, + 2.2869605142332414, + 2.2906336088154267, + 2.3016528925619832, + 2.3200183654729107, + 2.345730027548209, + 2.3787878787878785, + 2.4191919191919187, + 2.466942148760331, + 2.522038567493113, + 2.5844811753902666, + 2.654269972451791, + 2.731404958677686, + 2.8158861340679526, + 2.9077134986225897, + 3.006887052341598, + 3.1134067952249773, + 3.2272727272727266, + 3.3484848484848486, + 3.47704315886134, + 3.612947658402203, + 3.7561983471074374, + 3.906795224977042, + 4.064738292011021, + 4.230027548209367, + 4.402662993572086, + 4.582644628099175, + 4.769972451790634, + 4.964646464646465, + 5.166666666666668, + 5.376033057851241, + 5.592745638200183, + 5.8168044077135, + 6.048209366391184, + 6.286960514233241 + ], + [ + 18.242883379247015, + 17.761707988980717, + 17.28787878787879, + 16.821395775941234, + 16.362258953168045, + 15.910468319559227, + 15.466023875114782, + 15.028925619834709, + 14.599173553719009, + 14.176767676767676, + 13.761707988980717, + 13.353994490358124, + 12.953627180899906, + 12.560606060606059, + 12.174931129476583, + 11.796602387511477, + 11.425619834710744, + 11.061983471074381, + 10.705693296602387, + 10.356749311294765, + 10.015151515151516, + 9.680899908172636, + 9.353994490358126, + 9.034435261707989, + 8.722222222222221, + 8.417355371900825, + 8.119834710743802, + 7.829660238751147, + 7.5468319559228645, + 7.271349862258953, + 7.003213957759412, + 6.742424242424242, + 6.488980716253443, + 6.242883379247015, + 6.0041322314049586, + 5.772727272727273, + 5.548668503213959, + 5.331955922865013, + 5.12258953168044, + 4.920569329660238, + 4.725895316804408, + 4.538567493112947, + 4.358585858585858, + 4.185950413223141, + 4.020661157024793, + 3.8627180899908167, + 3.7121212121212115, + 3.5688705234159777, + 3.4329660238751147, + 3.3044077134986223, + 3.183195592286501, + 3.0693296602387514, + 2.962809917355372, + 2.8636363636363633, + 2.771808999081726, + 2.6873278236914597, + 2.6101928374655645, + 2.54040404040404, + 2.477961432506887, + 2.422865013774105, + 2.375114784205693, + 2.3347107438016526, + 2.3016528925619832, + 2.275941230486685, + 2.2575757575757573, + 2.2465564738292008, + 2.2428833792470155, + 2.2465564738292008, + 2.257575757575758, + 2.275941230486685, + 2.3016528925619832, + 2.3347107438016526, + 2.3751147842056928, + 2.4228650137741052, + 2.4779614325068873, + 2.5404040404040407, + 2.610192837465565, + 2.68732782369146, + 2.7718089990817267, + 2.8636363636363638, + 2.962809917355372, + 3.0693296602387514, + 3.183195592286501, + 3.3044077134986223, + 3.432966023875114, + 3.5688705234159768, + 3.712121212121211, + 3.862718089990816, + 4.0206611570247945, + 4.185950413223141, + 4.35858585858586, + 4.538567493112948, + 4.725895316804408, + 4.920569329660239, + 5.1225895316804415, + 5.331955922865014, + 5.548668503213959, + 5.772727272727273, + 6.004132231404958, + 6.242883379247015 + ], + [ + 18.202479338842977, + 17.721303948576676, + 17.247474747474747, + 16.780991735537192, + 16.321854912764007, + 15.870064279155187, + 15.425619834710744, + 14.988521579430671, + 14.558769513314967, + 14.136363636363637, + 13.721303948576676, + 13.313590449954084, + 12.913223140495866, + 12.520202020202019, + 12.134527089072542, + 11.756198347107437, + 11.385215794306703, + 11.02157943067034, + 10.665289256198347, + 10.316345270890725, + 9.974747474747474, + 9.640495867768596, + 9.313590449954086, + 8.994031221303949, + 8.681818181818182, + 8.376951331496786, + 8.079430670339761, + 7.789256198347108, + 7.506427915518824, + 7.230945821854913, + 6.962809917355371, + 6.7020202020202015, + 6.448576675849402, + 6.202479338842975, + 5.963728191000918, + 5.732323232323233, + 5.508264462809918, + 5.291551882460972, + 5.0821854912764, + 4.8801652892561975, + 4.685491276400367, + 4.498163452708907, + 4.318181818181818, + 4.1455463728191, + 3.980257116620752, + 3.822314049586776, + 3.6717171717171713, + 3.528466483011937, + 3.392561983471074, + 3.264003673094582, + 3.142791551882461, + 3.0289256198347108, + 2.9224058769513315, + 2.8232323232323226, + 2.7314049586776856, + 2.6469237832874195, + 2.5697887970615243, + 2.5, + 2.4375573921028466, + 2.3824609733700646, + 2.3347107438016526, + 2.2943067033976123, + 2.2612488521579426, + 2.2355371900826446, + 2.217171717171717, + 2.2061524334251605, + 2.2024793388429753, + 2.2061524334251605, + 2.217171717171717, + 2.2355371900826446, + 2.2612488521579426, + 2.294306703397612, + 2.3347107438016526, + 2.382460973370065, + 2.437557392102847, + 2.5000000000000004, + 2.5697887970615247, + 2.64692378328742, + 2.7314049586776865, + 2.8232323232323235, + 2.922405876951332, + 3.028925619834711, + 3.1427915518824605, + 3.2640036730945825, + 3.392561983471074, + 3.528466483011937, + 3.6717171717171713, + 3.822314049586776, + 3.9802571166207548, + 4.145546372819101, + 4.31818181818182, + 4.4981634527089085, + 4.685491276400368, + 4.880165289256199, + 5.082185491276402, + 5.291551882460975, + 5.508264462809917, + 5.732323232323234, + 5.963728191000918, + 6.202479338842975 + ], + [ + 18.16574839302112, + 17.68457300275482, + 17.210743801652896, + 16.744260789715334, + 16.28512396694215, + 15.833333333333332, + 15.38888888888889, + 14.951790633608816, + 14.522038567493112, + 14.099632690541782, + 13.68457300275482, + 13.27685950413223, + 12.876492194674011, + 12.483471074380164, + 12.097796143250687, + 11.719467401285582, + 11.348484848484848, + 10.984848484848484, + 10.628558310376492, + 10.27961432506887, + 9.938016528925619, + 9.603764921946741, + 9.276859504132231, + 8.957300275482094, + 8.645087235996327, + 8.34022038567493, + 8.042699724517906, + 7.752525252525253, + 7.46969696969697, + 7.194214876033058, + 6.926078971533516, + 6.665289256198347, + 6.411845730027548, + 6.16574839302112, + 5.926997245179064, + 5.695592286501378, + 5.471533516988063, + 5.254820936639118, + 5.045454545454545, + 4.8434343434343425, + 4.648760330578512, + 4.461432506887052, + 4.281450872359963, + 4.1088154269972454, + 3.943526170798897, + 3.785583103764921, + 3.6349862258953163, + 3.4917355371900825, + 3.355831037649219, + 3.227272727272727, + 3.106060606060606, + 2.9921946740128558, + 2.885674931129477, + 2.7865013774104677, + 2.6946740128558306, + 2.6101928374655645, + 2.5330578512396693, + 2.463269054178145, + 2.4008264462809916, + 2.3457300275482096, + 2.2979797979797976, + 2.2575757575757573, + 2.224517906336088, + 2.1988062442607896, + 2.180440771349862, + 2.169421487603306, + 2.1657483930211203, + 2.169421487603306, + 2.180440771349862, + 2.1988062442607896, + 2.224517906336088, + 2.2575757575757573, + 2.2979797979797976, + 2.34573002754821, + 2.400826446280992, + 2.4632690541781455, + 2.5330578512396698, + 2.610192837465565, + 2.6946740128558315, + 2.7865013774104685, + 2.885674931129477, + 2.992194674012856, + 3.1060606060606055, + 3.2272727272727275, + 3.355831037649219, + 3.491735537190082, + 3.6349862258953163, + 3.785583103764921, + 3.9435261707988998, + 4.108815426997246, + 4.281450872359965, + 4.4614325068870535, + 4.648760330578513, + 4.843434343434344, + 5.045454545454547, + 5.25482093663912, + 5.471533516988062, + 5.695592286501379, + 5.926997245179063, + 6.16574839302112 + ], + [ + 18.13269054178145, + 17.65151515151515, + 17.177685950413224, + 16.711202938475665, + 16.252066115702483, + 15.800275482093664, + 15.355831037649219, + 14.918732782369146, + 14.488980716253444, + 14.066574839302113, + 13.651515151515152, + 13.24380165289256, + 12.843434343434343, + 12.450413223140494, + 12.064738292011018, + 11.686409550045912, + 11.31542699724518, + 10.951790633608816, + 10.595500459136824, + 10.246556473829202, + 9.90495867768595, + 9.570707070707071, + 9.24380165289256, + 8.924242424242424, + 8.612029384756656, + 8.307162534435262, + 8.009641873278238, + 7.719467401285582, + 7.4366391184573, + 7.161157024793388, + 6.893021120293847, + 6.632231404958677, + 6.378787878787879, + 6.132690541781451, + 5.8939393939393945, + 5.662534435261708, + 5.438475665748394, + 5.221763085399449, + 5.012396694214876, + 4.810376492194674, + 4.615702479338843, + 4.428374655647383, + 4.248393021120294, + 4.075757575757576, + 3.910468319559228, + 3.7525252525252517, + 3.601928374655647, + 3.4586776859504127, + 3.3227731864095498, + 3.1942148760330578, + 3.0730027548209367, + 2.9591368227731865, + 2.852617079889807, + 2.7534435261707983, + 2.6616161616161613, + 2.577134986225895, + 2.5, + 2.4302112029384757, + 2.3677685950413223, + 2.3126721763085403, + 2.2649219467401283, + 2.224517906336088, + 2.1914600550964187, + 2.1657483930211203, + 2.147382920110193, + 2.1363636363636362, + 2.132690541781451, + 2.1363636363636362, + 2.147382920110193, + 2.1657483930211203, + 2.1914600550964183, + 2.2245179063360876, + 2.2649219467401283, + 2.3126721763085407, + 2.3677685950413228, + 2.430211202938476, + 2.5000000000000004, + 2.5771349862258957, + 2.661616161616162, + 2.7534435261707992, + 2.8526170798898076, + 2.959136822773187, + 3.073002754820936, + 3.194214876033058, + 3.3227731864095498, + 3.4586776859504127, + 3.601928374655647, + 3.7525252525252517, + 3.9104683195592305, + 4.075757575757577, + 4.248393021120296, + 4.428374655647384, + 4.615702479338844, + 4.810376492194675, + 5.012396694214877, + 5.22176308539945, + 5.438475665748394, + 5.662534435261708, + 5.893939393939393, + 6.13269054178145 + ], + [ + 18.103305785123965, + 17.622130394857667, + 17.148301193755742, + 16.681818181818183, + 16.222681359044998, + 15.770890725436178, + 15.326446280991735, + 14.889348025711662, + 14.45959595959596, + 14.037190082644628, + 13.622130394857669, + 13.214416896235075, + 12.814049586776857, + 12.421028466483012, + 12.035353535353535, + 11.65702479338843, + 11.286042240587696, + 10.92240587695133, + 10.56611570247934, + 10.217171717171716, + 9.875573921028465, + 9.541322314049587, + 9.214416896235077, + 8.89485766758494, + 8.582644628099173, + 8.277777777777779, + 7.980257116620754, + 7.690082644628099, + 7.407254361799816, + 7.131772268135904, + 6.863636363636363, + 6.602846648301194, + 6.349403122130394, + 6.1033057851239665, + 5.86455463728191, + 5.633149678604225, + 5.40909090909091, + 5.192378328741964, + 4.983011937557391, + 4.78099173553719, + 4.586317722681359, + 4.398989898989899, + 4.2190082644628095, + 4.0463728191000925, + 3.881083562901744, + 3.723140495867768, + 3.572543617998163, + 3.429292929292929, + 3.293388429752066, + 3.1648301193755737, + 3.0436179981634526, + 2.929752066115703, + 2.8232323232323235, + 2.7240587695133147, + 2.6322314049586772, + 2.547750229568411, + 2.470615243342516, + 2.4008264462809916, + 2.3383838383838382, + 2.283287419651056, + 2.2355371900826446, + 2.195133149678604, + 2.1620752984389346, + 2.1363636363636362, + 2.1179981634527087, + 2.106978879706152, + 2.103305785123967, + 2.106978879706152, + 2.117998163452709, + 2.1363636363636362, + 2.1620752984389346, + 2.195133149678604, + 2.2355371900826446, + 2.2832874196510566, + 2.3383838383838387, + 2.400826446280992, + 2.4706152433425164, + 2.5477502295684116, + 2.632231404958678, + 2.724058769513315, + 2.8232323232323235, + 2.929752066115703, + 3.0436179981634526, + 3.1648301193755746, + 3.293388429752066, + 3.429292929292929, + 3.5725436179981633, + 3.723140495867768, + 3.881083562901747, + 4.046372819100093, + 4.219008264462812, + 4.398989898989901, + 4.58631772268136, + 4.780991735537191, + 4.983011937557394, + 5.192378328741967, + 5.40909090909091, + 5.633149678604225, + 5.864554637281909, + 6.1033057851239665 + ], + [ + 18.07759412304867, + 17.596418732782368, + 17.122589531680443, + 16.656106519742885, + 16.1969696969697, + 15.74517906336088, + 15.300734618916437, + 14.863636363636363, + 14.433884297520661, + 14.011478420569329, + 13.59641873278237, + 13.188705234159777, + 12.788337924701558, + 12.395316804407713, + 12.009641873278236, + 11.631313131313131, + 11.260330578512397, + 10.896694214876034, + 10.540404040404042, + 10.191460055096417, + 9.849862258953168, + 9.515610651974288, + 9.188705234159778, + 8.869146005509641, + 8.556932966023876, + 8.25206611570248, + 7.954545454545455, + 7.6643709825528, + 7.381542699724518, + 7.106060606060606, + 6.8379247015610645, + 6.577134986225895, + 6.323691460055096, + 6.0775941230486685, + 5.838842975206612, + 5.607438016528926, + 5.383379247015611, + 5.166666666666666, + 4.957300275482093, + 4.755280073461892, + 4.5606060606060606, + 4.373278236914601, + 4.193296602387512, + 4.020661157024794, + 3.8553719008264453, + 3.6974288337924697, + 3.5468319559228645, + 3.4035812672176307, + 3.2676767676767673, + 3.1391184573002753, + 3.017906336088154, + 2.9040404040404044, + 2.797520661157025, + 2.6983471074380163, + 2.606519742883379, + 2.5220385674931127, + 2.4449035812672175, + 2.375114784205693, + 2.3126721763085403, + 2.257575757575758, + 2.2098255280073458, + 2.1694214876033056, + 2.1363636363636362, + 2.110651974288338, + 2.0922865013774103, + 2.081267217630854, + 2.0775941230486685, + 2.081267217630854, + 2.0922865013774103, + 2.110651974288338, + 2.1363636363636362, + 2.1694214876033056, + 2.2098255280073458, + 2.2575757575757582, + 2.3126721763085403, + 2.3751147842056937, + 2.444903581267218, + 2.522038567493113, + 2.6065197428833797, + 2.6983471074380168, + 2.797520661157025, + 2.9040404040404044, + 3.017906336088154, + 3.1391184573002757, + 3.2676767676767673, + 3.40358126721763, + 3.5468319559228645, + 3.6974288337924692, + 3.855371900826448, + 4.0206611570247945, + 4.193296602387513, + 4.373278236914602, + 4.560606060606061, + 4.7552800734618925, + 4.957300275482095, + 5.166666666666668, + 5.383379247015611, + 5.607438016528928, + 5.838842975206612, + 6.077594123048669 + ], + [ + 18.055555555555557, + 17.574380165289256, + 17.100550964187327, + 16.634067952249772, + 16.174931129476587, + 15.723140495867767, + 15.278696051423324, + 14.841597796143251, + 14.411845730027547, + 13.989439853076217, + 13.574380165289256, + 13.166666666666664, + 12.766299357208446, + 12.373278236914599, + 11.987603305785122, + 11.609274563820017, + 11.238292011019283, + 10.87465564738292, + 10.518365472910927, + 10.169421487603305, + 9.827823691460054, + 9.493572084481176, + 9.166666666666666, + 8.847107438016529, + 8.534894398530762, + 8.230027548209366, + 7.932506887052342, + 7.642332415059688, + 7.359504132231405, + 7.084022038567493, + 6.815886134067951, + 6.555096418732782, + 6.301652892561983, + 6.055555555555555, + 5.816804407713499, + 5.585399449035813, + 5.361340679522498, + 5.144628099173553, + 4.93526170798898, + 4.7332415059687785, + 4.538567493112947, + 4.351239669421488, + 4.171258034894398, + 3.9986225895316805, + 3.833333333333332, + 3.6753902662993565, + 3.5247933884297513, + 3.3815426997245175, + 3.2456382001836546, + 3.1170798898071626, + 2.9958677685950414, + 2.8820018365472913, + 2.775482093663912, + 2.676308539944903, + 2.584481175390266, + 2.5, + 2.4228650137741043, + 2.35307621671258, + 2.290633608815427, + 2.2355371900826446, + 2.187786960514233, + 2.147382920110193, + 2.114325068870523, + 2.0886134067952247, + 2.070247933884297, + 2.059228650137741, + 2.0555555555555554, + 2.059228650137741, + 2.070247933884297, + 2.0886134067952247, + 2.114325068870523, + 2.1473829201101924, + 2.1877869605142326, + 2.235537190082645, + 2.290633608815427, + 2.3530762167125805, + 2.422865013774105, + 2.5, + 2.5844811753902666, + 2.6763085399449036, + 2.775482093663912, + 2.8820018365472913, + 2.995867768595041, + 3.1170798898071626, + 3.245638200183654, + 3.381542699724517, + 3.5247933884297513, + 3.675390266299356, + 3.833333333333335, + 3.9986225895316814, + 4.1712580348944, + 4.3512396694214885, + 4.538567493112948, + 4.733241505968779, + 4.935261707988982, + 5.144628099173555, + 5.361340679522498, + 5.585399449035814, + 5.816804407713498, + 6.055555555555555 + ], + [ + 18.037190082644628, + 17.556014692378326, + 17.0821854912764, + 16.615702479338843, + 16.156565656565657, + 15.70477502295684, + 15.260330578512395, + 14.823232323232322, + 14.393480257116622, + 13.97107438016529, + 13.55601469237833, + 13.148301193755737, + 12.747933884297519, + 12.354912764003672, + 11.969237832874196, + 11.59090909090909, + 11.219926538108357, + 10.856290174471992, + 10.5, + 10.151056014692378, + 9.809458218549127, + 9.475206611570247, + 9.148301193755739, + 8.8287419651056, + 8.516528925619834, + 8.211662075298438, + 7.914141414141414, + 7.62396694214876, + 7.341138659320477, + 7.065656565656566, + 6.797520661157024, + 6.536730945821855, + 6.283287419651056, + 6.037190082644628, + 5.798438934802571, + 5.567033976124885, + 5.3429752066115705, + 5.126262626262625, + 4.9168962350780525, + 4.714876033057851, + 4.52020202020202, + 4.33287419651056, + 4.152892561983471, + 3.980257116620753, + 3.814967860422405, + 3.657024793388429, + 3.506427915518824, + 3.36317722681359, + 3.227272727272727, + 3.098714416896235, + 2.977502295684114, + 2.8636363636363638, + 2.7571166207529845, + 2.6579430670339756, + 2.5661157024793386, + 2.4816345270890725, + 2.404499540863177, + 2.3347107438016526, + 2.2722681359044996, + 2.217171717171717, + 2.1694214876033056, + 2.1290174471992653, + 2.095959595959596, + 2.070247933884297, + 2.0518824609733697, + 2.0408631772268135, + 2.037190082644628, + 2.0408631772268135, + 2.05188246097337, + 2.070247933884297, + 2.095959595959596, + 2.1290174471992653, + 2.1694214876033056, + 2.2171717171717176, + 2.2722681359044996, + 2.334710743801653, + 2.4044995408631773, + 2.4816345270890725, + 2.566115702479339, + 2.657943067033976, + 2.7571166207529845, + 2.8636363636363638, + 2.9775022956841135, + 3.098714416896235, + 3.2272727272727266, + 3.3631772268135895, + 3.506427915518824, + 3.6570247933884286, + 3.8149678604224073, + 3.980257116620754, + 4.152892561983473, + 4.332874196510561, + 4.520202020202021, + 4.714876033057852, + 4.916896235078054, + 5.126262626262627, + 5.3429752066115705, + 5.567033976124886, + 5.79843893480257, + 6.037190082644628 + ], + [ + 18.02249770431589, + 17.541322314049587, + 17.06749311294766, + 16.601010101010104, + 16.141873278236915, + 15.690082644628099, + 15.245638200183654, + 14.80853994490358, + 14.378787878787879, + 13.956382001836548, + 13.541322314049587, + 13.133608815426996, + 12.733241505968778, + 12.340220385674929, + 11.954545454545453, + 11.576216712580347, + 11.205234159779614, + 10.841597796143251, + 10.485307621671259, + 10.136363636363637, + 9.794765840220386, + 9.460514233241506, + 9.133608815426996, + 8.814049586776859, + 8.501836547291092, + 8.196969696969697, + 7.8994490358126725, + 7.609274563820017, + 7.3264462809917354, + 7.050964187327824, + 6.782828282828282, + 6.522038567493112, + 6.268595041322314, + 6.022497704315886, + 5.7837465564738295, + 5.5523415977961434, + 5.328282828282829, + 5.111570247933884, + 4.902203856749311, + 4.700183654729109, + 4.505509641873278, + 4.318181818181818, + 4.138200183654729, + 3.965564738292011, + 3.800275482093663, + 3.642332415059687, + 3.491735537190082, + 3.348484848484848, + 3.2125803489439853, + 3.0840220385674932, + 2.962809917355372, + 2.848943985307622, + 2.7424242424242427, + 2.643250688705234, + 2.551423324150597, + 2.4669421487603302, + 2.389807162534435, + 2.3200183654729107, + 2.257575757575758, + 2.2024793388429753, + 2.1547291092745633, + 2.114325068870523, + 2.0812672176308538, + 2.0555555555555554, + 2.037190082644628, + 2.0261707988980717, + 2.022497704315886, + 2.0261707988980717, + 2.037190082644628, + 2.0555555555555554, + 2.0812672176308538, + 2.114325068870523, + 2.1547291092745633, + 2.2024793388429758, + 2.257575757575758, + 2.320018365472911, + 2.3898071625344355, + 2.4669421487603307, + 2.5514233241505972, + 2.6432506887052343, + 2.7424242424242427, + 2.848943985307622, + 2.9628099173553717, + 3.0840220385674932, + 3.212580348943985, + 3.3484848484848477, + 3.491735537190082, + 3.6423324150596867, + 3.8002754820936655, + 3.965564738292012, + 4.138200183654731, + 4.318181818181819, + 4.505509641873279, + 4.70018365472911, + 4.9022038567493125, + 5.111570247933885, + 5.328282828282829, + 5.552341597796145, + 5.7837465564738295, + 6.022497704315887 + ], + [ + 18.01147842056933, + 17.53030303030303, + 17.056473829201103, + 16.589990817263548, + 16.13085399449036, + 15.679063360881543, + 15.234618916437098, + 14.797520661157025, + 14.367768595041323, + 13.945362718089992, + 13.530303030303031, + 13.12258953168044, + 12.722222222222221, + 12.329201101928373, + 11.943526170798897, + 11.565197428833791, + 11.194214876033058, + 10.830578512396695, + 10.474288337924701, + 10.125344352617079, + 9.78374655647383, + 9.44949494949495, + 9.12258953168044, + 8.803030303030303, + 8.490817263544535, + 8.18595041322314, + 7.888429752066116, + 7.598255280073461, + 7.315426997245179, + 7.039944903581267, + 6.771808999081726, + 6.511019283746556, + 6.257575757575758, + 6.01147842056933, + 5.772727272727273, + 5.541322314049587, + 5.317263544536273, + 5.1005509641873275, + 4.891184573002754, + 4.689164370982552, + 4.494490358126722, + 4.307162534435262, + 4.127180899908173, + 3.954545454545455, + 3.7892561983471067, + 3.6313131313131306, + 3.480716253443526, + 3.3374655647382916, + 3.2015610651974287, + 3.0730027548209367, + 2.9517906336088156, + 2.8379247015610654, + 2.731404958677686, + 2.6322314049586772, + 2.54040404040404, + 2.4559228650137737, + 2.378787878787879, + 2.3089990817263546, + 2.246556473829201, + 2.1914600550964187, + 2.143709825528007, + 2.1033057851239665, + 2.070247933884297, + 2.044536271808999, + 2.0261707988980717, + 2.015151515151515, + 2.01147842056933, + 2.015151515151515, + 2.0261707988980717, + 2.044536271808999, + 2.070247933884297, + 2.1033057851239665, + 2.143709825528007, + 2.191460055096419, + 2.246556473829201, + 2.3089990817263546, + 2.378787878787879, + 2.455922865013774, + 2.5404040404040407, + 2.6322314049586777, + 2.731404958677686, + 2.8379247015610654, + 2.951790633608815, + 3.073002754820937, + 3.2015610651974287, + 3.3374655647382916, + 3.480716253443526, + 3.6313131313131306, + 3.7892561983471094, + 3.954545454545456, + 4.127180899908175, + 4.307162534435263, + 4.494490358126723, + 4.689164370982554, + 4.891184573002756, + 5.100550964187329, + 5.317263544536273, + 5.541322314049587, + 5.772727272727272, + 6.011478420569329 + ], + [ + 18.00413223140496, + 17.522956841138658, + 17.049127640036733, + 16.582644628099175, + 16.12350780532599, + 15.67171717171717, + 15.227272727272727, + 14.790174471992653, + 14.360422405876951, + 13.938016528925619, + 13.52295684113866, + 13.115243342516067, + 12.714876033057848, + 12.321854912764003, + 11.936179981634526, + 11.557851239669422, + 11.186868686868687, + 10.823232323232324, + 10.466942148760332, + 10.117998163452707, + 9.776400367309458, + 9.442148760330578, + 9.115243342516068, + 8.795684113865931, + 8.483471074380166, + 8.17860422405877, + 7.881083562901745, + 7.590909090909091, + 7.308080808080808, + 7.032598714416896, + 6.7644628099173545, + 6.503673094582185, + 6.250229568411386, + 6.0041322314049586, + 5.765381083562902, + 5.533976124885216, + 5.309917355371901, + 5.093204775022956, + 4.883838383838383, + 4.681818181818182, + 4.487144168962351, + 4.299816345270891, + 4.119834710743802, + 3.9471992653810837, + 3.781910009182736, + 3.6239669421487597, + 3.4733700642791545, + 3.3301193755739207, + 3.1942148760330578, + 3.0656565656565657, + 2.9444444444444446, + 2.8305785123966944, + 2.724058769513315, + 2.6248852157943063, + 2.5330578512396693, + 2.448576675849403, + 2.3714416896235075, + 2.3016528925619832, + 2.2392102846648303, + 2.184113865932048, + 2.1363636363636362, + 2.095959595959596, + 2.0629017447199263, + 2.037190082644628, + 2.0188246097337004, + 2.0078053259871442, + 2.0041322314049586, + 2.0078053259871442, + 2.018824609733701, + 2.037190082644628, + 2.0629017447199267, + 2.095959595959596, + 2.1363636363636362, + 2.1841138659320483, + 2.2392102846648303, + 2.3016528925619837, + 2.371441689623508, + 2.448576675849403, + 2.5330578512396698, + 2.624885215794307, + 2.724058769513315, + 2.8305785123966944, + 2.944444444444444, + 3.0656565656565657, + 3.1942148760330573, + 3.3301193755739202, + 3.4733700642791545, + 3.6239669421487593, + 3.781910009182738, + 3.9471992653810846, + 4.119834710743803, + 4.299816345270892, + 4.4871441689623515, + 4.6818181818181825, + 4.883838383838385, + 5.093204775022958, + 5.309917355371901, + 5.533976124885218, + 5.765381083562902, + 6.004132231404959 + ], + [ + 18.000459136822773, + 17.519283746556475, + 17.045454545454547, + 16.578971533516988, + 16.119834710743802, + 15.668044077134985, + 15.22359963269054, + 14.786501377410467, + 14.356749311294767, + 13.934343434343434, + 13.519283746556475, + 13.111570247933882, + 12.711202938475664, + 12.318181818181817, + 11.932506887052341, + 11.554178145087235, + 11.183195592286502, + 10.819559228650139, + 10.463269054178145, + 10.114325068870523, + 9.772727272727273, + 9.438475665748394, + 9.111570247933884, + 8.792011019283747, + 8.47979797979798, + 8.174931129476583, + 7.87741046831956, + 7.587235996326905, + 7.304407713498622, + 7.028925619834711, + 6.760789715335169, + 6.5, + 6.246556473829201, + 6.000459136822773, + 5.761707988980716, + 5.530303030303031, + 5.3062442607897164, + 5.08953168044077, + 4.8801652892561975, + 4.678145087235996, + 4.483471074380165, + 4.296143250688705, + 4.116161616161616, + 3.9435261707988984, + 3.77823691460055, + 3.6202938475665745, + 3.4696969696969693, + 3.3264462809917354, + 3.190541781450872, + 3.06198347107438, + 2.940771349862259, + 2.8269054178145088, + 2.72038567493113, + 2.6212121212121207, + 2.5293847566574836, + 2.4449035812672175, + 2.3677685950413223, + 2.297979797979798, + 2.2355371900826446, + 2.180440771349862, + 2.1326905417814506, + 2.0922865013774103, + 2.059228650137741, + 2.0335169880624426, + 2.015151515151515, + 2.0041322314049586, + 2.000459136822773, + 2.0041322314049586, + 2.015151515151515, + 2.033516988062442, + 2.059228650137741, + 2.0922865013774103, + 2.1326905417814506, + 2.180440771349863, + 2.235537190082645, + 2.2979797979797985, + 2.3677685950413228, + 2.444903581267218, + 2.5293847566574845, + 2.6212121212121215, + 2.72038567493113, + 2.826905417814509, + 2.940771349862259, + 3.06198347107438, + 3.1905417814508716, + 3.3264462809917346, + 3.469696969696969, + 3.6202938475665736, + 3.7782369146005523, + 3.943526170798899, + 4.116161616161618, + 4.296143250688706, + 4.483471074380166, + 4.678145087235997, + 4.880165289256199, + 5.089531680440772, + 5.306244260789716, + 5.530303030303031, + 5.7617079889807155, + 6.000459136822773 + ], + [ + 18.000459136822773, + 17.519283746556475, + 17.045454545454547, + 16.578971533516988, + 16.119834710743802, + 15.668044077134985, + 15.22359963269054, + 14.786501377410467, + 14.356749311294767, + 13.934343434343434, + 13.519283746556475, + 13.111570247933882, + 12.711202938475664, + 12.318181818181817, + 11.932506887052341, + 11.554178145087235, + 11.183195592286502, + 10.819559228650139, + 10.463269054178145, + 10.114325068870523, + 9.772727272727273, + 9.438475665748394, + 9.111570247933884, + 8.792011019283747, + 8.47979797979798, + 8.174931129476583, + 7.87741046831956, + 7.587235996326905, + 7.304407713498622, + 7.028925619834711, + 6.760789715335169, + 6.5, + 6.246556473829201, + 6.000459136822773, + 5.761707988980716, + 5.530303030303031, + 5.3062442607897164, + 5.08953168044077, + 4.8801652892561975, + 4.678145087235996, + 4.483471074380165, + 4.296143250688705, + 4.116161616161616, + 3.9435261707988984, + 3.77823691460055, + 3.6202938475665745, + 3.4696969696969693, + 3.3264462809917354, + 3.190541781450872, + 3.06198347107438, + 2.940771349862259, + 2.8269054178145088, + 2.72038567493113, + 2.6212121212121207, + 2.5293847566574836, + 2.4449035812672175, + 2.3677685950413223, + 2.297979797979798, + 2.2355371900826446, + 2.180440771349862, + 2.1326905417814506, + 2.0922865013774103, + 2.059228650137741, + 2.0335169880624426, + 2.015151515151515, + 2.0041322314049586, + 2.000459136822773, + 2.0041322314049586, + 2.015151515151515, + 2.033516988062442, + 2.059228650137741, + 2.0922865013774103, + 2.1326905417814506, + 2.180440771349863, + 2.235537190082645, + 2.2979797979797985, + 2.3677685950413228, + 2.444903581267218, + 2.5293847566574845, + 2.6212121212121215, + 2.72038567493113, + 2.826905417814509, + 2.940771349862259, + 3.06198347107438, + 3.1905417814508716, + 3.3264462809917346, + 3.469696969696969, + 3.6202938475665736, + 3.7782369146005523, + 3.943526170798899, + 4.116161616161618, + 4.296143250688706, + 4.483471074380166, + 4.678145087235997, + 4.880165289256199, + 5.089531680440772, + 5.306244260789716, + 5.530303030303031, + 5.7617079889807155, + 6.000459136822773 + ], + [ + 18.00413223140496, + 17.522956841138658, + 17.049127640036733, + 16.582644628099175, + 16.12350780532599, + 15.67171717171717, + 15.227272727272727, + 14.790174471992653, + 14.360422405876951, + 13.938016528925619, + 13.52295684113866, + 13.115243342516067, + 12.714876033057848, + 12.321854912764003, + 11.936179981634526, + 11.557851239669422, + 11.186868686868687, + 10.823232323232324, + 10.466942148760332, + 10.117998163452707, + 9.776400367309458, + 9.442148760330578, + 9.115243342516068, + 8.795684113865931, + 8.483471074380166, + 8.17860422405877, + 7.881083562901745, + 7.590909090909091, + 7.308080808080808, + 7.032598714416896, + 6.7644628099173545, + 6.503673094582185, + 6.250229568411386, + 6.0041322314049586, + 5.765381083562902, + 5.533976124885216, + 5.309917355371901, + 5.093204775022956, + 4.883838383838383, + 4.681818181818182, + 4.487144168962351, + 4.299816345270891, + 4.119834710743802, + 3.9471992653810837, + 3.781910009182736, + 3.6239669421487597, + 3.4733700642791545, + 3.3301193755739207, + 3.1942148760330578, + 3.0656565656565657, + 2.9444444444444446, + 2.8305785123966944, + 2.724058769513315, + 2.6248852157943063, + 2.5330578512396693, + 2.448576675849403, + 2.3714416896235075, + 2.3016528925619832, + 2.2392102846648303, + 2.184113865932048, + 2.1363636363636362, + 2.095959595959596, + 2.0629017447199263, + 2.037190082644628, + 2.0188246097337004, + 2.0078053259871442, + 2.0041322314049586, + 2.0078053259871442, + 2.018824609733701, + 2.037190082644628, + 2.0629017447199267, + 2.095959595959596, + 2.1363636363636362, + 2.1841138659320483, + 2.2392102846648303, + 2.3016528925619837, + 2.371441689623508, + 2.448576675849403, + 2.5330578512396698, + 2.624885215794307, + 2.724058769513315, + 2.8305785123966944, + 2.944444444444444, + 3.0656565656565657, + 3.1942148760330573, + 3.3301193755739202, + 3.4733700642791545, + 3.6239669421487593, + 3.781910009182738, + 3.9471992653810846, + 4.119834710743803, + 4.299816345270892, + 4.4871441689623515, + 4.6818181818181825, + 4.883838383838385, + 5.093204775022958, + 5.309917355371901, + 5.533976124885218, + 5.765381083562902, + 6.004132231404959 + ], + [ + 18.01147842056933, + 17.53030303030303, + 17.056473829201103, + 16.589990817263548, + 16.13085399449036, + 15.679063360881543, + 15.234618916437098, + 14.797520661157025, + 14.367768595041323, + 13.945362718089992, + 13.530303030303031, + 13.12258953168044, + 12.722222222222221, + 12.329201101928373, + 11.943526170798897, + 11.565197428833791, + 11.194214876033058, + 10.830578512396695, + 10.474288337924701, + 10.125344352617079, + 9.78374655647383, + 9.44949494949495, + 9.12258953168044, + 8.803030303030303, + 8.490817263544535, + 8.18595041322314, + 7.888429752066116, + 7.598255280073461, + 7.315426997245179, + 7.039944903581267, + 6.771808999081726, + 6.511019283746556, + 6.257575757575758, + 6.01147842056933, + 5.772727272727273, + 5.541322314049587, + 5.317263544536273, + 5.1005509641873275, + 4.891184573002754, + 4.689164370982552, + 4.494490358126722, + 4.307162534435262, + 4.127180899908173, + 3.954545454545455, + 3.7892561983471067, + 3.6313131313131306, + 3.480716253443526, + 3.3374655647382916, + 3.2015610651974287, + 3.0730027548209367, + 2.9517906336088156, + 2.8379247015610654, + 2.731404958677686, + 2.6322314049586772, + 2.54040404040404, + 2.4559228650137737, + 2.378787878787879, + 2.3089990817263546, + 2.246556473829201, + 2.1914600550964187, + 2.143709825528007, + 2.1033057851239665, + 2.070247933884297, + 2.044536271808999, + 2.0261707988980717, + 2.015151515151515, + 2.01147842056933, + 2.015151515151515, + 2.0261707988980717, + 2.044536271808999, + 2.070247933884297, + 2.1033057851239665, + 2.143709825528007, + 2.191460055096419, + 2.246556473829201, + 2.3089990817263546, + 2.378787878787879, + 2.455922865013774, + 2.5404040404040407, + 2.6322314049586777, + 2.731404958677686, + 2.8379247015610654, + 2.951790633608815, + 3.073002754820937, + 3.2015610651974287, + 3.3374655647382916, + 3.480716253443526, + 3.6313131313131306, + 3.7892561983471094, + 3.954545454545456, + 4.127180899908175, + 4.307162534435263, + 4.494490358126723, + 4.689164370982554, + 4.891184573002756, + 5.100550964187329, + 5.317263544536273, + 5.541322314049587, + 5.772727272727272, + 6.011478420569329 + ], + [ + 18.02249770431589, + 17.541322314049587, + 17.06749311294766, + 16.601010101010104, + 16.141873278236915, + 15.690082644628099, + 15.245638200183654, + 14.80853994490358, + 14.378787878787879, + 13.956382001836548, + 13.541322314049587, + 13.133608815426996, + 12.733241505968778, + 12.340220385674929, + 11.954545454545453, + 11.576216712580347, + 11.205234159779614, + 10.841597796143251, + 10.485307621671259, + 10.136363636363637, + 9.794765840220386, + 9.460514233241506, + 9.133608815426996, + 8.814049586776859, + 8.501836547291092, + 8.196969696969697, + 7.8994490358126725, + 7.609274563820018, + 7.3264462809917354, + 7.050964187327824, + 6.782828282828282, + 6.522038567493112, + 6.268595041322314, + 6.022497704315886, + 5.7837465564738295, + 5.5523415977961434, + 5.328282828282829, + 5.111570247933884, + 4.902203856749311, + 4.700183654729109, + 4.505509641873278, + 4.318181818181818, + 4.138200183654729, + 3.965564738292011, + 3.8002754820936633, + 3.642332415059687, + 3.491735537190082, + 3.348484848484848, + 3.2125803489439853, + 3.0840220385674932, + 2.962809917355372, + 2.848943985307622, + 2.7424242424242427, + 2.643250688705234, + 2.551423324150597, + 2.4669421487603307, + 2.389807162534435, + 2.3200183654729107, + 2.257575757575758, + 2.2024793388429753, + 2.1547291092745637, + 2.1143250688705235, + 2.0812672176308538, + 2.0555555555555554, + 2.037190082644628, + 2.0261707988980717, + 2.022497704315886, + 2.0261707988980717, + 2.0371900826446283, + 2.0555555555555554, + 2.081267217630854, + 2.1143250688705235, + 2.1547291092745637, + 2.2024793388429758, + 2.257575757575758, + 2.320018365472911, + 2.3898071625344355, + 2.4669421487603307, + 2.5514233241505972, + 2.6432506887052343, + 2.7424242424242427, + 2.848943985307622, + 2.9628099173553717, + 3.0840220385674932, + 3.212580348943985, + 3.3484848484848477, + 3.491735537190082, + 3.6423324150596867, + 3.8002754820936655, + 3.965564738292012, + 4.138200183654731, + 4.318181818181819, + 4.505509641873279, + 4.70018365472911, + 4.9022038567493125, + 5.111570247933885, + 5.328282828282829, + 5.552341597796145, + 5.7837465564738295, + 6.022497704315887 + ], + [ + 18.037190082644628, + 17.556014692378326, + 17.0821854912764, + 16.615702479338843, + 16.156565656565657, + 15.70477502295684, + 15.260330578512395, + 14.823232323232322, + 14.393480257116622, + 13.97107438016529, + 13.55601469237833, + 13.148301193755737, + 12.747933884297519, + 12.354912764003672, + 11.969237832874196, + 11.59090909090909, + 11.219926538108357, + 10.856290174471994, + 10.5, + 10.151056014692378, + 9.809458218549128, + 9.475206611570249, + 9.148301193755739, + 8.828741965105602, + 8.516528925619834, + 8.211662075298438, + 7.914141414141415, + 7.62396694214876, + 7.341138659320477, + 7.065656565656566, + 6.797520661157024, + 6.536730945821855, + 6.283287419651056, + 6.037190082644628, + 5.798438934802571, + 5.567033976124886, + 5.342975206611571, + 5.126262626262625, + 4.9168962350780525, + 4.714876033057851, + 4.52020202020202, + 4.33287419651056, + 4.152892561983471, + 3.9802571166207534, + 3.814967860422405, + 3.6570247933884295, + 3.5064279155188243, + 3.3631772268135904, + 3.227272727272727, + 3.098714416896235, + 2.977502295684114, + 2.8636363636363638, + 2.757116620752985, + 2.6579430670339756, + 2.5661157024793386, + 2.4816345270890725, + 2.4044995408631773, + 2.334710743801653, + 2.2722681359044996, + 2.217171717171717, + 2.1694214876033056, + 2.1290174471992653, + 2.095959595959596, + 2.0702479338842976, + 2.05188246097337, + 2.0408631772268135, + 2.037190082644628, + 2.0408631772268135, + 2.05188246097337, + 2.070247933884297, + 2.095959595959596, + 2.1290174471992653, + 2.1694214876033056, + 2.217171717171718, + 2.2722681359045, + 2.3347107438016534, + 2.4044995408631777, + 2.481634527089073, + 2.5661157024793395, + 2.6579430670339765, + 2.757116620752985, + 2.863636363636364, + 2.977502295684114, + 3.098714416896235, + 3.2272727272727266, + 3.3631772268135895, + 3.506427915518824, + 3.6570247933884286, + 3.8149678604224073, + 3.980257116620754, + 4.152892561983473, + 4.332874196510561, + 4.520202020202021, + 4.714876033057852, + 4.916896235078054, + 5.126262626262627, + 5.3429752066115705, + 5.567033976124886, + 5.79843893480257, + 6.037190082644628 + ], + [ + 18.055555555555557, + 17.574380165289256, + 17.100550964187327, + 16.634067952249772, + 16.174931129476587, + 15.723140495867767, + 15.278696051423324, + 14.841597796143251, + 14.411845730027547, + 13.989439853076217, + 13.574380165289256, + 13.166666666666664, + 12.766299357208446, + 12.373278236914599, + 11.987603305785122, + 11.609274563820017, + 11.238292011019283, + 10.87465564738292, + 10.51836547291093, + 10.169421487603305, + 9.827823691460054, + 9.493572084481176, + 9.166666666666666, + 8.847107438016529, + 8.534894398530762, + 8.230027548209367, + 7.932506887052343, + 7.642332415059688, + 7.359504132231405, + 7.084022038567493, + 6.815886134067951, + 6.5550964187327825, + 6.301652892561983, + 6.055555555555555, + 5.816804407713499, + 5.585399449035814, + 5.361340679522498, + 5.144628099173553, + 4.93526170798898, + 4.7332415059687785, + 4.538567493112947, + 4.351239669421488, + 4.171258034894398, + 3.9986225895316805, + 3.8333333333333326, + 3.6753902662993565, + 3.5247933884297518, + 3.3815426997245175, + 3.2456382001836546, + 3.1170798898071626, + 2.9958677685950414, + 2.8820018365472913, + 2.775482093663912, + 2.676308539944903, + 2.584481175390266, + 2.5, + 2.4228650137741043, + 2.3530762167125805, + 2.290633608815427, + 2.2355371900826446, + 2.187786960514233, + 2.147382920110193, + 2.1143250688705235, + 2.0886134067952247, + 2.0702479338842976, + 2.059228650137741, + 2.0555555555555554, + 2.059228650137741, + 2.0702479338842976, + 2.0886134067952247, + 2.1143250688705235, + 2.147382920110193, + 2.187786960514233, + 2.2355371900826455, + 2.2906336088154275, + 2.353076216712581, + 2.4228650137741052, + 2.5000000000000004, + 2.584481175390267, + 2.676308539944904, + 2.7754820936639124, + 2.8820018365472917, + 2.9958677685950414, + 3.1170798898071626, + 3.245638200183654, + 3.381542699724517, + 3.5247933884297513, + 3.675390266299356, + 3.833333333333335, + 3.9986225895316814, + 4.1712580348944, + 4.3512396694214885, + 4.538567493112948, + 4.733241505968779, + 4.935261707988982, + 5.144628099173555, + 5.361340679522498, + 5.585399449035814, + 5.816804407713498, + 6.055555555555555 + ], + [ + 18.07759412304867, + 17.596418732782368, + 17.122589531680443, + 16.656106519742885, + 16.1969696969697, + 15.74517906336088, + 15.300734618916437, + 14.863636363636363, + 14.433884297520661, + 14.011478420569329, + 13.59641873278237, + 13.188705234159777, + 12.788337924701558, + 12.395316804407713, + 12.009641873278236, + 11.631313131313131, + 11.260330578512397, + 10.896694214876034, + 10.540404040404042, + 10.191460055096417, + 9.849862258953168, + 9.515610651974288, + 9.188705234159778, + 8.869146005509641, + 8.556932966023876, + 8.25206611570248, + 7.954545454545455, + 7.6643709825528, + 7.381542699724518, + 7.106060606060606, + 6.8379247015610645, + 6.577134986225895, + 6.323691460055096, + 6.0775941230486685, + 5.838842975206612, + 5.607438016528926, + 5.383379247015611, + 5.166666666666666, + 4.957300275482093, + 4.755280073461892, + 4.5606060606060606, + 4.373278236914601, + 4.193296602387512, + 4.020661157024794, + 3.8553719008264453, + 3.6974288337924697, + 3.5468319559228645, + 3.4035812672176307, + 3.2676767676767673, + 3.1391184573002753, + 3.017906336088154, + 2.9040404040404044, + 2.797520661157025, + 2.6983471074380163, + 2.606519742883379, + 2.5220385674931127, + 2.4449035812672175, + 2.375114784205693, + 2.3126721763085403, + 2.257575757575758, + 2.2098255280073458, + 2.1694214876033056, + 2.1363636363636362, + 2.110651974288338, + 2.0922865013774103, + 2.081267217630854, + 2.0775941230486685, + 2.081267217630854, + 2.0922865013774103, + 2.110651974288338, + 2.1363636363636362, + 2.1694214876033056, + 2.2098255280073458, + 2.2575757575757582, + 2.3126721763085403, + 2.3751147842056937, + 2.444903581267218, + 2.522038567493113, + 2.6065197428833797, + 2.6983471074380168, + 2.797520661157025, + 2.9040404040404044, + 3.017906336088154, + 3.1391184573002757, + 3.2676767676767673, + 3.40358126721763, + 3.5468319559228645, + 3.6974288337924692, + 3.855371900826448, + 4.0206611570247945, + 4.193296602387513, + 4.373278236914602, + 4.560606060606061, + 4.7552800734618925, + 4.957300275482095, + 5.166666666666668, + 5.383379247015611, + 5.607438016528928, + 5.838842975206612, + 6.077594123048669 + ], + [ + 18.103305785123965, + 17.622130394857667, + 17.148301193755742, + 16.681818181818183, + 16.222681359044998, + 15.770890725436178, + 15.326446280991735, + 14.889348025711662, + 14.45959595959596, + 14.037190082644628, + 13.622130394857669, + 13.214416896235075, + 12.814049586776857, + 12.421028466483012, + 12.035353535353535, + 11.65702479338843, + 11.286042240587696, + 10.92240587695133, + 10.56611570247934, + 10.217171717171716, + 9.875573921028465, + 9.541322314049587, + 9.214416896235077, + 8.89485766758494, + 8.582644628099173, + 8.277777777777779, + 7.980257116620754, + 7.690082644628099, + 7.407254361799816, + 7.131772268135904, + 6.863636363636363, + 6.602846648301194, + 6.349403122130394, + 6.1033057851239665, + 5.86455463728191, + 5.633149678604225, + 5.40909090909091, + 5.192378328741964, + 4.983011937557391, + 4.78099173553719, + 4.586317722681359, + 4.398989898989899, + 4.2190082644628095, + 4.0463728191000925, + 3.881083562901744, + 3.723140495867768, + 3.572543617998163, + 3.429292929292929, + 3.293388429752066, + 3.1648301193755737, + 3.0436179981634526, + 2.929752066115703, + 2.8232323232323235, + 2.7240587695133147, + 2.6322314049586772, + 2.547750229568411, + 2.470615243342516, + 2.4008264462809916, + 2.3383838383838382, + 2.283287419651056, + 2.2355371900826446, + 2.195133149678604, + 2.1620752984389346, + 2.1363636363636362, + 2.1179981634527087, + 2.106978879706152, + 2.103305785123967, + 2.106978879706152, + 2.117998163452709, + 2.1363636363636362, + 2.1620752984389346, + 2.195133149678604, + 2.2355371900826446, + 2.2832874196510566, + 2.3383838383838387, + 2.400826446280992, + 2.4706152433425164, + 2.5477502295684116, + 2.632231404958678, + 2.724058769513315, + 2.8232323232323235, + 2.929752066115703, + 3.0436179981634526, + 3.1648301193755746, + 3.293388429752066, + 3.429292929292929, + 3.5725436179981633, + 3.723140495867768, + 3.881083562901747, + 4.046372819100093, + 4.219008264462812, + 4.398989898989901, + 4.58631772268136, + 4.780991735537191, + 4.983011937557394, + 5.192378328741967, + 5.40909090909091, + 5.633149678604225, + 5.864554637281909, + 6.1033057851239665 + ], + [ + 18.13269054178145, + 17.65151515151515, + 17.177685950413224, + 16.711202938475665, + 16.252066115702483, + 15.800275482093664, + 15.355831037649219, + 14.918732782369146, + 14.488980716253444, + 14.066574839302113, + 13.651515151515152, + 13.24380165289256, + 12.843434343434343, + 12.450413223140494, + 12.064738292011018, + 11.686409550045912, + 11.31542699724518, + 10.951790633608816, + 10.595500459136824, + 10.246556473829202, + 9.90495867768595, + 9.570707070707071, + 9.24380165289256, + 8.924242424242424, + 8.612029384756656, + 8.307162534435262, + 8.009641873278238, + 7.719467401285582, + 7.4366391184573, + 7.161157024793388, + 6.893021120293847, + 6.632231404958677, + 6.378787878787879, + 6.132690541781451, + 5.8939393939393945, + 5.662534435261708, + 5.438475665748394, + 5.221763085399449, + 5.012396694214876, + 4.810376492194674, + 4.615702479338843, + 4.428374655647383, + 4.248393021120294, + 4.075757575757576, + 3.910468319559228, + 3.7525252525252517, + 3.601928374655647, + 3.4586776859504127, + 3.3227731864095498, + 3.1942148760330578, + 3.0730027548209367, + 2.9591368227731865, + 2.852617079889807, + 2.7534435261707983, + 2.6616161616161613, + 2.577134986225895, + 2.5, + 2.4302112029384757, + 2.3677685950413223, + 2.3126721763085403, + 2.2649219467401283, + 2.224517906336088, + 2.1914600550964187, + 2.1657483930211203, + 2.147382920110193, + 2.1363636363636362, + 2.132690541781451, + 2.1363636363636362, + 2.147382920110193, + 2.1657483930211203, + 2.1914600550964183, + 2.2245179063360876, + 2.2649219467401283, + 2.3126721763085407, + 2.3677685950413228, + 2.430211202938476, + 2.5000000000000004, + 2.5771349862258957, + 2.661616161616162, + 2.7534435261707992, + 2.8526170798898076, + 2.959136822773187, + 3.073002754820936, + 3.194214876033058, + 3.3227731864095498, + 3.4586776859504127, + 3.601928374655647, + 3.7525252525252517, + 3.9104683195592305, + 4.075757575757577, + 4.248393021120296, + 4.428374655647384, + 4.615702479338844, + 4.810376492194675, + 5.012396694214877, + 5.22176308539945, + 5.438475665748394, + 5.662534435261708, + 5.893939393939393, + 6.13269054178145 + ], + [ + 18.16574839302112, + 17.68457300275482, + 17.210743801652896, + 16.744260789715334, + 16.28512396694215, + 15.833333333333332, + 15.38888888888889, + 14.951790633608816, + 14.522038567493112, + 14.099632690541782, + 13.68457300275482, + 13.27685950413223, + 12.876492194674011, + 12.483471074380164, + 12.097796143250687, + 11.719467401285582, + 11.348484848484848, + 10.984848484848484, + 10.628558310376492, + 10.27961432506887, + 9.938016528925619, + 9.603764921946741, + 9.276859504132231, + 8.957300275482094, + 8.645087235996327, + 8.34022038567493, + 8.042699724517906, + 7.752525252525253, + 7.46969696969697, + 7.194214876033058, + 6.926078971533516, + 6.665289256198347, + 6.411845730027548, + 6.16574839302112, + 5.926997245179064, + 5.695592286501378, + 5.471533516988063, + 5.254820936639118, + 5.045454545454545, + 4.8434343434343425, + 4.648760330578512, + 4.461432506887052, + 4.281450872359963, + 4.1088154269972454, + 3.943526170798897, + 3.785583103764921, + 3.6349862258953163, + 3.4917355371900825, + 3.355831037649219, + 3.227272727272727, + 3.106060606060606, + 2.9921946740128558, + 2.885674931129477, + 2.7865013774104677, + 2.6946740128558306, + 2.6101928374655645, + 2.5330578512396693, + 2.463269054178145, + 2.4008264462809916, + 2.3457300275482096, + 2.2979797979797976, + 2.2575757575757573, + 2.224517906336088, + 2.1988062442607896, + 2.180440771349862, + 2.169421487603306, + 2.1657483930211203, + 2.169421487603306, + 2.180440771349862, + 2.1988062442607896, + 2.224517906336088, + 2.2575757575757573, + 2.2979797979797976, + 2.34573002754821, + 2.400826446280992, + 2.4632690541781455, + 2.5330578512396698, + 2.610192837465565, + 2.6946740128558315, + 2.7865013774104685, + 2.885674931129477, + 2.992194674012856, + 3.1060606060606055, + 3.2272727272727275, + 3.355831037649219, + 3.491735537190082, + 3.6349862258953163, + 3.785583103764921, + 3.9435261707988998, + 4.108815426997246, + 4.281450872359965, + 4.4614325068870535, + 4.648760330578513, + 4.843434343434344, + 5.045454545454547, + 5.25482093663912, + 5.471533516988062, + 5.695592286501379, + 5.926997245179063, + 6.16574839302112 + ], + [ + 18.202479338842977, + 17.721303948576676, + 17.247474747474747, + 16.780991735537192, + 16.321854912764007, + 15.870064279155187, + 15.425619834710744, + 14.988521579430671, + 14.558769513314967, + 14.136363636363637, + 13.721303948576676, + 13.313590449954084, + 12.913223140495866, + 12.520202020202019, + 12.134527089072542, + 11.756198347107437, + 11.385215794306703, + 11.02157943067034, + 10.665289256198347, + 10.316345270890725, + 9.974747474747474, + 9.640495867768596, + 9.313590449954086, + 8.994031221303949, + 8.681818181818182, + 8.376951331496786, + 8.079430670339761, + 7.789256198347108, + 7.506427915518825, + 7.230945821854913, + 6.962809917355371, + 6.702020202020202, + 6.448576675849403, + 6.202479338842975, + 5.963728191000919, + 5.732323232323233, + 5.508264462809918, + 5.291551882460973, + 5.0821854912764, + 4.880165289256198, + 4.685491276400367, + 4.498163452708908, + 4.318181818181818, + 4.1455463728191, + 3.9802571166207525, + 3.8223140495867765, + 3.6717171717171713, + 3.5284664830119374, + 3.3925619834710745, + 3.2640036730945825, + 3.1427915518824614, + 3.028925619834711, + 2.922405876951332, + 2.823232323232323, + 2.731404958677686, + 2.6469237832874195, + 2.5697887970615243, + 2.5, + 2.437557392102847, + 2.3824609733700646, + 2.334710743801653, + 2.294306703397613, + 2.261248852157943, + 2.2355371900826446, + 2.217171717171717, + 2.206152433425161, + 2.2024793388429753, + 2.206152433425161, + 2.2171717171717176, + 2.2355371900826446, + 2.261248852157943, + 2.2943067033976123, + 2.334710743801653, + 2.382460973370065, + 2.437557392102847, + 2.5000000000000004, + 2.5697887970615247, + 2.64692378328742, + 2.7314049586776865, + 2.8232323232323235, + 2.922405876951332, + 3.028925619834711, + 3.1427915518824614, + 3.2640036730945825, + 3.392561983471074, + 3.528466483011937, + 3.6717171717171713, + 3.822314049586776, + 3.9802571166207548, + 4.145546372819101, + 4.31818181818182, + 4.4981634527089085, + 4.685491276400368, + 4.880165289256199, + 5.082185491276402, + 5.291551882460975, + 5.508264462809919, + 5.732323232323234, + 5.963728191000918, + 6.202479338842975 + ], + [ + 18.242883379247015, + 17.761707988980717, + 17.28787878787879, + 16.821395775941234, + 16.362258953168045, + 15.910468319559229, + 15.466023875114784, + 15.02892561983471, + 14.599173553719009, + 14.176767676767678, + 13.761707988980717, + 13.353994490358126, + 12.953627180899908, + 12.560606060606059, + 12.174931129476583, + 11.796602387511477, + 11.425619834710744, + 11.061983471074381, + 10.705693296602389, + 10.356749311294767, + 10.015151515151516, + 9.680899908172636, + 9.353994490358126, + 9.034435261707989, + 8.722222222222221, + 8.417355371900827, + 8.119834710743802, + 7.829660238751147, + 7.546831955922865, + 7.271349862258953, + 7.003213957759412, + 6.742424242424242, + 6.488980716253444, + 6.242883379247016, + 6.004132231404959, + 5.772727272727273, + 5.548668503213959, + 5.3319559228650135, + 5.122589531680441, + 4.920569329660239, + 4.725895316804408, + 4.538567493112948, + 4.358585858585859, + 4.185950413223141, + 4.020661157024793, + 3.8627180899908167, + 3.712121212121212, + 3.5688705234159777, + 3.4329660238751147, + 3.3044077134986227, + 3.1831955922865016, + 3.0693296602387514, + 2.962809917355372, + 2.8636363636363633, + 2.7718089990817263, + 2.68732782369146, + 2.610192837465565, + 2.5404040404040407, + 2.4779614325068873, + 2.4228650137741052, + 2.375114784205693, + 2.334710743801653, + 2.3016528925619832, + 2.2759412304866853, + 2.257575757575758, + 2.246556473829201, + 2.242883379247016, + 2.246556473829201, + 2.257575757575758, + 2.2759412304866853, + 2.3016528925619832, + 2.3347107438016526, + 2.375114784205693, + 2.4228650137741057, + 2.4779614325068877, + 2.540404040404041, + 2.6101928374655654, + 2.6873278236914606, + 2.771808999081727, + 2.863636363636364, + 2.9628099173553726, + 3.069329660238752, + 3.183195592286501, + 3.304407713498623, + 3.4329660238751147, + 3.5688705234159777, + 3.712121212121212, + 3.8627180899908167, + 4.020661157024795, + 4.185950413223142, + 4.358585858585861, + 4.538567493112949, + 4.725895316804409, + 4.92056932966024, + 5.122589531680442, + 5.331955922865015, + 5.548668503213959, + 5.772727272727273, + 6.004132231404958, + 6.242883379247015 + ], + [ + 18.286960514233243, + 17.805785123966942, + 17.331955922865014, + 16.86547291092746, + 16.406336088154273, + 15.954545454545453, + 15.51010101010101, + 15.073002754820937, + 14.643250688705233, + 14.220844811753903, + 13.805785123966942, + 13.39807162534435, + 12.997704315886132, + 12.604683195592285, + 12.219008264462808, + 11.840679522497704, + 11.469696969696969, + 11.106060606060606, + 10.749770431588615, + 10.400826446280991, + 10.05922865013774, + 9.724977043158862, + 9.398071625344352, + 9.078512396694215, + 8.766299357208448, + 8.461432506887054, + 8.163911845730027, + 7.873737373737374, + 7.590909090909091, + 7.315426997245179, + 7.047291092745637, + 6.7865013774104685, + 6.533057851239669, + 6.286960514233241, + 6.048209366391185, + 5.8168044077135, + 5.592745638200184, + 5.376033057851239, + 5.166666666666666, + 4.9646464646464645, + 4.7699724517906334, + 4.582644628099174, + 4.4026629935720845, + 4.2300275482093666, + 4.064738292011018, + 3.9067952249770426, + 3.756198347107438, + 3.6129476584022036, + 3.4770431588613406, + 3.3484848484848486, + 3.2272727272727275, + 3.1134067952249773, + 3.006887052341598, + 2.907713498622589, + 2.815886134067952, + 2.731404958677686, + 2.6542699724517904, + 2.5844811753902666, + 2.522038567493113, + 2.4669421487603307, + 2.419191919191919, + 2.378787878787879, + 2.3457300275482096, + 2.3200183654729107, + 2.3016528925619837, + 2.290633608815427, + 2.2869605142332414, + 2.290633608815427, + 2.3016528925619837, + 2.3200183654729107, + 2.3457300275482096, + 2.378787878787879, + 2.419191919191919, + 2.4669421487603316, + 2.522038567493113, + 2.584481175390267, + 2.6542699724517913, + 2.731404958677686, + 2.815886134067953, + 2.9077134986225897, + 3.0068870523415985, + 3.1134067952249778, + 3.2272727272727275, + 3.3484848484848486, + 3.47704315886134, + 3.612947658402203, + 3.7561983471074374, + 3.906795224977042, + 4.064738292011021, + 4.230027548209367, + 4.402662993572086, + 4.582644628099175, + 4.769972451790634, + 4.964646464646465, + 5.166666666666668, + 5.376033057851241, + 5.592745638200185, + 5.8168044077135, + 6.048209366391184, + 6.286960514233241 + ], + [ + 18.33471074380165, + 17.853535353535353, + 17.379706152433428, + 16.91322314049587, + 16.454086317722684, + 16.002295684113864, + 15.557851239669422, + 15.120752984389348, + 14.691000918273645, + 14.268595041322314, + 13.853535353535353, + 13.445821854912761, + 13.045454545454543, + 12.652433425160696, + 12.26675849403122, + 11.888429752066115, + 11.517447199265382, + 11.153810835629017, + 10.797520661157026, + 10.448576675849402, + 10.106978879706151, + 9.772727272727273, + 9.445821854912763, + 9.126262626262626, + 8.814049586776859, + 8.509182736455465, + 8.21166207529844, + 7.921487603305785, + 7.638659320477503, + 7.36317722681359, + 7.095041322314049, + 6.83425160697888, + 6.58080808080808, + 6.3347107438016526, + 6.095959595959596, + 5.864554637281911, + 5.640495867768596, + 5.42378328741965, + 5.214416896235077, + 5.012396694214876, + 4.8177226813590455, + 4.630394857667585, + 4.450413223140496, + 4.277777777777779, + 4.11248852157943, + 3.954545454545454, + 3.803948576675849, + 3.660697887970615, + 3.524793388429752, + 3.3962350780532597, + 3.2750229568411386, + 3.161157024793389, + 3.0546372819100096, + 2.955463728191001, + 2.8636363636363633, + 2.779155188246097, + 2.702020202020202, + 2.6322314049586777, + 2.5697887970615243, + 2.5146923783287423, + 2.4669421487603307, + 2.42653810835629, + 2.3934802571166207, + 2.3677685950413223, + 2.349403122130395, + 2.3383838383838382, + 2.334710743801653, + 2.3383838383838382, + 2.3494031221303953, + 2.3677685950413223, + 2.3934802571166207, + 2.42653810835629, + 2.4669421487603307, + 2.5146923783287427, + 2.5697887970615247, + 2.632231404958678, + 2.7020202020202024, + 2.7791551882460976, + 2.863636363636364, + 2.9554637281910012, + 3.0546372819100096, + 3.161157024793389, + 3.2750229568411386, + 3.3962350780532606, + 3.5247933884297513, + 3.660697887970615, + 3.8039485766758485, + 3.9545454545454533, + 4.112488521579433, + 4.277777777777779, + 4.450413223140497, + 4.630394857667586, + 4.8177226813590455, + 5.0123966942148765, + 5.214416896235079, + 5.423783287419653, + 5.640495867768596, + 5.864554637281911, + 6.095959595959595, + 6.3347107438016526 + ], + [ + 18.38613406795225, + 17.90495867768595, + 17.431129476584026, + 16.964646464646464, + 16.50550964187328, + 16.053719008264462, + 15.60927456382002, + 15.172176308539946, + 14.742424242424242, + 14.320018365472912, + 13.90495867768595, + 13.49724517906336, + 13.09687786960514, + 12.703856749311294, + 12.318181818181817, + 11.939853076216712, + 11.568870523415978, + 11.205234159779614, + 10.848943985307622, + 10.5, + 10.158402203856749, + 9.82415059687787, + 9.49724517906336, + 9.177685950413222, + 8.865472910927457, + 8.56060606060606, + 8.263085399449036, + 7.972910927456382, + 7.690082644628099, + 7.414600550964187, + 7.146464646464645, + 6.8856749311294765, + 6.632231404958677, + 6.38613406795225, + 6.147382920110193, + 5.915977961432508, + 5.691919191919192, + 5.475206611570247, + 5.265840220385675, + 5.0638200183654725, + 4.869146005509641, + 4.681818181818182, + 4.501836547291093, + 4.3292011019283745, + 4.163911845730027, + 4.005968778696051, + 3.855371900826446, + 3.712121212121212, + 3.576216712580349, + 3.4476584022038566, + 3.3264462809917354, + 3.2125803489439857, + 3.1060606060606064, + 3.0068870523415976, + 2.91505968778696, + 2.830578512396694, + 2.753443526170799, + 2.6836547291092745, + 2.621212121212121, + 2.566115702479339, + 2.5183654729109275, + 2.477961432506887, + 2.4449035812672175, + 2.419191919191919, + 2.400826446280992, + 2.389807162534435, + 2.38613406795225, + 2.389807162534435, + 2.400826446280992, + 2.419191919191919, + 2.4449035812672175, + 2.477961432506887, + 2.5183654729109275, + 2.5661157024793395, + 2.6212121212121215, + 2.683654729109275, + 2.7534435261707992, + 2.8305785123966944, + 2.915059687786961, + 3.006887052341598, + 3.1060606060606064, + 3.2125803489439857, + 3.3264462809917354, + 3.4476584022038574, + 3.576216712580349, + 3.712121212121212, + 3.855371900826446, + 4.005968778696051, + 4.16391184573003, + 4.329201101928376, + 4.501836547291095, + 4.681818181818183, + 4.869146005509643, + 5.063820018365474, + 5.265840220385677, + 5.47520661157025, + 5.691919191919192, + 5.9159779614325085, + 6.147382920110193, + 6.38613406795225 + ], + [ + 18.441230486685033, + 17.960055096418735, + 17.486225895316807, + 17.019742883379248, + 16.560606060606062, + 16.108815426997243, + 15.6643709825528, + 15.227272727272727, + 14.797520661157025, + 14.375114784205692, + 13.960055096418733, + 13.55234159779614, + 13.151974288337922, + 12.758953168044076, + 12.373278236914599, + 11.994949494949495, + 11.62396694214876, + 11.260330578512397, + 10.904040404040405, + 10.555096418732782, + 10.213498622589531, + 9.879247015610652, + 9.552341597796143, + 9.232782369146005, + 8.920569329660239, + 8.615702479338843, + 8.318181818181818, + 8.028007346189163, + 7.745179063360881, + 7.46969696969697, + 7.201561065197428, + 6.940771349862258, + 6.68732782369146, + 6.441230486685033, + 6.202479338842975, + 5.971074380165289, + 5.7470156106519745, + 5.530303030303029, + 5.3209366391184565, + 5.118916437098255, + 4.924242424242424, + 4.736914600550964, + 4.556932966023876, + 4.384297520661157, + 4.2190082644628095, + 4.061065197428833, + 3.9104683195592282, + 3.7672176308539944, + 3.631313131313131, + 3.502754820936639, + 3.381542699724518, + 3.2676767676767677, + 3.161157024793389, + 3.0619834710743796, + 2.9701561065197426, + 2.8856749311294765, + 2.8085399449035813, + 2.738751147842057, + 2.6763085399449036, + 2.621212121212121, + 2.5734618916437095, + 2.5330578512396693, + 2.5, + 2.4742883379247016, + 2.455922865013774, + 2.4449035812672175, + 2.4412304866850323, + 2.4449035812672175, + 2.455922865013774, + 2.4742883379247016, + 2.5, + 2.5330578512396693, + 2.5734618916437095, + 2.621212121212122, + 2.676308539944904, + 2.7387511478420574, + 2.8085399449035817, + 2.885674931129477, + 2.9701561065197435, + 3.0619834710743805, + 3.161157024793389, + 3.267676767676768, + 3.381542699724518, + 3.502754820936639, + 3.6313131313131306, + 3.7672176308539935, + 3.910468319559228, + 4.0610651974288325, + 4.219008264462811, + 4.384297520661158, + 4.556932966023877, + 4.736914600550965, + 4.924242424242425, + 5.118916437098256, + 5.320936639118458, + 5.530303030303031, + 5.7470156106519745, + 5.971074380165291, + 6.202479338842975, + 6.441230486685033 + ], + [ + 18.5, + 18.0188246097337, + 17.544995408631774, + 17.078512396694215, + 16.61937557392103, + 16.16758494031221, + 15.723140495867767, + 15.286042240587694, + 14.856290174471994, + 14.433884297520661, + 14.018824609733702, + 13.611111111111109, + 13.21074380165289, + 12.817722681359044, + 12.432047750229568, + 12.053719008264462, + 11.68273645546373, + 11.319100091827364, + 10.962809917355372, + 10.61386593204775, + 10.272268135904499, + 9.938016528925619, + 9.61111111111111, + 9.291551882460972, + 8.979338842975206, + 8.67447199265381, + 8.376951331496787, + 8.086776859504132, + 7.8039485766758485, + 7.528466483011938, + 7.260330578512396, + 6.999540863177226, + 6.746097337006428, + 6.5, + 6.2612488521579435, + 6.029843893480257, + 5.805785123966943, + 5.5890725436179975, + 5.379706152433425, + 5.177685950413222, + 4.983011937557392, + 4.795684113865932, + 4.615702479338843, + 4.443067033976125, + 4.277777777777777, + 4.119834710743801, + 3.969237832874196, + 3.825987144168962, + 3.6900826446280988, + 3.561524334251607, + 3.440312213039486, + 3.3264462809917354, + 3.2199265381083566, + 3.120752984389348, + 3.0289256198347103, + 2.944444444444444, + 2.867309458218549, + 2.7975206611570247, + 2.7350780532598717, + 2.6799816345270893, + 2.6322314049586772, + 2.591827364554637, + 2.5587695133149677, + 2.5330578512396693, + 2.514692378328742, + 2.5036730945821857, + 2.5, + 2.5036730945821857, + 2.514692378328742, + 2.5330578512396693, + 2.5587695133149677, + 2.591827364554637, + 2.6322314049586772, + 2.6799816345270897, + 2.7350780532598717, + 2.797520661157025, + 2.8673094582185494, + 2.9444444444444446, + 3.028925619834711, + 3.1207529843893482, + 3.2199265381083566, + 3.3264462809917354, + 3.440312213039485, + 3.561524334251607, + 3.6900826446280988, + 3.8259871441689617, + 3.969237832874196, + 4.119834710743801, + 4.2777777777777795, + 4.443067033976126, + 4.615702479338845, + 4.795684113865933, + 4.983011937557393, + 5.177685950413224, + 5.379706152433426, + 5.589072543617998, + 5.805785123966942, + 6.029843893480258, + 6.261248852157943, + 6.5 + ], + [ + 18.562442607897154, + 18.081267217630852, + 17.607438016528928, + 17.14095500459137, + 16.681818181818183, + 16.230027548209364, + 15.785583103764921, + 15.348484848484848, + 14.918732782369146, + 14.496326905417813, + 14.081267217630854, + 13.673553719008261, + 13.273186409550043, + 12.880165289256198, + 12.49449035812672, + 12.116161616161616, + 11.745179063360881, + 11.381542699724518, + 11.025252525252526, + 10.676308539944904, + 10.334710743801653, + 10.000459136822773, + 9.673553719008265, + 9.353994490358126, + 9.04178145087236, + 8.736914600550964, + 8.43939393939394, + 8.149219467401284, + 7.866391184573002, + 7.590909090909091, + 7.322773186409549, + 7.061983471074379, + 6.808539944903581, + 6.562442607897154, + 6.323691460055096, + 6.09228650137741, + 5.868227731864096, + 5.6515151515151505, + 5.442148760330578, + 5.240128558310376, + 5.045454545454545, + 4.858126721763085, + 4.678145087235997, + 4.505509641873278, + 4.340220385674931, + 4.1822773186409545, + 4.03168044077135, + 3.8884297520661155, + 3.752525252525252, + 3.62396694214876, + 3.502754820936639, + 3.388888888888889, + 3.28236914600551, + 3.183195592286501, + 3.0913682277318637, + 3.0068870523415976, + 2.9297520661157024, + 2.859963269054178, + 2.7975206611570247, + 2.742424242424242, + 2.6946740128558306, + 2.6542699724517904, + 2.621212121212121, + 2.5955004591368227, + 2.577134986225895, + 2.5661157024793386, + 2.5624426078971534, + 2.5661157024793386, + 2.577134986225895, + 2.5955004591368227, + 2.621212121212121, + 2.6542699724517904, + 2.6946740128558306, + 2.742424242424243, + 2.797520661157025, + 2.8599632690541785, + 2.929752066115703, + 3.006887052341598, + 3.0913682277318646, + 3.1831955922865016, + 3.28236914600551, + 3.3888888888888893, + 3.502754820936639, + 3.62396694214876, + 3.7525252525252517, + 3.8884297520661146, + 4.031680440771349, + 4.182277318640954, + 4.340220385674932, + 4.505509641873279, + 4.678145087235998, + 4.858126721763086, + 5.045454545454546, + 5.240128558310377, + 5.442148760330579, + 5.651515151515152, + 5.868227731864096, + 6.092286501377412, + 6.323691460055096, + 6.562442607897154 + ], + [ + 18.62855831037649, + 18.147382920110193, + 17.673553719008268, + 17.207070707070706, + 16.747933884297524, + 16.296143250688704, + 15.851698806244261, + 15.414600550964188, + 14.984848484848484, + 14.562442607897154, + 14.147382920110193, + 13.739669421487601, + 13.339302112029383, + 12.946280991735536, + 12.560606060606059, + 12.182277318640955, + 11.81129476584022, + 11.447658402203857, + 11.091368227731865, + 10.742424242424242, + 10.400826446280991, + 10.066574839302111, + 9.739669421487601, + 9.420110192837464, + 9.107897153351699, + 8.803030303030303, + 8.505509641873278, + 8.215335169880625, + 7.932506887052341, + 7.65702479338843, + 7.3888888888888875, + 7.128099173553719, + 6.8746556473829195, + 6.6285583103764925, + 6.389807162534435, + 6.15840220385675, + 5.934343434343434, + 5.717630853994489, + 5.508264462809917, + 5.306244260789715, + 5.111570247933884, + 4.924242424242424, + 4.7442607897153355, + 4.571625344352617, + 4.406336088154269, + 4.248393021120293, + 4.097796143250688, + 3.954545454545454, + 3.818640955004591, + 3.690082644628099, + 3.568870523415978, + 3.455004591368228, + 3.3484848484848486, + 3.24931129476584, + 3.1574839302112023, + 3.073002754820936, + 2.995867768595041, + 2.926078971533517, + 2.8636363636363633, + 2.8085399449035813, + 2.7607897153351697, + 2.720385674931129, + 2.6873278236914597, + 2.6616161616161613, + 2.6432506887052343, + 2.6322314049586777, + 2.628558310376492, + 2.6322314049586777, + 2.6432506887052343, + 2.6616161616161613, + 2.6873278236914597, + 2.720385674931129, + 2.7607897153351697, + 2.8085399449035817, + 2.8636363636363638, + 2.926078971533517, + 2.9958677685950414, + 3.0730027548209367, + 3.157483930211203, + 3.2493112947658402, + 3.3484848484848486, + 3.455004591368228, + 3.5688705234159777, + 3.6900826446280997, + 3.818640955004591, + 3.954545454545454, + 4.097796143250688, + 4.248393021120293, + 4.406336088154272, + 4.5716253443526185, + 4.744260789715337, + 4.924242424242426, + 5.111570247933885, + 5.3062442607897164, + 5.508264462809919, + 5.717630853994491, + 5.934343434343434, + 6.158402203856751, + 6.389807162534435, + 6.6285583103764925 + ], + [ + 18.698347107438018, + 18.217171717171716, + 17.743342516069788, + 17.276859504132233, + 16.817722681359047, + 16.365932047750228, + 15.921487603305785, + 15.484389348025712, + 15.054637281910008, + 14.632231404958677, + 14.217171717171716, + 13.809458218549125, + 13.409090909090907, + 13.01606978879706, + 12.630394857667584, + 12.252066115702478, + 11.881083562901745, + 11.51744719926538, + 11.16115702479339, + 10.812213039485766, + 10.470615243342515, + 10.136363636363637, + 9.809458218549127, + 9.48989898989899, + 9.177685950413222, + 8.872819100091828, + 8.575298438934803, + 8.285123966942148, + 8.002295684113866, + 7.726813590449954, + 7.458677685950413, + 7.197887970615243, + 6.944444444444444, + 6.698347107438016, + 6.459595959595959, + 6.228191000918274, + 6.004132231404959, + 5.787419651056013, + 5.5780532598714405, + 5.376033057851239, + 5.181359044995409, + 4.994031221303948, + 4.814049586776859, + 4.641414141414142, + 4.4761248852157935, + 4.3181818181818175, + 4.167584940312212, + 4.024334251606978, + 3.8884297520661155, + 3.759871441689623, + 3.638659320477502, + 3.524793388429752, + 3.418273645546373, + 3.319100091827364, + 3.2272727272727266, + 3.1427915518824605, + 3.0656565656565653, + 2.995867768595041, + 2.9334251606978876, + 2.8783287419651056, + 2.830578512396694, + 2.7901744719926533, + 2.757116620752984, + 2.7314049586776856, + 2.713039485766758, + 2.7020202020202015, + 2.6983471074380163, + 2.7020202020202015, + 2.7130394857667586, + 2.7314049586776856, + 2.757116620752984, + 2.7901744719926533, + 2.830578512396694, + 2.878328741965106, + 2.933425160697888, + 2.9958677685950414, + 3.0656565656565657, + 3.142791551882461, + 3.2272727272727275, + 3.3191000918273645, + 3.418273645546373, + 3.524793388429752, + 3.638659320477502, + 3.759871441689624, + 3.8884297520661146, + 4.024334251606978, + 4.167584940312212, + 4.318181818181817, + 4.476124885215796, + 4.641414141414142, + 4.814049586776861, + 4.994031221303949, + 5.181359044995409, + 5.37603305785124, + 5.578053259871442, + 5.787419651056016, + 6.004132231404959, + 6.228191000918274, + 6.4595959595959584, + 6.698347107438016 + ], + [ + 18.771808999081728, + 18.290633608815426, + 17.816804407713498, + 17.350321395775943, + 16.891184573002757, + 16.439393939393938, + 15.994949494949495, + 15.557851239669422, + 15.128099173553718, + 14.705693296602387, + 14.290633608815426, + 13.882920110192835, + 13.482552800734616, + 13.08953168044077, + 12.703856749311292, + 12.325528007346188, + 11.954545454545453, + 11.59090909090909, + 11.2346189164371, + 10.885674931129476, + 10.544077134986225, + 10.209825528007347, + 9.882920110192837, + 9.5633608815427, + 9.251147842056932, + 8.946280991735538, + 8.648760330578511, + 8.358585858585858, + 8.075757575757574, + 7.800275482093664, + 7.532139577594122, + 7.271349862258953, + 7.017906336088154, + 6.771808999081726, + 6.533057851239669, + 6.301652892561984, + 6.0775941230486685, + 5.860881542699723, + 5.6515151515151505, + 5.449494949494949, + 5.254820936639118, + 5.067493112947658, + 4.887511478420569, + 4.714876033057851, + 4.549586776859503, + 4.3916437098255265, + 4.241046831955922, + 4.097796143250688, + 3.961891643709825, + 3.833333333333333, + 3.712121212121212, + 3.5982552800734617, + 3.4917355371900825, + 3.3925619834710736, + 3.3007346189164366, + 3.2162534435261705, + 3.139118457300275, + 3.0693296602387505, + 3.0068870523415976, + 2.951790633608815, + 2.9040404040404035, + 2.8636363636363633, + 2.830578512396694, + 2.804866850321395, + 2.786501377410468, + 2.7754820936639115, + 2.771808999081726, + 2.7754820936639115, + 2.786501377410468, + 2.804866850321395, + 2.830578512396694, + 2.8636363636363633, + 2.9040404040404035, + 2.951790633608816, + 3.0068870523415976, + 3.0693296602387514, + 3.1391184573002757, + 3.2162534435261705, + 3.3007346189164375, + 3.392561983471074, + 3.491735537190083, + 3.598255280073462, + 3.712121212121212, + 3.833333333333333, + 3.9618916437098246, + 4.0977961432506875, + 4.241046831955922, + 4.3916437098255265, + 4.549586776859505, + 4.714876033057852, + 4.887511478420571, + 5.067493112947659, + 5.254820936639119, + 5.44949494949495, + 5.651515151515152, + 5.860881542699726, + 6.077594123048669, + 6.301652892561984, + 6.533057851239668, + 6.771808999081726 + ], + [ + 18.84894398530762, + 18.36776859504132, + 17.893939393939394, + 17.427456382001836, + 16.968319559228654, + 16.516528925619834, + 16.072084481175388, + 15.634986225895316, + 15.205234159779614, + 14.782828282828284, + 14.367768595041323, + 13.960055096418731, + 13.559687786960513, + 13.166666666666664, + 12.780991735537189, + 12.402662993572083, + 12.03168044077135, + 11.668044077134986, + 11.311753902662993, + 10.96280991735537, + 10.621212121212121, + 10.286960514233241, + 9.960055096418731, + 9.640495867768594, + 9.328282828282827, + 9.023415977961431, + 8.725895316804408, + 8.435720844811753, + 8.152892561983471, + 7.8774104683195585, + 7.609274563820017, + 7.348484848484848, + 7.095041322314049, + 6.8489439853076215, + 6.610192837465565, + 6.378787878787879, + 6.154729109274564, + 5.938016528925619, + 5.728650137741046, + 5.526629935720845, + 5.3319559228650135, + 5.144628099173554, + 4.9646464646464645, + 4.792011019283747, + 4.626721763085398, + 4.468778696051422, + 4.3181818181818175, + 4.174931129476583, + 4.03902662993572, + 3.9104683195592282, + 3.789256198347107, + 3.675390266299357, + 3.5688705234159777, + 3.469696969696969, + 3.377869605142332, + 3.2933884297520652, + 3.2162534435261705, + 3.146464646464646, + 3.084022038567493, + 3.0289256198347103, + 2.9811753902662987, + 2.9407713498622585, + 2.9077134986225888, + 2.882001836547291, + 2.8636363636363633, + 2.8526170798898067, + 2.8489439853076215, + 2.8526170798898067, + 2.8636363636363633, + 2.882001836547291, + 2.9077134986225888, + 2.940771349862258, + 2.9811753902662987, + 3.0289256198347108, + 3.0840220385674932, + 3.146464646464646, + 3.2162534435261705, + 3.293388429752066, + 3.3778696051423323, + 3.4696969696969697, + 3.5688705234159777, + 3.675390266299357, + 3.7892561983471067, + 3.9104683195592287, + 4.03902662993572, + 4.174931129476583, + 4.3181818181818175, + 4.468778696051422, + 4.626721763085401, + 4.7920110192837475, + 4.964646464646466, + 5.144628099173555, + 5.331955922865014, + 5.5266299357208455, + 5.728650137741047, + 5.938016528925621, + 6.154729109274564, + 6.378787878787879, + 6.610192837465563, + 6.848943985307621 + ], + [ + 18.929752066115704, + 18.448576675849402, + 17.974747474747474, + 17.50826446280992, + 17.049127640036733, + 16.597337006427914, + 16.15289256198347, + 15.715794306703398, + 15.286042240587694, + 14.863636363636363, + 14.448576675849402, + 14.04086317722681, + 13.640495867768593, + 13.247474747474746, + 12.861799816345268, + 12.483471074380164, + 12.11248852157943, + 11.748852157943066, + 11.392561983471076, + 11.043617998163452, + 10.7020202020202, + 10.367768595041323, + 10.040863177226813, + 9.721303948576676, + 9.409090909090908, + 9.104224058769512, + 8.806703397612488, + 8.516528925619834, + 8.23370064279155, + 7.95821854912764, + 7.690082644628098, + 7.429292929292929, + 7.17584940312213, + 6.929752066115702, + 6.691000918273645, + 6.459595959595959, + 6.235537190082645, + 6.0188246097336995, + 5.809458218549127, + 5.607438016528925, + 5.412764003673094, + 5.225436179981634, + 5.045454545454545, + 4.872819100091827, + 4.707529843893479, + 4.549586776859503, + 4.398989898989898, + 4.2557392102846645, + 4.119834710743801, + 3.991276400367309, + 3.870064279155188, + 3.756198347107438, + 3.6496786042240585, + 3.5505050505050497, + 3.4586776859504127, + 3.3741965105601466, + 3.297061524334251, + 3.2272727272727266, + 3.1648301193755737, + 3.109733700642791, + 3.0619834710743796, + 3.0215794306703394, + 2.9885215794306697, + 2.9628099173553712, + 2.9444444444444438, + 2.9334251606978876, + 2.929752066115702, + 2.9334251606978876, + 2.944444444444444, + 2.9628099173553712, + 2.9885215794306697, + 3.021579430670339, + 3.0619834710743796, + 3.1097337006427916, + 3.1648301193755737, + 3.227272727272727, + 3.2970615243342514, + 3.3741965105601466, + 3.458677685950413, + 3.55050505050505, + 3.649678604224059, + 3.7561983471074383, + 3.870064279155188, + 3.991276400367309, + 4.119834710743801, + 4.255739210284664, + 4.398989898989898, + 4.549586776859503, + 4.707529843893481, + 4.872819100091828, + 5.045454545454547, + 5.225436179981635, + 5.412764003673095, + 5.607438016528926, + 5.809458218549128, + 6.018824609733702, + 6.2355371900826455, + 6.45959595959596, + 6.6910009182736445, + 6.929752066115702 + ], + [ + 19.01423324150597, + 18.53305785123967, + 18.059228650137744, + 17.592745638200185, + 17.133608815427, + 16.68181818181818, + 16.237373737373737, + 15.800275482093664, + 15.370523415977964, + 14.948117539026631, + 14.533057851239672, + 14.125344352617079, + 13.72497704315886, + 13.331955922865014, + 12.946280991735538, + 12.567952249770432, + 12.196969696969699, + 11.833333333333334, + 11.477043158861342, + 11.12809917355372, + 10.786501377410469, + 10.452249770431589, + 10.12534435261708, + 9.805785123966942, + 9.493572084481176, + 9.18870523415978, + 8.891184573002757, + 8.601010101010102, + 8.318181818181818, + 8.042699724517908, + 7.774563820018366, + 7.513774104683196, + 7.260330578512397, + 7.01423324150597, + 6.775482093663912, + 6.544077134986227, + 6.3200183654729125, + 6.1033057851239665, + 5.8939393939393945, + 5.691919191919192, + 5.497245179063361, + 5.309917355371901, + 5.129935720844813, + 4.957300275482095, + 4.792011019283747, + 4.6340679522497705, + 4.483471074380166, + 4.3402203856749315, + 4.204315886134069, + 4.075757575757576, + 3.9545454545454555, + 3.8406795224977053, + 3.734159779614326, + 3.634986225895317, + 3.54315886134068, + 3.4586776859504136, + 3.381542699724519, + 3.3117539026629945, + 3.249311294765841, + 3.1942148760330586, + 3.146464646464647, + 3.106060606060607, + 3.073002754820937, + 3.047291092745639, + 3.0289256198347116, + 3.017906336088155, + 3.01423324150597, + 3.017906336088155, + 3.0289256198347116, + 3.047291092745639, + 3.073002754820937, + 3.1060606060606064, + 3.146464646464647, + 3.194214876033059, + 3.2493112947658416, + 3.3117539026629945, + 3.381542699724519, + 3.4586776859504145, + 3.5431588613406806, + 3.634986225895318, + 3.734159779614326, + 3.8406795224977053, + 3.954545454545455, + 4.075757575757577, + 4.204315886134069, + 4.3402203856749315, + 4.483471074380166, + 4.6340679522497705, + 4.792011019283749, + 4.957300275482096, + 5.129935720844815, + 5.309917355371903, + 5.497245179063363, + 5.691919191919194, + 5.893939393939396, + 6.103305785123968, + 6.320018365472912, + 6.544077134986228, + 6.775482093663912, + 7.01423324150597 + ], + [ + 19.10238751147842, + 18.62121212121212, + 18.147382920110196, + 17.680899908172638, + 17.221763085399452, + 16.769972451790633, + 16.32552800734619, + 15.888429752066116, + 15.458677685950413, + 15.036271808999082, + 14.621212121212121, + 14.21349862258953, + 13.813131313131311, + 13.420110192837464, + 13.034435261707989, + 12.656106519742883, + 12.28512396694215, + 11.921487603305785, + 11.565197428833795, + 11.21625344352617, + 10.874655647382921, + 10.540404040404042, + 10.213498622589531, + 9.893939393939394, + 9.581726354453627, + 9.276859504132233, + 8.979338842975208, + 8.689164370982553, + 8.406336088154271, + 8.130853994490359, + 7.862718089990818, + 7.601928374655648, + 7.348484848484849, + 7.102387511478421, + 6.863636363636364, + 6.632231404958679, + 6.408172635445364, + 6.191460055096418, + 5.982093663911845, + 5.780073461891644, + 5.585399449035814, + 5.398071625344353, + 5.218089990817264, + 5.045454545454547, + 4.880165289256198, + 4.722222222222222, + 4.571625344352617, + 4.428374655647383, + 4.29247015610652, + 4.163911845730028, + 4.042699724517907, + 3.928833792470157, + 3.822314049586778, + 3.723140495867769, + 3.6313131313131315, + 3.5468319559228654, + 3.46969696969697, + 3.399908172635446, + 3.3374655647382925, + 3.2823691460055104, + 3.234618916437099, + 3.194214876033058, + 3.161157024793389, + 3.1354453627180905, + 3.117079889807163, + 3.1060606060606064, + 3.102387511478421, + 3.1060606060606064, + 3.1170798898071634, + 3.1354453627180905, + 3.161157024793389, + 3.194214876033058, + 3.234618916437099, + 3.282369146005511, + 3.337465564738293, + 3.3999081726354463, + 3.4696969696969706, + 3.546831955922866, + 3.6313131313131324, + 3.723140495867769, + 3.822314049586778, + 3.928833792470157, + 4.042699724517907, + 4.163911845730029, + 4.2924701561065195, + 4.428374655647383, + 4.571625344352617, + 4.722222222222221, + 4.880165289256201, + 5.045454545454547, + 5.2180899908172655, + 5.398071625344354, + 5.585399449035814, + 5.780073461891645, + 5.982093663911847, + 6.191460055096421, + 6.408172635445364, + 6.632231404958679, + 6.863636363636363, + 7.102387511478421 + ], + [ + 19.194214876033058, + 18.713039485766757, + 18.239210284664832, + 17.772727272727273, + 17.31359044995409, + 16.861799816345272, + 16.417355371900825, + 15.980257116620752, + 15.550505050505052, + 15.12809917355372, + 14.71303948576676, + 14.305325987144167, + 13.904958677685949, + 13.511937557392102, + 13.126262626262626, + 12.74793388429752, + 12.376951331496787, + 12.013314967860424, + 11.65702479338843, + 11.308080808080808, + 10.966483011937557, + 10.632231404958679, + 10.305325987144169, + 9.98576675849403, + 9.673553719008265, + 9.368686868686869, + 9.071166207529846, + 8.78099173553719, + 8.498163452708908, + 8.222681359044996, + 7.954545454545454, + 7.693755739210285, + 7.440312213039486, + 7.194214876033058, + 6.955463728191002, + 6.7240587695133165, + 6.500000000000001, + 6.283287419651056, + 6.073921028466483, + 5.871900826446281, + 5.67722681359045, + 5.4898989898989905, + 5.309917355371901, + 5.137281910009183, + 4.971992653810835, + 4.814049586776859, + 4.663452708907254, + 4.520202020202021, + 4.384297520661157, + 4.255739210284665, + 4.134527089072544, + 4.020661157024794, + 3.9141414141414153, + 3.814967860422406, + 3.723140495867769, + 3.638659320477503, + 3.561524334251607, + 3.491735537190083, + 3.42929292929293, + 3.3741965105601475, + 3.326446280991736, + 3.2860422405876957, + 3.2529843893480264, + 3.2272727272727275, + 3.2089072543618005, + 3.197887970615244, + 3.194214876033058, + 3.197887970615244, + 3.2089072543618005, + 3.2272727272727275, + 3.2529843893480264, + 3.2860422405876957, + 3.326446280991736, + 3.3741965105601484, + 3.42929292929293, + 3.491735537190084, + 3.561524334251608, + 3.638659320477503, + 3.72314049586777, + 3.8149678604224064, + 3.9141414141414153, + 4.0206611570247945, + 4.134527089072544, + 4.255739210284665, + 4.384297520661157, + 4.52020202020202, + 4.663452708907254, + 4.814049586776859, + 4.971992653810838, + 5.137281910009184, + 5.309917355371903, + 5.489898989898991, + 5.677226813590451, + 5.871900826446282, + 6.073921028466485, + 6.283287419651058, + 6.500000000000002, + 6.7240587695133165, + 6.955463728191001, + 7.194214876033058 + ], + [ + 19.28971533516988, + 18.80853994490358, + 18.334710743801654, + 17.868227731864096, + 17.409090909090914, + 16.957300275482094, + 16.512855831037648, + 16.075757575757578, + 15.646005509641874, + 15.223599632690544, + 14.808539944903583, + 14.400826446280991, + 14.000459136822773, + 13.607438016528924, + 13.221763085399449, + 12.843434343434343, + 12.47245179063361, + 12.108815426997246, + 11.752525252525253, + 11.40358126721763, + 11.061983471074381, + 10.727731864095501, + 10.400826446280991, + 10.081267217630854, + 9.769054178145087, + 9.46418732782369, + 9.166666666666668, + 8.876492194674013, + 8.59366391184573, + 8.318181818181818, + 8.050045913682277, + 7.789256198347108, + 7.535812672176309, + 7.289715335169881, + 7.050964187327825, + 6.819559228650139, + 6.595500459136824, + 6.378787878787879, + 6.169421487603306, + 5.9674012855831045, + 5.772727272727273, + 5.585399449035814, + 5.405417814508724, + 5.2327823691460065, + 5.067493112947658, + 4.909550045913682, + 4.758953168044077, + 4.615702479338843, + 4.47979797979798, + 4.3512396694214885, + 4.230027548209367, + 4.116161616161617, + 4.0096418732782375, + 3.9104683195592287, + 3.8186409550045917, + 3.734159779614325, + 3.6570247933884303, + 3.587235996326906, + 3.5247933884297526, + 3.46969696969697, + 3.4219467401285586, + 3.3815426997245184, + 3.3484848484848486, + 3.3227731864095507, + 3.304407713498623, + 3.2933884297520666, + 3.2897153351698813, + 3.2933884297520666, + 3.304407713498623, + 3.3227731864095507, + 3.3484848484848486, + 3.381542699724518, + 3.4219467401285586, + 3.4696969696969706, + 3.524793388429753, + 3.587235996326906, + 3.6570247933884303, + 3.734159779614326, + 3.818640955004592, + 3.9104683195592296, + 4.0096418732782375, + 4.116161616161617, + 4.2300275482093666, + 4.3512396694214885, + 4.47979797979798, + 4.615702479338843, + 4.758953168044077, + 4.909550045913682, + 5.067493112947661, + 5.232782369146007, + 5.405417814508726, + 5.5853994490358145, + 5.772727272727274, + 5.9674012855831045, + 6.169421487603307, + 6.378787878787881, + 6.595500459136824, + 6.819559228650139, + 7.050964187327823, + 7.2897153351698805 + ], + [ + 19.38888888888889, + 18.90771349862259, + 18.433884297520663, + 17.967401285583104, + 17.50826446280992, + 17.056473829201103, + 16.612029384756656, + 16.174931129476583, + 15.745179063360883, + 15.32277318640955, + 14.907713498622591, + 14.499999999999998, + 14.09963269054178, + 13.706611570247933, + 13.320936639118457, + 12.942607897153351, + 12.571625344352618, + 12.207988980716253, + 11.851698806244261, + 11.502754820936639, + 11.161157024793388, + 10.82690541781451, + 10.5, + 10.180440771349861, + 9.868227731864096, + 9.5633608815427, + 9.265840220385677, + 8.975665748393022, + 8.692837465564738, + 8.417355371900827, + 8.149219467401284, + 7.8884297520661155, + 7.634986225895317, + 7.388888888888889, + 7.150137741046833, + 6.918732782369147, + 6.694674012855832, + 6.477961432506887, + 6.268595041322314, + 6.0665748393021115, + 5.871900826446281, + 5.684573002754822, + 5.504591368227732, + 5.331955922865014, + 5.166666666666666, + 5.00872359963269, + 4.858126721763085, + 4.714876033057852, + 4.578971533516988, + 4.4504132231404965, + 4.329201101928375, + 4.215335169880625, + 4.108815426997246, + 4.009641873278237, + 3.9178145087236, + 3.8333333333333335, + 3.7561983471074383, + 3.686409550045914, + 3.623966942148761, + 3.5688705234159785, + 3.5211202938475665, + 3.4807162534435263, + 3.447658402203857, + 3.4219467401285586, + 3.403581267217631, + 3.392561983471075, + 3.3888888888888893, + 3.392561983471075, + 3.403581267217631, + 3.4219467401285586, + 3.447658402203857, + 3.4807162534435263, + 3.5211202938475665, + 3.568870523415979, + 3.623966942148761, + 3.6864095500459144, + 3.7561983471074387, + 3.833333333333334, + 3.9178145087236, + 4.0096418732782375, + 4.108815426997246, + 4.215335169880625, + 4.3292011019283745, + 4.4504132231404965, + 4.578971533516988, + 4.714876033057851, + 4.858126721763085, + 5.00872359963269, + 5.166666666666669, + 5.331955922865015, + 5.504591368227734, + 5.6845730027548225, + 5.871900826446282, + 6.066574839302113, + 6.268595041322316, + 6.477961432506888, + 6.694674012855831, + 6.918732782369148, + 7.150137741046832, + 7.388888888888889 + ], + [ + 19.49173553719008, + 19.010560146923783, + 18.53673094582186, + 18.0702479338843, + 17.611111111111114, + 17.159320477502295, + 16.714876033057852, + 16.27777777777778, + 15.848025711662075, + 15.425619834710744, + 15.010560146923783, + 14.602846648301192, + 14.202479338842974, + 13.809458218549127, + 13.42378328741965, + 13.045454545454545, + 12.67447199265381, + 12.310835629017447, + 11.954545454545457, + 11.605601469237833, + 11.264003673094582, + 10.929752066115704, + 10.602846648301194, + 10.283287419651057, + 9.97107438016529, + 9.666207529843895, + 9.368686868686869, + 9.078512396694215, + 8.795684113865931, + 8.52020202020202, + 8.25206611570248, + 7.99127640036731, + 7.737832874196511, + 7.491735537190083, + 7.252984389348026, + 7.021579430670341, + 6.797520661157026, + 6.58080808080808, + 6.3714416896235075, + 6.169421487603306, + 5.974747474747475, + 5.787419651056015, + 5.607438016528926, + 5.434802571166208, + 5.26951331496786, + 5.111570247933884, + 4.960973370064279, + 4.8177226813590455, + 4.681818181818182, + 4.55325987144169, + 4.432047750229569, + 4.318181818181818, + 4.21166207529844, + 4.112488521579431, + 4.020661157024794, + 3.9361799816345275, + 3.859044995408632, + 3.7892561983471076, + 3.7268135904499546, + 3.671717171717172, + 3.6239669421487606, + 3.5835629017447204, + 3.550505050505051, + 3.524793388429752, + 3.506427915518825, + 3.4954086317722686, + 3.491735537190083, + 3.4954086317722686, + 3.506427915518825, + 3.524793388429752, + 3.550505050505051, + 3.5835629017447204, + 3.6239669421487606, + 3.671717171717173, + 3.7268135904499546, + 3.7892561983471085, + 3.8590449954086328, + 3.9361799816345275, + 4.0206611570247945, + 4.112488521579431, + 4.21166207529844, + 4.318181818181819, + 4.432047750229569, + 4.55325987144169, + 4.681818181818182, + 4.817722681359045, + 4.960973370064279, + 5.111570247933884, + 5.269513314967862, + 5.434802571166209, + 5.607438016528928, + 5.787419651056016, + 5.974747474747476, + 6.169421487603307, + 6.371441689623509, + 6.580808080808083, + 6.7975206611570265, + 7.021579430670341, + 7.2529843893480255, + 7.491735537190083 + ], + [ + 19.598255280073463, + 19.11707988980716, + 18.643250688705237, + 18.17676767676768, + 17.717630853994493, + 17.265840220385673, + 16.82139577594123, + 16.384297520661157, + 15.954545454545455, + 15.532139577594123, + 15.117079889807163, + 14.70936639118457, + 14.308999081726352, + 13.915977961432507, + 13.53030303030303, + 13.151974288337925, + 12.78099173553719, + 12.417355371900827, + 12.061065197428835, + 11.712121212121213, + 11.370523415977962, + 11.036271808999082, + 10.709366391184574, + 10.389807162534435, + 10.07759412304867, + 9.772727272727273, + 9.475206611570249, + 9.185032139577594, + 8.902203856749312, + 8.6267217630854, + 8.358585858585858, + 8.097796143250688, + 7.84435261707989, + 7.598255280073462, + 7.359504132231406, + 7.12809917355372, + 6.904040404040405, + 6.68732782369146, + 6.477961432506887, + 6.275941230486685, + 6.081267217630854, + 5.8939393939393945, + 5.713957759412305, + 5.541322314049587, + 5.376033057851239, + 5.218089990817264, + 5.067493112947658, + 4.924242424242424, + 4.788337924701561, + 4.659779614325069, + 4.538567493112948, + 4.424701561065198, + 4.318181818181818, + 4.2190082644628095, + 4.127180899908173, + 4.042699724517906, + 3.965564738292011, + 3.895775941230487, + 3.833333333333334, + 3.7782369146005514, + 3.7304866850321394, + 3.690082644628099, + 3.65702479338843, + 3.6313131313131315, + 3.612947658402204, + 3.601928374655648, + 3.598255280073462, + 3.601928374655648, + 3.612947658402204, + 3.6313131313131315, + 3.65702479338843, + 3.690082644628099, + 3.7304866850321394, + 3.778236914600552, + 3.833333333333334, + 3.8957759412304873, + 3.965564738292011, + 4.042699724517907, + 4.127180899908174, + 4.21900826446281, + 4.318181818181818, + 4.4247015610651985, + 4.538567493112948, + 4.659779614325069, + 4.788337924701561, + 4.924242424242424, + 5.067493112947658, + 5.218089990817263, + 5.376033057851242, + 5.541322314049588, + 5.713957759412307, + 5.893939393939395, + 6.081267217630856, + 6.275941230486687, + 6.477961432506888, + 6.6873278236914615, + 6.904040404040405, + 7.128099173553721, + 7.359504132231404, + 7.598255280073463 + ], + [ + 19.708448117539028, + 19.227272727272727, + 18.7534435261708, + 18.286960514233243, + 17.827823691460058, + 17.376033057851238, + 16.931588613406795, + 16.494490358126722, + 16.064738292011018, + 15.642332415059688, + 15.227272727272728, + 14.819559228650135, + 14.419191919191917, + 14.026170798898072, + 13.640495867768594, + 13.26216712580349, + 12.891184573002755, + 12.52754820936639, + 12.1712580348944, + 11.822314049586776, + 11.480716253443527, + 11.146464646464647, + 10.819559228650137, + 10.5, + 10.187786960514234, + 9.882920110192838, + 9.585399449035814, + 9.295224977043159, + 9.012396694214877, + 8.736914600550964, + 8.468778696051423, + 8.207988980716253, + 7.954545454545455, + 7.708448117539027, + 7.469696969696971, + 7.2382920110192845, + 7.01423324150597, + 6.797520661157025, + 6.588154269972451, + 6.38613406795225, + 6.191460055096419, + 6.004132231404959, + 5.82415059687787, + 5.651515151515152, + 5.486225895316804, + 5.328282828282828, + 5.177685950413223, + 5.034435261707989, + 4.898530762167126, + 4.769972451790634, + 4.648760330578513, + 4.534894398530763, + 4.428374655647383, + 4.3292011019283745, + 4.237373737373737, + 4.152892561983471, + 4.075757575757576, + 4.005968778696052, + 3.9435261707988984, + 3.888429752066116, + 3.8406795224977044, + 3.800275482093664, + 3.7672176308539944, + 3.7415059687786965, + 3.723140495867769, + 3.7121212121212124, + 3.708448117539027, + 3.7121212121212124, + 3.723140495867769, + 3.7415059687786965, + 3.7672176308539944, + 3.8002754820936637, + 3.8406795224977044, + 3.8884297520661164, + 3.943526170798899, + 4.005968778696052, + 4.075757575757576, + 4.152892561983472, + 4.237373737373738, + 4.329201101928375, + 4.428374655647383, + 4.534894398530763, + 4.648760330578512, + 4.769972451790634, + 4.898530762167126, + 5.034435261707989, + 5.177685950413223, + 5.328282828282828, + 5.486225895316807, + 5.651515151515153, + 5.824150596877872, + 6.004132231404959, + 6.191460055096419, + 6.38613406795225, + 6.588154269972453, + 6.7975206611570265, + 7.01423324150597, + 7.2382920110192845, + 7.469696969696969, + 7.708448117539026 + ], + [ + 19.82231404958678, + 19.341138659320478, + 18.86730945821855, + 18.400826446280995, + 17.941689623507806, + 17.48989898989899, + 17.045454545454547, + 16.608356290174473, + 16.17860422405877, + 15.75619834710744, + 15.341138659320478, + 14.933425160697887, + 14.533057851239668, + 14.14003673094582, + 13.754361799816344, + 13.376033057851238, + 13.005050505050505, + 12.641414141414142, + 12.28512396694215, + 11.936179981634528, + 11.594582185491277, + 11.260330578512397, + 10.933425160697887, + 10.61386593204775, + 10.301652892561982, + 9.996786042240588, + 9.699265381083563, + 9.409090909090908, + 9.126262626262626, + 8.850780532598716, + 8.582644628099173, + 8.321854912764003, + 8.068411386593205, + 7.822314049586777, + 7.58356290174472, + 7.352157943067034, + 7.12809917355372, + 6.911386593204774, + 6.7020202020202015, + 6.5, + 6.305325987144169, + 6.117998163452709, + 5.938016528925621, + 5.765381083562902, + 5.600091827364555, + 5.4421487603305785, + 5.291551882460973, + 5.1483011937557395, + 5.0123966942148765, + 4.883838383838384, + 4.762626262626263, + 4.648760330578513, + 4.542240587695134, + 4.443067033976124, + 4.351239669421488, + 4.2667584940312215, + 4.189623507805326, + 4.1198347107438025, + 4.057392102846649, + 4.002295684113866, + 3.9545454545454546, + 3.9141414141414144, + 3.881083562901745, + 3.855371900826446, + 3.837006427915519, + 3.8259871441689626, + 3.822314049586777, + 3.8259871441689626, + 3.837006427915519, + 3.855371900826446, + 3.881083562901745, + 3.9141414141414144, + 3.9545454545454546, + 4.002295684113867, + 4.057392102846649, + 4.1198347107438025, + 4.189623507805327, + 4.2667584940312215, + 4.3512396694214885, + 4.443067033976125, + 4.542240587695134, + 4.648760330578513, + 4.762626262626263, + 4.883838383838384, + 5.012396694214876, + 5.148301193755739, + 5.291551882460973, + 5.442148760330578, + 5.600091827364556, + 5.765381083562903, + 5.938016528925622, + 6.117998163452711, + 6.305325987144171, + 6.500000000000002, + 6.702020202020204, + 6.911386593204776, + 7.12809917355372, + 7.352157943067036, + 7.58356290174472, + 7.822314049586778 + ], + [ + 19.939853076216714, + 19.458677685950413, + 18.984848484848484, + 18.51836547291093, + 18.059228650137744, + 17.607438016528924, + 17.16299357208448, + 16.725895316804408, + 16.296143250688704, + 15.873737373737374, + 15.458677685950413, + 15.050964187327821, + 14.650596877869603, + 14.257575757575756, + 13.871900826446279, + 13.493572084481174, + 13.12258953168044, + 12.758953168044076, + 12.402662993572086, + 12.053719008264462, + 11.712121212121211, + 11.377869605142333, + 11.050964187327823, + 10.731404958677686, + 10.419191919191919, + 10.114325068870524, + 9.816804407713498, + 9.526629935720845, + 9.24380165289256, + 8.96831955922865, + 8.70018365472911, + 8.43939393939394, + 8.18595041322314, + 7.939853076216712, + 7.701101928374656, + 7.469696969696971, + 7.245638200183655, + 7.02892561983471, + 6.819559228650137, + 6.617539026629935, + 6.422865013774104, + 6.235537190082645, + 6.055555555555555, + 5.882920110192838, + 5.717630853994489, + 5.559687786960513, + 5.409090909090908, + 5.265840220385675, + 5.129935720844811, + 5.0013774104683195, + 4.880165289256198, + 4.766299357208448, + 4.659779614325069, + 4.5606060606060606, + 4.468778696051423, + 4.384297520661157, + 4.307162534435262, + 4.237373737373737, + 4.174931129476584, + 4.119834710743802, + 4.07208448117539, + 4.03168044077135, + 3.9986225895316805, + 3.9729109274563816, + 3.9545454545454546, + 3.943526170798898, + 3.9398530762167123, + 3.943526170798898, + 3.9545454545454546, + 3.9729109274563816, + 3.9986225895316805, + 4.03168044077135, + 4.07208448117539, + 4.1198347107438025, + 4.174931129476584, + 4.237373737373738, + 4.307162534435262, + 4.384297520661157, + 4.468778696051424, + 4.5606060606060606, + 4.659779614325069, + 4.766299357208449, + 4.880165289256198, + 5.0013774104683195, + 5.129935720844811, + 5.265840220385674, + 5.409090909090908, + 5.559687786960513, + 5.717630853994492, + 5.882920110192838, + 6.055555555555557, + 6.2355371900826455, + 6.422865013774105, + 6.617539026629936, + 6.819559228650139, + 7.0289256198347125, + 7.245638200183656, + 7.469696969696971, + 7.701101928374655, + 7.939853076216712 + ], + [ + 20.06106519742883, + 19.579889807162534, + 19.10606060606061, + 18.63957759412305, + 18.180440771349865, + 17.728650137741045, + 17.284205693296602, + 16.84710743801653, + 16.417355371900825, + 15.994949494949495, + 15.579889807162534, + 15.172176308539942, + 14.771808999081724, + 14.378787878787877, + 13.993112947658402, + 13.614784205693296, + 13.243801652892563, + 12.880165289256198, + 12.523875114784207, + 12.174931129476583, + 11.833333333333334, + 11.499081726354454, + 11.172176308539944, + 10.852617079889807, + 10.540404040404042, + 10.235537190082646, + 9.938016528925619, + 9.647842056932966, + 9.365013774104684, + 9.089531680440771, + 8.82139577594123, + 8.56060606060606, + 8.30716253443526, + 8.061065197428833, + 7.822314049586777, + 7.590909090909092, + 7.366850321395777, + 7.150137741046831, + 6.940771349862258, + 6.7387511478420565, + 6.544077134986226, + 6.356749311294766, + 6.1767676767676765, + 6.004132231404959, + 5.83884297520661, + 5.680899908172635, + 5.530303030303029, + 5.387052341597796, + 5.251147842056933, + 5.122589531680441, + 5.0013774104683195, + 4.88751147842057, + 4.7809917355371905, + 4.681818181818182, + 4.589990817263544, + 4.505509641873278, + 4.428374655647383, + 4.358585858585858, + 4.296143250688705, + 4.241046831955924, + 4.193296602387512, + 4.152892561983471, + 4.119834710743802, + 4.094123048668504, + 4.075757575757576, + 4.064738292011019, + 4.061065197428833, + 4.064738292011019, + 4.075757575757576, + 4.094123048668504, + 4.119834710743802, + 4.152892561983471, + 4.193296602387512, + 4.241046831955924, + 4.296143250688706, + 4.358585858585859, + 4.428374655647383, + 4.505509641873278, + 4.589990817263545, + 4.681818181818182, + 4.7809917355371905, + 4.88751147842057, + 5.0013774104683195, + 5.1225895316804415, + 5.251147842056932, + 5.387052341597796, + 5.530303030303029, + 5.680899908172634, + 5.838842975206614, + 6.004132231404959, + 6.176767676767678, + 6.356749311294767, + 6.544077134986226, + 6.738751147842057, + 6.94077134986226, + 7.150137741046834, + 7.366850321395777, + 7.590909090909092, + 7.822314049586776, + 8.061065197428833 + ], + [ + 20.18595041322314, + 19.70477502295684, + 19.230945821854913, + 18.764462809917354, + 18.305325987144172, + 17.853535353535353, + 17.40909090909091, + 16.971992653810837, + 16.542240587695133, + 16.119834710743802, + 15.704775022956841, + 15.29706152433425, + 14.896694214876032, + 14.503673094582183, + 14.117998163452707, + 13.739669421487601, + 13.368686868686869, + 13.005050505050505, + 12.648760330578513, + 12.29981634527089, + 11.95821854912764, + 11.62396694214876, + 11.29706152433425, + 10.977502295684113, + 10.665289256198346, + 10.36042240587695, + 10.062901744719927, + 9.772727272727272, + 9.48989898989899, + 9.214416896235077, + 8.946280991735536, + 8.685491276400366, + 8.432047750229568, + 8.18595041322314, + 7.947199265381084, + 7.715794306703398, + 7.491735537190083, + 7.275022956841138, + 7.065656565656565, + 6.863636363636363, + 6.668962350780532, + 6.4816345270890725, + 6.301652892561983, + 6.129017447199265, + 5.963728191000917, + 5.805785123966942, + 5.655188246097336, + 5.511937557392102, + 5.37603305785124, + 5.247474747474747, + 5.126262626262626, + 5.0123966942148765, + 4.905876951331496, + 4.8067033976124875, + 4.71487603305785, + 4.630394857667584, + 4.553259871441689, + 4.483471074380165, + 4.421028466483012, + 4.3659320477502295, + 4.3181818181818175, + 4.277777777777777, + 4.244719926538108, + 4.2190082644628095, + 4.200642791551882, + 4.189623507805326, + 4.18595041322314, + 4.189623507805326, + 4.200642791551882, + 4.2190082644628095, + 4.244719926538108, + 4.277777777777777, + 4.3181818181818175, + 4.3659320477502295, + 4.421028466483012, + 4.483471074380166, + 4.553259871441689, + 4.630394857667585, + 4.714876033057852, + 4.806703397612488, + 4.905876951331496, + 5.0123966942148765, + 5.126262626262626, + 5.247474747474747, + 5.376033057851239, + 5.511937557392102, + 5.655188246097336, + 5.805785123966941, + 5.96372819100092, + 6.129017447199266, + 6.301652892561986, + 6.481634527089074, + 6.668962350780532, + 6.863636363636363, + 7.0656565656565675, + 7.2750229568411395, + 7.491735537190083, + 7.715794306703398, + 7.947199265381084, + 8.18595041322314 + ], + [ + 20.31450872359963, + 19.833333333333332, + 19.359504132231407, + 18.89302112029385, + 18.433884297520663, + 17.982093663911844, + 17.5376492194674, + 17.100550964187327, + 16.670798898071624, + 16.248393021120293, + 15.833333333333332, + 15.42561983471074, + 15.025252525252522, + 14.632231404958675, + 14.2465564738292, + 13.868227731864094, + 13.497245179063361, + 13.133608815426996, + 12.777318640955006, + 12.428374655647382, + 12.086776859504132, + 11.752525252525253, + 11.425619834710742, + 11.106060606060606, + 10.79384756657484, + 10.488980716253444, + 10.191460055096417, + 9.901285583103764, + 9.618457300275482, + 9.34297520661157, + 9.074839302112029, + 8.814049586776859, + 8.560606060606059, + 8.314508723599632, + 8.075757575757574, + 7.84435261707989, + 7.620293847566575, + 7.403581267217629, + 7.194214876033056, + 6.992194674012855, + 6.797520661157025, + 6.610192837465564, + 6.430211202938475, + 6.257575757575758, + 6.092286501377409, + 5.934343434343433, + 5.783746556473828, + 5.640495867768594, + 5.504591368227731, + 5.376033057851239, + 5.254820936639118, + 5.140955004591368, + 5.034435261707989, + 4.93526170798898, + 4.8434343434343425, + 4.758953168044076, + 4.681818181818182, + 4.6120293847566565, + 4.5495867768595035, + 4.494490358126722, + 4.44674012855831, + 4.406336088154269, + 4.3732782369146, + 4.347566574839302, + 4.3292011019283745, + 4.3181818181818175, + 4.314508723599632, + 4.3181818181818175, + 4.3292011019283745, + 4.347566574839302, + 4.3732782369146, + 4.406336088154269, + 4.44674012855831, + 4.494490358126722, + 4.549586776859504, + 4.612029384756657, + 4.681818181818182, + 4.758953168044076, + 4.843434343434343, + 4.93526170798898, + 5.034435261707989, + 5.140955004591368, + 5.254820936639118, + 5.37603305785124, + 5.5045913682277305, + 5.640495867768594, + 5.783746556473828, + 5.9343434343434325, + 6.092286501377412, + 6.257575757575758, + 6.430211202938477, + 6.610192837465565, + 6.797520661157025, + 6.992194674012856, + 7.194214876033058, + 7.403581267217632, + 7.620293847566575, + 7.84435261707989, + 8.075757575757574, + 8.314508723599632 + ], + [ + 20.44674012855831, + 19.96556473829201, + 19.491735537190085, + 19.025252525252526, + 18.56611570247934, + 18.11432506887052, + 17.669880624426078, + 17.232782369146005, + 16.803030303030305, + 16.38062442607897, + 15.965564738292013, + 15.557851239669418, + 15.1574839302112, + 14.764462809917354, + 14.378787878787877, + 14.000459136822773, + 13.629476584022038, + 13.265840220385675, + 12.909550045913683, + 12.56060606060606, + 12.21900826446281, + 11.88475665748393, + 11.557851239669422, + 11.238292011019283, + 10.926078971533517, + 10.621212121212121, + 10.323691460055096, + 10.033516988062441, + 9.75068870523416, + 9.475206611570247, + 9.207070707070706, + 8.946280991735536, + 8.692837465564738, + 8.44674012855831, + 8.207988980716253, + 7.976584022038567, + 7.752525252525253, + 7.5358126721763075, + 7.326446280991735, + 7.124426078971533, + 6.929752066115702, + 6.742424242424242, + 6.562442607897153, + 6.389807162534435, + 6.224517906336087, + 6.0665748393021115, + 5.915977961432506, + 5.772727272727272, + 5.63682277318641, + 5.508264462809917, + 5.387052341597796, + 5.273186409550046, + 5.166666666666666, + 5.067493112947657, + 4.97566574839302, + 4.891184573002754, + 4.814049586776859, + 4.744260789715335, + 4.681818181818182, + 4.626721763085399, + 4.578971533516987, + 4.5385674931129465, + 4.505509641873278, + 4.479797979797979, + 4.461432506887052, + 4.450413223140496, + 4.44674012855831, + 4.450413223140496, + 4.461432506887052, + 4.479797979797979, + 4.505509641873278, + 4.5385674931129465, + 4.578971533516987, + 4.626721763085399, + 4.681818181818182, + 4.7442607897153355, + 4.814049586776859, + 4.8911845730027546, + 4.975665748393022, + 5.067493112947658, + 5.166666666666666, + 5.273186409550046, + 5.387052341597796, + 5.508264462809917, + 5.636822773186409, + 5.772727272727272, + 5.915977961432506, + 6.066574839302111, + 6.224517906336089, + 6.389807162534435, + 6.562442607897154, + 6.742424242424242, + 6.929752066115704, + 7.124426078971535, + 7.3264462809917354, + 7.535812672176309, + 7.752525252525253, + 7.976584022038569, + 8.207988980716252, + 8.44674012855831 + ], + [ + 20.582644628099175, + 20.101469237832873, + 19.627640036730945, + 19.16115702479339, + 18.702020202020204, + 18.250229568411385, + 17.805785123966942, + 17.36868686868687, + 16.938934802571165, + 16.516528925619834, + 16.101469237832873, + 15.693755739210282, + 15.293388429752063, + 14.900367309458217, + 14.51469237832874, + 14.136363636363635, + 13.7653810835629, + 13.401744719926537, + 13.045454545454545, + 12.696510560146923, + 12.354912764003672, + 12.020661157024794, + 11.693755739210282, + 11.374196510560147, + 11.06198347107438, + 10.757116620752985, + 10.459595959595958, + 10.169421487603305, + 9.886593204775021, + 9.61111111111111, + 9.34297520661157, + 9.082185491276398, + 8.8287419651056, + 8.582644628099173, + 8.343893480257115, + 8.11248852157943, + 7.8884297520661155, + 7.67171717171717, + 7.4623507805325975, + 7.260330578512395, + 7.065656565656565, + 6.878328741965104, + 6.698347107438016, + 6.525711662075298, + 6.36042240587695, + 6.2024793388429735, + 6.051882460973369, + 5.908631772268135, + 5.772727272727272, + 5.644168962350779, + 5.522956841138658, + 5.409090909090908, + 5.30257116620753, + 5.203397612488521, + 5.111570247933884, + 5.0270890725436175, + 4.949954086317722, + 4.8801652892561975, + 4.817722681359044, + 4.762626262626262, + 4.71487603305785, + 4.67447199265381, + 4.64141414141414, + 4.615702479338842, + 4.597337006427915, + 4.5863177226813585, + 4.582644628099173, + 4.5863177226813585, + 4.597337006427915, + 4.615702479338842, + 4.64141414141414, + 4.67447199265381, + 4.71487603305785, + 4.762626262626263, + 4.817722681359045, + 4.8801652892561975, + 4.949954086317723, + 5.0270890725436175, + 5.111570247933884, + 5.203397612488521, + 5.30257116620753, + 5.409090909090908, + 5.522956841138658, + 5.64416896235078, + 5.772727272727272, + 5.9086317722681345, + 6.051882460973369, + 6.2024793388429735, + 6.360422405876953, + 6.525711662075299, + 6.698347107438018, + 6.878328741965106, + 7.065656565656566, + 7.260330578512397, + 7.462350780532599, + 7.671717171717173, + 7.888429752066116, + 8.112488521579431, + 8.343893480257115, + 8.582644628099173 + ], + [ + 20.72222222222222, + 20.241046831955924, + 19.767217630854, + 19.30073461891644, + 18.841597796143255, + 18.389807162534435, + 17.945362718089992, + 17.50826446280992, + 17.078512396694215, + 16.656106519742885, + 16.241046831955924, + 15.833333333333332, + 15.432966023875114, + 15.039944903581267, + 14.654269972451791, + 14.275941230486685, + 13.904958677685952, + 13.541322314049587, + 13.185032139577597, + 12.836088154269973, + 12.494490358126724, + 12.160238751147844, + 11.833333333333334, + 11.513774104683197, + 11.201561065197431, + 10.896694214876035, + 10.599173553719009, + 10.308999081726355, + 10.026170798898073, + 9.750688705234161, + 9.48255280073462, + 9.22176308539945, + 8.96831955922865, + 8.722222222222223, + 8.483471074380166, + 8.252066115702481, + 8.028007346189167, + 7.811294765840221, + 7.601928374655648, + 7.399908172635446, + 7.205234159779616, + 7.0179063360881555, + 6.837924701561066, + 6.665289256198349, + 6.5, + 6.342056932966025, + 6.191460055096419, + 6.048209366391186, + 5.912304866850323, + 5.78374655647383, + 5.662534435261709, + 5.5486685032139595, + 5.44214876033058, + 5.342975206611571, + 5.251147842056934, + 5.166666666666668, + 5.089531680440773, + 5.019742883379248, + 4.957300275482095, + 4.902203856749313, + 4.854453627180901, + 4.814049586776861, + 4.780991735537191, + 4.755280073461893, + 4.736914600550966, + 4.725895316804409, + 4.722222222222223, + 4.725895316804409, + 4.736914600550966, + 4.755280073461893, + 4.780991735537191, + 4.814049586776861, + 4.854453627180901, + 4.902203856749313, + 4.957300275482096, + 5.019742883379249, + 5.089531680440773, + 5.166666666666668, + 5.251147842056935, + 5.342975206611571, + 5.44214876033058, + 5.5486685032139595, + 5.662534435261709, + 5.783746556473831, + 5.912304866850322, + 6.048209366391186, + 6.191460055096419, + 6.342056932966024, + 6.5000000000000036, + 6.665289256198349, + 6.837924701561068, + 7.017906336088156, + 7.205234159779616, + 7.399908172635447, + 7.60192837465565, + 7.811294765840223, + 8.028007346189167, + 8.252066115702481, + 8.483471074380166, + 8.722222222222223 + ], + [ + 20.86547291092746, + 20.384297520661157, + 19.910468319559232, + 19.443985307621674, + 18.984848484848488, + 18.53305785123967, + 18.088613406795226, + 17.651515151515152, + 17.221763085399452, + 16.799357208448118, + 16.38429752066116, + 15.976584022038567, + 15.576216712580349, + 15.183195592286502, + 14.797520661157025, + 14.41919191919192, + 14.048209366391186, + 13.684573002754822, + 13.32828282828283, + 12.979338842975208, + 12.637741046831957, + 12.303489439853077, + 11.976584022038569, + 11.65702479338843, + 11.344811753902665, + 11.039944903581269, + 10.742424242424244, + 10.452249770431589, + 10.169421487603307, + 9.893939393939394, + 9.625803489439853, + 9.365013774104684, + 9.111570247933885, + 8.865472910927458, + 8.626721763085401, + 8.395316804407715, + 8.1712580348944, + 7.954545454545455, + 7.745179063360882, + 7.543158861340681, + 7.3484848484848495, + 7.16115702479339, + 6.9811753902663005, + 6.808539944903583, + 6.643250688705234, + 6.485307621671259, + 6.334710743801653, + 6.191460055096419, + 6.055555555555557, + 5.926997245179065, + 5.805785123966944, + 5.691919191919194, + 5.585399449035814, + 5.486225895316805, + 5.394398530762167, + 5.309917355371901, + 5.2327823691460065, + 5.162993572084482, + 5.100550964187329, + 5.045454545454547, + 4.997704315886135, + 4.957300275482094, + 4.924242424242426, + 4.898530762167127, + 4.880165289256199, + 4.869146005509643, + 4.8654729109274575, + 4.869146005509643, + 4.880165289256199, + 4.898530762167127, + 4.924242424242426, + 4.957300275482094, + 4.997704315886135, + 5.045454545454547, + 5.100550964187329, + 5.162993572084483, + 5.2327823691460065, + 5.309917355371902, + 5.394398530762169, + 5.486225895316806, + 5.585399449035814, + 5.691919191919194, + 5.805785123966944, + 5.926997245179065, + 6.055555555555556, + 6.191460055096419, + 6.334710743801653, + 6.485307621671259, + 6.643250688705237, + 6.808539944903583, + 6.981175390266301, + 7.16115702479339, + 7.348484848484851, + 7.543158861340682, + 7.745179063360883, + 7.954545454545457, + 8.1712580348944, + 8.395316804407717, + 8.6267217630854, + 8.865472910927458 + ], + [ + 21.01239669421488, + 20.531221303948577, + 20.057392102846652, + 19.590909090909093, + 19.131772268135908, + 18.67998163452709, + 18.235537190082646, + 17.798438934802572, + 17.368686868686872, + 16.946280991735538, + 16.53122130394858, + 16.123507805325985, + 15.723140495867769, + 15.330119375573922, + 14.944444444444445, + 14.56611570247934, + 14.195133149678606, + 13.831496786042242, + 13.47520661157025, + 13.126262626262628, + 12.784664830119377, + 12.450413223140497, + 12.123507805325989, + 11.80394857667585, + 11.491735537190085, + 11.186868686868689, + 10.889348025711664, + 10.599173553719009, + 10.316345270890727, + 10.040863177226814, + 9.772727272727273, + 9.511937557392104, + 9.258494031221305, + 9.012396694214878, + 8.773645546372821, + 8.542240587695135, + 8.31818181818182, + 8.101469237832875, + 7.892102846648302, + 7.6900826446281005, + 7.4954086317722695, + 7.30808080808081, + 7.1280991735537205, + 6.955463728191003, + 6.790174471992654, + 6.632231404958679, + 6.481634527089073, + 6.338383838383839, + 6.202479338842977, + 6.073921028466485, + 5.9527089072543635, + 5.838842975206614, + 5.732323232323234, + 5.633149678604225, + 5.541322314049587, + 5.456841138659321, + 5.379706152433426, + 5.309917355371902, + 5.247474747474749, + 5.192378328741967, + 5.144628099173555, + 5.104224058769514, + 5.071166207529846, + 5.045454545454547, + 5.027089072543619, + 5.016069788797063, + 5.012396694214877, + 5.016069788797063, + 5.027089072543619, + 5.045454545454547, + 5.071166207529846, + 5.104224058769514, + 5.144628099173555, + 5.192378328741967, + 5.247474747474749, + 5.309917355371903, + 5.379706152433426, + 5.456841138659322, + 5.541322314049589, + 5.633149678604226, + 5.732323232323234, + 5.838842975206614, + 5.9527089072543635, + 6.073921028466485, + 6.202479338842976, + 6.338383838383839, + 6.481634527089073, + 6.632231404958679, + 6.790174471992657, + 6.955463728191003, + 7.128099173553721, + 7.30808080808081, + 7.495408631772271, + 7.690082644628102, + 7.892102846648303, + 8.101469237832877, + 8.31818181818182, + 8.542240587695137, + 8.77364554637282, + 9.012396694214878 + ], + [ + 21.16299357208448, + 20.681818181818183, + 20.207988980716255, + 19.741505968778696, + 19.282369146005514, + 18.830578512396695, + 18.386134067952252, + 17.94903581267218, + 17.519283746556475, + 17.096877869605144, + 16.681818181818183, + 16.27410468319559, + 15.873737373737372, + 15.480716253443527, + 15.09504132231405, + 14.716712580348943, + 14.34573002754821, + 13.982093663911847, + 13.625803489439855, + 13.276859504132233, + 12.935261707988982, + 12.601010101010102, + 12.274104683195592, + 11.954545454545455, + 11.642332415059688, + 11.337465564738292, + 11.039944903581269, + 10.749770431588614, + 10.466942148760332, + 10.19146005509642, + 9.923324150596878, + 9.662534435261708, + 9.40909090909091, + 9.162993572084481, + 8.924242424242426, + 8.69283746556474, + 8.468778696051425, + 8.25206611570248, + 8.042699724517906, + 7.840679522497705, + 7.646005509641874, + 7.4586776859504145, + 7.278696051423325, + 7.106060606060607, + 6.940771349862259, + 6.782828282828284, + 6.632231404958678, + 6.488980716253444, + 6.353076216712582, + 6.224517906336089, + 6.103305785123968, + 5.9894398530762185, + 5.882920110192838, + 5.7837465564738295, + 5.691919191919192, + 5.607438016528926, + 5.530303030303031, + 5.460514233241507, + 5.398071625344354, + 5.342975206611571, + 5.295224977043159, + 5.254820936639119, + 5.22176308539945, + 5.1960514233241515, + 5.177685950413224, + 5.166666666666668, + 5.162993572084482, + 5.166666666666668, + 5.177685950413224, + 5.1960514233241515, + 5.22176308539945, + 5.254820936639119, + 5.295224977043159, + 5.342975206611571, + 5.398071625344354, + 5.460514233241508, + 5.530303030303031, + 5.607438016528927, + 5.691919191919194, + 5.78374655647383, + 5.882920110192838, + 5.9894398530762185, + 6.103305785123968, + 6.224517906336089, + 6.353076216712581, + 6.488980716253444, + 6.632231404958679, + 6.782828282828282, + 6.940771349862262, + 7.106060606060609, + 7.278696051423328, + 7.458677685950416, + 7.646005509641874, + 7.840679522497705, + 8.04269972451791, + 8.252066115702481, + 8.468778696051425, + 8.69283746556474, + 8.924242424242426, + 9.162993572084481 + ], + [ + 21.317263544536274, + 20.836088154269973, + 20.362258953168045, + 19.89577594123049, + 19.436639118457304, + 18.984848484848484, + 18.54040404040404, + 18.10330578512397, + 17.673553719008265, + 17.251147842056934, + 16.836088154269973, + 16.42837465564738, + 16.028007346189163, + 15.634986225895316, + 15.249311294765839, + 14.870982552800735, + 14.5, + 14.136363636363637, + 13.780073461891645, + 13.431129476584022, + 13.089531680440771, + 12.755280073461893, + 12.428374655647382, + 12.108815426997246, + 11.796602387511479, + 11.491735537190085, + 11.194214876033058, + 10.904040404040405, + 10.621212121212121, + 10.34573002754821, + 10.07759412304867, + 9.816804407713498, + 9.5633608815427, + 9.317263544536273, + 9.078512396694215, + 8.847107438016529, + 8.623048668503216, + 8.40633608815427, + 8.196969696969697, + 7.994949494949495, + 7.800275482093665, + 7.612947658402204, + 7.432966023875116, + 7.260330578512398, + 7.095041322314049, + 6.937098255280073, + 6.7865013774104685, + 6.643250688705235, + 6.507346189164371, + 6.378787878787879, + 6.257575757575758, + 6.143709825528008, + 6.03719008264463, + 5.938016528925621, + 5.846189164370983, + 5.761707988980717, + 5.684573002754822, + 5.614784205693297, + 5.5523415977961434, + 5.497245179063362, + 5.44949494949495, + 5.40909090909091, + 5.37603305785124, + 5.350321395775942, + 5.331955922865014, + 5.320936639118458, + 5.317263544536273, + 5.320936639118458, + 5.331955922865014, + 5.350321395775942, + 5.37603305785124, + 5.40909090909091, + 5.44949494949495, + 5.497245179063363, + 5.552341597796144, + 5.614784205693297, + 5.6845730027548225, + 5.761707988980717, + 5.846189164370983, + 5.938016528925621, + 6.03719008264463, + 6.143709825528008, + 6.257575757575758, + 6.37878787878788, + 6.507346189164371, + 6.643250688705234, + 6.7865013774104685, + 6.937098255280073, + 7.095041322314053, + 7.260330578512399, + 7.432966023875117, + 7.612947658402206, + 7.8002754820936655, + 7.994949494949497, + 8.196969696969699, + 8.406336088154273, + 8.623048668503216, + 8.84710743801653, + 9.078512396694215, + 9.317263544536273 + ], + [ + 21.47520661157025, + 20.99403122130395, + 20.52020202020202, + 20.053719008264466, + 19.59458218549128, + 19.14279155188246, + 18.698347107438018, + 18.261248852157944, + 17.83149678604224, + 17.40909090909091, + 16.99403122130395, + 16.586317722681358, + 16.18595041322314, + 15.792929292929292, + 15.407254361799817, + 15.02892561983471, + 14.657943067033976, + 14.294306703397613, + 13.93801652892562, + 13.589072543617998, + 13.247474747474747, + 12.91322314049587, + 12.586317722681358, + 12.266758494031222, + 11.954545454545455, + 11.64967860422406, + 11.352157943067034, + 11.061983471074381, + 10.779155188246097, + 10.503673094582187, + 10.235537190082646, + 9.974747474747474, + 9.721303948576676, + 9.475206611570249, + 9.236455463728191, + 9.005050505050505, + 8.780991735537192, + 8.564279155188245, + 8.354912764003673, + 8.152892561983471, + 7.958218549127641, + 7.77089072543618, + 7.590909090909092, + 7.418273645546374, + 7.2529843893480255, + 7.095041322314049, + 6.944444444444445, + 6.801193755739211, + 6.6652892561983474, + 6.536730945821855, + 6.415518824609734, + 6.301652892561984, + 6.195133149678606, + 6.095959595959597, + 6.004132231404959, + 5.919651056014693, + 5.842516069788798, + 5.772727272727273, + 5.7102846648301195, + 5.655188246097338, + 5.607438016528926, + 5.567033976124886, + 5.533976124885216, + 5.508264462809918, + 5.4898989898989905, + 5.478879706152434, + 5.475206611570249, + 5.478879706152434, + 5.4898989898989905, + 5.508264462809918, + 5.533976124885216, + 5.567033976124886, + 5.607438016528926, + 5.655188246097339, + 5.71028466483012, + 5.772727272727273, + 5.842516069788799, + 5.919651056014693, + 6.004132231404959, + 6.095959595959597, + 6.195133149678606, + 6.301652892561984, + 6.415518824609734, + 6.536730945821856, + 6.6652892561983474, + 6.801193755739211, + 6.944444444444445, + 7.095041322314049, + 7.252984389348029, + 7.418273645546375, + 7.5909090909090935, + 7.770890725436182, + 7.958218549127642, + 8.152892561983473, + 8.354912764003675, + 8.564279155188249, + 8.780991735537192, + 9.005050505050507, + 9.236455463728191, + 9.475206611570249 + ], + [ + 21.63682277318641, + 21.15564738292011, + 20.681818181818183, + 20.215335169880625, + 19.756198347107443, + 19.304407713498623, + 18.85996326905418, + 18.422865013774107, + 17.993112947658403, + 17.570707070707073, + 17.15564738292011, + 16.747933884297517, + 16.3475665748393, + 15.954545454545455, + 15.568870523415978, + 15.190541781450873, + 14.819559228650139, + 14.455922865013775, + 14.099632690541783, + 13.750688705234161, + 13.40909090909091, + 13.07483930211203, + 12.74793388429752, + 12.428374655647383, + 12.116161616161616, + 11.81129476584022, + 11.513774104683197, + 11.223599632690542, + 10.94077134986226, + 10.665289256198347, + 10.397153351698806, + 10.136363636363637, + 9.882920110192838, + 9.63682277318641, + 9.398071625344354, + 9.166666666666668, + 8.942607897153353, + 8.725895316804408, + 8.516528925619834, + 8.314508723599634, + 8.119834710743802, + 7.932506887052343, + 7.7525252525252535, + 7.579889807162536, + 7.414600550964187, + 7.256657483930212, + 7.106060606060606, + 6.962809917355372, + 6.82690541781451, + 6.698347107438018, + 6.5771349862258965, + 6.463269054178147, + 6.356749311294767, + 6.257575757575758, + 6.16574839302112, + 6.081267217630854, + 6.004132231404959, + 5.934343434343435, + 5.871900826446282, + 5.8168044077135, + 5.769054178145088, + 5.728650137741048, + 5.695592286501379, + 5.66988062442608, + 5.651515151515152, + 5.640495867768596, + 5.6368227731864105, + 5.640495867768596, + 5.651515151515152, + 5.66988062442608, + 5.695592286501379, + 5.728650137741047, + 5.769054178145088, + 5.8168044077135, + 5.871900826446282, + 5.934343434343436, + 6.004132231404959, + 6.081267217630855, + 6.165748393021122, + 6.257575757575759, + 6.356749311294767, + 6.463269054178147, + 6.5771349862258965, + 6.698347107438018, + 6.82690541781451, + 6.962809917355372, + 7.106060606060607, + 7.25665748393021, + 7.41460055096419, + 7.579889807162537, + 7.752525252525256, + 7.9325068870523445, + 8.119834710743802, + 8.314508723599634, + 8.516528925619838, + 8.72589531680441, + 8.942607897153353, + 9.166666666666668, + 9.398071625344354, + 9.63682277318641 + ], + [ + 21.80211202938476, + 21.320936639118457, + 20.84710743801653, + 20.380624426078974, + 19.92148760330579, + 19.46969696969697, + 19.025252525252526, + 18.588154269972453, + 18.15840220385675, + 17.73599632690542, + 17.320936639118457, + 16.913223140495866, + 16.512855831037648, + 16.119834710743802, + 15.734159779614325, + 15.355831037649219, + 14.984848484848486, + 14.621212121212121, + 14.264921946740131, + 13.915977961432507, + 13.574380165289258, + 13.240128558310378, + 12.913223140495868, + 12.59366391184573, + 12.281450872359965, + 11.976584022038569, + 11.679063360881543, + 11.38888888888889, + 11.106060606060607, + 10.830578512396695, + 10.562442607897154, + 10.301652892561984, + 10.048209366391184, + 9.802112029384757, + 9.5633608815427, + 9.331955922865015, + 9.1078971533517, + 8.891184573002754, + 8.681818181818182, + 8.47979797979798, + 8.285123966942148, + 8.09779614325069, + 7.917814508723601, + 7.745179063360883, + 7.579889807162534, + 7.421946740128559, + 7.271349862258953, + 7.12809917355372, + 6.992194674012857, + 6.863636363636364, + 6.742424242424243, + 6.628558310376493, + 6.522038567493114, + 6.422865013774105, + 6.331037649219468, + 6.246556473829202, + 6.169421487603307, + 6.099632690541783, + 6.037190082644629, + 5.982093663911846, + 5.934343434343435, + 5.8939393939393945, + 5.860881542699725, + 5.835169880624427, + 5.8168044077135, + 5.805785123966943, + 5.802112029384757, + 5.805785123966943, + 5.8168044077135, + 5.835169880624427, + 5.860881542699725, + 5.8939393939393945, + 5.934343434343435, + 5.982093663911847, + 6.03719008264463, + 6.099632690541783, + 6.169421487603307, + 6.246556473829202, + 6.331037649219469, + 6.422865013774105, + 6.522038567493114, + 6.628558310376493, + 6.742424242424243, + 6.863636363636365, + 6.992194674012856, + 7.12809917355372, + 7.271349862258953, + 7.421946740128558, + 7.579889807162537, + 7.745179063360883, + 7.917814508723602, + 8.09779614325069, + 8.28512396694215, + 8.479797979797981, + 8.681818181818183, + 8.891184573002757, + 9.1078971533517, + 9.331955922865015, + 9.5633608815427, + 9.802112029384757 + ], + [ + 21.97107438016529, + 21.48989898989899, + 21.01606978879706, + 20.549586776859506, + 20.09044995408632, + 19.6386593204775, + 19.194214876033058, + 18.757116620752985, + 18.32736455463728, + 17.90495867768595, + 17.48989898989899, + 17.082185491276398, + 16.68181818181818, + 16.288797061524335, + 15.903122130394857, + 15.524793388429751, + 15.153810835629018, + 14.790174471992653, + 14.433884297520663, + 14.084940312213039, + 13.74334251606979, + 13.40909090909091, + 13.0821854912764, + 12.762626262626263, + 12.450413223140497, + 12.145546372819101, + 11.848025711662075, + 11.557851239669422, + 11.27502295684114, + 10.999540863177227, + 10.731404958677686, + 10.470615243342516, + 10.217171717171716, + 9.97107438016529, + 9.732323232323232, + 9.500918273645548, + 9.276859504132233, + 9.060146923783286, + 8.850780532598714, + 8.648760330578511, + 8.45408631772268, + 8.266758494031222, + 8.086776859504134, + 7.914141414141415, + 7.748852157943067, + 7.590909090909091, + 7.440312213039486, + 7.297061524334252, + 7.161157024793389, + 7.032598714416896, + 6.911386593204775, + 6.797520661157026, + 6.691000918273646, + 6.5918273645546375, + 6.5, + 6.415518824609734, + 6.338383838383839, + 6.268595041322315, + 6.206152433425161, + 6.1510560146923785, + 6.103305785123967, + 6.062901744719927, + 6.029843893480257, + 6.004132231404959, + 5.985766758494032, + 5.974747474747475, + 5.971074380165289, + 5.974747474747475, + 5.985766758494032, + 6.004132231404959, + 6.029843893480257, + 6.062901744719927, + 6.103305785123967, + 6.151056014692379, + 6.206152433425162, + 6.268595041322315, + 6.338383838383839, + 6.415518824609734, + 6.500000000000001, + 6.5918273645546375, + 6.691000918273646, + 6.797520661157026, + 6.911386593204775, + 7.032598714416897, + 7.161157024793388, + 7.297061524334252, + 7.440312213039485, + 7.59090909090909, + 7.74885215794307, + 7.914141414141415, + 8.086776859504134, + 8.266758494031222, + 8.454086317722682, + 8.648760330578513, + 8.850780532598716, + 9.06014692378329, + 9.276859504132233, + 9.500918273645548, + 9.732323232323232, + 9.97107438016529 + ], + [ + 22.143709825528006, + 21.66253443526171, + 21.188705234159784, + 20.722222222222225, + 20.26308539944904, + 19.81129476584022, + 19.366850321395777, + 18.929752066115704, + 18.5, + 18.07759412304867, + 17.66253443526171, + 17.254820936639117, + 16.8544536271809, + 16.46143250688705, + 16.075757575757578, + 15.69742883379247, + 15.326446280991737, + 14.962809917355372, + 14.60651974288338, + 14.257575757575758, + 13.915977961432507, + 13.581726354453629, + 13.254820936639117, + 12.935261707988982, + 12.623048668503214, + 12.31818181818182, + 12.020661157024794, + 11.73048668503214, + 11.447658402203857, + 11.172176308539946, + 10.904040404040405, + 10.643250688705233, + 10.389807162534435, + 10.143709825528008, + 9.90495867768595, + 9.673553719008265, + 9.449494949494952, + 9.232782369146005, + 9.023415977961433, + 8.82139577594123, + 8.6267217630854, + 8.439393939393941, + 8.259412304866851, + 8.086776859504134, + 7.921487603305785, + 7.763544536271809, + 7.612947658402204, + 7.46969696969697, + 7.333792470156107, + 7.205234159779615, + 7.084022038567494, + 6.9701561065197435, + 6.863636363636364, + 6.764462809917355, + 6.672635445362719, + 6.588154269972453, + 6.511019283746557, + 6.441230486685033, + 6.37878787878788, + 6.323691460055097, + 6.275941230486685, + 6.2355371900826455, + 6.202479338842975, + 6.176767676767677, + 6.15840220385675, + 6.147382920110194, + 6.143709825528008, + 6.147382920110194, + 6.15840220385675, + 6.176767676767677, + 6.202479338842975, + 6.2355371900826455, + 6.275941230486685, + 6.323691460055098, + 6.37878787878788, + 6.441230486685033, + 6.511019283746558, + 6.588154269972453, + 6.672635445362719, + 6.764462809917356, + 6.863636363636365, + 6.9701561065197435, + 7.084022038567493, + 7.205234159779616, + 7.333792470156107, + 7.469696969696971, + 7.612947658402204, + 7.763544536271809, + 7.921487603305788, + 8.086776859504134, + 8.259412304866853, + 8.439393939393941, + 8.626721763085401, + 8.821395775941232, + 9.023415977961434, + 9.232782369146008, + 9.449494949494952, + 9.673553719008266, + 9.90495867768595, + 10.143709825528008 + ], + [ + 22.32001836547291, + 21.83884297520661, + 21.365013774104685, + 20.898530762167127, + 20.43939393939394, + 19.98760330578512, + 19.54315886134068, + 19.106060606060606, + 18.676308539944905, + 18.25390266299357, + 17.838842975206614, + 17.43112947658402, + 17.0307621671258, + 16.637741046831955, + 16.252066115702476, + 15.873737373737372, + 15.502754820936639, + 15.139118457300276, + 14.782828282828284, + 14.433884297520661, + 14.09228650137741, + 13.75803489439853, + 13.431129476584022, + 13.111570247933884, + 12.799357208448118, + 12.494490358126722, + 12.196969696969697, + 11.906795224977042, + 11.62396694214876, + 11.348484848484848, + 11.080348943985307, + 10.819559228650137, + 10.566115702479339, + 10.320018365472912, + 10.081267217630854, + 9.849862258953168, + 9.625803489439853, + 9.409090909090908, + 9.199724517906336, + 8.997704315886134, + 8.803030303030303, + 8.615702479338843, + 8.435720844811755, + 8.263085399449036, + 8.097796143250687, + 7.939853076216711, + 7.789256198347107, + 7.646005509641872, + 7.5101010101010095, + 7.381542699724518, + 7.260330578512397, + 7.146464646464646, + 7.039944903581267, + 6.940771349862258, + 6.8489439853076215, + 6.764462809917355, + 6.68732782369146, + 6.617539026629935, + 6.5550964187327825, + 6.5, + 6.452249770431588, + 6.411845730027548, + 6.378787878787879, + 6.35307621671258, + 6.3347107438016526, + 6.323691460055096, + 6.320018365472911, + 6.323691460055096, + 6.3347107438016526, + 6.35307621671258, + 6.378787878787879, + 6.411845730027547, + 6.452249770431588, + 6.5, + 6.5550964187327825, + 6.617539026629936, + 6.68732782369146, + 6.764462809917355, + 6.848943985307622, + 6.940771349862259, + 7.039944903581267, + 7.146464646464647, + 7.260330578512397, + 7.381542699724518, + 7.510101010101009, + 7.646005509641872, + 7.789256198347106, + 7.939853076216712, + 8.09779614325069, + 8.263085399449036, + 8.435720844811755, + 8.615702479338843, + 8.803030303030305, + 8.997704315886136, + 9.199724517906336, + 9.40909090909091, + 9.625803489439853, + 9.84986225895317, + 10.081267217630852, + 10.320018365472912 + ], + [ + 22.5, + 22.0188246097337, + 21.544995408631774, + 21.078512396694215, + 20.61937557392103, + 20.167584940312214, + 19.723140495867767, + 19.286042240587694, + 18.856290174471994, + 18.433884297520663, + 18.018824609733702, + 17.611111111111107, + 17.21074380165289, + 16.817722681359044, + 16.432047750229565, + 16.053719008264462, + 15.682736455463727, + 15.319100091827364, + 14.962809917355372, + 14.61386593204775, + 14.272268135904499, + 13.93801652892562, + 13.61111111111111, + 13.291551882460972, + 12.979338842975206, + 12.67447199265381, + 12.376951331496787, + 12.086776859504132, + 11.803948576675849, + 11.528466483011938, + 11.260330578512395, + 10.999540863177227, + 10.746097337006429, + 10.5, + 10.261248852157944, + 10.029843893480258, + 9.805785123966942, + 9.589072543617998, + 9.379706152433425, + 9.177685950413224, + 8.983011937557393, + 8.795684113865931, + 8.615702479338843, + 8.443067033976124, + 8.277777777777777, + 8.1198347107438, + 7.969237832874196, + 7.825987144168962, + 7.690082644628099, + 7.561524334251607, + 7.440312213039486, + 7.3264462809917354, + 7.219926538108356, + 7.120752984389347, + 7.028925619834711, + 6.944444444444445, + 6.867309458218549, + 6.797520661157025, + 6.735078053259872, + 6.679981634527089, + 6.632231404958677, + 6.5918273645546375, + 6.558769513314967, + 6.533057851239669, + 6.514692378328742, + 6.503673094582186, + 6.5, + 6.503673094582186, + 6.514692378328742, + 6.533057851239669, + 6.558769513314967, + 6.5918273645546375, + 6.632231404958677, + 6.67998163452709, + 6.735078053259872, + 6.797520661157025, + 6.86730945821855, + 6.944444444444445, + 7.028925619834711, + 7.120752984389348, + 7.219926538108357, + 7.3264462809917354, + 7.440312213039485, + 7.561524334251606, + 7.690082644628099, + 7.825987144168961, + 7.969237832874196, + 8.1198347107438, + 8.277777777777779, + 8.443067033976126, + 8.615702479338845, + 8.795684113865933, + 8.983011937557393, + 9.177685950413224, + 9.379706152433426, + 9.589072543617998, + 9.805785123966942, + 10.029843893480258, + 10.261248852157943, + 10.5 + ] + ] + } + ], + "layout": { + "scene": { + "aspectmode": "data" + }, + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-3,3,100)\n", + "y = np.linspace(-3,3,100)\n", + "\n", + "mx, my = np.meshgrid(x,y)\n", + "mz = J(mx, my)\n", + "\n", + "trace = go.Surface(x=mx, y=my, z=mz)\n", + "layout = go.Layout(scene = {'aspectmode':'data'})\n", + "fig = go.Figure(data=[trace], layout=layout)\n", + "py.iplot(fig, show_link=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def grad_J(x,y):\n", + " return np.array([2*x-2, y]) # calculé à la main à partir de J (on aimerait que cela soit automatique)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "If you don't understand $J$'s gradient calculation, look no further. Find your course on this\n", + "subject, look at the memo, ask questions." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Le minimum est au point [1. 0.] La valeur de J en ce point est 2.0000001053122918\n" + ] + } + ], + "source": [ + "# Algo du gradient pour trouver le minimum\n", + "\n", + "x = np.array([0,0]) # un point au hasard, changez pour voir\n", + "µ = 0.1 # plus il est petit et moins on avance vite, cf formule ci-dessus\n", + "e = 0.0001 # mon epsilon pour la condition d'arrêt\n", + "\n", + "while True:\n", + " x_old = x\n", + " x = x - µ * grad_J(*x) # *x donne en arguments toutes les valeurs de x donc x[0] en 1er arg et x[1] en 2e\n", + " if np.square(x_old - x).sum() < e**2:\n", + " break\n", + "print(\"Le minimum est au point \", x, \"La valeur de J en ce point est \", J(*x))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "I invite you to move your figure to be above, zoom in to see what will happen and now\n", + "move the mouse over the figure. You should see an ellipse that shows the level line (all points having the same z value). The minimum is when this ellipse is only a point. It is precisely in [1, 0, 2]." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Study of the convergence of the gradient\n", + "\n", + "We store all the values ​​of the points between our initial point and the solution to be able to draw curves\n", + "of convergence.\n", + "\n", + "So the result of our gradient method must be a set of points." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def minimum_J(start_value, µ=0.1, e = 0.001):\n", + " x = [np.array(start_value)]\n", + " while True:\n", + " x.append(x[-1] - µ * grad_J(*x[-1]))\n", + " if np.square(x[-1] - x[-2]).sum() < e**2:\n", + " break\n", + " # la suite n'est que des tests pour se protéger\n", + " if np.square(x[-1] - x[-2]).sum() > 1E6: # au cas où on diverge\n", + " print(\"DIVERGE\")\n", + " break\n", + " if len(x) > 200: # c'est trop long, je crains la boucle infinie\n", + " print('Trop long, boucle infinie ?')\n", + " break\n", + " return np.array(x)\n", + "\n", + "\n", + "x = minimum_J(start_value = (0,1)) # je prends une valeur initiale qui n'est pas alignée avec la solution" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 369 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x[:,0], x[:,1], 'x:')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "type": "scatter3d", + "x": [ + 0, + 0.2, + 0.36000000000000004, + 0.488, + 0.5904, + 0.67232, + 0.7378560000000001, + 0.7902848, + 0.83222784, + 0.865782272, + 0.8926258176, + 0.9141006540800001, + 0.931280523264, + 0.9450244186112, + 0.95601953488896, + 0.9648156279111679, + 0.9718525023289344, + 0.9774820018631475, + 0.981985601490518, + 0.9855884811924144, + 0.9884707849539315, + 0.9907766279631451, + 0.9926213023705162, + 0.9940970418964129, + 0.9952776335171303, + 0.9962221068137043, + 0.9969776854509634, + 0.9975821483607707, + 0.9980657186886166, + 0.9984525749508932, + 0.9987620599607145, + 0.9990096479685716, + 0.9992077183748573, + 0.9993661746998859, + 0.9994929397599087, + 0.999594351807927, + 0.9996754814463416, + 0.9997403851570732, + 0.9997923081256586, + 0.9998338465005269, + 0.9998670772004215, + 0.9998936617603371, + 0.9999149294082696, + 0.9999319435266157, + 0.9999455548212925, + 0.9999564438570341 + ], + "y": [ + 1, + 0.9, + 0.81, + 0.7290000000000001, + 0.6561000000000001, + 0.5904900000000001, + 0.531441, + 0.4782969, + 0.43046721, + 0.387420489, + 0.3486784401, + 0.31381059609, + 0.282429536481, + 0.2541865828329, + 0.22876792454961, + 0.20589113209464902, + 0.1853020188851841, + 0.16677181699666568, + 0.15009463529699912, + 0.1350851717672992, + 0.12157665459056928, + 0.10941898913151235, + 0.09847709021836111, + 0.088629381196525, + 0.0797664430768725, + 0.07178979876918525, + 0.06461081889226672, + 0.05814973700304005, + 0.052334763302736044, + 0.047101286972462436, + 0.042391158275216195, + 0.03815204244769457, + 0.034336838202925116, + 0.030903154382632605, + 0.027812838944369346, + 0.02503155504993241, + 0.022528399544939168, + 0.02027555959044525, + 0.018248003631400726, + 0.016423203268260654, + 0.014780882941434589, + 0.01330279464729113, + 0.011972515182562017, + 0.010775263664305815, + 0.009697737297875235, + 0.00872796356808771 + ], + "z": [ + 3.5, + 3.045, + 2.73765, + 2.5278645, + 2.383005765, + 2.28171340245, + 2.2099342449765, + 2.158364427385845, + 2.1207985071136575, + 2.0930617161579814, + 2.072317542341353, + 2.0566172427386644, + 2.044605588021306, + 2.03532772399517, + 2.0281016629627513, + 2.0224335191768934, + 2.017960700726605, + 2.014413479712276, + 2.011588718326128, + 2.009331693690042, + 2.0075233642702957, + 2.0060713281830114, + 2.004903313827645, + 2.003962428520012, + 2.0032036434657665, + 2.0025911600805872, + 2.002096413344198, + 2.0016965419633106, + 2.0013732051691684, + 2.0011116601415138, + 2.000900037645498, + 2.0007287699686116, + 2.0005901369390604, + 2.0004779042099097, + 2.00038703411516, + 2.000313453924565, + 2.00025386970532, + 2.0002056165582194, + 2.0001665379541804, + 2.0001348884097805, + 2.000109254918735, + 2.0000884934805354, + 2.000071677796904, + 2.000058057785201, + 2.0000470260186267, + 2.0000380905711603 + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Nice, isn't it?\n", + "\n", + "#### Impact of µ\n", + "\n", + "Let's see how µ influences the convergence i.e. once we have the direction of the greatest slope\n", + "at a point how much should we advance. With a large µ we take big steps, with a small µ we take small steps.\n", + "\n", + "With µ = 0.1 we have taken small steps." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DIVERGE\n" + ] + }, + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 383 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# µ = 2\n", + "\n", + "x = minimum_J(start_value = (0,1), µ = 2)\n", + "plt.plot(x[:,0], x[:,1], 'x:')" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "type": "scatter3d", + "x": [ + 0, + 4, + -8, + 28, + -80, + 244, + -728, + 2188 + ], + "y": [ + 1, + -1, + 1, + -1, + 1, + -1, + 1, + -1 + ], + "z": [ + 3.5, + 11.5, + 83.5, + 731.5, + 6563.5, + 59051.5, + 531443.5, + 4782971.5 + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Not good, we diverged. The steps are too big. We're going in the right direction but so far that we go back\n", + "on the other side of the bowl.\n", + "\n", + "We can see that in y we go from 1 to -1 then to 1, -1 etc without ever stopping\n", + "to 0 which is the solution for y.\n", + "\n", + "**Question** Why does the value of x explode instead of like y?" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuIAAAHtCAYAAABcXRt3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOzdeXyU1dn/8e9kspKEEAhhCZBAgEMQkVUBlV2sW6lbXR73aot1oVVrf1318enTPtat1da1rdZasa37VgUVRNmqCKISDvu+JmzZt5nfHzMJCc4NmUwyS/J5v1687txzzpy5PES4OLnuc1xer1cAAAAAwisu0gEAAAAAHRGJOAAAABABJOIAAABABJCIAwAAABFAIg4AAABEAIk4AAAAEAEk4gAAAEAEkIgDAAAAEUAiDgAAAEQAiTgAAAAQASTiAAAAQASQiAMAAAAREB/pANrK8uXLvZGOAQAAAB3D6NGjXcG+hxVxAAAAIALa7Yp4vdGjR4f18woLCyVJBQUFYf3cWMV8BYf5Cg7zFTzmLDjMV3CYr+AwX8GJ1HwtX768xe9lRRwAAACIABJxAAAAIAJIxAEAAIAIIBEHAAAAIoBEHAAAAIgAEnEAAAAgAkjEAQAAgAggEQcAAAAigES8BZ5dsllFpVVBv6+otErPLtnc2uEAAAAgBrXJyZrGmDhJSyTlW2uzWvD+TEl3STpfUi9J+yS9I+kea+2W1ow1WM8u2axfvvaV/rZki+Z8d5yy0pKa9b6i0ipd9uRSrdtbKkm6anxe2wUJAACAqNdWK+K/knRyS97oT8IXS5otKVPSKkkpkq6TtNIYM7y1gmyJs0/spUHZaVq3t1SXPbm0WSvjjZPwQdlpOvvEXmGIFAAAANGsVRNxY4zLGHO3pJ+EMMxTkoZIeltSjrV2jKTekp6R1EXSC8YYd4ihtlhWWpLmfHdcs5Pxo5PwYFbRAQAA0H61WiJujOkp6RX5SkpaOsYQSRdIKpV0pbW2RJKstZWSrpdUKKlAvpKViGluMk4SDgAAACetkogbY2ZIWitppqTdavmK+BWSXJLesNbub9xgra2T9LT/9pIWjt9qjpeMk4QDAADgWFprRXyopDRJf5M0TNLSFo5ziv+62KG9ftzTWzh+qwqUjB+sqNPBijqScAAAABxTa+2a8h9Jo6y1KyXJGNPScQb6r5sc2ut3TOlhjEmz1pa29INaS30yXp94z3q9XJJ0qNJDEg4AAABHrZKIW2udVrCD1d1/LXZob1yukiVfLfkxFRYWhhpTs9wzuZtmvV6uQ5Wehtfy0iVr12pfpzbZJbJdqKiokBS+36dYx3wFh/kKHnMWHOYrOMxXcJiv4MTifEXbgT4p/muFQ3vj11Mc+kSNeRtKdd3L2zRvfUmkQwEAAECUibal2jod+x8Hjdu8zRmwoKAgpICao6i0Src+uVSHKj3qlOBSec2R0KrqvJoy0qigT0abxxGL6v/VGo7fp/aA+QoO8xU85iw4zFdwmK/gMF/BidR8LV++vMXvjbYV8TL/NdmhvXGxtdOqeVgdvTvK90/JUvdOR7Y5T0uKV68uTv85AAAA6KiiLRGvrw3v6tDerdHX+9o4luMKtEXhtPx0/fmCfvrxWUMUH+dSaVWt4z7jdneJqmrrIhA5AAAAIi3aEvE1/mueQ3uu/7rLWlve9uE4O9Y+4Qlul26clK9FP57iuM94RXWdrvzzMk29/0P985Ntqq3zOH0UAAAA2qFoS8Q/9V/HObTXv74sDLE4au5hPT0yUhwP/fnb0s3aW1KlHQcrdOdLq/TNPyxSnadZZe8AAABoB6ItEX/Zf/2WMaZJeYoxxi3pGv/tc+EMqrFgT8wMdOjP5qJSPbZgQ5N+pw3KkjvO1dbhAwAAIEpEJBE3xmQZY4YYY/Ibv26tXSXpLUmdJb1ojOnm758s6U+SCiRZSa+EOeQGb3+xK+gTM49Oxt/9ao9mjshRots3/WlJ8Zo1Kf84owAAAKA9idT2hTdLuku+kzLzjmqbJeljSVMkbTXGFEoaIClT0iFJ51trI1ZQfdX4PEnS2Sf2CurEzPpk/O0vdjWMccPEAXrk/XXK6ZKirqmJAd+393Clth0o1+hcp+dXAQAAEIuirTRF1trtkkZLeli+nVGGS6qVNEfSWGttxI9Lump8XouOrc9KS2pIwiUpp0uK/u/C4bpl2iDH9zz8wTpd+NgSXfv0f/TljkMtCRcAAABRqE1WxK21CyQ5Fjxba++WdPcx2oslzfb/6rC27S/XC//ZJkmab/dpvt2nZ64dq8kmO8KRAQAAIFRRtyKOI3733jrVNtpJpU9miibkZ0UwIgAAALQWEvEo9u0xfTQ2L7Ph/ofTBysxnt8yAACA9oCsLoqdMqCb/vm98Xrm2rE676Te+tbIHMe+f1+2RcUBTu8EAABAdCIRj3Iul0uTTbYeuWyk4z7j/9m0Xz975UtN/O18PTDX6lBFTZijBAAAQLBIxGOc1+vV/e9aSVJZdZ0e+WC9bvvHyghHBQAAgOMhEY9xH68v0n8272/y2vc4HAgAACDqkYjHuLF5XfWLc4eqm/9AoImDu+vk/hz+AwAAEO0idbImWklyglvfOa2/Lh3bV08v2qRJg533GJ/71W6VV9fpvJN6O9abAwAAIDxIxNuJ1KR43TzV+YTO6lqP7nlztbYfqNCjC9brtjOMzjyhh1wuEnIAAIBIoDSlg/jnp9u0/UCFJGntnlLdMucz7TxUGeGoAAAAOi4S8Q6gzuPVYws2NHntkrF9ldMlJUIRAQAAgES8A3DHufT8Dafo/JE5crmkpPg43XKMMhYAAAC0PRLxDiK3W6oeumSE3v3BRP3mghPVo3NywH77y6p165wVWrunJMwRAgAAdCw8rNnBDO6RrsE90h3bH/9wg17/fKfeWLVTM0/qrR9MH6y8rNQwRggAANAxsCKOBnsOV+qvizdLkrxe6dWVOzVv9Z7IBgUAANBOkYijwUufbVdVrafhPjs9SVeOz41gRAAAAO0XiTga3DgpX09cOVrGX7pyy9SBSk5wRzgqAACA9okacTRwuVw684Seml7QQ+98uVtnDO3h2PfOFz9X38xOuva0/kpL4tsIAAAgWGRQ+Bp3nEvnDO/l2P7F9kP656fbJUlPL96s70/O1zUT8hTv5gcsAAAAzUXmhKDdP9c2fL2/rFqvf75T7jhXBCMCAACIPSTiCMrekkqt3HawyWu3zzByuUjEAQAAgkEijqBkpydr4Z1TdOvUgUpNdGtsXqYmDsoK2Nfr9crj8YY5QgAAgNhAjTiClpGSoNtmGF09IU+HKmocV8P//eVu/XH+et0xw2iy6c6qOQAAQCOsiKPFuqUlaUD3tIBtdR6vHpy3Vl/tPKxrn/lEFz2+RKt3Hg5zhAAAANGLRBxt4tUVO7R+b2nD/YqtB5QYz7cbAABAPTIjtInCXU1Xv88f2UcDswOvngMAAHREJOJoEz8/d6jevOU0TR2SrQS3Sz+YPsixb0WNJ4yRAQAARAce1kSbGZaTob9cM1bb9perb9dOAfuUVXt0/SvbNGNtrW6dNkh9MgP3AwAAaG9YEUebc0rCJemV1Qd1sLJO//x0u6bcv0D3vbsmjJEBAABEDok4IuZAWbVeXn2o4b6mzqtEtzuCEQEAAIQPiTgiZsfBCnVNOVIdldkpQdedlhe5gAAAAMKIRBwRMywnQ0/M7KMfTuiunC4punFyvtKTEwL23V9WrYrqujBHCAAA0HZ4WBMR5Y5zacagdM06e/Qx+/3qzdX6eH2Rbp46UJeO7cee5AAAIOaRzSAqJMW7lRQfuD583Z4SvbJyh/aWVOmXr32lKfcv0Nbi8jBHCAAA0LpIxBH1Hpy3Vl7vkftOiW7lZKZELiAAAIBWQCKOqOb1epXbLVXJCUe+VW+fMVjuOFcEowIAAAgdiTiimsvl0v87a4gW/miKrh6fq9G5mTrzhJ4B+3q9Xq3cdjDMEQIAALQMD2siJmR3TtZ/zxymOo9XLlfg1fAFa/fp2qc/0YT8brp9htHo3MwwRwkAANB8rIgjpjiVpHi9Xj0w10qSFm8o1oWPLdbD768LZ2gAAABBIRFHu/DOl7v15Y7DTV6bOiQ7QtEAAAAcH4k42oW+XTvptIFZDfdnn9hTw3IyIhgRAADAsZGIo10YlpOh564/RXNuGKeT87rqtjMGO/ZdtrFYew5XhjE6AACAr+NhTbQr4/O7aXz+eMf2iuo63TxnhQ5X1OjqCXmaNSlfXVMTwxghAACADyvi6FCeXbJZ+0qqVFXr0ZMLN2rGQwtVWVMX6bAAAEAHRCKODqOkskaPfbihyWsXjs5RcoI7QhEBAICOjEQcHUZSvFt3zDDq0TlJkpSeFK9ZE/MjHBUAAOioqBFHh5EYH6crxuXqotF99NzSLYpzuZTpUB+++1ClPly7VxeO6qN4N/9eBQAArY9EHB1OcoJb158+4Jh9Hvlgnf6+bKse/3CjfjB9kM4b3ltxDocJAQAAtARLfcBRthaX6x+fbJMkbSoq0+wXVur1z3dGOCoAANDekIgDR3nkg3Wq9Xgb7vt17aRzhveKYEQAAKA9IhEHjvLDMwbrspP7yu0vRfnB9EFKoE4cAAC0MrIL4Ci9u6ToNxcM13u3TdJ3Jw7QzBE5jn0fnLdWX+44FMboAABAe0EiDjjon5Wqn55d0LAyfrRlG4v18PvrdO4jH+vG55Zr3Z6SMEcIAABiGYk40AJer1f3z7UN9//+crd++dpXEYwIAADEGhJxoAWWbzmgTzYfaPLa7TMGRygaAAAQi0jEgRYYnZupZ64dqxNzMiRJk013jcnrGuGoAABALOFAH6AFXC6XJptsTRrcXe9+tVu53VId+762cofW7SnVDRMHKCMlIYxRAgCAaEYiDoTA5XLpG8Oc9xivrvXovnetth+o0LNLNut7k/J1zYQ8pSbxvx4AAB0dpSlAG/rHJ1u1/UCFJOlwZa1+995aHSivjnBUAAAgGpCIA23E6/Vqzn+2NXnt8pP7qU9mpwhFBAAAokmr/HzcGJMp6S5J50vqJWmfpHck3WOt3dKC8fpI+rmks/zjHZa0WNK91tpFrREz0NZcLpf+NWu8nlm8WU98uEHVdR7dNGVgpMMCAABRIuQVcX8SvljSbEmZklZJSpF0naSVxpjhQY53gqQVkr4nKVtSob/pPEkfGmOuCzVmIFxSk+J105SB+ujHU/XElWOU3Tk5YL/9ZdU6/9FFeufLXfJ6vWGOEgAAREJrlKY8JWmIpLcl5Vhrx0jqLekZSV0kvWCMcQcx3rOSsiTNl9TPWnuSpB6S/leSW9Jjxpj+rRA3EDYZKQmaNLi7Y/tjC9ZrxdaDmvXcZ/rmHxZp8fqiMEYHAAAiIaRE3BgzRNIFkkolXWmtLZEka22lpOvlW80ukK9kpTnjDZU0SpJX0hXW2n3+8eqstT+X9ImkREmXhRI3EE32HK7Us0uOVHB9seOQVu86HMGIAABAOIS6In6FJJekN6y1+xs3WGvrJD3tv72kmePl+K/F1tqdAdo/81/7BRsoEK0+Wlek6jpPw33Pzsm6YlxuBCMCAADhEGoifor/utihfan/enozx9vuv2YZY3ICtJ/gv25t5nhA1LtodB/N/cFEnTWspyTplmkDlZwQuJqrzkP9OAAA7UWoiXj9FhCbHNrrf97ewxiTdrzBrLWFOpLU/9UYkyVJxhiXMebHkk6Trwzm2ZaHDESfQT3S9dgVo/XmLafp4tF9Hfv9ZuFe3btwrzYXlYUxOgAA0BZC3b6w/umzYof2xuUqWfIl0cdzvqS/S5ouaasxZq2knvI9sFko6TvW2u3HeD8Qs4blZDi2rdp+UIu2+BLwaQ9+qItH99Fd552glMRgnoUGAADRItREPMV/rXBob/x6ikOfo1XJV9Jyqv89JzVq2+lvb7bCwsLjd2pFFRUVEfncWMV8Nd9/z9vV8HWdx6sVm/Zq0/p4uVyuCEYV3fj+Ch5zFhzmKzjMV3CYr+DE4nyFWppSF8T4xy1uNcZ0kbRAvsN8PpI0UlKSpAGSHpY0TdJCY8z4lgQLxKqyao+KK5r+73bVyEyScAAAYlioK+Jl8u0VHviUEl8SXc9p1byxOyWNkPSFpHOttTX+1zdJmm2MqZL0I0l/lG+bw+MqKChoTrdWU/+vsHB/bqxivprvgxOH6ol/f6rnPj+gPt3SdfnUUQETcY/Hq/KaOqUltcrBuTGN76/gMWfBYb6Cw3wFh/kKTqTma/ny5S1+b6gr4vW14V0d2rs1+npfM8a70H+9r1ES3thv5FuFH2mM4axwdChxcS5NHpCmJ2b20SOXjXRcDf/3l7s18bfz9dTCjaqsOd4PrQAAQKSEmoiv8V/zHNrrN0PeZa0tb8Z49f3XBGq01h7QkYSejZbRIbnjXMruHPiHUHUerx6cZ7W/rFr/+3ahJt03Xx+ta86/gQEAQLiFmoh/6r+Oc2ivf31ZM8erP06wV6BGY0yypOyj+gLwe2XFDm3Yd2Rrw30lVerdpbnPSQMAgHAKNRF/2X/9ljGmSXmKMcYt6Rr/7XPNHG+B/3qdQ/sV8sV8SNLnzY4S6CDKq2uV2mg7wwtH9VF+9+Nu4Q8AACIgpETcWrtK0luSOkt60RjTTWpYuf6TpAJJVtIrjd9njMkyxgwxxuQfNeS9kmolzTTG/NYYk9roPRdJesB/+3/W2upQYgfao6vG5+mjH0/VdycOUHpyvG6dNsix77b95fJ6OakTAIBICXVFXJJmyXeC5hT5DuD5VL79vq+Rb+X6fGut56j33Czf4TzvN37RWrtc0g3yJeM/krTbGLPcGLNX0r/kS/j/Kl/CDiCArqmJ+unZBVr202nq27VTwD6HK2t07iMf68LHFmvJBqfzuAAAQFsKORH3n3I5Wr59vvdJGi5fIj1H0lj/sfXBjPeMpDHylbMcknSifNssvifpYmvtNdZalvGA4+iU6Lx94Z8+2qRDFTX6bOtBXfbUUn3/7y3fegkAALRMq2w0bK0tljTb/6s5/e+WdPcx2j+XdGVrxAagqf1l1frzRxubvDakZ+cIRQMAQMfVGqUpAGJIeXWtxg04ssV/19REXXda/whGBABAx8TRe0AH0yezk/58zVgt33JAD8y1mjok2/EUzl2HKlTn8apPZuBacwAA0HIk4kAHNTo3U8/fME4ej/MjF799x+rNVTt1+cn9dNOUgY4HCQEAgOBRmgJ0cHFxroCvr91ToldX7lBNnVd/XbJFE++br692HgpzdAAAtF8k4gACenDuWjXeZjy3ayoPdQIA0IpIxAEENH1oD/XJTGm4v23GYLkdVs8BAEDwqBEHENBFo/vomyf11j8+2aoP1xZpxtAeAft5vV69uWqXZpzQQ0nx7jBHCQBA7CIRB+AoMT5OV47P05Xj8xz7LLD7dMucFcrpkqLZ0wfpgpE5infzwzYAAI6Hvy0BtJjH49X9c60kacfBCt354ird9fpXEY4KAIDYQCIOoMXe+Wq3vtp5uMlrl5/SL0LRAAAQW0jEAbTYmLxMXTMhT4n+UpRzhvfSCb0zIhwVAACxgUQcQItlpyfr7m+eoPk/mqxLxvTVD6cPduw7b/UeLd+yP4zRAQAQ3XhYE0DIcrqk6N6Lhju2V1TX6aevfKF9JVWaOiRbt88YzMo5AKDDY0UcQJv765LN2ldSJUn6YM1eXfz4EpVU1kQ2KAAAIoxEHECbKq+u1eMfbmjy2tUT8pSenBChiAAAiA4k4gDaVKfEeD1+xWiNyc2UJKUnxet7EwdEOCoAACKPGnEAbW7cgG7616zxWrB2n/aVVKlLp8SA/XYdqtDTizZr1qR8dU0N3AcAgPaCRBxAWLhcLk0x2cfs88gH6/X8sq36+9It+s5p/XX9xAHqTAkLAKCdojQFQFTYWlyuf36yTZJUVl2nhz9Yr7dX7YpwVAAAtB0ScQBR4c8fb1Stx9twn9utky4c3SeCEQEA0LZIxAFEhZ+cXaCfn1PQUBv+g+mDlODmjygAQPtFjTiAqJCc4Nb1pw/QpSf300vLt+ubJ+U49v3Jy19o3ICuOm94b8XFucIYJQAArYflJgBRJS0pXldPyJPbIcFeurFYc/6zVbNfWKmzfv+R3v1qt7xeb8C+AABEMxJxADHD6/Xq/ndtw73dU6JnFm2Wy8WqOAAg9pCIA4gZa/eUasW2g01eu+NME6FoAAAIDYk4gJhheqbr/dsm6VsjesvlkqYOydZo/4mdAADEGh7WBBBT8rJS9btLR+rGyQMV73YuSfnXp9v0yn9266oRXVUQxvgAAGguEnEAMcn0THdsq6qt0+/eW6cdByu0ZGu5Zm716MdnDVGvjJQwRggAwLFRmgKg3fnHJ9u042CFJMkr6e0vdsvDxioAgChDIg6g3Vm4dl+T+8tP6aecLqyGAwCiC4k4gHbnqavG6PErRiu3S4KS3C59f0q+Y9/aOk8YIwMA4AhqxAG0Oy6XS98Y1lN9XPu1+WC1stOTA/YrLq3SuY98rMtP7qdrT+uvtCT+SAQAhA8r4gDaLXecS/ldkxzbH1uwQbsOVeqBeWs18bfz9Y9PtoYxOgBAR0ciDqBD2nWoQs8u3dJwv7+sWqVVdRGMCADQ0ZCIA+iQ1u4pVXL8kT8Ce2Uk679O6RfBiAAAHQ2JOIAOadLg7vrox1N1y9SBSk1065apg5Sc4A7Y93BljTzsfwgAaGU8mQSgw8pISdDtM4yumZCnzikJjv3u+Ofn2nGwQnfMMJpsusvlcj7REwCA5mJFHECH1y0tSQnuwH8cfr7toOau3qOvdh7Wtc98oosfX6KD5dVhjhAA0B6RiAPAMdw/1za5r/F4lXGM1XMAAJqLRBwAHFTW1Ck9uWkF349mGEpTAACtghpxAHCQnODWo/81Wl/uOKQH5lpV1nh06sBuAft6PF5tP1Chft06hTlKAECsIhEHgOMYlpOhp689WRXVdY6r4W9/uUuzX1ipi0b10a3TBymnS0qYowQAxBpKUwCgmVISA29vWFvn0YPz1qrO49U/Pt2mKfct0EvLt4c5OgBArCERB4AQvbxihzbuK2u4r/N6NbJflwhGBACIBSTiABCirLREDchKbbi/cFSOBnRPi2BEAIBYQCIOACGaOqSH5v5won574XD1z0rVrdMGOfZdue2gKmvqwhgdACBa8bAmALSCeHecvj22ry4a3UdxcYEf6DxUUaOr/rxMKYlu3Tx1kC4Z01eJ8ayHAEBHxd8AANCKnJJwSfrTRxt1uLJWew5X6RevfqnzH10kr9cbxugAANGERBwAwqC4tEp/+XhTk9fOGtaTw4EAoAMjEQeAMIh3x+mKcblKTvD9sdstNVHXnto/wlEBACKJGnEACIOMlAT95OwCfee0/vrD/PXK756m1KTAfwRvLS7X9oPlmpCfFeYoAQDhRCIOAGGU3TlZ98wcdsw+D8yzem3lTp06sJtun2E0ql9mmKIDAIQTpSkAEEXs7hK9/vlOSdKi9cW64NHFWryhKMJRAQDaAok4AESRB+ZaNd5IZUjPdI3r3y1yAQEA2gyJOABEkVmT83XqwCOJ921nDD7mlogAgNhFjTgARJFR/TL19+vHafGGIr25apfOGNojYD+v16snF27U+SNzlN05OcxRAgBaA4k4AEShCflZx9w15YM1e/Wbf6/Rg/PW6uoJeZo1KV9dUxPDGCEAIFSUpgBAjPF4vLp/7lpJUlWtR08u3KhfvPZlhKMCAASLRBwAYszc1XtUuOtwk9dumjwwQtEAAFqKRBwAYszUIdn6n28NU3Z6kiTp3OG9NLR35whHBQAIVqvUiBtjMiXdJel8Sb0k7ZP0jqR7rLVbWjBenKTrJV0j6QRJiZIKJT0l6XFrrdf53QDQviXGx+nKcbm6eHQf/W3JFk0tyHbs+8qK7aqu9ejCUX0U72btBQCiSch/KvuT8MWSZkvKlLRKUoqk6yStNMYMD3K8ZElvS3pC0imStkvaK2mkpEclzTHGsJcXgA4vOcGtGyYOUH73tIDt5dW1+t+3CvXjl77QGQ8t1Gsrd8jjYR0DAKJFayyPPCVpiHzJc461doyk3pKekdRF0gvGGHcQ490r6UxJ2ySNtNaeYK3NlXSepDJJl0j6r1aIGwDatWcWb1ZRabUkaVNRmf7fS19of3l1hKMCANQLKRE3xgyRdIGkUklXWmtLJMlaWylfaUmhpAL5SlaaM94ASTdJqpV0lrV2VX2btfZNSQ/4b68LJW4AaO9q6jx6etHmJq9de2qestKSIhMQAOBrQl0Rv0KSS9Ib1tr9jRustXWSnvbfXtLM8S6T5Jb0nLX2qwDtT0v6maS/tCxcAOgYEtxxevWmU3XJmL5yx7mUnhyv703Mj3RYAIBGQn1Y8xT/dbFD+1L/9fRmjjfNf30tUKO1drOkXzdzLADo0HK6pOjei4Zr1uR8rd1TooxOCQH77TxYobte/0qzpw1SMHWEAIDQhJqI129cu8mhvX7HlB7GmDRrbelxxhvmvxYaYzIkXStpoqQ0SaslPWmtXR1KwADQ0fTPSlX/rFTH9kc+WKd5q/do3uo9Oi03VVeOyFRBGOMDgI4q1NKU7v5rsUN743IV57Oa1bBbSv14fSV9Jekh+erLz5BvV5bPjTE3tDhaAEATm4vK9M9Ptzfcf7ylTKv3VkYwIgDoOEJdEU/xXysc2hu/nuLQp156o6/nSDoo6SxJC+RL4m+T9ENJjxtjNlhrP2hOgIWFhc3p1moqKioi8rmxivkKDvMVHObr+P7++QHVNdrSsFeaW6fmxDNnzcT3WHCYr+AwX8GJxfkKNRGv07FX1Ru3HW/z2uRGX6dKOtlaW1/ysl3SbcaYbPm2Lvy1pHFBxgoAOMrlw7tocLckPbtiv9bvr9YlJ6QrPi7wUQ1er1cuF8c4AEBrCTURL5Nvr/Bkh/bG+2Q5rZoHav9boyS8sV/Ll4ifYozJttbuPV6ABQXhrXSs/1dYuD83VjFfwWG+gsN8Nc/QodKV071aYPcp21OkOJcr4Jx999lPZXqm6/rTBygjJfCDnx0N32PBYb6Cw3wFJ1LztXz58ha/N9Qa8fra8K4O7d0afb3vOGMd1pFV81UOfdbKt1QpK/oAACAASURBVMe4JOUdLzgAQPO4XC5NGZKtOIcV78UbijR39R498sF6nX7vB/rj/PVNSloAAMELNRFf47/mObTn+q+7rLXlxxrIWlst591X6nl1JFmvaU6AAIDQeL1e3f+ubbg/XFmrReuL5HYoYQEANE+oifin/qtTvXb968uaOd5//NcxDu25khIkeSRtbuaYAIAQ7DxUqS3FTddS7jjTRCgaAGg/Qk3EX/Zfv2WMaVKeYoxxS7rGf/tcM8f7h/96kTEmJ0D7Tf7rh9baA8EECgBomZwuKVp45xTdMWOw0pPjNW1Itkb1ywzYt87jpWQFAJoppETcWrtK0luSOkt60RjTTWrYE/xPkgokWUmvNH6fMSbLGDPEGHP0ecuvS1oi3wE+bzZuN8ZcIulm/+3/hhI3ACA4qUnxunnqIH1851Td861hjv1eXL5NZ/1+od75cre8XhJyADiWUFfEJWmWfCdoTpG01RjzqaSd8q2GH5J0vrXWc9R7bpZUKOn9xi/6+10sX/I+QpI1xqwyxmyU9IKkREm/sNa+LwBA2GV0SlBOl8DHQlTV1unh99dr7Z5SzXpuub75h0VavfNwmCMEgNgRciJurd0uabSkh+XbGWW4fDubzJE01lob1K7q1todkkZJ+qV8D4MOlO+wn3clfcNa+6tQYwYAtL45y7Zqx8EjO9Ha3SXK6MQ2hwDgJNR9xCVJ1tpi+Y6gn93M/ndLuvsY7eWS/sf/CwAQA7YfqJDLJdVXpFx+Sj/H1XMAQOuUpgAAoJ+fO1RzfzBRZw3rqU6Jbt00ZaBj34Pl1WGMDACiU6usiAMAIEmDeqTrsStGa19JlbqnJwXsU1Rapcn3LdC0gmz9cPpg5WWlhjlKAIgOrIgDAFqdUxIuSY/O36DSqlq9tnKnpj34oe59Z41jXwBoz0jEAQBhs+tQhZ5btqXhvs7jVfc056QdANozEnEAQNgUl1arf7cjpSi9MpJ1+Sn9IhgRAEQOiTgAIGyG5WTo7dmn6/eXjlBet066ddogJSe4A/bdfahSpVW1YY4QAMKHhzUBAGHljnNp5ogcnXNir2P2+/mrX+qzrQf0/cn5umJcrmPCDgCxihVxAEBExLvjFO8O/NfQiq0H9F7hHu0vq9av3irU5PsWaGejw4IAoD0gEQcARJ0H5q5tct8zI1m9MpIjFA0AtA0ScQBAVKnzeDUqN1OpiUdKUX50ppHL5YpgVADQ+qgRBwBEFXecS7edMVhXj8/V4x9u0Pq9pTp1YFbAvh6PV0s3Fmt8fjcSdQAxh0QcABCVuqUl6WfnDJXX63Xs8+YXu3TrnBUak5up22cYjc/vFsYIASA0lKYAAKKa00p3bZ1Hv5vnqyX/dMsBXfbUUv1x/vpwhgYAISERBwDEpJc/26GNRWUN9+44l84+zpaIABBNSMQBADHpxD4Zmjoku+H+olF91D8r9RjvAIDoQiIOAIhJBb066y/XjNVLN07QxMHddev0QY5956/Zq+0HysMYHQAcHw9rAgBi2ujcTD173cmO7YcqajT7hRWqrPHospP76qapA5Wdzp7kACKPFXEAQLv21MKNOlxZq+o6j/66ZIvOe+Rj1dR5Ih0WAJCIAwDar+LSKv1l0aYmr101Pk8Jbv76AxB5/EkEAGi3MlISdPc3T1BOlxRJUlZaoq6ZkBfZoADAjxpxAEC7Fe+O07fH9NW3RuToH59sVVKCW6lJgf/q21RUpo/W7dOlY/spMZ51KgBtj0QcANDuJcbH6crxecfs89C8tXr985164sONmj19kC4YmaN4SlgAtCH+hAEAdHhrdh/WG6t2SpJ2HKzQnS+u0nuFeyMcFYD2jkQcANDhPfL+enm9R+6H9EzXjKE9IhcQgA6BRBwA0OHddd5QXT0+VwlulyTp9hlGcXGuCEcFoL0jEQcAdHjZnZP13zOHaf4dk3XbGYM1vSA7YD+v16u7X/9Ky7ccCHOEANojHtYEAMCvT2Yn3TptkGP7+4V79czizXpm8WZNHZKtCwYlKL9rUhgjBNCesCIOAEAzeDxe3T/XNtx/sGavnlvJyjiAliMRBwCgGZZsLNaa3SUN9y6XdNWIzAhGBCDWkYgDANAMpw7M0pwbxml0ri/5Pnd4b/WnLAVACKgRBwCgmcbnd9OLs8Zrgd2n/lmpqti3NWC/55Zu0ZbiMt04eaC6piaGOUoAsYJEHACAILhcLk0Z4ttVpXDf19vLq2v1u/fWqqi0Ws8v26rvnNZfN0wcoPTkhDBHCiDaUZoCAEArenrRZhWVVkuSyqrr9KePN6mq1hPhqABEIxJxAABaicfj1esrdzZ57dpT85SVRi05gK8jEQcAoJXExbn02s2n6ufnFKhraqLSk+P13dPzHft7vd4wRgcg2lAjDgBAK0pOcOv60wfo0pP7qXDXYWV0ClwbvuNgha57+hN9f0q+zhveW3FxrjBHCiDSWBEHAKANpCXFa2xeV8f2R95fJ7unRLNfWKmzfv+RFq4N8OQngHaNRBwAgDDbVFSmfy3f3nBv95Ro16GKCEYEIBJIxAEACLNPNu1vct8/K1UXjuoToWgARAqJOAAAYfbtsX313m2TNHNEb7lc0g+mD1K8O/BfyVW1dWGODkC48LAmAAAR0D8rVb+/dKRumTpQA7LSHPtd98wnSk9K0G0zBmtwj/QwRgigrZGIAwAQQQOznZPrxeuLtGh9sSTp3dW79a0ROfq/C09UUrw7XOEBaEOUpgAAEIW8Xq/um2sb3Ut7SypJwoF2hEQcAIAodLC8RrV1TQ/8uWOGiVA0ANoCpSkAAEShzNREvX7zqXr3qz16cJ5Vv66dNLJfZsC+NXUelVfVOR4eBCA6kYgDABClXC6XvjGsp84Y2kMllTWO/V5avl2/frtQ3504QNee2l+pSfz1DsQCSlMAAIhy7jiXunRKDNhWVVunh99fp8OVtbp/7lpN/O18fbyuKMwRAmgJEnEAAGLY88u2auehyob7kspaDeieGsGIADQXiTgAADEs3h2nzslHSlH+a1w/9e6SEsGIADQXiTgAADHsynG5+ujHU3XL1IHKSkvS9ycPdOy7bk+JvF6vYzuA8OJpDgAAYlxGSoJun2F089SBjvuM7yup0jf/sEgDs9N0+4zBmjS4u1wuV5gjBdAYK+IAALQTxzrs59EF61VRU6cvdhzSNU9/opue/yyMkQEIhEQcAIB2bufBCv196dYmr43N6xqhaADUIxEHAKCd83i9mj40u+G+d0ayLj+lXwQjAiBRIw4AQLvXJ7OTHv2v0fpyxyE9MNfqzBN6OpaxbC4qkyTlZbEFItDWSMQBAOgghuVk6OlrTz7mzim/emu15tt9unh0H906bRBbIQJtiNIUAAA6GKfdUj7bekDvFe5VncerFz7Zpsn3LdC6PSVhjg7oOEjEAQCAJOmBubbJ/Qk5nTUwOy1C0QDtH4k4AACQ1+vVJWP7qX+j2vAfzTDsNQ60IWrEAQCAXC6XvnlSb509rKde/myHlm3arwkDswL29Xi8+tfybZo5IkfJCc57lwM4tlZLxI0xmZLuknS+pF6S9kl6R9I91totrTD+BEkfSdpmrc0LdTwAAPB18e44fXtsX317bF/HPm+s2qkfv/SFHpy3VjdPHaRLxvRVYjw/ZAeC1Sr/1/iT8MWSZkvKlLRKUoqk6yStNMYMD3H8ZEl/FqU0AABEVG2dR797b50kac/hKv3i1S/167cLIxwVEJtaK7F9StIQSW9LyrHWjpHUW9IzkrpIesEYE8rPru7yjw8AACLo5c92aJN/r3FJcse5dM2EvMgFBMSwkBNxY8wQSRdIKpV0pbW2RJKstZWSrpdUKKlAvpKVlow/StIdkipCjRUAAIRm+tAe+t7EAUpO8KUQF4/uw+E/QAu1xor4FZJckt6w1u5v3GCtrZP0tP/2kmAHNsYk+N/vlfQ/IcYJAABC1DU1UT85u0ALfzRFV4/P1S3TBjn2fXXFDi3eUBTG6IDY0hoPa57ivy52aF/qv57egrF/Imm4pF9J+qIF7wcAAG0gu3Oy/nvmMMf2Q+U1+sVrX6qkslanDuymO2YYJYcxPiAWtMaK+ED/dZNDe/2OKT2MMc0+FcAYM0zSzyStkS8RBwAAMeLJjzaopLJWkrRofbGuefoTVdZ4IhwVEF1aIxHv7r8WO7Q3LlcJvCHpUfwPdv5FUoKk6621VS0PDwAAhNPhyho9vWhzk9e+26iuHIBPa5SmpPivTg9TNn49xaHP0W6TNFbSH621i1oamCQVFoZ3S6WKioqIfG6sYr6Cw3wFh/kKHnMWHObL2a+m99BfP9uvz3dXqkuyWxO6Vamiwreuxnw1D99fwYnF+WqNRLxOx15Zb9zmPd5gxphBkv5b0jb5asQBAECMKeierP87s7dW7qpQSVWdkhPiVFH79X7bD1Xr9TWHdemJXdS1Ewd+o2Npje/4Mvn2Cnd6BiOp0dfH3ILQGOOSryQlRdKs+q0QQ1FQUBDqEEGp/1dYuD83VjFfwWG+gsN8BY85Cw7zdXyNpybQfD06Z4XeWHNY8zaU6urxeZo1KV+ZqYnhDjMq8f0VnEjN1/Lly1v83tYo1qqvDe/q0N6t0df7jjPWTZJOkzTHWvt2qIEBAIDoVbjrsN74fKckqbLGoycWbtTH69nuEB1Ha6yIr5GULynPoT3Xf91lrS0/zlgX+a+XGWMucxrPGFNf4tLfWru5uYECAIDo8dfFm5vcF/TqrHNO7BWZYIAIaI1E/FNJ50gaJ+mxAO3j/NdlzRjri2PElClpqKQq/2dKUmXzwwQAANHknpnDdELvznrkg/XaW1Kl288YrLg4V6TDAsKmNRLxlyXdJelbxpiujU/X9G9DeI3/9rnjDWStvcWpzRhzrqQ3JO221p4WUsQAACDiEuPjdOX4PF00uq/e+mKXphVkB+zn9Xp18/MrNGlwd10wKkfxbrZBRPsQ8neytXaVpLckdZb0ojGmmyQZY5Il/UlSgSQr6ZXG7zPGZBljhhhj8kONAQAAxK6URLcuGt1HLlfg1fD3CvfqrS926c6XVmnGQwsb6sqBWNda/6ScJd8JmlMkbTXGfCppp3yr4YcknW+tPfo4rZslFUp6v5ViAAAA7YzH49UDc23D/caiMr1OIo52olUScWvtdkmjJT0s384owyXVSpojaay1NnZ2VgcAAFFj9a7D2rivrOHe5ZJunzE4ghEBrafVds631hZLmu3/1Zz+d0u6O4jx35TEExwAAHQgw3Iy9MEdk/TI++v14mfbde7wXhrSs3PAvl6v17G8BYhGHGEFAACiWp/MTrr3ouH63qQBSkpwO/b7y6LN+njdPt0+w2hYTkYYIwRahkQcAADEhAHd0xzbyqpq9ej89Souq9Z8u09nn9hTPz9nqHp3SQljhEBw2P8HAADEvGcWb1ZxWXXD/QK7T4nxpDmIbnyHAgCAmPfZlgNN7q87tb+y0pIiFA3QPCTiAAAg5v3p6jF6+tqxOqF3Z3VOjtcNEwc49q2sqQtjZIAzasQBAEDMc7lcmmKyNWlQd20uLlNGSkLAfjsOVujchz/SFeNydf3pAxz7AeHAijgAAGg34uJcx3yo8+H31ulAeY0e+WC9Tr/3A835z9YwRgc0RSIOAAA6hE1FZXrxs+0N94cra+Vm33FEEIk4AADoEDYXl6lLo1KUAVmpumBUTgQjQkdHIg4AADqEKSZbC++cojtmDFZ6crx+eMZgxbsDp0LFpVWq83jDHCE6Gh7WBAAAHUZqUrxunjpIV47LU3qycxp08/MrVFxWpdvOMDrzhB5yUcKCNsCKOAAA6HAyOiUoLi5wcr1ofZGWbCzW2j2lmvXccs384yKVVNaEOUJ0BCTiAAAAfl6vV/e9a5u81jk5QenJbHOI1kciDgAA4FdRU6f+WalqXIlyx5kmcgGhXaNGHAAAwK9TYrweumSEbpycrwfnrpXH69WIvl0C9q2p82hzUZkG9UgPc5RoL0jEAQAAjjK4R7oev3K0auo8jn1eXL5dP33lC808qbd+MH2w8rJSwxgh2gNKUwAAABwkOGxvWFlTp4ffXyevV3p15U5Ne/BDvbpiR5ijQ6wjEQcAAAjS88u2atehyoZ7d5xLpwzoGsGIEItIxAEAAII0oHuqTKPa8CvH5apXRkoEI0IsokYcAAAgSJNNtk4f1F1vrtqpJz7cqBsn5zv2XbyhSCf16aLUJNIuNMV3BAAAQAu441yaOSJH3zypt+PJm3tLKvWdZz5Vp0S3bpycryvG5So5wR3mSBGtKE0BAAAIgVMSLkmPzt+gipo6FZdV61dvFerbTyyR1+sNY3SIZiTiAAAAbWDHwQo9v2xrk9cuHNXnmIk7OhYScQAAgDaQnhyvWZMGKDXRV4qS0yVFl57cN8JRIZpQIw4AANAGOicn6LYZRldPyNPjH27Q0N6dlRQfuD587Z4S7ThYocmDu7Ni3oGQiAMAALShbmlJ+tk5Q4/Z595/r9H7a/ZqTG6m7jjTaNyAbmGKDpFEaQoAAEAEfbb1gN5fs1eS9OmWA7r0yaVavuVAhKNCOJCIAwAARNADc22T+9G5mRrVr0uEokE4kYgDAABE0E/OKtDUIdkN93fMMNSJdxDUiAMAAETQsJwM/eWasVq+Zb/mrd6r8fmB68PrPF797r21uvTkfsrpkhLmKNEWSMQBAACiwOjcrhqd29Wx/c1VO/XIB+v1xIcbdfkp/fT9KfnKTk8OY4RobZSmAAAARLmaOo8emrdWklRd59Ezizfrvnfscd6FaEciDgAAEOXeWrVLm4vLG+7j41y6eerACEaE1kBpCgAAQJQ7d3gvVdd59Pv31mnHwQpdPKavcrulRjoshIhEHAAAIMrFu+P07TF9NXNEb73wn206Y2gPx75/W7JZknTJ2H5KjKf4IZqRiAMAAMSIpHi3rp6Q59h+qLxGv33XqqSyVk8s3KjZ0wbp/JE5ineTkEcjflcAAADaiScWblBJZa0kafuBCv3qrUKV19RFOCo4IREHAABoBypr6vTCJ9uavDZrUr46JydEKCIcD4k4AABAO5Cc4NY7s0/XVeNzleB2KSstSVdPyI10WDgGasQBAADaiezOybpn5jDdcPoAbSkuV6fEwKnehn2luvv1r/TDMwZrVL/MMEeJeiTiAAAA7Uzfrp3Ut2snx/aH5q3VR+uK9NG6Ik0bkq07vzFEpmd6GCOERGkKAABAh7J652G9uWpXw/37a/Zq/d7SCEbUcZGIAwAAdCDvfLW7yf3QXp111rCeEYqmYyMRBwAA6EBuO2Ownr/hFI3q10WSdMeZgxUX5wrY1+PxhjO0DocacQAAgA5mQn6WXrqxm5Zt2q9T+ncN2Mfr9eqyp5bqpL5dNGtSvrqmJoY5yvaPFXEAAIAOyOVyadyAbnK5Aq+Gz1u9R8s27deTCzdq4m/n66F5a+X1skLemkjEAQAA0ITH49WD89Y23JdW1WrN7sOOSTtahkQcAAAATWw7UK4D5dUN9y6XdPsME8GI2icScQAAADSR2y1VH/5oin52doEyOyVo5km9NbhH4H3Gq2s9qq3zhDnC9oGHNQEAAPA1yQlu3TBxgC47pZ8qqusc+z27ZLP+vmyrfjB9kM4b3ttxBxZ8HSviAAAAcJSWFK/u6UkB28qqavXYgg3aVFSm2S+s1NkPf6TCXYfDHGHsIhEHAABAizy9aJOKy47Ukm/bX64enZMjGFFsIREHAABAixyurJW7USnKd07rz37jQSARBwAAQIv89OwCvXfbJM0c0VuZnRJ0/cQBjn33HK4MY2SxgYc1AQAA0GL9s1L1+0tH6lBFjTonJwTss/1AuaY+8KGmDcnWbWcM1iCHHVg6GlbEAQAAELKMlMBJuCQ9/P46Vdd69O8vd+vM3y3Uve+sCWNk0YtEHAAAAG1m475SvfTZjoZ7j1cakJUawYiiB4k4AAAA2kx5dZ2G9urccD+ge6rOH5kTwYiiB4k4AAAA2sywnAy9fvOpevyKURqUnabbzhiseHfgFHRrcbkOVdSEOcLI4WFNAAAAtCmXy6VvDOulM4b2lNO5m16vVz968XMV7jqs703K1zUT8pSa1L5T1Vb5rzPGZEq6S9L5knpJ2ifpHUn3WGu3tGC8IZLulDTVP16FpM8l/cla+7fWiBkAAADh1XjP8aN9vL5IyzbtlyTd967V04s26d+zJzY51fPZJZt19om9lJUW+KRPJ0WlVXr7i126anxeS8JuMyGXpviT8MWSZkvKlLRKUoqk6yStNMYMD3K88yStkHStpB6S1kiqlDRR0rPGmL8bY5x/FwEAABBTvF6v7n/XNnmtoFfnryXhv3ztK1325FIVlVY1e+yi0ipd9uRS/fK1r/Tsks2tE3AraY0a8ackDZH0tqQca+0YSb0lPSOpi6QXjDHu5gxkjOkh6e+Skv3jdrPWnmSt7SnfanuJpMsl3dIKcQMAACAK1Hq8mnFCT3VOPlKscccM06TP2Sf20qDsNK3bW9rsZLw+CV+3t1SDstN09om9Wj32UISUiPtLSC6QVCrpSmttiSRZayslXS+pUFKBfEl0c1wvKV3SZ5JmWWvL6xusta9K+on/9oehxA0AAIDokeCO001TBuqjO6fq5ikDdf7IHJ3Ut0uTPllpSZrz3XEa2Mxk/OgkfM53xwVd0tLWQl0Rv0KSS9Ib1tr9jRustXWSnvbfXtLM8Sb7ry9baz0B2t/0X/P8JTEAAABoJzI6JeiOM40eumREwPastCR9e0xfSdK6vaX65h8WaV9J5df6xUISLoWeiJ/ivy52aF/qv57ezPF+IekaSa86tDfe/b19P0YLAACAJipr6vSXjzc13O88WKGzfv9Rk5XxWEnCpdCT2YH+6yaH9vodU3oYY9KstaXHGsxau1RHkvdAZvqv+yQVNTtKAAAAxLznlm7R7sNHVsBdkopKq3XZk0t1z+RukqRbYyQJl0JPxLv7r8UO7Y3LVbLkqyVvEWNMT/m2NJSk56213paOBQAAgNhz2qAsmR7psntKJEleqeEBzlmv+x4tPFTpiYkkXAo9EU/xXysc2hu/nuLQ57iMManylat0kW8l/DfNfW9hYWFLP7ZFKioqIvK5sYr5Cg7zFRzmK3jMWXCYr+AwX8Fhvr5u9d7KhiRckjonxemeyd006/VyHar0PV6Ykex7bd+2jdoXqUCbKdREvE7HrjNv3NaiFWxjTJqkN+SrR6+TdIW1dk9LxgIAAED0WVtUpTX7KrXlYLU2H6zWd0Z309Ds5K/1y+2S2OS+tNqjak/sFkmEmoiXybdK/fWZ8mn88wCnVXNHxpju8u2UcrIkj6RrrbXvBjNGQUFBsB8bkvp/tYb7c2MV8xUc5is4zFfwmLPgMF/BYb6C097mq6bOowR34PXbJ/+xUq+sOFLpXJqQqYKCvIB9c/69RzsO+tJKj1f6xQdFOlTpUUayb+xDlR79ckFx2EpTli9f3uL3hpqIF8uXiHd1aO/W6OugfjpgjBkgaa6kfEm1kq6y1s5pSZAAAAAIr4Pl1frTR5u0ZneJ1u4pUVJ8nObdNilg38E90pvcNy4/OdopA7pqz+FK9c3spA/W7NXW/eUalJ3W8LDmLxcUN+wzHu114qFuX7jGf81zaM/1X3c1PpzneIwxwyUtki8JL5c0kyQcAAAgeng8Xm3bX679ZdUB291xLv1h/nq9V7hHW/eXa2NRmSpr6gL2NT3Tmtzb3c6J+IPfHqHfXzpSy7cc0N6SqoYHM7ukuNUlxa053x0X9AmckRJqIv6p/zrOob3+9WXNHdAYM0jSPEk9JR2QNN1a+3aLIwQAAECr+ccnWzXzj4s07O53dfpv5+u1lTsC9ktPTlBOlyN7ddR5vNq4ryxg36G9MnT+yBz9+BtD9Jdrxujhy0Y6fv7x9gmvP4EzFpLxUBPxl/3XbxljmpSnGGPc8h3OI0nPNWcwY0wn+R7MzJZvd5TJ1tolIcYIAACAZiiprNHyLfsdk2tJOlBeo8+3HVR5tW91e+0xykhMzyMlJy6XtHV/4AKJnhnJeuiSEbpxcr6mDunRJIFvrLmH9cRKMh5Sjbi1dpUx5i1J50h60RhzsbW22BiTLOkxSQWSrKRXGr/PGJMl377iNdbaDY2afibJyPdg5sXW2lWhxAcAAIDjq6qt09T7P2x4CDLOJZ15Qk8lJ7i/1rdxci0du4zkynG5OvvEXhrSM1353dOUkvj18Zor2BMz65Px+vdEY814axwTP0vSx5KmSNpqjCmUNEBSpqRDks631nqOes/Nku6S7+TNPEkyxiRJusnfXi7pV8aYY33uRdba3a0QPwAAQLtU5/FqS3GZ1u4pkd1dquF9MzTFZH+tX1K8Wy7XkXuPV1q/t1TDcjK+1tc0erCyc3K8MlISHD9/ypCvf1ZLvf3FrqBPzDw6GX/7i126anxeq8UUqpATcWvtdmPMaEm/lO8I+uGSDkqaI+kua+26Zg51oqT63+00Sacep7/TlokAAACQ9OePN+rXb69puL90bN+AibjkS7C3Hziy2/TaPSUBE/FeGf+/vTuPk6uq8z7+qe7qvao7SXe6OwlkI+mbkIQlYV8kIIgiyDIyyLA8KKg4QXFwRh9H2RyXQR9lBmV0gFFkEXQURAVFUPYksoQlgeQkELKnu9Odrar3rqrnj1tVqeVWp5dbXdXV3/frldftW/fUqXtPbp3+3dNnKefnnzoOq8FPQ3UZnsQIPotiAfQ5i6YMqVU7FoznWxAO7rSIY4xpB66P/htM+luAW1JeexUYnf9JERERkTHs5fd3Y5r3s645wIaWIPddfZxjN5K5Q5gW0Gr08+z6Xcyqq8Jq8FPvd27z9Hg8nNY0eWQXMEzDDaTrfGV5F4SDS4G4iIiIiLgrEolkbG2+4VdvJLVeZ+pGMi+lP/f65kDGfK9dehjXnzmXMu/w+3HL0CgQFxEREckD7+0KjpxJ6QAAIABJREFU8tvXt2OaA5iWAPMnFXP9Sc4tz/Mak7uRmGbnbiSN1eXMqquisbocq9GP1einPxyhpDg9EK8uz9zXW7JDgbiIiIjIKAiHI2zf20VDdTml3vQZpLft6eKHf303vl/uydwPuqnBz9NrW+P7maYQ9Hg8PPPPS4d/0pJVCsRFREREsuj7fza8+G4b65sDdPSG+P11p7DokIFnIwHYsreXcCTimOdxsyaxfW8XTQ1+rAa/Y36S/xSIi4iIiAxTsKcf0xygPxTm+Nm1jmnW7gzw+pa98X3TEnAMnBuqy6gu97K/ux+A7v4I7Z3OS8IvtepZmmH2Exk7FIiLiIiIDNGa7fv47P2vxRfAOfLQCTy2zHnm5XmNfp5e2xLfN837HdN5PB5uOKuJyjIv8xr9hHZvp7xkpIugSz5TIC4iIiISFQpH2LK7E9McYH1LgI8dOZWZdVVp6Sb7y+JBOMCGlgDhcISiovRBkE0JM5f4y71k6G0CwFUnz4r/vDawc5hXIWOFAnERERGRqOt+sYo/rjmwcPeUmnLHQLzeX0ZNRQn7uvoA6OwNsW1PF9NrK9PSnnRYLfd+8lisRj+N1eWjtgCO5D8F4iIiIlLQevpDvLl1H6YlgGneTygM37lokWPawyb7kvYHmo3EavTz6qbd9gI4jX76w2HHtHW+MvXnFkcKxEVERKSg7evs4+//e0V8v6KkmG9dsNCxG4mVsgDOuubMK1He8YmjmVBZ4riipchgKBAXERGRMem1zbt5zuzCtARY3xJk2elz+PiSQ9LSTfaXMaGyhL2ddjeSrr4QW/d0MqM2vcuJ1ehnYmUJVqOfeY3VHD19QsbPb6xxXgJeZLAUiIuIiEheikQi7Ar2UO93DnifM7u4I2EBnHU7M89G0tTg5+X3d8dfM80Bx0B8br2PVTeepX7cMioUiIuIiEje6OkPccvv3o7OWhKkPxzm7Vs/TPFBZiMBe37uTJZak+PLvDc1+DlmxkTHdArAZTQpEBcREZFR09UX5vUte6ipKGF2ysBIgNLiIp58u4XdHb3x17bu7nScuSR1JcoNLcGMn/uPS+eM4KxFskOBuIiIiGTdb1/fzr8/voXmYD+wiatPmcWN5x6els7uRuJj5cYD3UjWNQccA/GZdVVcfcosrAY/VqOfuQ3pgb1IPlMgLiIiIsMWDkfYusdeAGdDa5BrTzvMsRtJSXFRNAi3mQFmI7Ea/PFA3F/mZV9Xr2O6kuIix2BeZKxQIC4iIiLDdup3n0laYfKcRVOY5dSNpDG5tXqg/tx/f+yhLLXqsRr9TKnRAjhSuBSIi4iISJKOnn7W7twfXQAnwNx6H1ecONMx7fRJlUmBuGkOOAbiM2ur8BZBOGL/3NTgp6c/RJk3fQ7uBVNrWDDVtcsRyVsKxEVERCTJs2YXy36xKr5/ypy6jIG41ehnxcb2+L5pDvDhhY1p6bzFRdx53iE0+LwctWiB6+csMhYpEBcRERknnjGtvLl1L6Y5gGkJcM+VxzjOXDKU1SWbGvxMqCyJD5hcPCPzAjjTJ5QO/+RFCpACcRERkQIRiUQI9vTjLy9xPH738xtZ/t6B1uv1LQHHQHxmbSWl3iJ6+8MAtAV7aA/2UOsrS0t7ybGHculxh6oft8gwKBAXEREZw7a0d/KT599jfbSVe9G0Gn7x6RMc0zY1+JMCcdMc5MML09N5i4v44Lx6ioo8zGvw09Top7LUOWRwmiFFRAZHgbiIiEge6+ztZ0NLkJm1VdRUprd094XD/OJvW+L76weYjSS1y4lpcV4SHuDHly8ZxtmKyFAoEBcREclDP3hqPb99fTtb93QSicCPL1vMRxZNSUs3s7YqpRtJL23BHuocupEsmTGRT548M2EBHH9aGhEZPQrERURERlE4HGH73i7WNQcI9vRx4dGHOKYLdPexZXdnfH9dc8AxEC8u8jC33sfbO+zWbV+Zl+17uhwD8aYGPzefpxlLRPKFAnEREZFRsn1vF2f94Dk6e0MA1FaVZgzErZTW6oG6nNxwVpP9nkY/0yZUaOCkyBihQFxERGSEAt19rG8JYJqDrG+x59E+YXZtWrrG6nJC4Uh8v70jczeSWH9uj8fuftJQXZ7x8z84v8GFqxCR0aZAXEREZIRuf2oDP33p/fh+TUWJYyBeXORhboOPNdsPDJI0zQHq5qQH4vOnVPP7605hTr2PitL01SdFZOxTIC4iIuKgLxTmL2tbMM1BTMt+mvd185vPneTY7cNqTJ6L2xxkAZwt7Z3Ma6ymqdHHpCrnRW7KS4pZdEjNyC5CRPKaAnERERm3IpEIvaEwZd70Fucij4cv/vINuvvC8dfagr1M9jsPgkw0UH/ub1+4iO9ffKT6cYuIAnERERlfXt20m0df3x7t0x3gqpNmcsOHrLR09mwkflZv3xd/bX1LIGMgPqfeF58WcF5j5mkBy0vUzUREbArERUSkoHT1hni3NcjCadWOrc4b2zp4MGEBHDNA63VTQ3Igvq45wMlz6tLSVZV5efqG00Z45iIy3igQFxGRgvDFh1/n9a172bLbXgDn5a99kHp/+kwjqdMCDtSf+4x59fjLvViNdkt36ntFREZCgbiIiOS12AI4pjmAv9zL8Q6zkYDd0r25/cACOKY54BiIz23w4fFAJDqLYHuwl57+kGM/8Y8eMYWPHpG+iI6IiBsUiIuISN56+p0Wrn/4dTqiC+B86PCGjIF4U4Oft7Yd6EZimgOcOndyWrrKUi+3fmwBU2sq4gvgFBVp4KSIjD4F4iIiMuqCPf2sbwmwvjmAaQmw7PQ5jova1FeXxYNwGHg2knkJC+DMmFSJd4Dg+soTZw7/5EVEXKJAXERERt1ld6/kzYTW6zPm1Tu2Xs+pT+5Gsnl3J529/VSWpv/6OveIqRw3axJz6n2Ox0VE8o1qKhERccW+rj5WbmzHRFu5J/vKuOVjCxzTNjX4kwLxgbqRTJ9Uye6OXuY1+mlq8NPdF6bSYQ2cxppyGmsyLwMvIpJvFIiLiMigRSIRIhEc+1Rvae/ks/e/Ft+fUVvJLTgH4lbj4Gcu+d2yU6iu8GoBHBEpOArERURkQH9a08xL77ZhWgKsbwnwn584mtOaDt6NZMsA3UgOn1LNYZOrsKKt3MfNmpTx82sqS1y7FhGRfKJAXERknOvuC9G6v4fptZWOx59Z18ovX90a31/fHHAMxCtKi5kxqZJN0SkEIxHY0BLkyEMnpKU9aU4df/nSUncuQERkjFIgLiIyDrUGurnxt2tY3xJkc3sHh0ys5Pkvn+6YtimlG8m6AbqRfOyoaezr7MVqrMZq9KV1QRERkQMUiIuIFJhIJMKOfd2Y5v0cNtnHjNqqtDTV5SU89U4L4YRuJB09/Y75pa4muam9I+Nn33BW0/BPXERknFEgLiJSQO585l1+8ux7BKJB9b+eM4/PfOCwtHTlJcXMrK1iY9uBoHpDa5D0mbxhwdRq/uVsi6YGe4n3QyZWZOv0RUTGlaJcn4CISC7dt2ITbcGeIb+vLdjDfSs2uX06GXX09PPG1r388pUt/MfT6zOmKy8pjgfhAKY5mDFtU0JL9/RJlQS6+xzTTawqZdnpczjr8Aam11ZqFUoREZeoRVxExq37Vmzipsfe5v4Vm3noMyc4ruzopC3Yw6V3rWRDqx3kZnuVxp7+EEfe+mf6Y/1IgE+fOpuqsvQqfF7qtIAt+zPme90Zc7h26WHMrffF81q7ts2lsxYRkYNRi7iIjFvnLJrC3HofG1qDXHrXykG1jCcG4XPrfZyzaMqwP7810M2f327mR3/dwOcfep1fv7bNMV2ZtzhtRpNMS73HWrn9ZV6WzJjIsTMzTwu4cFoNRx06wTGgFxGR7FPtKyLjVp2vjIc+c0I8sL70rpUDtoynBuFDaUV38vhbO7n19+/E90uKPXx8ySGOaa0GPxt3HejPvb4lwNHTJ6alm+wv46X/ewZTa8q1AI6ISJ5TIC4i49pgg/GhBOG/fGUL7+zYz7rmABtagzz3L0vxl6cvSpM6G0mmVm6A+VOqMc0Be8Bko5+F02oypp02QYMpRUTGAgXiIjLuHSwYTw3C7/3ksQzU1nzX8xt5b1fybCSLHVqvU+fn3tASJBSOUOwwGPLzZ8zhCx+cO7wLFBGRvKQ+4iIiHAjGU/uMJwbhvjIvvaEwp373Gb71+NqMeaUuYmMyLIBT5yvjzPn1XHHCDL55wUIeuOb4jHmqm4mISOFRi7iISFRqy/jZtz8PQHtHL9MmVLB9bxfB6NSAj7y+nRvPPZyJVaVp+RwyMXlg5YaWzFMI3vN/jnXxCkREZCxRi7iISIJYMF5bVUp7Ry/tHb3UVpVy7yfTA+a+UNgxj5Li5NbrrXs6M37er17Zyn88vZ57XtjIr17ZSvO+7pFdgIiIjBlqERcRGYQJlemDLXv6nQPx2XW+pP3K0uKM+f5m1Tb+9v7u+P6D1xxPY015Wrqtuzv52I9exF9egr/cy6y6Kn70D4sd81zXvJ+d+7qpLvfiLy+hsaacaofBoiIiklsKxEVEEsT6hMdawsHumvKJu1YmpSv1FnHopEqnLOLdV2L85Zmr2sGm3d/dx55O+x9AKGFxn1QPv7yVe5dviu/feO7hXH3KLMe0n73/VUq9xfjLvfjLvXz00Ehaiz5AZ28/PX1hfOVeSor1x1QRETcoEBcRiXKaohCIv3bIxAq+dFYTHo+H3gyt4WAH6dMmVBDo7iPY0+84dWFMoDs1EHdOm54uc/W9P2Wp+kxp+0Nhnny7Jb7v8cDHrnAO2B97YwdffWQ1AOUlRfzDcTO46bzDHdP+8pUtBHtCdnBf5uWkOXXUVKhFXkQklQJxEREGnic8cQDnfz373kEX8rn0uOlcetx0ACKRSNLS9Kk+feosWgM9BLr7CXT3M6kyffAnDD5gd0pbnSEQT22N95V5KcowO0sgIbjv7gsz0CQud7/wPu+2Hhig+uQXP+AYiK/eto9lv1gVb41fNK2Gr33UObhf3xIg0N0X75ozqaqUMm/mLj8iImOBAnERGfcOtljPUFfgTOTxeBy7esRcceLMQZ3j6dZkXv36mdGAvY/yksxB6IKp1XT3heJpazOcZ1pwP8BS96lpfQOmTW6R92V4ENjd2cuW3QcGsmZ6CAC44y8b+MNbO+P7/3HJUVxw9LS0dN19Ib7867fwl3vxlXuZVFnKZ087zDHPnv4QxR4PXnW1GRX3rdjE3LIQEyqG9gDVFuzhidU7uXKQ3xWRsUSBuIiMa4NdMXMkwbgbvMVF1PnKBvV5XzyzaVB5Tqoq5Z4rjyHQ00ewuz8akHY4pvV4PPjLvQR7+olEDtLvfZDdaAabDgbfNWd/Vx+/e3NHfL+2KnMgfvfzG/l/f15PRYndR/7Tp87m0x+Y7Zj2V69uBYgPgF0yY+KAD0OS7L4Vm7jpsbeZXlPCbWdPHfT7Er+fgIJxKTgKxEVk3BrKsvWQ+2DcbVVlXs48vCHptbVrnRcquuGsJm44q4lwOEJHbz/eIudW5EgkwtWnzGJ/dz+vb93DhIpSfKXOv2pSW85j3W2cWkAzpU21fxjBfVdfiK6+EL0ZpqME+Pc/rmN3R298/5WvnekYiC9/r41vP7EWX5kdsB8/axLXnOoc3L+3y15J1R8N7qtKiwt24aZzFk3h/hWb2dAa5CtP7uCRprkH/d6kfj/PWTRllM5WZPQoEBeRceuJ1TsHHYTHpAbj4+1P5kVFngH7p3s8Hm74kMV9KzZx7/JNzK33sbuz17FszztyKsfPriXQ3Wf3j68qzdgCajX6CUUgGE2bafBnasBeMUCrdWrQXhSNgduCPdz82BpuPX8hNz+2hnXNgaQgHKC3PwTA3q4QL2wOMn++3eob7Oljzfb98XQr32un1FvElSfOTHvA+Pqja1ixsT2e9v6rj+PUuZMBO69zFk2hzldGW7CH259aH+8fP6WmnIsWH+J4TbsC3fxxTXPe3ZOx781FP3yOLfv6DvoQO9SHZJGxypVA3LKsicDNwIXAFGAX8CfgG8aYzbnOT0TESSxYiQU8gxULKsZbED4UiS2gmYKuqjIvsxL6mg/UAvqdi44Y1OdOn1TJ7ZccydPvtPD46mbaO3ppC/Y4/v/2h+xBp5HoWNp7l2/ig/MbuOzulewK9vLU2taMs+Nc9bNXuPOyxXzlyR1s2dfH5s7XeHx1M8VFyS3agZ5+bnrsbYI9/Ty6anvSA0bqYNkXNrRx6tzJ8W4c96/YzEOfOYFdgR4e/NuWeLqmBp9jIN4W7OGsHzzP3q4+vvsnQ0N1GV/44FzOPyq9Lz3Ao69vo6LEGx8su3BqDUVF2WuRr/OVcdvZU/nKkzsGvC8UhMt4MuIRKtGgeTlwPTAReAuoAD4FvGFZ1uBqzyzlJyIykCtPnDmsX/J1vjIF4QOIPazMrffFg662YE/G9G4FX7W+Mi48+hBuPX8hc+t9tAZ6Mn729y4+kve+dQ7P/vNpzKqromV/D+fe8SK7gr2UFhc5BuFlxVBZWsSG1iDn3vEiW/b1Mb2mhCtPmklpcZHj/O5Tqsv531e3pj1g7O1MbmX/0AK7m9A5i6Ykldu2PV1J6Zz+IhErv71d9l8Egj39vLerg+6+kGM5hcIR/umXb3LtA69x2T1/42M/eolMc/s89U4Ll961ks/c9yo3/OoNHntje4aU9sJTO/d1RccSpOc4oaKY286emvG+UBAu440bQ8XvBuYBTwDTjDHHAFOBe4EJwMOWZQ1lRIvb+YmISA4MNhjPRvA12M8uKvIws87Hf1+xxA6+Q2FKi4u4/5rjmFvvS0vfEwJfaQklRR56Q2FKiuC6E+r4+qNrHPuY11aWUl5axPttnUnX1hbsoT3a3aW4yEOZ18P06AJRqed+82NrkvJM7feeWH5VZcUpaZ278DhNXZnamh+zub2DFRvb+fM7LTyyajtvbN2bdDwx4L76569w4nf+ysKbn+Swf32Cl95t493WIOua97Nm+z72dduzpnz/4iOZWFnChtYgH/nPF3jsje0KwmVcGlHXFMuy5gEXAUHgCmNMAMAY021Z1jXA8cB87C4mvx7t/EREJLcONsA1m8HXYAfXtgV7WPbgqngQ3hsK8/VH13DnZYtZ9uCqeHeSmNZoQF9S5KEvHOFrT+2kz6EHSxH21I1OQfild62kszeU9Pqejl42t3fQF4rQHw7zk8uXcO0Dr7GhNchkfxkXLzmEUCTCzNoqnli9k75QmD0dvfz4ufdo2d/D3HofEypLeGXTnvg5vNsa5DtPrI3nuWTGRM4/aprD4FcvX31kNRt3BekPR+gPhbn9kqOYPdmX1pd+U1sHC29+kr5QmP5whIXTanhs2clA8uw24Qjc+cy7LH/vQD/460+s48NN1ezrPrBK7K5AD1/61ZvUVJTQ3tGrIFzGlZH2Eb8c8AC/N8bsTjxgjAlZlvUz4LvAJQwucHY7PxERybFMATEw7CB8X5e9aml/KExfKMJkXxk1lemtv7VVpXz2A7P5/lPr2dAa5KN3vMDjXzjV8UHg0IkVnDynliffbmFDa5Ar/+dl7rv6OMdgHA60BGcKwsPA5t2dFHlgx94uTrntr8yt99HdF3a85tv+tI6HX9kaz+PbFy5KKren3mnhoc+cQG1VKbO++kTS58XymlRZSrC3n2B0gajn1rfyg6c2xtP1hcKcf9Q0SoqLuOjoaezv7ifY08fEylJWb9+bNNA01mqeOs1kdUVJUot6X0IXntS0E6uSF6iKJU1N1x+O0N7RS21VqYJwGVdGGogfH90uz3B8ZXR7ao7yExGRPJAajJ99+/MAtHf0Uu8vo9RbxGnffYaOXrtPs7/MS1Ojn9987qSkfK77xSqCPf08a3Ylvf7NCxZy+Qkz4vtvbdvLPS+8j8cDj71xYF7xlv09jg8C3iIPW/d08fAr2+Jpm/d3s+zBVdx52WKu+fmrSYsPAfRn6FQ9pbqccCRCS8BuOQ9HiF+XaQnS2x9OCsJ/9+YOXn6/PSkIB+gPh9PK7aN3vMDJc+rSPvP+q4+LB6/V5SVUR7ukvJnSjaQvZJ90Q3U5P7jkqKRjF9z5kmPaq06ayRnz6uOz25SVFCWVaX/Yjq4jkQj11WWUdxcT6O6juy/MhJTZbULRh5fUeeFFxquRBuJzotv3MxyPzXDSYFmWzxiT3qSQ3fxERCRPxILKs29/Pt4/uraqlI8e0cjPXkqeECvQ05/Wagqw/L32tKkEwZ4BJdGOvd1JC/skSn0QqCwtprM3fVCjv9wbb8Hf39WXdjyT7v5QvNtFqtQgHODW370dL49EsUA4Vm7n/fBFdu7r5pFV6YMlaypK014D8Kas6ppaTolSV4CNpZ1eW8n02sr46++2BlLS2efp8Xj4y5eWJpx/mJ88+x6z6qrwFtkrmPrL7KFpC6ZV87nTZvPwK1vZ09lHVZmXcm8R7R29Y35+fpGhGGkgPjm6bc9wPLF7SR123+/RzC/j4hTZ0tXVlZPPHatUXkOj8hoaldfQZbvM9naF6A8dCLD7Q/3s3r3HMW1HV3faefT1O7ekbt/ZzNq13fH9bducVwgFqC4rige+NeVFTK8pYXVLeiC+qL6Ut1vDjkHyQPZ09lFW7KEnlN5kXuSBbyytZdfWjcTa9DNdU8eeXUnX9IkFfm5f3p2UZvbEUg6bVIox6yjzps+/UNndyycXT8JbZA8KPbQmnPH/9vIFlfxdUznFRR47faCZtWtb09KFwhH+99IZeD2eeNpMeZ45Fc6cemDRqK6uLrq6uujp2srjb+xgT2df0mqbsakNL/rhc9x29lQmVIzvuRlUhw3NWCyvkQbiFdFtV4bjia9XZEiTzfxERCRP7O0K8ZUnd7CvO0xNuR007usO88xG5zaVfoepAFNnxKss8TCxwktlSXIQGnaYOu8DM6sIRSKsbk4OZh2SUl/l5eQZVbzd2p1+cAT8penBssNl8oOPTGV+fXlKuuSEHuCrp9VzSI1zazjAjImlzJiY+XiiprrBtUAXF3nwlQ4/QN7bHeKW53bEp35MDLhj84xv2dfHV57coWBcCt5IA/EQA0+BmHgs0xSl2cyP+fPnDyaZa2JPYaP9uWOVymtoVF5Do/IaumyVWVuwhy/ctZIt+/riXTOApIGSN557OH2hCDNqKzl0UiWlxUVUpAR8P7liMn2hMOFIhHAETmuaTKlDS3D1lC7qG3cTIUI4DFMnVDC3wWd3M+kJUxsdRNje0UulQ/x5/Yfmce9Lm9jXbacN9vTRk6lTeIqJlSWOXVNKvUXs6wlz07PtSV0vLlwc4v6VB7rmLJkxkUXz5jC3wZ9Ufr/53YE+3N4iD/3hCN9dvndMdeNYsWpNPAjPNED3kaa58fsitazGG9VhQ5Or8nrttdeG/d6RBuId2HN7l2c4nvjNydTKnc38REQkxwaaojBxIOL3njQHDbpOmZs+UNHJtAkVTDv6wIqSTucAzrO2pKa987LFXHv/a2xsy9zdJVG5t5gZk0rYHB3cOauukv+99qSkz0vsB/1vFyzk3y5YmDG/2Pls29PleO5jpU91W7An3to90Cw5g512UqQQjHRBn1hf7kkZjtcm/LwrQ5ps5iciIjl0sHnCh7oCp5vn4PTZ61sCaUH4sgdXOQbhdVWleB3WwNm5v5utCTOsePAM+1qHcu5ul5ubYtcR645ysMB6rF2fyHCNNBBfF93OzHA8NpfUTmNMZ4Y02cxPRERyZLCL9WQz6Brqg8C5d7yYFoQ7zSEO9lzm/REocfhNGsb+BTtjUiUb2zri1zSUa82Hhxi3PLF6Jxtag/E+4YNp3U69vidW7xyFMxUZXSMNxF+Nbk/IcDz2+t9ylJ+IiOTAUFfMzEZQOZQHgTsvW5y0xP03L1yYMQiv95XFV9UsKYJvnTWFufW+tHRh7OkKZ9VVJl3TYK41Hx5i3HTliTP5xvkLhjz4MnZ93zh/AVeeODN7JyiSIyMNxB+Jbi+wLCupO4llWcXAVdHdB3KUn4iI5ECsBXQoK2a62QI6lAcBpyXur7jnZccgfEp1OVXlxfSFI5QWF9EXhh+tbOObFy6ktDj9V+rO/d109w4tGM+Hh5hsuPLEmcOaAaXOV6YgXArWiAJxY8xbwONANfBry7JqASzLKgfuAeYDBng08X2WZdVZljXPsqzD3MhPRETyS6wFdKiD7NxqAR3Kg0Bi2j984RQm+0rtoDxlNpZpE8q54qQZvN/WGU87vaaELfv6uG/5pnggD5DYdXzn/m4uPubQtAeMTA8euX6IEZHRM9JZUwCuBV4ETge2WJa1FpgNTAT2ARcaY1KX8roOuBl7pcyZLuQnIiJ5ZriBtBstoLH3n7NoykED2dS0f/ziB7j5sTXcev5Cbn5sDaY5wKlNdSw7fS51vjJ8Zd542tvOnsoLm4N8+cIlHL9iEyfMrmXlxnZOmF3LTb9dw57OXi47YQZXnjiTvz/mUJ5YvTPp2mIBdOLrQzn3RE55iUh+G3EgbozZZlnWEuAm4HzgCGAv8BBwszFmQy7zExGR8WkowWhqcHznZUsA4ttMaSdUFHPevJqk15ui838//NkTk96X6QHD6fVcPsSIyOhxo0UcY0w7cH3032DS3wLc4lZ+IiIiIiJjzUgHa4qIiIiIyDAoEBcRERERyQEF4iIiIiIiOaBAXEREREQkBxSIi4iIiIjkgAJxEREREZEcUCAuIiIiIpIDCsRFRERERHLAE4lEcn0OWfHaa68V5oWJiIiISN5ZsmSJZ6jvUYu4iIiIiEgOFGyLuIiIiIhIPlOLuIiIiIhIDigQFxERERHJAQXiIiIiIiI5oEBcRERERCQHFIiLiIiIiOSAN9cnkO8sy5oI3AxcCEwBdgF/Ar5hjNmc6/zyTRbKax7wZeCMaH5dwJvAPcaY+90671zJ9v1gWdZJwAvAVmPMzJHml2tZuL+KgGuAq4AFQCmwFrgb+IkxZkxPK5WYZNqGAAAKBElEQVSF8joE+DrwkWh++4HlwG3GmJfcOu98Eb0/VgCHGWPqhvH+gq7vU7lQXgVd36caaXk55FdQ9X0qF+6vvKzv1SI+gGgluhy4HpgIvAVUAJ8C3rAs64hc5pdvslBe5wGvA58EGoB1QDfwAeA+y7IetCxryJPn54ts3w+WZZUD/0OBfM+zcH+VA08A/w0cD2wDWoGjgf8CHtL9lZTfAuzv42eBeuxfYADnAc9ZlvUpl049n3wTOG44byz0+j6DkZRXQdf3GQy7vFIVWn2fwUjur7yt7wv5P8wNdwPzsP/zphljjgGmAvcCE4CHLcsqzmF++ca167MsqwF4ECiP5ltrjDnSGNOI3boUAP4B+LzbFzGKsn0/3BzNv1C4XV63AWcDW4GjjTELjDEzsAPLDuAS4DL3Tn/UuV1e9wF1wDPAdGPMkdgB07eAYuDHlmXNcu/0c8eyLI9lWbcAXx1BNoVe38eNtLzGSX0f59L9larQ6vs4l8orb+t7BeIZRP9EdhEQBK4wxgQAjDHd2H/aWAvMx64kRj2/fJOF67sG8AOrgGuNMZ2xA8aY33LgC/lPrlzAKMv2/WBZ1mLgn7H/tDvmZeH7OBtYBvQDHzHGvBU7Zoz5A/D96O6YbOXNQnkdDiwGIsDlxphd0fxCxpivA69g/5n3UpcvZdRZltUIPIod2Aw3j4Ku7xO5UV4UeH2fyKXySs2zoOr7RC59H/O6vlcgntnlgAf4vTFmd+IBY0wI+Fl095Ic5Zdv3L6+pdHtI8aYsMPxP0S3M6N/Ah5rsnY/WJZVEn1/BPi3EZ5nvnC7vC7FbsV9wBjztsPxnwFfA346vNPNObfLa1p0226M2eFwfFV0O32oJ5pPLMv6ELAeOB9oZvgtcIVe3wOultfS6LZQ63vA1fJKzLMQ63vA1fLK6/pegzUzOz66XZ7h+Mro9tQc5Zdv3L6+G4EHgFczHK9K+Hks3sfZvB++ChyB3Z9u9TDen4/cLq8PRrePOR00xmwCvj3IvPKR2+W1LbqtsyxrmjFme8rxBdHtlkHml68OB3zA/ditr4uGmU+h1/cxbpVXodf3MW6VV6JCrO9j3CqvvK7vx/INnW1zotv3MxyPjXhvsCzLZ4wJjnJ++cbV6zPGrOTALysn50e3u4C2QZ9l/sjK/WBZ1kLsJ/t12BXzWSM6y/zhdnktjG7XWpZVgz1A7APYlf47wF3GmHdGcsI55vb3ca1lWcuBk4CfW5b1CWNMW3Rw05eBU7C7Ydznwrnn0svAYmPMGwCWZQ03n0Kv72NcKa9xUN/HuHV/EX1/odb3MW6VV17X9wrEM5sc3bZnOJ7458Y67F9Co5lfvhm164v2GftydPcXY3SKOdfLKzrw66dACXCNMaZnpBV9HnGtvKKj52P5HQr8hQNdL8D+ZbbMsqx/NMbcPbzTzblsfB8vxB5QdyawxbKs9UAj9oDNtcDVxphtA7w/7xljMrVgD1Wh1/eAq+WVUYHU94C75VXg9T3gTnmNhfpefcQzq4huMw1+SHy9IkOabOaXb0bl+izLqgJ+iz3rQBvwneHmlWPZKK8bgGOB/yrAOZ3dLC9/ws8PRd/7kej7DgVux26k+IllWWcM/VTzQjburx7sVsuu6Htis6YA7IgeF1uh1/ejooDq+2wo5PreTXlf36tFPLMQAz+oJB4bzBO62/nlm6xfn2VZPuD32P0vQ9izN7QMJ6884Gp5WZY1F7gVe2omN6fEyhdulld5ws9VwHHGmFgXgm3ADZZl1WNPZfVt4IQhnms+cPv+moA9beFRwJ+Br2D/SXca8EXgC8DzlmWdZYxZMdyTLiCFXt9nXYHV964aB/W9m/K+vleLeGYd0W15huNlCT8PZsogt/PLN1m9PsuyJmP/SWkpEAY+aYx5cqj55BHXyivaT/en2E/418amSiswbt5ficfvT6iUE8UG7hwfraTHGre/j1/GDsJXA+caY94wxvQaY943xlwPfA/7l9ydwz3hAlPo9X1WFWB975pxUt+7Ke/rewXimcX69k3KcLw24eddOcgv32Tt+qJzgK7AXlGrH7tlZKwvd+xmeS3DHiz3kDHmiZGeWJ5ys7z2c6AV8q0MadZj32sAMw92cnnI7e/j30W33zPG9Dkc/w52q+XRlmXNcTg+3hR6fZ81BVrfu2k81Pduyvv6Xl1TMlsHHEbm/5QZ0e3OxMUHRjG/fJOV64suA/0k9qCwTuDiAql83Cyvj0e3l1qWlWlBlRmWZcUqo1nR6ZrGEtfKyxjTa1nW+8DsAZJFOFB5OwWe+c7t72Ms/Tqng8aYPZZl7cL+ns4A3h38qRakQq/vs6KA63s3jYf63jVjob5Xi3hmsflMM/UXir3+txzll29cv75oP7insCvlPcCZBVQpu1leq4GXMvyLTcnUk/Ba9zDON9fcvr9ejm6PyXB8BvZsBGFg0yDzzCdul9f+6HaK08HozAT1KWnHs0Kv711X4PW9m8ZDfe+2vK7vFYhn9kh0e4FlWUl/XoxOG3RVdPeBHOWXb1y9PsuyKrEH6tRjj5ZfWmCDwFwrL2PM540xpzj9wx5UB9Cc8HqzWxcxitz+/vwyuv24ZVnTHI4vi26fM8bsGcqJ5gm3y+vZ6DbTEtCXY/8+2Qe8OeizLFyFXt+7ahzU964ZJ/W92/K6vlcgnoEx5i3gcaAa+LVlWbUQb/m5B5gPGODRxPdZllVnWdY8y7IOcyO/scLt8sJepMDCfkK9OJp/wchCeRW0LJTX77D7ofqAPyQetyzrEuC66O63snA5WZeF8roNuw/l+ZZlfTc6rVzsPR8Hvh/d/XdjTG82rikfjdf6frjGa30/XOO1vh+usVrfq4/4wK4FXgROx17AYi12P6OJ2C0/FxpjwinvuQ64GXvltJku5DeWuFJelmWVceAJtRP45kEWKvj4GH3qd/v+KnSulZcxJmxZ1sXYMzMcBRjLst7BrqhnRZPdaIz5S/YuJ+vcLK/XLMv6NHA38C/A56IL+hzKgcUyfo4dsI8n47m+H47xXN8Px3iu74djTNb3ahEfQHSVuCXAHdgj24/AbhV6CDjWGLM2l/nlGxevbxFQE/3ZB5x8kH+ZpgjLa4V+P7gtC9/H7cBi4CbswXVzsBd/eBL4sDHmm+6d/ejLQnndi93H8gHsQHIRdmPO09itmFeN5VUP3abv96CNi/peciuf63tPJKJ6U0RERERktKlFXEREREQkBxSIi4iIiIjkgAJxEREREZEcUCAuIiIiIpIDCsRFRERERHJAgbiIiIiISA4oEBcRERERyQEF4iIiIiIiOaBAXEREREQkBxSIi4iIiIjkgAJxEREREZEcUCAuIiIiIpIDCsRFRERERHJAgbiIiIiISA4oEBcRERERyQEF4iIiIiIiOaBAXEREREQkBxSIi4iIiIjkwP8HeXyOlZfByakAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 369 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# µ = 0.8\n", + "\n", + "x = minimum_J(start_value = (0,1), µ = 0.8)\n", + "plt.plot(x[:,0], x[:,1], 'x:')" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "type": "scatter3d", + "x": [ + 0, + 1.6, + 0.6399999999999999, + 1.2160000000000002, + 0.8703999999999998, + 1.07776, + 0.953344, + 1.0279936, + 0.9832038399999999, + 1.010077696, + 0.9939533824, + 1.00362797056, + 0.9978232176640001, + 1.0013060694016, + 0.99921635835904, + 1.000470184984576, + 0.9997178890092544 + ], + "y": [ + 1, + 0.19999999999999996, + 0.03999999999999998, + 0.007999999999999993, + 0.0015999999999999981, + 0.00031999999999999954, + 6.399999999999988e-05, + 1.2799999999999972e-05, + 2.559999999999994e-06, + 5.119999999999987e-07, + 1.023999999999997e-07, + 2.047999999999993e-08, + 4.095999999999986e-09, + 8.191999999999969e-10, + 1.638399999999993e-10, + 3.276799999999986e-11, + 6.553599999999971e-12 + ], + "z": [ + 3.5, + 2.3800000000000003, + 2.1304, + 2.046688, + 2.01679744, + 2.0060466688, + 2.002176784384, + 2.00078364172288, + 2.0002821109940223, + 2.0001015599567995, + 2.000036561584406, + 2.0000131621703847, + 2.0000047383813384, + 2.000001705817282, + 2.0000006140942217, + 2.0000002210739196, + 2.000000079586611 + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We converged but it's less pretty than the first time. On the other hand" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "17" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "we converged in 17 iterations. Let's see how many iterations it took for µ = 0.1:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "46" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = minimum_J(start_value = (0,1), µ = 0.1)\n", + "len(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "µ = 0.8 gives a less attractive curve but we converge almost 3 times faster than with µ = 0.1. So it's better." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Trop long, boucle infinie ?\n" + ] + }, + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 369 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# µ = 1\n", + "\n", + "x = minimum_J(start_value = (0,1), µ = 1)\n", + "plt.plot(x[:,0], x[:,1], 'x:')" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "type": "scatter3d", + "x": [ + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0 + ], + "y": [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "z": [ + 3.5, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We started from [0.1] to go to [2.0] then to [0.0] then to [2.0].\n", + "\n", + "As we have seen that from [2.0] we go to [0.0] this means that we oscillate infinitely between [0.0] and [2.0].\n", + "\n", + "Knowing that the solution is [1,0] this means that we are going in the right direction but we do\n", + "a step twice too big each time.\n", + "\n", + "**Morality** The value of µ is important. If it is too small we waste time, if it is too big we cannot find the solution." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma51 x.T A x sur un maillage en Numpy .ipynb b/PVCM/cama/en/ma51 x.T A x sur un maillage en Numpy .ipynb new file mode 100644 index 0000000..d80df36 --- /dev/null +++ b/PVCM/cama/en/ma51 x.T A x sur un maillage en Numpy .ipynb @@ -0,0 +1,32043 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "import plotly.offline as py\n", + "import plotly.graph_objects as go\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Let's calculate ${\\bf x}^T \\, A \\, {\\bf x} $ with Numpy\n", + "\n", + "The goal is to plot the $J_A({\\bf x})$ curve with ${\\bf x} \\in ℝ^2$ so that the poor little humans we\n", + "are able to see something.\n", + "\n", + "$$\n", + "J_A({\\bf x}) = {\\bf x}^T \\, A \\, {\\bf x}\n", + "$$\n", + "\n", + "Later we will take ${\\bf x} \\in ℝ^n$.\n", + "\n", + "For a value **x** this calculation is simple: `x.T @A@ x` but we want to do this calculation for a set of\n", + "**x**." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We start by building a mesh, i.e. a set of ${\\bf x}$ points for which we will calculate\n", + "$J_A({\\bf x})$. For this we use `np.meshgrid`. Let's see what it gives." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "shape of M: (2, 4, 3)\n", + "[[[-1. 0. 1.]\n", + " [-1. 0. 1.]\n", + " [-1. 0. 1.]\n", + " [-1. 0. 1.]]\n", + "\n", + " [[-1. -1. -1.]\n", + " [ 0. 0. 0.]\n", + " [ 1. 1. 1.]\n", + " [ 2. 2. 2.]]]\n", + "\n", + "shape of M: (4, 3, 2)\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[[-1., -1.],\n", + " [ 0., -1.],\n", + " [ 1., -1.]],\n", + "\n", + " [[-1., 0.],\n", + " [ 0., 0.],\n", + " [ 1., 0.]],\n", + "\n", + " [[-1., 1.],\n", + " [ 0., 1.],\n", + " [ 1., 1.]],\n", + "\n", + " [[-1., 2.],\n", + " [ 0., 2.],\n", + " [ 1., 2.]]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.linspace(-1,1,3)\n", + "y = np.linspace(-1,2,4)\n", + "\n", + "mesh = np.meshgrid(x,y) # donne les x puis les y du maillage\n", + "M = np.array(mesh)\n", + "print(\"shape of M:\", M.shape)\n", + "print(M)\n", + "M = M.transpose([1,2,0]) # je préfère avoir un tableau 4x3 de points\n", + "print(\"\\nshape of M:\", M.shape)\n", + "M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "I want to apply ${\\bf x}^T \\, A \\, {\\bf x}$ to each point of my mesh. I start with the identity matrix\n", + "so that I can easily check the calculations.\n", + "\n", + "First I compute ${\\bf x}^T \\, A$ for all points of the mesh.\n", + "\n", + "### Test case with A = 2 Id\n", + "\n", + "I look on a very small mesh how to write the calculations. I take for A twice\n", + "the identity matrix to be able to check the head calculations." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[-2., -2.],\n", + " [ 0., -2.],\n", + " [ 2., -2.]],\n", + "\n", + " [[-2., 0.],\n", + " [ 0., 0.],\n", + " [ 2., 0.]],\n", + "\n", + " [[-2., 2.],\n", + " [ 0., 2.],\n", + " [ 2., 2.]],\n", + "\n", + " [[-2., 4.],\n", + " [ 0., 4.],\n", + " [ 2., 4.]]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = 2 * np.diag([1, 1])\n", + "MA = np.einsum(\"ijk, ka -> ija\", M, A) # voici un cas où la notation d'Einstein simplifie bien la vie\n", + "MA # k est en double et pas dans le résultat, donc on somme sur lui" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "I find `2 M` which is consistent.\n", + "\n", + "In another case we could check some points:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0., -2.])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# vérification sur un point particulier\n", + "M[0,1] @ A" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Note that I wrote ${\\bf x} \\, A$ and not ${\\bf x}^T \\, A$ but when we have a vector Numpy adapts and favors the vector matrix product which gives a vector. Thus `m[0,1] @A == m[0,1].T@ A` because, as\n", + "says the doc, \"Transposing a 1-D array returns an unchanged view of the original array\".\n", + "\n", + "If we want to have a difference between a vertical vector and a horizontal vector we must use\n", + "2D `array` of size 1xn or nx1." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 4., 2., 4.],\n", + " [ 2., 0., 2.],\n", + " [ 4., 2., 4.],\n", + " [10., 8., 10.]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.einsum(\"ijk, ijk -> ij\", MA, M) # comme k n'est pas dans le résultat, c'est sur lui qu'on fait la somme" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "As A is 2 times the identity, we must find for any point 2 times its norm squared. It's good.\n", + "\n", + "### A real case\n", + "\n", + "We take a mesh of 100x100 and a random matrix A:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-0.02 0.05]\n", + " [ 0.03 -0.02]]\n" + ] + } + ], + "source": [ + "np.random.seed(2)\n", + "A = np.random.randint(-10,10, size=(2,2)) / 100\n", + "print(A)\n", + "\n", + "x = np.linspace(-20,20,100)\n", + "y = np.linspace(-20,20,100)\n", + "\n", + "mx, my = np.meshgrid(x,y) \n", + "M = np.array(np.meshgrid(x,y)).transpose([1,2,0])\n", + "\n", + "MA = np.einsum(\"ijk, ka -> ija\", M, A)\n", + "mz = np.einsum(\"ijk, ijk -> ij\", MA, M)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "linkText": "Export to plot.ly", + "plotlyServerURL": "https://plot.ly", + "showLink": false + }, + "data": [ + { + "type": "surface", + "x": [ + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ] + ], + "y": [ + [ + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20 + ], + [ + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595 + ], + [ + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919 + ], + [ + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879 + ], + [ + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384 + ], + [ + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798 + ], + [ + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574 + ], + [ + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173 + ], + [ + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768 + ], + [ + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363 + ], + [ + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958 + ], + [ + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555 + ], + [ + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152 + ], + [ + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747 + ], + [ + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343 + ], + [ + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394 + ], + [ + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536 + ], + [ + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131 + ], + [ + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727 + ], + [ + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324 + ], + [ + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919 + ], + [ + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516 + ], + [ + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111 + ], + [ + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708 + ], + [ + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303 + ], + [ + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899 + ], + [ + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495 + ], + [ + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092 + ], + [ + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687 + ], + [ + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284 + ], + [ + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879 + ], + [ + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476 + ], + [ + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071 + ], + [ + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666 + ], + [ + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263 + ], + [ + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858 + ], + [ + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455 + ], + [ + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505 + ], + [ + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647 + ], + [ + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242 + ], + [ + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373 + ], + [ + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436 + ], + [ + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031 + ], + [ + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263 + ], + [ + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214 + ], + [ + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201 + ], + [ + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153 + ], + [ + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104 + ], + [ + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055 + ], + [ + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066 + ], + [ + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066 + ], + [ + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055 + ], + [ + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104 + ], + [ + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153 + ], + [ + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166 + ], + [ + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214 + ], + [ + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263 + ], + [ + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031 + ], + [ + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325 + ], + [ + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373 + ], + [ + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242 + ], + [ + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647 + ], + [ + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048 + ], + [ + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453 + ], + [ + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858 + ], + [ + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263 + ], + [ + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668 + ], + [ + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069 + ], + [ + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474 + ], + [ + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879 + ], + [ + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284 + ], + [ + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685 + ], + [ + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909 + ], + [ + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495 + ], + [ + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899 + ], + [ + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301 + ], + [ + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706 + ], + [ + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111 + ], + [ + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516 + ], + [ + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917 + ], + [ + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325 + ], + [ + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727 + ], + [ + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128 + ], + [ + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536 + ], + [ + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938 + ], + [ + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346 + ], + [ + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747 + ], + [ + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149 + ], + [ + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557 + ], + [ + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958 + ], + [ + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636 + ], + [ + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768 + ], + [ + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717 + ], + [ + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578 + ], + [ + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798 + ], + [ + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838 + ], + [ + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879 + ], + [ + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919 + ], + [ + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596 + ], + [ + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20 + ] + ], + "z": [ + [ + 16, + 15.673502703805733, + 15.340475461687582, + 15.000918273645546, + 14.654831139679624, + 14.302214059789817, + 13.943067033976124, + 13.577390062238548, + 13.205183144577084, + 12.826446280991735, + 12.441179471482503, + 12.049382716049383, + 11.65105601469238, + 11.246199367411489, + 10.83481277420671, + 10.416896235078053, + 9.99244975002551, + 9.561473319049076, + 9.123966942148758, + 8.679930619324558, + 8.229364350576471, + 7.7722681359045, + 7.3086419753086425, + 6.838485868788898, + 6.36179981634527, + 5.878583817977757, + 5.388837873686358, + 4.892561983471074, + 4.389756147331905, + 3.8804203652688507, + 3.36455463728191, + 2.842158963371086, + 2.3132333435363743, + 1.7777777777777766, + 1.235792266095296, + 0.6872768084889289, + 0.13223140495867813, + -0.4293439444954603, + -0.9974492398734816, + -1.5720844811753905, + -2.153249668401185, + -2.7409448015508597, + -3.335169880624425, + -3.9359249056218752, + -4.543209876543212, + -5.157024793388428, + -5.777369656157533, + -6.404244464850526, + -7.0376492194674025, + -7.677583920008165, + -8.324048566472806, + -8.97704315886134, + -9.636567697173758, + -10.302622181410062, + -10.975206611570245, + -11.65432098765432, + -12.339965309662281, + -13.032139577594126, + -13.73084379144985, + -14.436077951229466, + -15.147842056932967, + -15.866136108560353, + -16.59096010611162, + -17.322314049586772, + -18.060197938985816, + -18.804611774308746, + -19.555555555555557, + -20.313029282726248, + -21.077032955820833, + -21.847566574839302, + -22.624630139781658, + -23.40822365064789, + -24.198347107438014, + -24.995000510152025, + -25.79818385878992, + -26.607897153351693, + -27.424140393837362, + -28.24691358024691, + -29.07621671258035, + -29.912049790837663, + -30.75441281501888, + -31.603305785123965, + -32.458728701152936, + -33.32068156310581, + -34.189164370982546, + -35.06417712478319, + -35.945719824507705, + -36.8337924701561, + -37.728395061728406, + -38.629527599224566, + -39.53719008264462, + -40.45138251198858, + -41.3721048872564, + -42.29935720844812, + -43.23313947556372, + -44.173451688603194, + -45.12029384756658, + -46.07366595245383, + -47.033568003264975, + -48 + ], + [ + 15.673502703805731, + 15.360065299459237, + 15.040097949188857, + 14.713600652994591, + 14.38057341087644, + 14.041016222834404, + 13.69492908886848, + 13.342312008978677, + 12.983164983164983, + 12.617488011427405, + 12.245281093765941, + 11.866544230180594, + 11.481277420671361, + 11.089480665238241, + 10.691153963881234, + 10.286297316600347, + 9.874910723395573, + 9.456994184266911, + 9.032547699214366, + 8.601571268237937, + 8.164064891337617, + 7.720028568513417, + 7.26946229976533, + 6.812366085093357, + 6.348739924497499, + 5.878583817977758, + 5.4018977655341285, + 4.918681767166616, + 4.428935822875217, + 3.932659932659934, + 3.4298540965207636, + 2.92051831445771, + 2.4046525864707693, + 1.8822569125599422, + 1.3533312927252323, + 0.8178757269666361, + 0.27589021528415536, + -0.2726252423222113, + -0.8276706458524625, + -1.389245995306601, + -1.9573512906846247, + -2.5319865319865285, + -3.1131517192123237, + -3.7008468523620035, + -4.295071931435569, + -4.895826956433014, + -5.503111927354349, + -6.116926844199571, + -6.737271706968676, + -7.364146515661668, + -7.9975512702785405, + -8.637485970819302, + -9.28395061728395, + -9.936945209672484, + -10.596469747984896, + -11.262524232221198, + -11.93510866238139, + -12.614223038465465, + -13.299867360473415, + -13.992041628405264, + -14.690745842260993, + -15.39598000204061, + -16.107744107744104, + -16.826038159371485, + -17.55086215692276, + -18.282216100397918, + -19.02009998979696, + -19.76451382511988, + -20.515457606366695, + -21.272931333537393, + -22.03693500663198, + -22.807468625650436, + -23.584532190592792, + -24.368125701459032, + -25.15824915824916, + -25.954902560963163, + -26.758085909601057, + -27.56779920416284, + -28.384042444648504, + -29.20681563105805, + -30.036118763391492, + -30.87195184164881, + -31.71431486583001, + -32.56320783593511, + -33.41863075196407, + -34.28058361391695, + -35.14906642179369, + -36.024079175594316, + -36.90562187531885, + -37.79369452096724, + -38.68829711253953, + -39.58942965003571, + -40.49709213345576, + -41.41128456279971, + -42.33200693806754, + -43.259259259259245, + -44.193041526374856, + -45.133353739414346, + -46.080195898377724, + -47.03356800326497 + ], + [ + 15.34047546168758, + 15.040097949188858, + 14.733190490766244, + 14.419753086419751, + 14.099785736149373, + 13.773288439955104, + 13.440261197836953, + 13.100704009794919, + 12.754616875828997, + 12.40199979593919, + 12.042852770125496, + 11.677175798387918, + 11.304968880726456, + 10.926232017141107, + 10.54096520763187, + 10.149168452198754, + 9.750841750841753, + 9.34598510356086, + 8.934598510356086, + 8.516681971227428, + 8.092235486174879, + 7.66125905519845, + 7.223752678298133, + 6.77971635547393, + 6.329150086725844, + 5.872053872053873, + 5.408427711458014, + 4.938271604938272, + 4.461585552494643, + 3.978369554127131, + 3.4886236098357317, + 2.9923477196204487, + 2.4895418834812784, + 1.9802061014182222, + 1.4643403734312832, + 0.9419446995204572, + 0.41301907968574714, + -0.12243648607284907, + -0.6644219977553298, + -1.212937455361697, + -1.7679828588919504, + -2.329558208346083, + -2.897663503724108, + -3.4722987450260163, + -4.053463932251811, + -4.641159065401486, + -5.23538414447505, + -5.836139169472501, + -6.443424140393837, + -7.057239057239058, + -7.67758392000816, + -8.304458728701151, + -8.93786348331803, + -9.577798183858791, + -10.224262830323433, + -10.877257422711967, + -11.536781961024385, + -12.202836445260687, + -12.875420875420872, + -13.554535251504944, + -14.240179573512904, + -14.93235384144475, + -15.631058055300475, + -16.33629221508009, + -17.04805632078359, + -17.766350372410976, + -18.49117436996225, + -19.2225283134374, + -19.960412202836444, + -20.70482603815937, + -21.455769819406182, + -22.213243546576876, + -22.977247219671458, + -23.747780838689927, + -24.524844403632283, + -25.308437914498512, + -26.09856137128864, + -26.895214774002653, + -27.698398122640548, + -28.50811141720232, + -29.324354657687994, + -30.14712784409754, + -30.976430976430965, + -31.8122640546883, + -32.654627078869495, + -33.5035200489746, + -34.35894296500357, + -35.22089582695642, + -36.08937863483318, + -36.964391388633814, + -37.84593408835832, + -38.73400673400673, + -39.62860932557902, + -40.5297418630752, + -41.437404346495256, + -42.35159677583919, + -43.27231915110703, + -44.19957147229874, + -45.133353739414346, + -46.07366595245383 + ], + [ + 15.000918273645546, + 14.71360065299459, + 14.419753086419753, + 14.11937557392103, + 13.812468115498417, + 13.499030711151924, + 13.17906336088154, + 12.852566064687277, + 12.519538822569126, + 12.179981634527088, + 11.833894500561167, + 11.48127742067136, + 11.122130394857669, + 10.75645342312009, + 10.384246505458623, + 10.005509641873278, + 9.620242832364045, + 9.228446076930924, + 8.83011937557392, + 8.425262728293031, + 8.013876135088253, + 7.595959595959595, + 7.17151311090705, + 6.740536679930618, + 6.303030303030302, + 5.858993980206102, + 5.408427711458014, + 4.951331496786042, + 4.487705336190184, + 4.0175492296704425, + 3.5408631772268135, + 3.057647178859301, + 2.5679012345679015, + 2.071625344352616, + 1.568819508213447, + 1.0594837261503918, + 0.5436179981634524, + 0.02122232425262638, + -0.507703295582083, + -1.0431588613406806, + -1.5851443730231631, + -2.133659830629526, + -2.6887052341597792, + -3.250280583613918, + -3.8183858789919407, + -4.393021120293846, + -4.97418630751964, + -5.561881440669319, + -6.156106519742885, + -6.756861544740335, + -7.364146515661666, + -7.977961432506888, + -8.598306295275995, + -9.225181103968985, + -9.858585858585856, + -10.49852055912662, + -11.144985205591269, + -11.7979797979798, + -12.457504336292214, + -13.123558820528517, + -13.796143250688706, + -14.475257626772784, + -15.160901948780735, + -15.85307621671258, + -16.55178043056831, + -17.257014590347925, + -17.968778696051427, + -18.68707274767881, + -19.411896745230077, + -20.143250688705237, + -20.88113457810428, + -21.6255484134272, + -22.376492194674015, + -23.133965921844712, + -23.897969594939294, + -24.668503213957756, + -25.445566778900115, + -26.229160289766348, + -27.01928374655648, + -27.815937149270482, + -28.619120497908384, + -29.428833792470158, + -30.24507703295582, + -31.067850219365376, + -31.897153351698805, + -32.732986429956135, + -33.57534945413734, + -34.42424242424242, + -35.27966534027141, + -36.141618202224265, + -37.01010101010101, + -37.88511376390164, + -38.766656463626155, + -39.65472910927457, + -40.54933170084685, + -41.45046423834302, + -42.358126721763085, + -43.27231915110703, + -44.19304152637487, + -45.12029384756657 + ], + [ + 14.654831139679622, + 14.38057341087644, + 14.099785736149371, + 13.812468115498419, + 13.518620548923579, + 13.218243036424855, + 12.911335578002245, + 12.59789817365575, + 12.27793082338537, + 11.951433527191103, + 11.61840628507295, + 11.278849097030914, + 10.932761963064994, + 10.580144883175187, + 10.220997857361493, + 9.855320885623916, + 9.483113967962455, + 9.104377104377104, + 8.71911029486787, + 8.327313539434751, + 7.928986838077746, + 7.524130190796857, + 7.1127435975920825, + 6.694827058463421, + 6.2703805734108755, + 5.8394041424344465, + 5.4018977655341285, + 4.957861442709928, + 4.50729517396184, + 4.050198959289869, + 3.586572798694011, + 3.1164166921742686, + 2.63973063973064, + 2.156514641363125, + 1.6667686970717268, + 1.1704928068564422, + 0.6676869707172737, + 0.1583511886542186, + -0.3575145393327208, + -0.8799102132435475, + -1.408835833078259, + -1.9442913988368515, + -2.486276910519334, + -3.034792368125702, + -3.5898377716559553, + -4.151413121110089, + -4.719518416488112, + -5.294153657790022, + -5.8753188450158165, + -6.463013978165495, + -7.057239057239056, + -7.657994082236506, + -8.265279053157842, + -8.879093970003064, + -9.499438832772165, + -10.126313641465156, + -10.759718396082034, + -11.399653096622796, + -12.046117743087438, + -12.699112335475972, + -13.35863687378839, + -14.024691358024695, + -14.697275788184877, + -15.37639016426895, + -16.06203448627691, + -16.754208754208754, + -17.452912968064485, + -18.158147127844096, + -18.869911233547597, + -19.588205285174983, + -20.313029282726255, + -21.044383226201404, + -21.782267115600447, + -22.526680950923378, + -23.27762473217019, + -24.03509845934088, + -24.799102132435465, + -25.569635751453934, + -26.34669931639629, + -27.130292827262522, + -27.920416284052656, + -28.717069686766656, + -29.520253035404544, + -30.329966329966332, + -31.146209570451994, + -31.96898275686155, + -32.798285889194986, + -33.634118967452295, + -34.476481991633506, + -35.3253749617386, + -36.18079787776757, + -37.04275073972043, + -37.911233547597185, + -38.786246301397824, + -39.66778900112233, + -40.55586164677074, + -41.45046423834303, + -42.3515967758392, + -43.25925925925927, + -44.17345168860321 + ], + [ + 14.302214059789815, + 14.041016222834402, + 13.773288439955104, + 13.499030711151923, + 13.218243036424852, + 12.930925415773899, + 12.63707784919906, + 12.336700336700336, + 12.029792878277728, + 11.71635547393123, + 11.396388123660849, + 11.069890827466583, + 10.736863585348434, + 10.397306397306398, + 10.051219263340473, + 9.698602183450667, + 9.339455157636978, + 8.973778185899398, + 8.601571268237935, + 8.222834404652588, + 7.837567595143351, + 7.445770839710233, + 7.047444138353229, + 6.642587491072339, + 6.231200897867564, + 5.813284358738905, + 5.388837873686358, + 4.957861442709928, + 4.5203550658096106, + 4.076318742985411, + 3.625752474237323, + 3.168656259565352, + 2.7050300989694938, + 2.2348739924497494, + 1.7581879400061218, + 1.274971941638608, + 0.7852259973472102, + 0.28895010713192537, + -0.21385572900724314, + -0.7231915110702989, + -1.23905723905724, + -1.7614529129680618, + -2.290378532802774, + -2.825834098561371, + -3.367819610243853, + -3.9163350678502162, + -4.471380471380469, + -5.032955820834609, + -5.601061116212632, + -6.17569635751454, + -6.756861544740331, + -7.34455667789001, + -7.938781756963574, + -8.539536781961026, + -9.146821752882355, + -9.760636669727576, + -10.380981532496683, + -11.007856341189676, + -11.641261095806547, + -12.28119579634731, + -12.927660442811957, + -13.58065503520049, + -14.240179573512904, + -14.906234057749206, + -15.578818487909396, + -16.257932863993467, + -16.94357718600143, + -17.63575145393327, + -18.334455667788998, + -19.039689827568615, + -19.751453933272117, + -20.469747984899495, + -21.194571982450768, + -21.925925925925924, + -22.663809815324967, + -23.408223650647887, + -24.1591674318947, + -24.9166411590654, + -25.680644832159985, + -26.451178451178443, + -27.22824201612081, + -28.011835526987042, + -28.801958983777155, + -29.598612386491176, + -30.401795735129063, + -31.211509029690852, + -32.027752270176514, + -32.850525456586055, + -33.6798285889195, + -34.51566166717682, + -35.35802469135801, + -36.20691766146311, + -37.062340577492094, + -37.92429343944496, + -38.7927762473217, + -39.66778900112233, + -40.54933170084686, + -41.43740434649525, + -42.33200693806755, + -43.23313947556372 + ], + [ + 13.94306703397612, + 13.69492908886848, + 13.440261197836953, + 13.17906336088154, + 12.911335578002245, + 12.63707784919906, + 12.356290174471992, + 12.06897255382104, + 11.7751249872462, + 11.474747474747474, + 11.167840016324865, + 10.854402611978369, + 10.53443526170799, + 10.207937965513723, + 9.874910723395569, + 9.535353535353535, + 9.189266401387615, + 8.836649321497806, + 8.477502295684113, + 8.111825323946537, + 7.7396184062850715, + 7.360881542699724, + 6.975614733190491, + 6.583817977757371, + 6.1854912764003664, + 5.7806346291194775, + 5.369248035914702, + 4.951331496786042, + 4.526885011733496, + 4.095908580757067, + 3.6584022038567494, + 3.214365881032549, + 2.7637996122844615, + 2.306703397612488, + 1.8430772370166313, + 1.3729211304968878, + 0.8962350780532609, + 0.4130190796857469, + -0.07672686460565137, + -0.5730027548209364, + -1.075808590960107, + -1.585144373023158, + -2.1010101010100994, + -2.6234057749209256, + -3.1523313947556377, + -3.687786960514231, + -4.2297724721967125, + -4.77828792980308, + -5.333333333333333, + -5.894908682787472, + -6.463013978165491, + -7.0376492194674, + -7.618814406693194, + -8.206509539842875, + -8.800734618916433, + -9.401489643913886, + -10.008774614835222, + -10.62258953168044, + -11.242934394449541, + -11.869809203142534, + -12.50321395775941, + -13.143148658300172, + -13.789613304764815, + -14.442607897153348, + -15.102132435465766, + -15.768186919702071, + -16.44077134986226, + -17.119885725946325, + -17.80553004795429, + -18.497704315886132, + -19.196408529741863, + -19.901642689521474, + -20.613406795224975, + -21.33170084685236, + -22.056524844403633, + -22.787878787878782, + -23.525762677277825, + -24.270176512600756, + -25.021120293847567, + -25.778594021018257, + -26.54259769411285, + -27.313131313131308, + -28.090194878073653, + -28.873788388939907, + -29.66391184573002, + -30.46056524844404, + -31.26374859708193, + -32.0734618916437, + -32.88970513212938, + -33.71247831853892, + -34.54178145087235, + -35.37761452912968, + -36.21997755331088, + -37.06887052341598, + -37.92429343944495, + -38.78624630139781, + -39.65472910927457, + -40.52974186307519, + -41.41128456279972, + -42.299357208448114 + ], + [ + 13.577390062238548, + 13.342312008978675, + 13.10070400979492, + 12.852566064687279, + 12.597898173655746, + 12.336700336700337, + 12.068972553821038, + 11.794714825017856, + 11.513927150290787, + 11.226609529639832, + 10.932761963064992, + 10.632384450566269, + 10.32547699214366, + 10.012039587797165, + 9.69207223752678, + 9.365574941332516, + 9.032547699214367, + 8.69299051117233, + 8.346903377206406, + 7.9942862973166005, + 7.635139271502906, + 7.26946229976533, + 6.897255382103866, + 6.518518518518517, + 6.133251709009284, + 5.7414549535761665, + 5.343128252219161, + 4.938271604938271, + 4.526885011733496, + 4.108968472604836, + 3.6845219875522903, + 3.2535455565758604, + 2.8160391796755433, + 2.3720028568513407, + 1.921436588103254, + 1.4643403734312819, + 1.0007142128354245, + 0.530558106315681, + 0.05387205387205385, + -0.42934394449546054, + -0.9190898887868608, + -1.4153657790021412, + -1.918171615141312, + -2.4275073972043675, + -2.943373125191309, + -3.4657687991021313, + -3.9946944189368425, + -4.53014998469544, + -5.072135496377923, + -5.62065095398429, + -6.175696357514539, + -6.737271706968677, + -7.3053770023467015, + -7.88001224364861, + -8.4611774308744, + -9.04887256402408, + -9.643097643097645, + -10.243852668095094, + -10.851137639016425, + -11.464952555861647, + -12.085297418630752, + -12.712172227323748, + -13.345576981940617, + -13.98551168248138, + -14.631976328946028, + -15.284970921334558, + -15.944495459646978, + -16.610549943883278, + -17.283134374043463, + -17.96224875012754, + -18.6478930721355, + -19.34006734006734, + -20.03877155392307, + -20.744005713702684, + -21.455769819406186, + -22.174063871033567, + -22.89888786858484, + -23.630241812059992, + -24.36812570145904, + -25.11253953678196, + -25.863483318028777, + -26.62095704519947, + -27.38496071829405, + -28.155494337312522, + -28.93255790225487, + -29.716151413121118, + -30.506274869911238, + -31.302928272625238, + -32.10611162126314, + -32.91582491582491, + -33.732068156310575, + -34.55484134272014, + -35.38414447505357, + -36.2199775533109, + -37.062340577492094, + -37.91123354759718, + -38.76665646362616, + -39.62860932557902, + -40.49709213345578, + -41.372104887256405 + ], + [ + 13.205183144577084, + 12.983164983164983, + 12.754616875828999, + 12.519538822569128, + 12.277930823385368, + 12.029792878277728, + 11.7751249872462, + 11.513927150290787, + 11.246199367411492, + 10.971941638608307, + 10.691153963881238, + 10.403836343230283, + 10.109988776655445, + 9.80961126415672, + 9.502703805734107, + 9.189266401387615, + 8.869299051117235, + 8.542801754922968, + 8.209774512804817, + 7.8702173247627805, + 7.524130190796857, + 7.171513110907052, + 6.812366085093359, + 6.44668911335578, + 6.074482195694317, + 5.69574533210897, + 5.310478522599736, + 4.918681767166616, + 4.520355065809612, + 4.115498418528723, + 3.704111825323947, + 3.286195286195288, + 2.861748801142742, + 2.4307723701663098, + 1.9932659932659935, + 1.5492296704417918, + 1.0986634016937054, + 0.6415671870217328, + 0.17794102642587606, + -0.2922150800938679, + -0.7689011325374973, + -1.2521171309050074, + -1.7418630751964068, + -2.238138965411692, + -2.740944801550863, + -3.2502805836139146, + -3.7661463116008553, + -4.2885419855116815, + -4.817467605346394, + -5.352923171104991, + -5.89490868278747, + -6.443424140393836, + -6.99846954392409, + -7.560044893378229, + -8.128150188756248, + -8.702785430058157, + -9.283950617283951, + -9.871645750433629, + -10.465870829507192, + -11.06662585450464, + -11.673910825425978, + -12.2877257422712, + -12.908070605040301, + -13.53494541373329, + -14.16835016835017, + -14.80828486889093, + -15.45474951535558, + -16.107744107744107, + -16.76726864605652, + -17.433323130292827, + -18.105907560453016, + -18.785021936537085, + -19.470666258545045, + -20.16284052647689, + -20.86154474033262, + -21.566778900112233, + -22.278543005815735, + -22.996837057443116, + -23.721661054994392, + -24.45301499846954, + -25.19089888786859, + -25.93531272319151, + -26.68625650443832, + -27.443730231609024, + -28.2077339047036, + -28.978267523722074, + -29.755331088664423, + -30.53892459953066, + -31.329048056320786, + -32.125701459034794, + -32.92888480767268, + -33.73859810223446, + -34.554841342720124, + -35.37761452912969, + -36.206917661463116, + -37.04275073972043, + -37.88511376390164, + -38.734006734006726, + -39.589429650035726, + -40.45138251198857 + ], + [ + 12.826446280991735, + 12.617488011427405, + 12.401999795939188, + 12.17998163452709, + 11.951433527191103, + 11.716355473931232, + 11.474747474747474, + 11.226609529639834, + 10.971941638608307, + 10.710743801652892, + 10.443016018773594, + 10.16875828997041, + 9.887970615243344, + 9.60065299459239, + 9.306805428017547, + 9.006427915518824, + 8.699520457096217, + 8.386083052749719, + 8.066115702479339, + 7.739618406285074, + 7.4065911641669215, + 7.067033976124886, + 6.720946842158964, + 6.368329762269157, + 6.009182736455463, + 5.643505764717887, + 5.271298847056423, + 4.892561983471075, + 4.507295173961841, + 4.115498418528723, + 3.717171717171718, + 3.312315069890829, + 2.9009284766860537, + 2.4830119375573916, + 2.058565452504847, + 1.6275890215284154, + 1.1900826446281, + 0.7460463218038977, + 0.29548005305581193, + -0.16161616161616155, + -0.6252423222120203, + -1.0953984287317597, + -1.5720844811753887, + -2.055300479542903, + -2.545046423834304, + -3.0413223140495846, + -3.5441281501887545, + -4.053463932251811, + -4.569329660238752, + -5.091725334149578, + -5.620650953984286, + -6.156106519742882, + -6.6980920314253645, + -7.2466074890317325, + -7.801652892561981, + -8.36322824201612, + -8.931333537394144, + -9.505968778696053, + -10.087133965921842, + -10.674829099071522, + -11.269054178145087, + -11.869809203142538, + -12.477094174063868, + -13.090909090909088, + -13.711253953678195, + -14.338128762371186, + -14.971533516988064, + -15.611468217528822, + -16.25793286399347, + -16.910927456382, + -17.570451994694423, + -18.236506478930718, + -18.909090909090907, + -19.588205285174983, + -20.273849607182942, + -20.96602387511478, + -21.664728088970513, + -22.369962248750127, + -23.08172635445363, + -23.80002040608101, + -24.524844403632287, + -25.256198347107436, + -25.994082236506472, + -26.73849607182941, + -27.489439853076213, + -28.24691358024692, + -29.010917253341496, + -29.781450872359958, + -30.55851443730232, + -31.342107948168554, + -32.13223140495867, + -32.92888480767269, + -33.732068156310575, + -34.541781450872364, + -35.358024691358025, + -36.18079787776757, + -37.01010101010101, + -37.845934088358334, + -38.688297112539544, + -39.53719008264463 + ], + [ + 12.4411794714825, + 12.245281093765943, + 12.042852770125494, + 11.833894500561165, + 11.61840628507295, + 11.396388123660849, + 11.167840016324865, + 10.932761963064994, + 10.691153963881236, + 10.443016018773594, + 10.188348127742067, + 9.927150290786654, + 9.659422507907356, + 9.385164779104173, + 9.104377104377102, + 8.817059483726151, + 8.523211917151311, + 8.222834404652586, + 7.915926946229976, + 7.602489541883482, + 7.2825221916131, + 6.956024895418835, + 6.622997653300684, + 6.283440465258646, + 5.937353331292725, + 5.584736251402919, + 5.225589225589225, + 4.859912253851648, + 4.487705336190185, + 4.108968472604837, + 3.7237016630956026, + 3.3319049076624845, + 2.9335782063054796, + 2.528721559024589, + 2.1173349658198144, + 1.699418426691154, + 1.2749719416386087, + 0.8439955106621775, + 0.4064891337618619, + -0.03754718906234045, + -0.4881134578104287, + -0.9452096724823975, + -1.408835833078256, + -1.878991939598, + -2.3556779920416293, + -2.8388939904091393, + -3.328639934700539, + -3.824915824915824, + -4.327721661054994, + -4.83705744311805, + -5.352923171104988, + -5.875318845015814, + -6.4042444648505255, + -6.9397000306091225, + -7.481685542291601, + -8.030200999897968, + -8.585246403428222, + -9.146821752882358, + -9.71492704826038, + -10.289562289562287, + -10.870727476788083, + -11.458422609937761, + -12.052647689011323, + -12.653402714008772, + -13.260687684930106, + -13.87450260177533, + -14.494847464544435, + -15.12172227323742, + -15.7551270278543, + -16.395061728395063, + -17.041526374859707, + -17.694520967248238, + -18.354045505560656, + -19.020099989796957, + -19.69268441995715, + -20.371798796041215, + -21.05744311804918, + -21.749617385981022, + -22.448321599836753, + -23.15355575961636, + -23.86531986531987, + -24.583613916947247, + -25.308437914498512, + -26.039791857973675, + -26.77767574737271, + -27.52208958269565, + -28.273033363942453, + -29.030507091113144, + -29.794510764207736, + -30.5650443832262, + -31.342107948168547, + -32.125701459034794, + -32.91582491582491, + -33.71247831853893, + -34.515661667176815, + -35.32537496173859, + -36.141618202224265, + -36.964391388633814, + -37.79369452096725, + -38.629527599224566 + ], + [ + 12.049382716049381, + 11.866544230180594, + 11.677175798387918, + 11.48127742067136, + 11.278849097030914, + 11.069890827466585, + 10.854402611978369, + 10.632384450566269, + 10.403836343230282, + 10.16875828997041, + 9.927150290786654, + 9.679012345679013, + 9.424344454647485, + 9.163146617692073, + 8.895418834812773, + 8.621161106009591, + 8.340373431282524, + 8.053055810631568, + 7.759208244056728, + 7.458830731558004, + 7.151923273135393, + 6.838485868788899, + 6.518518518518519, + 6.192021222324252, + 5.858993980206101, + 5.519436792164066, + 5.173349658198143, + 4.820732578308336, + 4.461585552494643, + 4.095908580757066, + 3.7237016630956026, + 3.3449647995102554, + 2.959697990001021, + 2.5679012345679, + 2.169574533210897, + 1.7647178859300068, + 1.3533312927252326, + 0.9354147535965716, + 0.5109682685440269, + 0.07999183756759498, + -0.35751453933272237, + -0.801550862156921, + -1.2521171309050083, + -1.7092133455769818, + -2.1728395061728403, + -2.64299561269258, + -3.119681665136209, + -3.602897663503724, + -4.092643607795123, + -4.588919498010408, + -5.091725334149575, + -5.60106111621263, + -6.116926844199571, + -6.639322518110398, + -7.168248137945105, + -7.703703703703702, + -8.245689215386186, + -8.794204672992553, + -9.3492500765228, + -9.910825425976938, + -10.478930721354963, + -11.053565962656872, + -11.63473114988266, + -12.222426283032343, + -12.816651362105906, + -13.417406387103357, + -14.024691358024693, + -14.63850627486991, + -15.258851137639015, + -15.885725946332009, + -16.51913070094888, + -17.15906540148964, + -17.80553004795429, + -18.458524640342823, + -19.11804917865524, + -19.78410366289154, + -20.456688093051728, + -21.1358024691358, + -21.821446791143764, + -22.5136210590756, + -23.212325272931338, + -23.917559432710945, + -24.62932353841444, + -25.347617590041835, + -26.0724415875931, + -26.80379553106826, + -27.5416794204673, + -28.28609325579022, + -29.037037037037038, + -29.794510764207732, + -30.55851443730231, + -31.329048056320786, + -32.10611162126313, + -32.88970513212938, + -33.6798285889195, + -34.4764819916335, + -35.2796653402714, + -36.08937863483318, + -36.90562187531885, + -37.72839506172839 + ], + [ + 11.65105601469238, + 11.48127742067136, + 11.304968880726458, + 11.122130394857669, + 10.932761963064992, + 10.736863585348434, + 10.534435261707989, + 10.32547699214366, + 10.109988776655445, + 9.887970615243342, + 9.659422507907358, + 9.424344454647485, + 9.18273645546373, + 8.934598510356087, + 8.679930619324558, + 8.418732782369146, + 8.15100499948985, + 7.876747270686664, + 7.595959595959595, + 7.308641975308643, + 7.0147944087338026, + 6.714416896235078, + 6.407509437812468, + 6.094072033465973, + 5.774104683195592, + 5.4476073870013275, + 5.114580144883175, + 4.7750229568411395, + 4.428935822875217, + 4.076318742985411, + 3.7171717171717176, + 3.351494745434141, + 2.9792878277726773, + 2.600550964187327, + 2.2152841546780944, + 1.8234873992449747, + 1.4251606978879712, + 1.020304050607081, + 0.6089174574023068, + 0.19100091827364518, + -0.23344556677890127, + -0.6644219977553292, + -1.1019283746556465, + -1.545964697479849, + -1.996530966227937, + -2.4536271808999066, + -2.9172533414957647, + -3.387409448015508, + -3.8640955004591375, + -4.347311498826652, + -4.837057443118049, + -5.333333333333333, + -5.836139169472504, + -6.34547495153556, + -6.861340679522495, + -7.383736353433323, + -7.912661973268035, + -8.448117539026631, + -8.99010305070911, + -9.538618508315478, + -10.093663911845729, + -10.65523926129987, + -11.223344556677887, + -11.797979797979798, + -12.379144985205592, + -12.96684011835527, + -13.561065197428837, + -14.161820222426282, + -14.769105193347617, + -15.382920110192838, + -16.003264972961944, + -16.63013978165493, + -17.26354453627181, + -17.903479236812572, + -18.54994388327722, + -19.202938475665746, + -19.862463013978164, + -20.528517498214466, + -21.20110192837466, + -21.880216304458727, + -22.565860626466694, + -23.258034894398527, + -23.956739108254254, + -24.661973268033876, + -25.37373737373737, + -26.092031425364766, + -26.816855422916028, + -27.548209366391184, + -28.28609325579023, + -29.03050709111315, + -29.78145087235996, + -30.53892459953066, + -31.302928272625238, + -32.07346189164372, + -32.85052545658606, + -33.634118967452295, + -34.42424242424243, + -35.22089582695643, + -36.02407917559434, + -36.833792470156105 + ], + [ + 11.246199367411487, + 11.08948066523824, + 10.926232017141107, + 10.756453423120089, + 10.580144883175185, + 10.397306397306398, + 10.207937965513722, + 10.012039587797164, + 9.809611264156718, + 9.600652994592389, + 9.385164779104173, + 9.163146617692071, + 8.934598510356087, + 8.699520457096215, + 8.457912457912457, + 8.209774512804815, + 7.9551066217732895, + 7.693908784817875, + 7.426181001938577, + 7.151923273135395, + 6.871135598408324, + 6.583817977757372, + 6.289970411182532, + 5.989592898683807, + 5.6826854402611975, + 5.369248035914703, + 5.049280685644321, + 4.722783389450056, + 4.389756147331905, + 4.050198959289869, + 3.7041118253239462, + 3.35149474543414, + 2.9923477196204473, + 2.6266707478828684, + 2.2544638302214057, + 1.875726966636057, + 1.490460157126824, + 1.0986634016937047, + 0.7003367003367007, + 0.2954800530558104, + -0.11590654014896562, + -0.5338230792776231, + -0.9582695643301697, + -1.3892459953066014, + -1.826752372206919, + -2.2707886950311176, + -2.7213549637792047, + -3.178451178451178, + -3.6420773390470367, + -4.112233445566781, + -4.588919498010406, + -5.07213549637792, + -5.561881440669319, + -6.058157330884605, + -6.560963167023772, + -7.070298949086826, + -7.586164677073768, + -8.108560350984595, + -8.637485970819302, + -9.172941536577898, + -9.714927048260382, + -10.263442505866749, + -10.818487909397, + -11.380063258851136, + -11.94816855422916, + -12.522803795531068, + -13.103968982756863, + -13.691664115906537, + -14.285889194980104, + -14.886644219977555, + -15.49392919089889, + -16.107744107744104, + -16.72808897051321, + -17.3549637792062, + -17.98836853382308, + -18.628303234363838, + -19.274767880828485, + -19.92776247321702, + -20.587287011529437, + -21.253341495765735, + -21.92592592592593, + -22.605040302009996, + -23.290684624017953, + -23.982858891949803, + -24.681563105805527, + -25.386797265585148, + -26.098561371288646, + -26.816855422916024, + -27.5416794204673, + -28.273033363942456, + -29.01091725334149, + -29.75533108866442, + -30.50627486991123, + -31.263748597081936, + -32.02775227017651, + -32.79828588919497, + -33.57534945413733, + -34.35894296500357, + -35.149066421793705, + -35.945719824507705 + ], + [ + 10.834812774206709, + 10.691153963881236, + 10.54096520763187, + 10.384246505458623, + 10.220997857361493, + 10.051219263340473, + 9.87491072339557, + 9.692072237526784, + 9.502703805734107, + 9.30680542801755, + 9.104377104377102, + 8.895418834812773, + 8.679930619324558, + 8.457912457912457, + 8.22936435057647, + 7.9942862973166, + 7.752678298132844, + 7.504540353025201, + 7.249872461993673, + 6.988674625038262, + 6.720946842158961, + 6.446689113355779, + 6.16590143862871, + 5.878583817977756, + 5.584736251402917, + 5.284358738904194, + 4.977451280481583, + 4.664013876135088, + 4.344046525864707, + 4.017549229670442, + 3.6845219875522903, + 3.3449647995102545, + 2.9988776655443328, + 2.646260585654524, + 2.2871135598408325, + 1.921436588103254, + 1.5492296704417918, + 1.1704928068564429, + 0.78522599734721, + 0.3934292419140901, + -0.004897459442915197, + -0.40975410672380197, + -0.821140699928578, + -1.2390572390572392, + -1.6635037241097854, + -2.094480155086214, + -2.5319865319865307, + -2.9760228548107337, + -3.426589123558821, + -3.883685338230794, + -4.347311498826649, + -4.817467605346392, + -5.294153657790022, + -5.7773696561575365, + -6.267115600448932, + -6.763391490664217, + -7.266197326803388, + -7.775533108866443, + -8.29139883685338, + -8.813794510764206, + -9.342720130598918, + -9.878175696357514, + -10.420161208039993, + -10.96867666564636, + -11.523722069176612, + -12.085297418630752, + -12.653402714008775, + -13.228037955310679, + -13.809203142536475, + -14.396898275686155, + -14.991123354759718, + -15.591878379757166, + -16.1991633506785, + -16.81297826752372, + -17.433323130292827, + -18.060197938985812, + -18.693602693602692, + -19.333537394143455, + -19.9800020406081, + -20.63299663299663, + -21.292521171309055, + -21.958575655545353, + -22.63116008570553, + -23.310274461789618, + -23.995918783797567, + -24.688093051729417, + -25.386797265585145, + -26.092031425364752, + -26.80379553106826, + -27.522089582695642, + -28.246913580246904, + -28.97826752372207, + -29.716151413121107, + -30.460565248444038, + -31.211509029690845, + -31.968982756861536, + -32.73298642995613, + -33.50352004897459, + -34.280583613916946, + -35.064177124783185 + ], + [ + 10.416896235078053, + 10.286297316600345, + 10.149168452198754, + 10.005509641873278, + 9.855320885623916, + 9.698602183450669, + 9.535353535353535, + 9.365574941332516, + 9.189266401387613, + 9.006427915518824, + 8.81705948372615, + 8.621161106009591, + 8.418732782369148, + 8.209774512804817, + 7.994286297316599, + 7.7722681359045, + 7.543720028568515, + 7.308641975308641, + 7.067033976124884, + 6.818896031017244, + 6.564228139985714, + 6.303030303030303, + 6.035302520151005, + 5.761044791347821, + 5.480257116620752, + 5.192939495969799, + 4.8990919293949595, + 4.598714416896235, + 4.291806958473625, + 3.9783695541271307, + 3.658402203856749, + 3.331904907662484, + 2.9988776655443328, + 2.6593204775022947, + 2.313233343536374, + 1.960616263646566, + 1.6014692378328745, + 1.235792266095296, + 0.8635853484338339, + 0.4848484848484844, + 0.09958167533924978, + -0.2922150800938663, + -0.6905417814508716, + -1.0953984287317624, + -1.5067850219365382, + -1.924701561065196, + -2.349148046117742, + -2.7801244770941738, + -3.217630853994491, + -3.6616671768186935, + -4.112233445566778, + -4.5693296602387505, + -5.032955820834609, + -5.503111927354354, + -5.979797979797978, + -6.463013978165492, + -6.952759922456893, + -7.449035812672178, + -7.951841648811342, + -8.4611774308744, + -8.977043158861342, + -9.499438832772167, + -10.028364452606873, + -10.563820018365472, + -11.105805530047954, + -11.654320987654321, + -12.209366391184577, + -12.770941740638708, + -13.339047036016733, + -13.913682277318642, + -14.494847464544435, + -15.08254259769411, + -15.676767676767678, + -16.277522701765125, + -16.884807672686463, + -17.498622589531678, + -18.118967452300783, + -18.745842260993776, + -19.37924701561065, + -20.019181716151408, + -20.665646362616066, + -21.31864095500459, + -21.978165493317007, + -22.644219977553313, + -23.316804407713498, + -23.995918783797578, + -24.68156310580553, + -25.37373737373737, + -26.072441587593104, + -26.777675747372715, + -27.48943985307621, + -28.207733904703602, + -28.93255790225487, + -29.66391184573003, + -30.401795735129067, + -31.14620957045199, + -31.89715335169881, + -32.6546270788695, + -33.418630751964095, + -34.18916437098255 + ], + [ + 9.992449750025509, + 9.874910723395573, + 9.75084175084175, + 9.620242832364045, + 9.483113967962453, + 9.339455157636978, + 9.189266401387613, + 9.032547699214366, + 8.869299051117235, + 8.699520457096215, + 8.523211917151313, + 8.340373431282522, + 8.15100499948985, + 7.9551066217732895, + 7.752678298132842, + 7.543720028568514, + 7.3282318130803, + 7.106213651668197, + 6.877665544332212, + 6.642587491072341, + 6.400979491888583, + 6.152841546780941, + 5.898173655749414, + 5.636975818794001, + 5.369248035914702, + 5.09499030711152, + 4.8142026323844505, + 4.526885011733497, + 4.233037445158658, + 3.9326599326599334, + 3.6257524742373226, + 3.312315069890828, + 2.9923477196204478, + 2.66585042342618, + 2.3328231813080302, + 1.993265993265993, + 1.647178859300072, + 1.2945617794102642, + 0.9354147535965726, + 0.5697377818589938, + 0.19753086419752952, + -0.18120599938781612, + -0.5664728088970505, + -0.9582695643301706, + -1.3565962656871762, + -1.7614529129680632, + -2.1728395061728385, + -2.5907560453014997, + -3.0152025303540464, + -3.4461789613304785, + -3.883685338230792, + -4.327721661054994, + -4.778287929803083, + -5.235384144475056, + -5.69901030507091, + -6.169166411590654, + -6.6458524640342835, + -7.129068462401797, + -7.618814406693193, + -8.115090296908479, + -8.617896133047648, + -9.127231915110706, + -9.64309764309764, + -10.165493317008467, + -10.694418936843181, + -11.229874502601776, + -11.77186001428426, + -12.320375471890625, + -12.875420875420875, + -13.436996224875015, + -14.005101520253039, + -14.57973676155494, + -15.160901948780737, + -15.748597081930416, + -16.34282216100398, + -16.943577186001427, + -17.55086215692276, + -18.164677073767983, + -18.785021936537092, + -19.411896745230077, + -20.04530149984696, + -20.685236200387717, + -21.331700846852357, + -21.984695439240898, + -22.644219977553313, + -23.310274461789618, + -23.982858891949803, + -24.661973268033872, + -25.347617590041835, + -26.039791857973675, + -26.738496071829402, + -27.44373023160902, + -28.15549433731252, + -28.873788388939907, + -29.598612386491176, + -30.329966329966325, + -31.067850219365376, + -31.812264054688292, + -32.56320783593512, + -33.32068156310581 + ], + [ + 9.561473319049075, + 9.456994184266913, + 9.34598510356086, + 9.228446076930924, + 9.104377104377104, + 8.973778185899397, + 8.836649321497806, + 8.69299051117233, + 8.542801754922968, + 8.386083052749719, + 8.222834404652586, + 8.053055810631568, + 7.876747270686666, + 7.693908784817876, + 7.5045403530252, + 7.308641975308642, + 7.106213651668199, + 6.897255382103866, + 6.681767166615651, + 6.459749005203552, + 6.231200897867564, + 5.996122844607694, + 5.7545148454239365, + 5.506376900316294, + 5.251709009284767, + 4.990511172329354, + 4.722783389450056, + 4.448525660646872, + 4.167737985919803, + 3.8804203652688507, + 3.586572798694011, + 3.286195286195287, + 2.9792878277726764, + 2.66585042342618, + 2.3458830731558002, + 2.019385776961534, + 1.6863585348433834, + 1.3468013468013467, + 1.0007142128354252, + 0.6480971329456174, + 0.28895010713192404, + -0.07672686460565115, + -0.4489337822671149, + -0.8276706458524643, + -1.2129374553616987, + -1.6047342107948155, + -2.0030609121518204, + -2.4079175594327107, + -2.819304152637487, + -3.2372206917661477, + -3.6616671768186912, + -4.0926436077951225, + -4.53014998469544, + -4.974186307519642, + -5.424752576267727, + -5.881848790939699, + -6.345474951535558, + -6.815631058055303, + -7.292317110498926, + -7.7755331088664414, + -8.265279053157842, + -8.761554943373127, + -9.264360779512293, + -9.773696561575347, + -10.289562289562289, + -10.811957963473116, + -11.340883583307827, + -11.876339149066421, + -12.418324660748901, + -12.96684011835527, + -13.521885521885524, + -14.083460871339657, + -14.651566166717682, + -15.226201408019591, + -15.807366595245384, + -16.39506172839506, + -16.989286807468623, + -17.590041832466074, + -18.197326803387412, + -18.811141720232627, + -19.43148658300174, + -20.058361391694724, + -20.691766146311597, + -21.331700846852364, + -21.978165493317007, + -22.631160085705545, + -23.290684624017956, + -23.956739108254254, + -24.629323538414454, + -25.30843791449852, + -25.994082236506472, + -26.686256504438326, + -27.384960718294046, + -28.090194878073667, + -28.80195898377717, + -29.520253035404544, + -30.24507703295582, + -30.976430976430976, + -31.714314865830026, + -32.45872870115294 + ], + [ + 9.123966942148758, + 9.032547699214364, + 8.934598510356086, + 8.830119375573922, + 8.71911029486787, + 8.601571268237935, + 8.477502295684113, + 8.346903377206408, + 8.209774512804817, + 8.066115702479339, + 7.915926946229976, + 7.759208244056728, + 7.595959595959597, + 7.426181001938579, + 7.2498724619936725, + 7.067033976124884, + 6.877665544332212, + 6.681767166615651, + 6.479338842975206, + 6.270380573410877, + 6.05489235792266, + 5.832874196510561, + 5.604326089174574, + 5.369248035914702, + 5.127640036730946, + 4.879502091623304, + 4.624834200591776, + 4.363636363636364, + 4.095908580757065, + 3.8216508519538834, + 3.540863177226814, + 3.253545556575861, + 2.959697990001021, + 2.6593204775022956, + 2.3524130190796866, + 2.0389756147331908, + 1.7190082644628106, + 1.3925109682685444, + 1.059483726150394, + 0.7199265381083565, + 0.3738394041424339, + 0.021222324252629265, + -0.3379247015610639, + -0.7036016732986424, + -1.0758085909601065, + -1.4545454545454524, + -1.8398122640546868, + -2.2316090194878067, + -2.629935720844812, + -3.0347923681257023, + -3.4461789613304745, + -3.8640955004591357, + -4.2885419855116815, + -4.719518416488114, + -5.157024793388428, + -5.601061116212629, + -6.051627384960718, + -6.508723599632691, + -6.972349760228545, + -7.442505866748289, + -7.919191919191919, + -8.402407917559433, + -8.89215386185083, + -9.388429752066113, + -9.891235588205284, + -10.400571370268338, + -10.91643709825528, + -11.438832772166103, + -11.967758392000814, + -12.50321395775941, + -13.045199469441894, + -13.593714927048257, + -14.148760330578508, + -14.71033568003265, + -15.278440975410673, + -15.853076216712576, + -16.434241403938373, + -17.021936537088052, + -17.616161616161616, + -18.216916641159063, + -18.824201612080405, + -19.438016528925615, + -20.058361391694717, + -20.685236200387717, + -21.31864095500459, + -21.958575655545356, + -22.605040302009996, + -23.258034894398527, + -23.917559432710952, + -24.583613916947247, + -25.25619834710743, + -25.935312723191515, + -26.62095704519946, + -27.313131313131315, + -28.011835526987042, + -28.71706968676665, + -29.428833792470154, + -30.14712784409754, + -30.871951841648816, + -31.603305785123965 + ], + [ + 8.679930619324557, + 8.601571268237935, + 8.516681971227426, + 8.425262728293031, + 8.32731353943475, + 8.222834404652586, + 8.111825323946535, + 7.9942862973166005, + 7.8702173247627805, + 7.739618406285073, + 7.6024895418834815, + 7.458830731558004, + 7.3086419753086425, + 7.151923273135395, + 6.988674625038261, + 6.8188960310172435, + 6.642587491072341, + 6.45974900520355, + 6.270380573410876, + 6.074482195694317, + 5.872053872053871, + 5.663095602489542, + 5.447607387001327, + 5.225589225589225, + 4.997041118253239, + 4.761963064993369, + 4.520355065809611, + 4.27221712070197, + 4.017549229670442, + 3.75635139271503, + 3.4886236098357313, + 3.2143658810325486, + 2.93357820630548, + 2.6462605856545247, + 2.352413019079686, + 2.0520355065809612, + 1.7451280481583518, + 1.431690643811856, + 1.1117232935414763, + 0.7852259973472093, + 0.4521987552290574, + 0.11264156718702323, + -0.23344556677889916, + -0.5860626466687072, + -0.9452096724824005, + -1.3108866442199756, + -1.68309356188144, + -2.061830425466789, + -2.4470972349760234, + -2.8388939904091437, + -3.237220691766145, + -3.642077339047036, + -4.053463932251812, + -4.471380471380472, + -4.895826956433016, + -5.326803387409448, + -5.764309764309764, + -6.208346087133966, + -6.658912355882052, + -7.116008570554024, + -7.579634731149882, + -8.049790837669626, + -8.526476890113251, + -9.009692888480766, + -9.499438832772167, + -9.99571472298745, + -10.498520559126622, + -11.007856341189672, + -11.523722069176614, + -12.046117743087441, + -12.575043362922152, + -13.110498928680745, + -13.652484440363228, + -14.200999897969595, + -14.75604530149985, + -15.317620650953982, + -15.885725946332007, + -16.460361187633914, + -17.04152637485971, + -17.629221508009383, + -18.223446587082954, + -18.8242016120804, + -19.43148658300173, + -20.045301499846957, + -20.66564636261606, + -21.292521171309055, + -21.92592592592593, + -22.56586062646668, + -23.212325272931338, + -23.865319865319865, + -24.524844403632276, + -25.190898887868585, + -25.86348331802877, + -26.54259769411285, + -27.228242016120802, + -27.920416284052642, + -28.61912049790838, + -29.32435465768799, + -30.036118763391492, + -30.754412815018878 + ], + [ + 8.229364350576471, + 8.164064891337619, + 8.09223548617488, + 8.013876135088257, + 7.928986838077746, + 7.837567595143353, + 7.739618406285073, + 7.635139271502908, + 7.524130190796858, + 7.4065911641669215, + 7.282522191613101, + 7.151923273135394, + 7.0147944087338026, + 6.871135598408326, + 6.720946842158963, + 6.564228139985715, + 6.4009794918885845, + 6.231200897867564, + 6.054892357922661, + 5.872053872053873, + 5.6826854402611975, + 5.486787062544638, + 5.284358738904194, + 5.075400469339863, + 4.859912253851647, + 4.637894092439548, + 4.409345985103561, + 4.17426793184369, + 3.9326599326599325, + 3.6845219875522908, + 3.4298540965207636, + 3.168656259565352, + 2.9009284766860532, + 2.6266707478828684, + 2.3458830731558007, + 2.0585654525048467, + 1.7647178859300077, + 1.4643403734312828, + 1.1574329150086733, + 0.8439955106621775, + 0.5240281603917962, + 0.19753086419753263, + -0.1354963779206192, + -0.4750535659626566, + -0.8211406999285791, + -1.173757779818384, + -1.5329048056320769, + -1.8985817773696554, + -2.2707886950311194, + -2.6495255586164688, + -3.0347923681256996, + -3.4265891235588195, + -3.8249158249158244, + -4.229772472196716, + -4.641159065401487, + -5.059075604530149, + -5.483522089582696, + -5.914498520559128, + -6.35200489745944, + -6.7960412202836435, + -7.246607489031731, + -7.703703703703704, + -8.167329864299559, + -8.637485970819302, + -9.114172023262931, + -9.597388021630445, + -10.087133965921847, + -10.583409856137127, + -11.086215692276298, + -11.595551474339354, + -12.111417202326294, + -12.633812876237116, + -13.162738496071828, + -13.698194061830424, + -14.240179573512908, + -14.78869503111927, + -15.343740434649524, + -15.905315784103662, + -16.473421079481685, + -17.04805632078359, + -17.629221508009387, + -18.216916641159063, + -18.811141720232623, + -19.41189674523008, + -20.019181716151408, + -20.632996632996637, + -21.25334149576574, + -21.880216304458724, + -22.513621059075607, + -23.153555759616363, + -23.80002040608101, + -24.453014998469545, + -25.11253953678196, + -25.778594021018264, + -26.45117845117845, + -27.130292827262515, + -27.815937149270486, + -28.508111417202322, + -29.20681563105806, + -29.91204979083767 + ], + [ + 7.772268135904499, + 7.720028568513417, + 7.661259055198449, + 7.595959595959596, + 7.524130190796857, + 7.445770839710234, + 7.360881542699724, + 7.269462299765331, + 7.171513110907051, + 7.067033976124885, + 6.956024895418835, + 6.838485868788899, + 6.714416896235079, + 6.583817977757373, + 6.446689113355779, + 6.303030303030303, + 6.152841546780942, + 5.996122844607693, + 5.83287419651056, + 5.663095602489543, + 5.4867870625446375, + 5.303948576675849, + 5.114580144883175, + 4.918681767166615, + 4.7162534435261705, + 4.507295173961841, + 4.291806958473625, + 4.069788797061525, + 3.841240689725538, + 3.606162636465667, + 3.3645546372819104, + 3.116416692174269, + 2.861748801142741, + 2.6005509641873275, + 2.3328231813080302, + 2.0585654525048462, + 1.7777777777777781, + 1.4904601571268237, + 1.196612590551985, + 0.8962350780532597, + 0.5893276196306492, + 0.275890215284156, + -0.04407713498622512, + -0.3705744311804918, + -0.7036016732986438, + -1.043158861340678, + -1.3892459953066008, + -1.7418630751964086, + -2.1010101010101017, + -2.46668707274768, + -2.8388939904091406, + -3.2176308539944904, + -3.6028976635037244, + -3.9946944189368443, + -4.393021120293846, + -4.797877767574737, + -5.209264360779512, + -5.627180899908174, + -6.0516273849607165, + -6.482603815937148, + -6.920110192837465, + -7.36414651566167, + -7.814712784409752, + -8.271808999081724, + -8.735435159677584, + -9.205591266197327, + -9.682277318640956, + -10.165493317008467, + -10.655239261299867, + -11.151515151515152, + -11.654320987654321, + -12.163656769717374, + -12.679522497704315, + -13.201918171615143, + -13.730843791449853, + -14.266299357208446, + -14.80828486889093, + -15.356800326497297, + -15.91184573002755, + -16.473421079481685, + -17.041526374859714, + -17.616161616161616, + -18.197326803387405, + -18.785021936537092, + -19.37924701561065, + -19.980002040608106, + -20.58728701152944, + -21.20110192837465, + -21.821446791143764, + -22.448321599836753, + -23.08172635445362, + -23.72166105499439, + -24.368125701459032, + -25.02112029384757, + -25.680644832159985, + -26.346699316396283, + -27.019283746556475, + -27.698398122640548, + -28.384042444648514, + -29.076216712580347 + ], + [ + 7.308641975308641, + 7.26946229976533, + 7.2237526782981325, + 7.17151311090705, + 7.112743597592082, + 7.047444138353229, + 6.975614733190491, + 6.897255382103867, + 6.812366085093358, + 6.7209468421589635, + 6.622997653300684, + 6.518518518518518, + 6.407509437812468, + 6.289970411182533, + 6.16590143862871, + 6.035302520151005, + 5.898173655749415, + 5.754514845423936, + 5.604326089174574, + 5.447607387001327, + 5.284358738904192, + 5.114580144883175, + 4.938271604938272, + 4.755433119069482, + 4.566064687276809, + 4.37016630956025, + 4.167737985919804, + 3.9587797163554743, + 3.7432915008672585, + 3.521273339455158, + 3.292725232119172, + 3.057647178859301, + 2.8160391796755437, + 2.567901234567901, + 2.313233343536374, + 2.0520355065809612, + 1.7843077237016636, + 1.5100499948984798, + 1.229262320171412, + 0.9419446995204571, + 0.6480971329456171, + 0.34771962044689475, + 0.04081216202428417, + -0.27262524232221175, + -0.592592592592593, + -0.9190898887868569, + -1.2521171309050083, + -1.5916743189470457, + -1.9377614529129683, + -2.2903785328027766, + -2.649525558616466, + -3.015202530354045, + -3.387409448015508, + -3.766146311600858, + -4.151413121110089, + -4.543209876543209, + -4.941536577900214, + -5.346393225181105, + -5.757779818385876, + -6.175696357514537, + -6.6001428425670845, + -7.031119273543517, + -7.46862565044383, + -7.9126619732680314, + -8.36322824201612, + -8.820324456688093, + -9.283950617283951, + -9.754106723803691, + -10.23079277624732, + -10.714008774614834, + -11.203754718906236, + -11.700030609121516, + -12.202836445260687, + -12.712172227323743, + -13.228037955310683, + -13.750433629221504, + -14.279359249056217, + -14.814814814814813, + -15.356800326497297, + -15.90531578410366, + -16.46036118763392, + -17.021936537088052, + -17.59004183246607, + -18.164677073767983, + -18.745842260993772, + -19.33353739414346, + -19.92776247321702, + -20.528517498214462, + -21.135802469135804, + -21.749617385981022, + -22.36996224875012, + -22.996837057443116, + -23.630241812059992, + -24.270176512600756, + -24.9166411590654, + -25.56963575145393, + -26.229160289766355, + -26.89521477400265, + -27.567799204162846, + -28.246913580246915 + ], + [ + 6.838485868788899, + 6.812366085093358, + 6.779716355473932, + 6.74053667993062, + 6.694827058463423, + 6.642587491072341, + 6.583817977757373, + 6.518518518518519, + 6.446689113355781, + 6.368329762269157, + 6.283440465258648, + 6.192021222324252, + 6.094072033465974, + 5.989592898683809, + 5.8785838179777565, + 5.761044791347821, + 5.636975818794002, + 5.506376900316294, + 5.369248035914702, + 5.225589225589227, + 5.075400469339863, + 4.918681767166616, + 4.755433119069483, + 4.585654525048464, + 4.409345985103561, + 4.226507499234772, + 4.037139067442098, + 3.8412406897255384, + 3.6388123660850935, + 3.4298540965207636, + 3.214365881032548, + 2.9923477196204478, + 2.7637996122844615, + 2.5287215590245893, + 2.287113559840833, + 2.0389756147331903, + 1.7843077237016636, + 1.5231098867462505, + 1.2553821038669528, + 0.981124375063769, + 0.7003367003366995, + 0.4130190796857476, + 0.11917151311090768, + -0.18120599938781767, + -0.48811345781042836, + -0.8015508621569215, + -1.1215182124273029, + -1.4480155086215694, + -1.781042750739721, + -2.1205999387817585, + -2.466687072747678, + -2.819304152637486, + -3.178451178451179, + -3.5441281501887576, + -3.9163350678502185, + -4.295071931435568, + -4.680338740944802, + -5.072135496377922, + -5.470462197734923, + -5.875318845015814, + -6.28670543822059, + -6.704621977349252, + -7.1290684624017935, + -7.560044893378225, + -7.997551270278544, + -8.441587593102746, + -8.892153861850833, + -9.349250076522804, + -9.812876237118662, + -10.283032343638405, + -10.759718396082034, + -11.242934394449545, + -11.732680338740945, + -12.228956228956228, + -12.7317620650954, + -13.24109784715845, + -13.756963575145392, + -14.27935924905622, + -14.808284868890933, + -15.343740434649522, + -15.885725946332013, + -16.434241403938373, + -16.989286807468623, + -17.55086215692277, + -18.118967452300783, + -18.6936026936027, + -19.274767880828488, + -19.862463013978164, + -20.45668809305173, + -21.05744311804918, + -21.66472808897051, + -22.278543005815735, + -22.898887868584836, + -23.525762677277832, + -24.159167431894705, + -24.799102132435465, + -25.445566778900115, + -26.098561371288643, + -26.758085909601068, + -27.424140393837362 + ], + [ + 6.36179981634527, + 6.348739924497501, + 6.329150086725845, + 6.303030303030303, + 6.2703805734108755, + 6.231200897867565, + 6.1854912764003664, + 6.133251709009285, + 6.074482195694317, + 6.009182736455465, + 5.937353331292726, + 5.858993980206101, + 5.774104683195594, + 5.682685440261198, + 5.5847362514029175, + 5.480257116620753, + 5.369248035914704, + 5.251709009284767, + 5.127640036730946, + 4.99704111825324, + 4.859912253851648, + 4.716253443526171, + 4.566064687276809, + 4.409345985103561, + 4.246097337006428, + 4.07631874298541, + 3.900010203040506, + 3.717171717171717, + 3.527803285379043, + 3.331904907662484, + 3.1294765840220387, + 2.920518314457709, + 2.7050300989694938, + 2.483011937557392, + 2.254463830221406, + 2.0193857769615344, + 1.7777777777777781, + 1.529639832670136, + 1.2749719416386087, + 1.0137741046831956, + 0.746046321803897, + 0.47178859300071563, + 0.1910009182736464, + -0.09631670237730827, + -0.3901642689521483, + -0.6905417814508708, + -0.9974492398734811, + -1.3108866442199771, + -1.6308539944903586, + -1.957351290684625, + -2.290378532802774, + -2.629935720844811, + -2.9760228548107333, + -3.3286399347005418, + -3.6877869605142317, + -4.05346393225181, + -4.425670849913274, + -4.804407713498624, + -5.189674523007854, + -5.581471278440974, + -5.97979797979798, + -6.38465462707887, + -6.796041220283643, + -7.213957759412303, + -7.63840424446485, + -8.069380675441282, + -8.5068870523416, + -8.950923375165797, + -9.401489643913886, + -9.85858585858586, + -10.322212019181716, + -10.792368125701458, + -11.269054178145087, + -11.7522701765126, + -12.242016120804, + -12.738292011019281, + -13.241097847158454, + -13.750433629221508, + -14.26629935720845, + -14.788695031119271, + -15.317620650953987, + -15.85307621671258, + -16.395061728395056, + -16.943577186001427, + -17.498622589531678, + -18.060197938985823, + -18.62830323436384, + -19.202938475665746, + -19.784103662891543, + -20.37179879604122, + -20.96602387511478, + -21.566778900112233, + -22.174063871033567, + -22.78787878787879, + -23.40822365064789, + -24.03509845934088, + -24.66850321395776, + -25.30843791449852, + -25.954902560963173, + -26.6078971533517 + ], + [ + 5.878583817977757, + 5.878583817977759, + 5.872053872053873, + 5.858993980206102, + 5.8394041424344465, + 5.813284358738905, + 5.780634629119478, + 5.741454953576166, + 5.695745332108969, + 5.6435057647178875, + 5.584736251402918, + 5.519436792164066, + 5.4476073870013275, + 5.369248035914703, + 5.284358738904192, + 5.192939495969799, + 5.09499030711152, + 4.990511172329354, + 4.879502091623304, + 4.761963064993369, + 4.637894092439547, + 4.507295173961841, + 4.37016630956025, + 4.2265074992347715, + 4.07631874298541, + 3.9196000408121625, + 3.75635139271503, + 3.586572798694011, + 3.4102642587491077, + 3.227425772880319, + 3.0380573410876446, + 2.8421589633710855, + 2.63973063973064, + 2.4307723701663093, + 2.2152841546780944, + 1.9932659932659933, + 1.7647178859300074, + 1.5296398326701357, + 1.2880318334863794, + 1.0398938883787368, + 0.7852259973472087, + 0.5240281603917978, + 0.2563003775124993, + -0.017957351290684764, + -0.2987450260177541, + -0.586062646668706, + -0.8799102132435462, + -1.1802877257422715, + -1.487195184164882, + -1.800632588511378, + -2.1205999387817562, + -2.4470972349760225, + -2.7801244770941747, + -3.119681665136212, + -3.4657687991021318, + -3.8183858789919394, + -4.177532904805632, + -4.543209876543211, + -4.915416794204672, + -5.294153657790021, + -5.679420467299256, + -6.0712172227323755, + -6.469543924089377, + -6.874400571370268, + -7.285787164575044, + -7.703703703703706, + -8.128150188756251, + -8.55912661973268, + -8.996632996632997, + -9.4406693194572, + -9.891235588205287, + -10.348331802877258, + -10.811957963473114, + -11.282114069992858, + -11.758800122436488, + -12.242016120804, + -12.731762065095399, + -13.228037955310683, + -13.730843791449855, + -14.240179573512906, + -14.756045301499853, + -15.278440975410673, + -15.80736659524538, + -16.342822161003983, + -16.88480767268646, + -17.433323130292834, + -17.98836853382308, + -18.549943883277216, + -19.118049178655244, + -19.692684419957146, + -20.27384960718294, + -20.861544740332622, + -21.45576981940618, + -22.056524844403636, + -22.663809815324967, + -23.27762473217018, + -23.897969594939294, + -24.52484440363228, + -25.158249158249166, + -25.79818385878992 + ], + [ + 5.388837873686358, + 5.401897765534129, + 5.408427711458015, + 5.408427711458014, + 5.4018977655341285, + 5.388837873686359, + 5.369248035914703, + 5.343128252219161, + 5.310478522599736, + 5.271298847056423, + 5.225589225589226, + 5.173349658198143, + 5.114580144883176, + 5.049280685644323, + 4.977451280481582, + 4.8990919293949595, + 4.814202632384451, + 4.722783389450056, + 4.624834200591776, + 4.520355065809611, + 4.409345985103561, + 4.291806958473625, + 4.167737985919804, + 4.037139067442098, + 3.900010203040506, + 3.75635139271503, + 3.6061626364656667, + 3.449443934292419, + 3.2861952861952863, + 3.116416692174268, + 2.9401081522293646, + 2.7572696663605765, + 2.567901234567902, + 2.372002856851341, + 2.169574533210897, + 1.9606162636465667, + 1.7451280481583515, + 1.5231098867462505, + 1.2945617794102646, + 1.0594837261503929, + 0.8178757269666355, + 0.5697377818589953, + 0.31506989082746734, + 0.05387205387205396, + -0.2138557290072446, + -0.4881134578104262, + -0.7689011325374953, + -1.0562187531884497, + -1.3500663197632898, + -1.650443832262015, + -1.9573512906846229, + -2.270788695031119, + -2.5907560453015, + -2.9172533414957664, + -3.2502805836139155, + -3.5898377716559526, + -3.9359249056218752, + -4.288541985511683, + -4.647689011325372, + -5.013365983062952, + -5.385572900724416, + -5.764309764309766, + -6.149576573818996, + -6.5413733292521155, + -6.939700030609122, + -7.3445566778900115, + -7.755943271094788, + -8.173859810223446, + -8.598306295275991, + -9.029282726252424, + -9.466789103152742, + -9.910825425976938, + -10.361391694725027, + -10.818487909397, + -11.282114069992858, + -11.752270176512598, + -12.228956228956228, + -12.712172227323741, + -13.20191817161514, + -13.698194061830423, + -14.200999897969599, + -14.71033568003265, + -15.226201408019586, + -15.748597081930416, + -16.277522701765122, + -16.812978267523725, + -17.3549637792062, + -17.903479236812565, + -18.458524640342823, + -19.02009998979696, + -19.588205285174976, + -20.16284052647689, + -20.74400571370268, + -21.331700846852364, + -21.925925925925924, + -22.52668095092337, + -23.133965921844712, + -23.747780838689927, + -24.368125701459043, + -24.995000510152025 + ], + [ + 4.892561983471075, + 4.918681767166617, + 4.938271604938272, + 4.951331496786043, + 4.957861442709928, + 4.957861442709929, + 4.951331496786043, + 4.938271604938272, + 4.918681767166617, + 4.892561983471075, + 4.859912253851649, + 4.820732578308337, + 4.7750229568411395, + 4.722783389450057, + 4.664013876135088, + 4.598714416896236, + 4.526885011733498, + 4.448525660646872, + 4.363636363636364, + 4.27221712070197, + 4.17426793184369, + 4.069788797061525, + 3.9587797163554743, + 3.8412406897255384, + 3.717171717171717, + 3.5865727986940117, + 3.4494439342924195, + 3.3057851239669427, + 3.15559636771758, + 2.9988776655443328, + 2.8356290174471996, + 2.665850423426182, + 2.489541883481278, + 2.3067033976124884, + 2.117334965819815, + 1.921436588103255, + 1.7190082644628104, + 1.5100499948984798, + 1.2945617794102646, + 1.0725436179981633, + 0.8439955106621766, + 0.6089174574023068, + 0.36730945821854966, + 0.11917151311090696, + -0.13549637792062108, + -0.39669421487603207, + -0.6644219977553306, + -0.9386797265585145, + -1.2194674012855837, + -1.5067850219365386, + -1.8006325885113759, + -2.101010101010101, + -2.407917559432712, + -2.7213549637792074, + -3.0413223140495864, + -3.3678196102438527, + -3.7008468523620044, + -4.040404040404042, + -4.3864911743699615, + -4.739108254259769, + -5.098255280073463, + -5.463932251811041, + -5.836139169472501, + -6.21487603305785, + -6.600142842567086, + -6.991939598000205, + -7.3902662993572115, + -7.795122946638098, + -8.206509539842873, + -8.624426078971535, + -9.048872564024082, + -9.47984899500051, + -9.917355371900825, + -10.361391694725029, + -10.811957963473118, + -11.269054178145087, + -11.732680338740945, + -12.20283644526069, + -12.679522497704319, + -13.162738496071828, + -13.652484440363235, + -14.148760330578515, + -14.651566166717679, + -15.16090194878074, + -15.676767676767676, + -16.199163350678507, + -16.72808897051322, + -17.263544536271805, + -17.805530047954292, + -18.35404550556066, + -18.909090909090907, + -19.470666258545048, + -20.03877155392307, + -20.613406795224982, + -21.194571982450775, + -21.782267115600447, + -22.376492194674015, + -22.97724721967146, + -23.584532190592803, + -24.198347107438018 + ], + [ + 4.389756147331904, + 4.428935822875218, + 4.461585552494644, + 4.487705336190184, + 4.5072951739618405, + 4.520355065809611, + 4.526885011733497, + 4.526885011733496, + 4.520355065809612, + 4.507295173961841, + 4.487705336190185, + 4.461585552494644, + 4.428935822875218, + 4.389756147331906, + 4.344046525864707, + 4.291806958473625, + 4.233037445158659, + 4.167737985919804, + 4.095908580757066, + 4.0175492296704425, + 3.9326599326599325, + 3.841240689725539, + 3.743291500867259, + 3.6388123660850935, + 3.5278032853790426, + 3.4102642587491077, + 3.2861952861952863, + 3.15559636771758, + 3.0184675033159882, + 2.874808692990512, + 2.724619936741149, + 2.567901234567902, + 2.404652586470769, + 2.23487399244975, + 2.0585654525048467, + 1.8757269666360576, + 1.6863585348433836, + 1.490460157126824, + 1.2880318334863794, + 1.0790735639220488, + 0.8635853484338327, + 0.6415671870217335, + 0.413019079685747, + 0.177941026425875, + -0.06366697275788225, + -0.3118049178655227, + -0.5664728088970508, + -0.8276706458524639, + -1.0953984287317626, + -1.3696561575349466, + -1.6504438322620132, + -1.9377614529129679, + -2.231609019487808, + -2.531986531986533, + -2.838893990409141, + -3.1523313947556364, + -3.472298745026018, + -3.798796041220285, + -4.131823283338433, + -4.471380471380471, + -4.817467605346393, + -5.170084685236201, + -5.529231711049891, + -5.89490868278747, + -6.267115600448934, + -6.645852464034283, + -7.031119273543518, + -7.422916028976634, + -7.821242730333639, + -8.226099377614531, + -8.637485970819306, + -9.055402509947964, + -9.47984899500051, + -9.910825425976942, + -10.34833180287726, + -10.792368125701458, + -11.242934394449545, + -11.70003060912152, + -12.163656769717377, + -12.633812876237117, + -13.11049892868075, + -13.59371492704826, + -14.083460871339655, + -14.579736761554948, + -15.082542597694111, + -15.591878379757173, + -16.107744107744107, + -16.630139781654933, + -17.15906540148965, + -17.694520967248238, + -18.236506478930718, + -18.785021936537092, + -19.340067340067336, + -19.90164268952148, + -20.4697479848995, + -21.044383226201404, + -21.625548413427204, + -22.213243546576876, + -22.80746862565045, + -23.408223650647894 + ], + [ + 3.8804203652688516, + 3.9326599326599334, + 3.9783695541271316, + 4.0175492296704425, + 4.050198959289869, + 4.0763187429854115, + 4.095908580757067, + 4.108968472604837, + 4.115498418528723, + 4.115498418528722, + 4.108968472604838, + 4.095908580757066, + 4.076318742985411, + 4.050198959289871, + 4.0175492296704425, + 3.9783695541271316, + 3.9326599326599343, + 3.8804203652688507, + 3.821650851953883, + 3.7563513927150303, + 3.684521987552291, + 3.606162636465667, + 3.5212733394551585, + 3.4298540965207636, + 3.3319049076624836, + 3.227425772880319, + 3.116416692174268, + 2.9988776655443328, + 2.8748086929905114, + 2.7442097745128056, + 2.607080910111214, + 2.463422099785737, + 2.3132333435363748, + 2.156514641363126, + 1.9932659932659935, + 1.823487399244975, + 1.6471788593000718, + 1.4643403734312825, + 1.2749719416386087, + 1.0790735639220488, + 0.8766452402816035, + 0.6676869707172748, + 0.45219875522905884, + 0.2301805938169575, + 0.0016324864809708073, + -0.23344556677889916, + -0.4750535659626564, + -0.7231915110702989, + -0.977859402101827, + -1.23905723905724, + -1.5067850219365364, + -1.7810427507397204, + -2.06183042546679, + -2.3491480461177443, + -2.6429956126925815, + -2.943373125191307, + -3.2502805836139177, + -3.5637179879604135, + -3.883685338230792, + -4.210182634425058, + -4.5432098765432105, + -4.882767064585248, + -5.228854198551167, + -5.581471278440974, + -5.940618304254668, + -6.306295275992246, + -6.678502193653711, + -7.057239057239057, + -7.442505866748291, + -7.834302622181411, + -8.232629323538415, + -8.637485970819302, + -9.04887256402408, + -9.466789103152742, + -9.891235588205287, + -10.322212019181716, + -10.759718396082032, + -11.203754718906236, + -11.654320987654323, + -12.111417202326294, + -12.575043362922155, + -13.045199469441895, + -13.521885521885519, + -14.005101520253039, + -14.494847464544433, + -14.991123354759722, + -15.49392919089889, + -16.003264972961944, + -16.519130700948885, + -17.041526374859707, + -17.570451994694416, + -18.10590756045302, + -18.647893072135496, + -19.196408529741866, + -19.751453933272117, + -20.313029282726248, + -20.881134578104277, + -21.455769819406182, + -22.036935006631985, + -22.624630139781658 + ], + [ + 3.364554637281909, + 3.429854096520763, + 3.4886236098357317, + 3.540863177226813, + 3.5865727986940104, + 3.625752474237323, + 3.658402203856749, + 3.6845219875522908, + 3.704111825323947, + 3.7171717171717176, + 3.7237016630956026, + 3.723701663095602, + 3.717171717171718, + 3.704111825323947, + 3.68452198755229, + 3.658402203856749, + 3.625752474237323, + 3.5865727986940104, + 3.540863177226814, + 3.4886236098357317, + 3.4298540965207627, + 3.3645546372819104, + 3.292725232119172, + 3.2143658810325473, + 3.1294765840220387, + 3.038057341087644, + 2.9401081522293646, + 2.835629017447199, + 2.7246199367411488, + 2.607080910111214, + 2.483011937557392, + 2.352413019079686, + 2.2152841546780944, + 2.0716253443526167, + 1.921436588103255, + 1.764717885930007, + 1.6014692378328745, + 1.431690643811856, + 1.2553821038669528, + 1.0725436179981633, + 0.8831751862054887, + 0.6872768084889306, + 0.4848484848484853, + 0.27589021528415464, + 0.06040199979593869, + -0.16161616161616071, + -0.39016426895214723, + -0.625242322212019, + -0.8668503213957764, + -1.114988266503419, + -1.3696561575349446, + -1.630853994490358, + -1.8985817773696565, + -2.1728395061728403, + -2.453627180899907, + -2.7409448015508615, + -3.034792368125702, + -3.335169880624427, + -3.6420773390470345, + -3.9555147433935307, + -4.275482093663912, + -4.601979389858179, + -4.935006631976328, + -5.274563820018365, + -5.6206509539842875, + -5.973268033874095, + -6.332415059687788, + -6.6980920314253645, + -7.070298949086828, + -7.449035812672176, + -7.834302622181411, + -8.226099377614528, + -8.624426078971533, + -9.029282726252424, + -9.4406693194572, + -9.858585858585856, + -10.283032343638403, + -10.714008774614836, + -11.151515151515152, + -11.595551474339352, + -12.046117743087443, + -12.50321395775941, + -12.966840118355266, + -13.436996224875015, + -13.913682277318639, + -14.396898275686159, + -14.886644219977555, + -15.382920110192835, + -15.885725946332009, + -16.395061728395063, + -16.910927456381998, + -17.433323130292827, + -17.962248750127536, + -18.49770431588614, + -19.039689827568615, + -19.58820528517498, + -20.143250688705237, + -20.704826038159368, + -21.2729313335374, + -21.847566574839302 + ], + [ + 2.842158963371085, + 2.9205183144577105, + 2.992347719620448, + 3.0576471788593005, + 3.1164166921742695, + 3.1686562595653514, + 3.21436588103255, + 3.253545556575861, + 3.2861952861952877, + 3.312315069890829, + 3.3319049076624845, + 3.3449647995102554, + 3.3514947454341417, + 3.35149474543414, + 3.3449647995102545, + 3.3319049076624836, + 3.3123150698908286, + 3.2861952861952863, + 3.2535455565758604, + 3.214365881032549, + 3.168656259565351, + 3.1164166921742686, + 3.057647178859301, + 2.9923477196204473, + 2.920518314457709, + 2.8421589633710855, + 2.757269666360576, + 2.6658504234261815, + 2.567901234567902, + 2.463422099785737, + 2.352413019079686, + 2.2348739924497507, + 2.11080501989593, + 1.9802061014182226, + 1.8430772370166313, + 1.699418426691154, + 1.549229670441792, + 1.3925109682685441, + 1.2292623201714115, + 1.0594837261503929, + 0.8831751862054888, + 0.7003367003367013, + 0.5109682685440265, + 0.31506989082746656, + 0.11264156718702123, + -0.09631670237730755, + -0.31180491786552345, + -0.5338230792776246, + -0.7623711866136114, + -0.9974492398734836, + -1.2390572390572385, + -1.4871951841648812, + -1.741863075196409, + -2.0030609121518226, + -2.2707886950311185, + -2.545046423834303, + -2.825834098561372, + -3.1131517192123264, + -3.406999285787164, + -3.707376798285889, + -4.0142842567085, + -4.327721661054996, + -4.647689011325374, + -4.97418630751964, + -5.307213549637792, + -5.64677073767983, + -5.992857871645753, + -6.345474951535557, + -6.704621977349251, + -7.07029894908683, + -7.442505866748293, + -7.82124273033364, + -8.206509539842873, + -8.598306295275993, + -8.996632996633, + -9.401489643913884, + -9.812876237118662, + -10.230792776247323, + -10.655239261299869, + -11.086215692276298, + -11.52372206917662, + -11.967758392000816, + -12.418324660748901, + -12.875420875420879, + -13.339047036016733, + -13.809203142536482, + -14.285889194980106, + -14.769105193347615, + -15.258851137639022, + -15.755127027854302, + -16.257932863993467, + -16.76726864605653, + -17.283134374043467, + -17.805530047954292, + -18.334455667789, + -18.869911233547594, + -19.41189674523008, + -19.960412202836444, + -20.515457606366702, + -21.077032955820837 + ], + [ + 2.313233343536374, + 2.4046525864707693, + 2.489541883481278, + 2.5679012345679006, + 2.6397306397306393, + 2.7050300989694938, + 2.7637996122844615, + 2.816039179675543, + 2.861748801142741, + 2.900928476686053, + 2.9335782063054796, + 2.959697990001021, + 2.9792878277726764, + 2.9923477196204473, + 2.998877665544332, + 2.9988776655443323, + 2.9923477196204473, + 2.979287827772676, + 2.9596979900010205, + 2.933578206305479, + 2.9009284766860524, + 2.861748801142741, + 2.8160391796755433, + 2.7637996122844606, + 2.705030098969493, + 2.6397306397306397, + 2.5679012345679015, + 2.4895418834812775, + 2.4046525864707684, + 2.3132333435363743, + 2.215284154678095, + 2.1108050198959294, + 1.999795939189879, + 1.8822569125599429, + 1.7581879400061222, + 1.6275890215284154, + 1.4904601571268241, + 1.3468013468013469, + 1.196612590551985, + 1.039893888378737, + 0.8766452402816037, + 0.7068666462605866, + 0.5305581063156826, + 0.3477196204468933, + 0.15835118865421866, + -0.03754718906233956, + -0.23997551270278483, + -0.4489337822671154, + -0.6644219977553314, + -0.8864401591674327, + -1.1149882665034172, + -1.3500663197632892, + -1.5916743189470464, + -1.8398122640546888, + -2.094480155086215, + -2.355677992041628, + -2.6234057749209265, + -2.8976635037241105, + -3.1784511784511773, + -3.4657687991021318, + -3.7596163656769717, + -4.059993878175698, + -4.366901336598304, + -4.6803387409448005, + -5.000306091215182, + -5.3268033874094485, + -5.6598306295276, + -5.999387817569635, + -6.345474951535557, + -6.698092031425365, + -7.057239057239058, + -7.422916028976633, + -7.795122946638097, + -8.173859810223448, + -8.559126619732682, + -8.950923375165797, + -9.349250076522804, + -9.754106723803694, + -10.165493317008469, + -10.583409856137127, + -11.00785634118968, + -11.438832772166105, + -11.876339149066418, + -12.320375471890625, + -12.770941740638708, + -13.228037955310686, + -13.69166411590654, + -14.16182022242628, + -14.638506274869915, + -15.121722273237424, + -15.61146821752882, + -16.10774410774411, + -16.610549943883274, + -17.119885725946336, + -17.635751453933274, + -18.158147127844096, + -18.687072747678812, + -19.2225283134374, + -19.76451382511989, + -20.313029282726255 + ], + [ + 1.7777777777777768, + 1.882256912559943, + 1.9802061014182226, + 2.071625344352616, + 2.156514641363125, + 2.2348739924497494, + 2.306703397612489, + 2.372002856851341, + 2.4307723701663098, + 2.483011937557392, + 2.5287215590245893, + 2.5679012345679, + 2.6005509641873275, + 2.6266707478828693, + 2.6462605856545243, + 2.6593204775022956, + 2.665850423426181, + 2.6658504234261806, + 2.6593204775022956, + 2.646260585654525, + 2.626670747882869, + 2.600550964187328, + 2.567901234567901, + 2.528721559024589, + 2.483011937557392, + 2.4307723701663098, + 2.372002856851341, + 2.3067033976124884, + 2.23487399244975, + 2.156514641363126, + 2.0716253443526167, + 1.9802061014182228, + 1.882256912559943, + 1.7777777777777772, + 1.6667686970717273, + 1.5492296704417914, + 1.4251606978879707, + 1.2945617794102642, + 1.1574329150086728, + 1.0137741046831956, + 0.8635853484338329, + 0.7068666462605864, + 0.5436179981634531, + 0.3738394041424345, + 0.19753086419753052, + 0.014692378328742872, + -0.1746760534639317, + -0.37057443118049155, + -0.5730027548209369, + -0.7819610243852675, + -0.9974492398734814, + -1.2194674012855826, + -1.4480155086215691, + -1.6830935618814409, + -1.9247015610651963, + -2.172839506172839, + -2.427507397204367, + -2.68870523415978, + -2.956433017039076, + -3.2306907458422605, + -3.511478420569329, + -3.798796041220284, + -4.092643607795122, + -4.393021120293846, + -4.699928578716457, + -5.013365983062952, + -5.333333333333334, + -5.6598306295275975, + -5.992857871645749, + -6.332415059687786, + -6.67850219365371, + -7.0311192735435135, + -7.390266299357208, + -7.755943271094786, + -8.12815018875625, + -8.506887052341595, + -8.892153861850831, + -9.28395061728395, + -9.682277318640955, + -10.087133965921842, + -10.498520559126622, + -10.916437098255278, + -11.340883583307821, + -11.771860014284258, + -12.20936639118457, + -12.653402714008777, + -13.10396898275686, + -13.561065197428828, + -14.024691358024693, + -14.494847464544435, + -14.971533516988057, + -15.454749515355577, + -15.944495459646973, + -16.44077134986226, + -16.943577186001427, + -17.452912968064478, + -17.968778696051423, + -18.491174369962245, + -19.02009998979696, + -19.555555555555554 + ], + [ + 1.235792266095297, + 1.3533312927252328, + 1.4643403734312836, + 1.5688195082134473, + 1.6667686970717277, + 1.7581879400061227, + 1.8430772370166313, + 1.921436588103255, + 1.993265993265994, + 2.0585654525048476, + 2.117334965819815, + 2.1695745332108975, + 2.215284154678095, + 2.2544638302214066, + 2.287113559840832, + 2.313233343536374, + 2.3328231813080302, + 2.3458830731558002, + 2.3524130190796866, + 2.352413019079686, + 2.3458830731558007, + 2.3328231813080302, + 2.3132333435363743, + 2.2871135598408325, + 2.254463830221406, + 2.215284154678095, + 2.1695745332108975, + 2.117334965819814, + 2.0585654525048467, + 1.993265993265994, + 1.9214365881032553, + 1.8430772370166317, + 1.7581879400061222, + 1.6667686970717275, + 1.5688195082134477, + 1.4643403734312825, + 1.3533312927252326, + 1.2357922660952965, + 1.1117232935414758, + 0.9811243750637693, + 0.843995510662177, + 0.7003367003367011, + 0.5501479440873385, + 0.39342924191409046, + 0.2301805938169572, + 0.06040199979594002, + -0.1159065401489639, + -0.2987450260177531, + -0.4881134578104278, + -0.6840118355269879, + -0.8864401591674312, + -1.095398428731762, + -1.3108866442199778, + -1.5329048056320789, + -1.7614529129680638, + -1.9965309662279354, + -2.238138965411693, + -2.4862769105193356, + -2.740944801550861, + -3.0021426385062746, + -3.2698704213855727, + -3.544128150188757, + -3.8249158249158235, + -4.112233445566778, + -4.406081012141618, + -4.706458524640343, + -5.013365983062954, + -5.326803387409448, + -5.646770737679828, + -5.973268033874095, + -6.306295275992246, + -6.645852464034281, + -6.991939598000204, + -7.3445566778900115, + -7.703703703703705, + -8.06938067544128, + -8.441587593102746, + -8.820324456688093, + -9.205591266197327, + -9.597388021630444, + -9.995714722987454, + -10.40057137026834, + -10.811957963473112, + -11.229874502601778, + -11.65432098765432, + -12.085297418630756, + -12.522803795531068, + -12.966840118355268, + -13.41740638710336, + -13.87450260177533, + -14.338128762371184, + -14.808284868890931, + -15.284970921334555, + -15.768186919702073, + -16.257932863993467, + -16.75420875420875, + -17.257014590347925, + -17.766350372410976, + -18.282216100397925, + -18.804611774308743 + ], + [ + 0.687276808488928, + 0.8178757269666361, + 0.941944699520457, + 1.059483726150391, + 1.170492806856442, + 1.2749719416386078, + 1.3729211304968878, + 1.464340373431281, + 1.5492296704417914, + 1.627589021528415, + 1.6994184266911536, + 1.7647178859300063, + 1.8234873992449745, + 1.8757269666360572, + 1.9214365881032538, + 1.960616263646566, + 1.9932659932659929, + 2.019385776961534, + 2.0389756147331903, + 2.052035506580961, + 2.058565452504846, + 2.0585654525048462, + 2.052035506580961, + 2.03897561473319, + 2.0193857769615344, + 1.9932659932659933, + 1.9606162636465665, + 1.9214365881032545, + 1.8757269666360572, + 1.823487399244975, + 1.764717885930007, + 1.699418426691154, + 1.6275890215284154, + 1.5492296704417914, + 1.4643403734312825, + 1.3729211304968878, + 1.2749719416386083, + 1.170492806856443, + 1.0594837261503929, + 0.941944699520457, + 0.8178757269666357, + 0.6872768084889302, + 0.5501479440873384, + 0.4064891337618611, + 0.2563003775124984, + 0.09958167533925186, + -0.06366697275788136, + -0.2334455667788999, + -0.40975410672380386, + -0.592592592592593, + -0.781961024385266, + -0.9778594021018259, + -1.1802877257422713, + -1.3892459953066016, + -1.6047342107948157, + -1.8267523722069172, + -2.0553004795429035, + -2.2903785328027757, + -2.5319865319865307, + -2.7801244770941733, + -3.034792368125701, + -3.2959902050811145, + -3.56371798796041, + -3.837975716763594, + -4.118763391490663, + -4.406081012141618, + -4.699928578716458, + -5.00030609121518, + -5.307213549637791, + -5.6206509539842875, + -5.940618304254668, + -6.267115600448932, + -6.6001428425670845, + -6.939700030609121, + -7.2857871645750425, + -7.638404244464848, + -7.997551270278541, + -8.36322824201612, + -8.735435159677582, + -9.11417202326293, + -9.499438832772167, + -9.891235588205284, + -10.289562289562285, + -10.69441893684318, + -11.105805530047952, + -11.523722069176618, + -11.94816855422916, + -12.379144985205588, + -12.816651362105908, + -13.260687684930108, + -13.711253953678192, + -14.168350168350168, + -14.631976328946022, + -15.102132435465771, + -15.578818487909395, + -16.062034486276907, + -16.55178043056831, + -17.04805632078359, + -17.55086215692277, + -18.060197938985816 + ], + [ + 0.13223140495867725, + 0.27589021528415625, + 0.41301907968574714, + 0.5436179981634526, + 0.6676869707172739, + 0.7852259973472102, + 0.8962350780532606, + 1.0007142128354247, + 1.0986634016937056, + 1.1900826446280997, + 1.2749719416386087, + 1.353331292725232, + 1.425160697887971, + 1.4904601571268241, + 1.5492296704417914, + 1.6014692378328743, + 1.6471788593000716, + 1.686358534843383, + 1.7190082644628104, + 1.7451280481583515, + 1.7647178859300072, + 1.7777777777777781, + 1.7843077237016636, + 1.7843077237016627, + 1.7777777777777777, + 1.7647178859300072, + 1.7451280481583515, + 1.7190082644628097, + 1.6863585348433834, + 1.647178859300072, + 1.6014692378328745, + 1.5492296704417918, + 1.4904601571268241, + 1.4251606978879705, + 1.3533312927252323, + 1.2749719416386085, + 1.1900826446280994, + 1.098663401693705, + 1.0007142128354252, + 0.89623507805326, + 0.7852259973472092, + 0.6676869707172743, + 0.543617998163453, + 0.41301907968574636, + 0.2758902152841544, + 0.13223140495867836, + -0.017957351290684292, + -0.1746760534639322, + -0.3379247015610655, + -0.5077032955820842, + -0.6840118355269865, + -0.8668503213957759, + -1.0562187531884506, + -1.2521171309050103, + -1.454545454545454, + -1.6635037241097845, + -1.8789919395980004, + -2.1010101010101017, + -2.329558208346086, + -2.564636261605958, + -2.8062442607897156, + -3.054382205897358, + -3.3090500969288836, + -3.5702479338842967, + -3.8379757167635957, + -4.11223344556678, + -4.393021120293849, + -4.680338740944801, + -4.974186307519641, + -5.274563820018366, + -5.581471278440976, + -5.89490868278747, + -6.214876033057851, + -6.541373329252117, + -6.87440057137027, + -7.213957759412303, + -7.560044893378227, + -7.912661973268034, + -8.271808999081728, + -8.637485970819302, + -9.009692888480771, + -9.388429752066116, + -9.773696561575347, + -10.16549331700847, + -10.563820018365472, + -10.968676665646367, + -11.380063258851138, + -11.797979797979796, + -12.222426283032346, + -12.653402714008774, + -13.090909090909088, + -13.534945413733293, + -13.985511682481377, + -14.442607897153355, + -14.906234057749211, + -15.376390164268948, + -15.853076216712584, + -16.336292215080093, + -16.826038159371496, + -17.32231404958678 + ], + [ + -0.42934394449546076, + -0.27262524232221264, + -0.12243648607284996, + 0.02122232425262638, + 0.15835118865421727, + 0.28895010713192537, + 0.41301907968574625, + 0.5305581063156808, + 0.6415671870217321, + 0.7460463218038975, + 0.843995510662177, + 0.9354147535965716, + 1.0203040506070806, + 1.0986634016937047, + 1.1704928068564426, + 1.235792266095296, + 1.2945617794102642, + 1.3468013468013462, + 1.3925109682685441, + 1.431690643811856, + 1.464340373431282, + 1.4904601571268237, + 1.51004999489848, + 1.5231098867462496, + 1.5296398326701353, + 1.5296398326701355, + 1.52310988674625, + 1.5100499948984794, + 1.4904601571268237, + 1.4643403734312825, + 1.4316906438118557, + 1.3925109682685441, + 1.3468013468013469, + 1.294561779410264, + 1.2357922660952965, + 1.170492806856443, + 1.0986634016937047, + 1.0203040506070808, + 0.9354147535965719, + 0.8439955106621773, + 0.7460463218038973, + 0.641567187021733, + 0.5305581063156823, + 0.41301907968574636, + 0.28895010713192504, + 0.1583511886542196, + 0.021222324252627656, + -0.1224364860728496, + -0.2726252423222122, + -0.4293439444954601, + -0.592592592592592, + -0.7623711866136105, + -0.9386797265585146, + -1.1215182124273038, + -1.3108866442199765, + -1.5067850219365366, + -1.7092133455769818, + -1.9181716151413126, + -2.1336598306295267, + -2.3556779920416275, + -2.5842260993776147, + -2.8193041526374865, + -3.060912151821241, + -3.3090500969288836, + -3.5637179879604117, + -3.824915824915825, + -4.092643607795123, + -4.366901336598305, + -4.647689011325374, + -4.935006631976329, + -5.2288541985511685, + -5.529231711049891, + -5.836139169472502, + -6.149576573818997, + -6.469543924089379, + -6.796041220283643, + -7.129068462401795, + -7.4686256504438315, + -7.814712784409755, + -8.167329864299559, + -8.526476890113255, + -8.892153861850831, + -9.264360779512291, + -9.643097643097644, + -10.028364452606874, + -10.420161208039998, + -10.818487909397, + -11.223344556677887, + -11.634731149882667, + -12.052647689011323, + -12.477094174063867, + -12.908070605040301, + -13.345576981940614, + -13.78961330476482, + -14.240179573512906, + -14.697275788184875, + -15.160901948780737, + -15.631058055300475, + -16.10774410774411, + -16.590960106111623 + ], + [ + -0.9974492398734824, + -0.8276706458524625, + -0.6644219977553298, + -0.5077032955820839, + -0.35751453933272126, + -0.2138557290072436, + -0.07672686460565137, + 0.05387205387205363, + 0.1779410264258754, + 0.2954800530558117, + 0.4064891337618617, + 0.5109682685440267, + 0.6089174574023062, + 0.7003367003367007, + 0.7852259973472093, + 0.8635853484338334, + 0.9354147535965724, + 1.0007142128354247, + 1.0594837261503935, + 1.1117232935414758, + 1.1574329150086728, + 1.1966125905519844, + 1.2292623201714115, + 1.2553821038669524, + 1.2749719416386083, + 1.2880318334863792, + 1.2945617794102646, + 1.2945617794102642, + 1.2880318334863792, + 1.2749719416386087, + 1.2553821038669526, + 1.2292623201714112, + 1.1966125905519847, + 1.1574329150086726, + 1.1117232935414756, + 1.059483726150393, + 1.0007142128354252, + 0.9354147535965719, + 0.8635853484338336, + 0.7852259973472095, + 0.7003367003367001, + 0.6089174574023064, + 0.5109682685440264, + 0.4064891337618611, + 0.2954800530558104, + 0.17794102642587545, + 0.053872053872054154, + -0.07672686460565245, + -0.21385572900724442, + -0.35751453933272176, + -0.507703295582083, + -0.6644219977553311, + -0.8276706458524643, + -0.9974492398734829, + -1.1737577798183854, + -1.3565962656871746, + -1.5459646974798493, + -1.7418630751964095, + -1.9442913988368526, + -2.153249668401183, + -2.3687378838893993, + -2.590756045301501, + -2.8193041526374847, + -3.054382205897357, + -3.2959902050811145, + -3.544128150188757, + -3.798796041220285, + -4.059993878175696, + -4.327721661054994, + -4.601979389858178, + -4.882767064585247, + -5.1700846852361995, + -5.463932251811039, + -5.764309764309765, + -6.0712172227323755, + -6.384654627078869, + -6.70462197734925, + -7.031119273543517, + -7.364146515661668, + -7.703703703703702, + -8.049790837669628, + -8.402407917559433, + -8.761554943373124, + -9.127231915110706, + -9.499438832772165, + -9.878175696357518, + -10.263442505866749, + -10.655239261299865, + -11.053565962656874, + -11.458422609937763, + -11.869809203142534, + -12.2877257422712, + -12.712172227323741, + -13.143148658300177, + -13.58065503520049, + -14.02469135802469, + -14.47525762677278, + -14.932353841444751, + -15.395980002040613, + -15.866136108560353 + ], + [ + -1.572084481175391, + -1.389245995306601, + -1.2129374553616974, + -1.0431588613406801, + -0.8799102132435475, + -0.7231915110702993, + -0.5730027548209367, + -0.42934394449546076, + -0.2922150800938681, + -0.16161616161616177, + -0.03754718906234089, + 0.07999183756759498, + 0.1910009182736454, + 0.2954800530558104, + 0.3934292419140899, + 0.4848484848484844, + 0.5697377818589939, + 0.6480971329456173, + 0.7199265381083564, + 0.7852259973472093, + 0.8439955106621773, + 0.8962350780532597, + 0.9419446995204572, + 0.9811243750637687, + 1.0137741046831954, + 1.0398938883787368, + 1.0594837261503927, + 1.0725436179981633, + 1.0790735639220486, + 1.0790735639220486, + 1.0725436179981633, + 1.0594837261503927, + 1.039893888378737, + 1.0137741046831954, + 0.981124375063769, + 0.941944699520457, + 0.8962350780532599, + 0.8439955106621773, + 0.7852259973472095, + 0.7199265381083563, + 0.6480971329456175, + 0.5697377818589944, + 0.4848484848484851, + 0.39342924191409046, + 0.2954800530558105, + 0.1910009182736461, + 0.07999183756759548, + -0.03754718906234042, + -0.16161616161616174, + -0.2922150800938684, + -0.4293439444954591, + -0.5730027548209363, + -0.723191511070299, + -0.879910213243547, + -1.0431588613406788, + -1.2129374553616974, + -1.3892459953066014, + -1.5720844811753905, + -1.7614529129680634, + -1.9573512906846235, + -2.1597796143250685, + -2.3687378838893993, + -2.584226099377613, + -2.8062442607897147, + -3.034792368125701, + -3.2698704213855727, + -3.51147842056933, + -3.7596163656769708, + -4.014284256708498, + -4.275482093663912, + -4.5432098765432105, + -4.817467605346391, + -5.098255280073461, + -5.385572900724416, + -5.679420467299256, + -5.9797979797979774, + -6.286705438220588, + -6.6001428425670845, + -6.920110192837465, + -7.24660748903173, + -7.579634731149886, + -7.919191919191918, + -8.265279053157839, + -8.61789613304765, + -8.977043158861338, + -9.34272013059892, + -9.714927048260382, + -10.093663911845727, + -10.478930721354965, + -10.870727476788081, + -11.269054178145083, + -11.673910825425978, + -12.085297418630748, + -12.503213957759414, + -12.927660442811959, + -13.358636873788384, + -13.796143250688708, + -14.240179573512904, + -14.690745842260995, + -15.147842056932967 + ], + [ + -2.1532496684011853, + -1.9573512906846253, + -1.7679828588919504, + -1.5851443730231631, + -1.408835833078259, + -1.2390572390572396, + -1.0758085909601065, + -0.9190898887868602, + -0.768901132537497, + -0.6252423222120198, + -0.48811345781042803, + -0.3575145393327226, + -0.23344556677890127, + -0.1159065401489654, + -0.0048974594429154195, + 0.09958167533925, + 0.19753086419752997, + 0.28895010713192426, + 0.3738394041424342, + 0.45219875522905784, + 0.524028160391796, + 0.589327619630649, + 0.6480971329456173, + 0.7003367003366994, + 0.7460463218038967, + 0.7852259973472087, + 0.8178757269666354, + 0.8439955106621765, + 0.8635853484338327, + 0.8766452402816033, + 0.8831751862054886, + 0.8831751862054888, + 0.8766452402816037, + 0.8635853484338327, + 0.8439955106621769, + 0.8178757269666357, + 0.7852259973472092, + 0.7460463218038972, + 0.7003367003367001, + 0.6480971329456178, + 0.5893276196306496, + 0.5240281603917969, + 0.4521987552290584, + 0.37383940414243444, + 0.28895010713192515, + 0.1975308641975313, + 0.0995816753392514, + -0.0048974594429138235, + -0.11590654014896445, + -0.23344556677890038, + -0.3575145393327206, + -0.4881134578104271, + -0.625242322212019, + -0.7689011325374963, + -0.9190898887868575, + -1.0758085909601054, + -1.2390572390572387, + -1.4088358330782573, + -1.5851443730231596, + -1.767982858891949, + -1.9573512906846235, + -2.1532496684011835, + -2.3556779920416266, + -2.5646362616059575, + -2.7801244770941733, + -3.0021426385062746, + -3.230690745842261, + -3.465768799102131, + -3.707376798285888, + -3.9555147433935307, + -4.210182634425059, + -4.47138047138047, + -4.739108254259768, + -5.013365983062952, + -5.294153657790021, + -5.581471278440973, + -5.875318845015813, + -6.175696357514537, + -6.482603815937148, + -6.796041220283642, + -7.116008570554026, + -7.44250586674829, + -7.775533108866439, + -8.115090296908479, + -8.461177430874397, + -8.81379451076421, + -9.172941536577898, + -9.538618508315475, + -9.910825425976942, + -10.289562289562287, + -10.67482909907152, + -11.066625854504641, + -11.464952555861643, + -11.869809203142536, + -12.281195796347308, + -12.699112335475967, + -13.123558820528517, + -13.554535251504946, + -13.992041628405268, + -14.436077951229464 + ], + [ + -2.7409448015508597, + -2.5319865319865285, + -2.329558208346084, + -2.133659830629526, + -1.9442913988368513, + -1.7614529129680618, + -1.5851443730231578, + -1.415365779002141, + -1.2521171309050074, + -1.0953984287317593, + -0.9452096724823975, + -0.8015508621569207, + -0.664421997755329, + -0.5338230792776226, + -0.40975410672380175, + -0.2922150800938663, + -0.1812059993878159, + -0.07672686460565092, + 0.021222324252629488, + 0.11264156718702356, + 0.1975308641975324, + 0.27589021528415625, + 0.34771962044689464, + 0.41301907968574736, + 0.4717885930007155, + 0.5240281603917978, + 0.5697377818589949, + 0.6089174574023066, + 0.6415671870217334, + 0.6676869707172746, + 0.6872768084889305, + 0.7003367003367011, + 0.7068666462605866, + 0.7068666462605863, + 0.7003367003367009, + 0.6872768084889302, + 0.6676869707172742, + 0.641567187021733, + 0.6089174574023063, + 0.5697377818589944, + 0.5240281603917969, + 0.47178859300071474, + 0.4130190796857467, + 0.3477196204468933, + 0.2758902152841546, + 0.19753086419753127, + 0.11264156718702191, + 0.02122232425262726, + -0.0767268646056528, + -0.18120599938781815, + -0.29221508009386793, + -0.40975410672380386, + -0.5338230792776253, + -0.6644219977553318, + -0.8015508621569227, + -0.9452096724824, + -1.0953984287317629, + -1.2521171309050108, + -1.4153657790021428, + -1.5851443730231614, + -1.7614529129680652, + -1.9442913988368544, + -2.1336598306295276, + -2.3295582083460875, + -2.531986531986533, + -2.7409448015508633, + -2.9564330170390796, + -3.178451178451179, + -3.406999285787166, + -3.6420773390470376, + -3.8836853382307943, + -4.131823283338435, + -4.386491174369963, + -4.647689011325377, + -4.915416794204675, + -5.189674523007856, + -5.470462197734927, + -5.757779818385881, + -6.05162738496072, + -6.352004897459443, + -6.658912355882057, + -6.97234976022855, + -7.292317110498928, + -7.618814406693197, + -7.951841648811346, + -8.291398836853386, + -8.637485970819306, + -8.990103050709111, + -9.349250076522807, + -9.714927048260384, + -10.087133965921844, + -10.465870829507196, + -10.851137639016427, + -11.24293439444955, + -11.641261095806552, + -12.04611774308744, + -12.457504336292217, + -12.875420875420877, + -13.299867360473428, + -13.730843791449855 + ], + [ + -3.3351698806244254, + -3.1131517192123237, + -2.897663503724108, + -2.6887052341597797, + -2.486276910519334, + -2.290378532802774, + -2.1010101010100994, + -1.9181716151413117, + -1.7418630751964073, + -1.5720844811753891, + -1.408835833078256, + -1.2521171309050088, + -1.1019283746556465, + -0.9582695643301693, + -0.8211406999285782, + -0.6905417814508714, + -0.5664728088970508, + -0.4489337822671151, + -0.33792470156106424, + -0.23344556677889972, + -0.13549637792061953, + -0.044077134986225674, + 0.04081216202428406, + 0.11917151311090746, + 0.19100091827364607, + 0.25630037751249923, + 0.31506989082746706, + 0.3673094582185493, + 0.4130190796857467, + 0.4521987552290586, + 0.4848484848484853, + 0.5109682685440265, + 0.5305581063156826, + 0.543617998163453, + 0.5501479440873384, + 0.5501479440873385, + 0.543617998163453, + 0.5305581063156823, + 0.5109682685440264, + 0.48484848484848503, + 0.4521987552290584, + 0.4130190796857467, + 0.3673094582185494, + 0.31506989082746667, + 0.2563003775124987, + 0.1910009182736459, + 0.11917151311090722, + 0.04081216202428327, + -0.044077134986226084, + -0.13549637792062075, + -0.2334455667788999, + -0.3379247015610652, + -0.44893378226711583, + -0.5664728088970519, + -0.6905417814508721, + -0.8211406999285789, + -0.9582695643301706, + -1.101928374655648, + -1.2521171309050092, + -1.4088358330782573, + -1.5720844811753907, + -1.741863075196409, + -1.9181716151413113, + -2.1010101010101008, + -2.2903785328027757, + -2.486276910519335, + -2.688705234159781, + -2.8976635037241096, + -3.1131517192123255, + -3.335169880624427, + -3.5637179879604135, + -3.7987960412202835, + -4.040404040404041, + -4.288541985511683, + -4.543209876543211, + -4.804407713498622, + -5.072135496377921, + -5.346393225181105, + -5.627180899908174, + -5.9144985205591265, + -6.208346087133969, + -6.508723599632691, + -6.815631058055299, + -7.129068462401798, + -7.449035812672177, + -7.775533108866446, + -8.108560350984595, + -8.44811753902663, + -8.794204672992555, + -9.14682175288236, + -9.50596877869605, + -9.87164575043363, + -10.24385266809509, + -10.622589531680443, + -11.007856341189676, + -11.399653096622792, + -11.797979797979801, + -12.202836445260688, + -12.614223038465468, + -13.032139577594126 + ], + [ + -3.9359249056218757, + -3.7008468523620026, + -3.472298745026017, + -3.2502805836139173, + -3.0347923681257014, + -2.8258340985613706, + -2.6234057749209256, + -2.4275073972043675, + -2.238138965411693, + -2.0553004795429035, + -1.878991939598, + -1.7092133455769818, + -1.5459646974798489, + -1.3892459953066014, + -1.2390572390572392, + -1.0953984287317622, + -0.9582695643301706, + -0.8276706458524643, + -0.7036016732986425, + -0.5860626466687073, + -0.4750535659626567, + -0.37057443118049216, + -0.2726252423222115, + -0.18120599938781812, + -0.09631670237730838, + -0.017957351290684764, + 0.05387205387205385, + 0.11917151311090668, + 0.17794102642587495, + 0.23018059381695744, + 0.2758902152841546, + 0.3150698908274665, + 0.34771962044689336, + 0.37383940414243433, + 0.3934292419140904, + 0.406489133761861, + 0.41301907968574636, + 0.41301907968574636, + 0.4064891337618611, + 0.39342924191409046, + 0.3738394041424344, + 0.3477196204468933, + 0.31506989082746667, + 0.2758902152841547, + 0.23018059381695735, + 0.17794102642587517, + 0.11917151311090718, + 0.05387205387205392, + -0.01795735129068475, + -0.09631670237730873, + -0.18120599938781728, + -0.2726252423222119, + -0.3705744311804919, + -0.47505356596265713, + -0.5860626466687069, + -0.7036016732986428, + -0.8276706458524641, + -0.9582695643301706, + -1.0953984287317615, + -1.2390572390572387, + -1.3892459953066014, + -1.545964697479849, + -1.709213345576981, + -1.8789919395979997, + -2.0553004795429035, + -2.2381389654116925, + -2.4275073972043675, + -2.6234057749209256, + -2.825834098561371, + -3.034792368125702, + -3.2502805836139177, + -3.4722987450260168, + -3.7008468523620035, + -3.9359249056218752, + -4.177532904805632, + -4.425670849913272, + -4.680338740944801, + -4.941536577900214, + -5.209264360779512, + -5.483522089582694, + -5.7643097643097665, + -6.051627384960718, + -6.3454749515355555, + -6.6458524640342835, + -6.952759922456891, + -7.26619732680339, + -7.586164677073769, + -7.9126619732680314, + -8.245689215386186, + -8.585246403428222, + -8.93133353739414, + -9.283950617283951, + -9.643097643097642, + -10.008774614835223, + -10.380981532496683, + -10.759718396082029, + -11.144985205591269, + -11.536781961024385, + -11.935108662381392, + -12.33996530966228 + ], + [ + -4.543209876543212, + -4.295071931435567, + -4.053463932251811, + -3.8183858789919416, + -3.5898377716559553, + -3.3678196102438527, + -3.1523313947556373, + -2.9433731251913087, + -2.740944801550863, + -2.545046423834303, + -2.355677992041629, + -2.1728395061728403, + -1.996530966227937, + -1.8267523722069186, + -1.6635037241097854, + -1.5067850219365377, + -1.3565962656871755, + -1.2129374553616987, + -1.0758085909601063, + -0.9452096724824008, + -0.8211406999285791, + -0.7036016732986439, + -0.5925925925925928, + -0.4881134578104285, + -0.39016426895214806, + -0.2987450260177542, + -0.2138557290072447, + -0.1354963779206212, + -0.06366697275788247, + 0.0016324864809706963, + 0.06040199979593863, + 0.11264156718702123, + 0.1583511886542186, + 0.19753086419753046, + 0.2301805938169571, + 0.25630037751249846, + 0.27589021528415436, + 0.2889501071319251, + 0.2954800530558104, + 0.2954800530558105, + 0.28895010713192515, + 0.2758902152841546, + 0.2563003775124987, + 0.23018059381695738, + 0.19753086419753071, + 0.1583511886542191, + 0.11264156718702183, + 0.06040199979593924, + 0.0016324864809712653, + -0.06366697275788202, + -0.13549637792062003, + -0.21385572900724392, + -0.2987450260177532, + -0.39016426895214784, + -0.4881134578104269, + -0.5925925925925922, + -0.7036016732986428, + -0.8211406999285787, + -0.9452096724823988, + -1.0758085909601056, + -1.2129374553616974, + -1.3565962656871746, + -1.506785021936536, + -1.6635037241097839, + -1.826752372206917, + -1.9965309662279354, + -2.17283950617284, + -2.3556779920416275, + -2.5450464238343016, + -2.740944801550862, + -2.9433731251913073, + -3.1523313947556355, + -3.367819610243852, + -3.589837771655953, + -3.818385878991939, + -4.053463932251809, + -4.295071931435567, + -4.543209876543209, + -4.797877767574736, + -5.059075604530148, + -5.3268033874094485, + -5.60106111621263, + -5.8818487909396975, + -6.169166411590654, + -6.463013978165491, + -6.76339149066422, + -7.070298949086827, + -7.383736353433321, + -7.703703703703704, + -8.030200999897968, + -8.363228242016117, + -8.702785430058157, + -9.048872564024077, + -9.401489643913887, + -9.760636669727578, + -10.126313641465153, + -10.49852055912662, + -10.877257422711967, + -11.262524232221203, + -11.654320987654321 + ], + [ + -5.157024793388427, + -4.895826956433012, + -4.641159065401485, + -4.393021120293845, + -4.151413121110088, + -3.9163350678502162, + -3.68778696051423, + -3.465768799102131, + -3.2502805836139146, + -3.0413223140495838, + -2.8388939904091393, + -2.6429956126925798, + -2.4536271808999066, + -2.2707886950311176, + -2.094480155086214, + -1.9247015610651956, + -1.7614529129680632, + -1.6047342107948157, + -1.4545454545454526, + -1.310886644219976, + -1.173757779818384, + -1.0431588613406784, + -0.9190898887868567, + -0.8015508621569215, + -0.6905417814508709, + -0.5860626466687061, + -0.48811345781042637, + -0.39669421487603207, + -0.3118049178655228, + -0.23344556677889916, + -0.16161616161616066, + -0.0963167023773076, + -0.03754718906233956, + 0.014692378328742817, + 0.060401999795939965, + 0.099581675339252, + 0.13223140495867836, + 0.15835118865421963, + 0.17794102642587548, + 0.1910009182736461, + 0.19753086419753133, + 0.19753086419753127, + 0.1910009182736459, + 0.17794102642587517, + 0.15835118865421913, + 0.13223140495867797, + 0.09958167533925125, + 0.060401999795939236, + 0.014692378328741847, + -0.03754718906234087, + -0.0963167023773084, + -0.16161616161616177, + -0.23344556677890047, + -0.3118049178655245, + -0.3966942148760332, + -0.4881134578104278, + -0.5860626466687078, + -0.6905417814508732, + -0.801550862156923, + -0.919089888786859, + -1.0431588613406801, + -1.173757779818387, + -1.3108866442199778, + -1.454545454545455, + -1.6047342107948177, + -1.7614529129680656, + -1.9247015610651992, + -2.094480155086216, + -2.2707886950311202, + -2.4536271808999097, + -2.642995612692584, + -2.8388939904091424, + -3.0413223140495877, + -3.2502805836139186, + -3.4657687991021344, + -3.6877869605142335, + -3.9163350678502207, + -4.151413121110092, + -4.39302112029385, + -4.6411590654014905, + -4.895826956433021, + -5.157024793388431, + -5.4247525762677276, + -5.699010305070914, + -5.979797979797981, + -6.267115600448938, + -6.560963167023776, + -6.861340679522499, + -7.168248137945112, + -7.481685542291605, + -7.801652892561983, + -8.128150188756253, + -8.461177430874402, + -8.800734618916442, + -9.146821752882362, + -9.499438832772167, + -9.858585858585862, + -10.224262830323438, + -10.596469747984905, + -10.975206611570252 + ], + [ + -5.777369656157533, + -5.503111927354349, + -5.23538414447505, + -4.97418630751964, + -4.719518416488112, + -4.471380471380469, + -4.2297724721967125, + -3.9946944189368425, + -3.7661463116008553, + -3.544128150188754, + -3.328639934700539, + -3.119681665136209, + -2.9172533414957647, + -2.7213549637792047, + -2.531986531986531, + -2.349148046117742, + -2.1728395061728385, + -2.003060912151821, + -1.839812264054687, + -1.6830935618814398, + -1.5329048056320773, + -1.3892459953066005, + -1.2521171309050088, + -1.1215182124273029, + -0.9974492398734816, + -0.879910213243546, + -0.7689011325374954, + -0.6644219977553307, + -0.5664728088970507, + -0.47505356596265647, + -0.3901642689521473, + -0.3118049178655235, + -0.23997551270278483, + -0.17467605346393178, + -0.11590654014896401, + -0.06366697275788125, + -0.017957351290684265, + 0.02122232425262771, + 0.05387205387205418, + 0.07999183756759551, + 0.09958167533925141, + 0.11264156718702195, + 0.11917151311090726, + 0.11917151311090722, + 0.11264156718702184, + 0.09958167533925126, + 0.07999183756759526, + 0.05387205387205393, + 0.021222324252627225, + -0.017957351290684813, + -0.06366697275788176, + -0.11590654014896443, + -0.17467605346393245, + -0.2399755127027858, + -0.3118049178655239, + -0.39016426895214784, + -0.4750535659626572, + -0.5664728088970519, + -0.664421997755331, + -0.7689011325374964, + -0.8799102132435469, + -0.9974492398734829, + -1.121518212427303, + -1.2521171309050096, + -1.3892459953066019, + -1.532904805632079, + -1.6830935618814418, + -1.8398122640546883, + -2.0030609121518217, + -2.1728395061728403, + -2.3491480461177443, + -2.531986531986532, + -2.7213549637792065, + -2.9172533414957664, + -3.1196816651362123, + -3.328639934700541, + -3.544128150188757, + -3.766146311600858, + -3.9946944189368447, + -4.229772472196714, + -4.471380471380474, + -4.719518416488114, + -4.9741863075196395, + -5.235384144475056, + -5.503111927354352, + -5.777369656157539, + -6.0581573308846055, + -6.345474951535557, + -6.6393225181104, + -6.939700030609123, + -7.246607489031731, + -7.560044893378229, + -7.880012243648608, + -8.206509539842877, + -8.539536781961026, + -8.87909397000306, + -9.225181103968985, + -9.577798183858791, + -9.936945209672487, + -10.302622181410062 + ], + [ + -6.404244464850525, + -6.11692684419957, + -5.836139169472501, + -5.561881440669319, + -5.294153657790021, + -5.032955820834608, + -4.77828792980308, + -4.53014998469544, + -4.288541985511682, + -4.053463932251811, + -3.8249158249158235, + -3.602897663503723, + -3.387409448015508, + -3.1784511784511777, + -2.9760228548107333, + -2.7801244770941738, + -2.5907560453015, + -2.407917559432711, + -2.2316090194878067, + -2.0618304254667885, + -1.8985817773696556, + -1.7418630751964086, + -1.5916743189470457, + -1.4480155086215694, + -1.3108866442199774, + -1.1802877257422713, + -1.0562187531884502, + -0.9386797265585147, + -0.8276706458524641, + -0.7231915110702991, + -0.6252423222120191, + -0.5338230792776248, + -0.44893378226711544, + -0.3705744311804916, + -0.2987450260177532, + -0.23344556677889988, + -0.17467605346393222, + -0.12243648607284952, + -0.07672686460565248, + -0.03754718906234042, + -0.004897459442913865, + 0.02122232425262724, + 0.04081216202428328, + 0.053872053872053925, + 0.060401999795939236, + 0.06040199979593923, + 0.05387205387205392, + 0.04081216202428327, + 0.021222324252627253, + -0.004897459442914093, + -0.037547189062340475, + -0.07672686460565245, + -0.12243648607284978, + -0.17467605346393245, + -0.23344556677889994, + -0.2987450260177532, + -0.3705744311804919, + -0.4489337822671159, + -0.5338230792776244, + -0.6252423222120191, + -0.7231915110702989, + -0.8276706458524643, + -0.938679726558514, + -1.05621875318845, + -1.1802877257422713, + -1.3108866442199778, + -1.4480155086215698, + -1.591674318947046, + -1.7418630751964086, + -1.8985817773696565, + -2.0618304254667894, + -2.2316090194878067, + -2.4079175594327107, + -2.5907560453014997, + -2.7801244770941747, + -2.976022854810733, + -3.178451178451178, + -3.387409448015509, + -3.6028976635037244, + -3.824915824915824, + -4.0534639322518125, + -4.288541985511682, + -4.530149984695438, + -4.778287929803083, + -5.032955820834609, + -5.294153657790024, + -5.561881440669321, + -5.836139169472502, + -6.116926844199574, + -6.4042444648505255, + -6.698092031425363, + -6.99846954392409, + -7.305377002346698, + -7.618814406693198, + -7.938781756963576, + -8.265279053157839, + -8.598306295275995, + -8.937863483318027, + -9.283950617283955, + -9.63656769717376 + ], + [ + -7.0376492194674025, + -6.737271706968675, + -6.443424140393837, + -6.156106519742885, + -5.875318845015816, + -5.601061116212631, + -5.333333333333333, + -5.072135496377922, + -4.817467605346393, + -4.569329660238751, + -4.327721661054994, + -4.092643607795123, + -3.864095500459137, + -3.6420773390470362, + -3.426589123558821, + -3.217630853994491, + -3.0152025303540464, + -2.819304152637487, + -2.629935720844812, + -2.447097234976024, + -2.2707886950311194, + -2.1010101010101017, + -1.937761452912968, + -1.7810427507397213, + -1.6308539944903584, + -1.4871951841648818, + -1.3500663197632898, + -1.219467401285584, + -1.0953984287317626, + -0.9778594021018269, + -0.8668503213957763, + -0.7623711866136115, + -0.6644219977553314, + -0.5730027548209369, + -0.4881134578104278, + -0.40975410672380386, + -0.3379247015610655, + -0.2726252423222122, + -0.21385572900724448, + -0.16161616161616177, + -0.11590654014896447, + -0.07672686460565281, + -0.04407713498622608, + -0.01795735129068475, + 0.0016324864809712653, + 0.014692378328741845, + 0.021222324252627222, + 0.021222324252627257, + 0.014692378328741939, + 0.0016324864809712785, + -0.017957351290684525, + -0.04407713498622581, + -0.07672686460565245, + -0.11590654014896444, + -0.16161616161616132, + -0.21385572900724398, + -0.2726252423222119, + -0.3379247015610652, + -0.4097541067238032, + -0.48811345781042714, + -0.5730027548209363, + -0.6644219977553311, + -0.76237118661361, + -0.8668503213957753, + -0.977859402101826, + -1.0953984287317617, + -1.2194674012855833, + -1.3500663197632885, + -1.4871951841648805, + -1.630853994490358, + -1.7810427507397204, + -1.9377614529129672, + -2.1010101010101003, + -2.270788695031119, + -2.4470972349760225, + -2.62993572084481, + -2.819304152637485, + -3.0152025303540446, + -3.21763085399449, + -3.426589123558819, + -3.6420773390470367, + -3.864095500459136, + -4.092643607795121, + -4.327721661054995, + -4.56932966023875, + -4.817467605346395, + -5.07213549637792, + -5.333333333333331, + -5.601061116212633, + -5.875318845015814, + -6.156106519742881, + -6.443424140393837, + -6.7372717069686745, + -7.0376492194674025, + -7.344556677890011, + -7.657994082236503, + -7.977961432506888, + -8.304458728701151, + -8.637485970819307, + -8.97704315886134 + ], + [ + -7.677583920008165, + -7.364146515661668, + -7.057239057239058, + -6.756861544740335, + -6.463013978165495, + -6.17569635751454, + -5.894908682787472, + -5.62065095398429, + -5.352923171104991, + -5.091725334149578, + -4.83705744311805, + -4.588919498010409, + -4.3473114988266515, + -4.112233445566781, + -3.883685338230794, + -3.6616671768186935, + -3.446178961330478, + -3.237220691766148, + -3.0347923681257023, + -2.8388939904091433, + -2.6495255586164688, + -2.4666870727476806, + -2.290378532802776, + -2.1205999387817585, + -1.957351290684625, + -1.8006325885113779, + -1.6504438322620152, + -1.5067850219365386, + -1.3696561575349464, + -1.23905723905724, + -1.114988266503419, + -0.9974492398734834, + -0.8864401591674327, + -0.7819610243852675, + -0.6840118355269877, + -0.5925925925925931, + -0.5077032955820842, + -0.42934394449546015, + -0.35751453933272176, + -0.2922150800938684, + -0.2334455667789004, + -0.18120599938781817, + -0.13549637792062075, + -0.09631670237730873, + -0.06366697275788202, + -0.03754718906234088, + -0.017957351290684813, + -0.004897459442914092, + 0.0016324864809712783, + 0.0016324864809713078, + -0.004897459442913922, + -0.017957351290684525, + -0.037547189062340475, + -0.06366697275788177, + -0.09631670237730808, + -0.13549637792062003, + -0.18120599938781728, + -0.23344556677889988, + -0.2922150800938673, + -0.3575145393327205, + -0.4293439444954591, + -0.507703295582083, + -0.5925925925925916, + -0.6840118355269861, + -0.7819610243852659, + -0.8864401591674314, + -0.9974492398734819, + -1.1149882665034168, + -1.239057239057238, + -1.3696561575349446, + -1.5067850219365364, + -1.6504438322620127, + -1.800632588511375, + -1.9573512906846229, + -2.1205999387817562, + -2.290378532802773, + -2.4666870727476775, + -2.649525558616466, + -2.8388939904091406, + -3.0347923681256987, + -3.2372206917661464, + -3.446178961330475, + -3.6616671768186886, + -3.8836853382307925, + -4.112233445566777, + -4.347311498826651, + -4.588919498010406, + -4.837057443118046, + -5.091725334149577, + -5.352923171104988, + -5.620650953984284, + -5.894908682787469, + -6.175696357514536, + -6.463013978165494, + -6.756861544740331, + -7.057239057239053, + -7.364146515661667, + -7.677583920008159, + -7.997551270278544, + -8.324048566472808 + ], + [ + -8.324048566472808, + -7.9975512702785405, + -7.677583920008159, + -7.364146515661667, + -7.057239057239056, + -6.756861544740331, + -6.463013978165491, + -6.175696357514539, + -5.894908682787469, + -5.620650953984286, + -5.352923171104988, + -5.091725334149576, + -4.837057443118048, + -4.588919498010406, + -4.347311498826649, + -4.112233445566778, + -3.8836853382307925, + -3.6616671768186912, + -3.446178961330475, + -3.237220691766145, + -3.0347923681256996, + -2.8388939904091406, + -2.649525558616466, + -2.466687072747678, + -2.290378532802774, + -2.1205999387817562, + -1.9573512906846229, + -1.8006325885113759, + -1.6504438322620132, + -1.5067850219365364, + -1.3696561575349446, + -1.2390572390572385, + -1.1149882665034172, + -0.9974492398734814, + -0.8864401591674314, + -0.7819610243852659, + -0.6840118355269865, + -0.5925925925925919, + -0.507703295582083, + -0.4293439444954591, + -0.3575145393327205, + -0.2922150800938679, + -0.23344556677889988, + -0.18120599938781728, + -0.13549637792062003, + -0.0963167023773084, + -0.06366697275788177, + -0.037547189062340475, + -0.017957351290684525, + -0.004897459442913922, + 0.0016324864809713078, + 0.0016324864809712783, + -0.004897459442914092, + -0.017957351290684813, + -0.03754718906234068, + -0.06366697275788202, + -0.09631670237730873, + -0.13549637792062075, + -0.18120599938781773, + -0.2334455667789004, + -0.2922150800938684, + -0.35751453933272176, + -0.4293439444954598, + -0.5077032955820838, + -0.5925925925925931, + -0.6840118355269877, + -0.7819610243852678, + -0.8864401591674322, + -0.997449239873483, + -1.114988266503419, + -1.23905723905724, + -1.369656157534946, + -1.5067850219365377, + -1.6504438322620152, + -1.8006325885113779, + -1.9573512906846242, + -2.1205999387817576, + -2.290378532802776, + -2.4666870727476806, + -2.6495255586164683, + -2.8388939904091446, + -3.0347923681257023, + -3.2372206917661455, + -3.446178961330478, + -3.661667176818692, + -3.8836853382307956, + -4.112233445566781, + -4.34731149882665, + -4.58891949801041, + -4.83705744311805, + -5.091725334149576, + -5.352923171104991, + -5.620650953984287, + -5.894908682787473, + -6.17569635751454, + -6.463013978165492, + -6.756861544740335, + -7.057239057239058, + -7.364146515661671, + -7.677583920008165 + ], + [ + -8.97704315886134, + -8.637485970819304, + -8.304458728701151, + -7.977961432506888, + -7.657994082236507, + -7.344556677890011, + -7.037649219467401, + -6.737271706968678, + -6.443424140393837, + -6.156106519742883, + -5.875318845015814, + -5.601061116212631, + -5.333333333333333, + -5.07213549637792, + -4.817467605346393, + -4.5693296602387505, + -4.327721661054995, + -4.092643607795123, + -3.864095500459136, + -3.642077339047036, + -3.42658912355882, + -3.21763085399449, + -3.0152025303540446, + -2.8193041526374856, + -2.629935720844811, + -2.4470972349760225, + -2.270788695031119, + -2.1010101010101008, + -1.9377614529129676, + -1.7810427507397204, + -1.630853994490358, + -1.487195184164881, + -1.3500663197632892, + -1.2194674012855828, + -1.0953984287317617, + -0.977859402101826, + -0.8668503213957758, + -0.7623711866136105, + -0.6644219977553311, + -0.5730027548209363, + -0.48811345781042714, + -0.40975410672380386, + -0.3379247015610652, + -0.2726252423222119, + -0.21385572900724398, + -0.16161616161616177, + -0.11590654014896444, + -0.07672686460565245, + -0.04407713498622581, + -0.017957351290684525, + 0.0016324864809712785, + 0.014692378328741939, + 0.021222324252627257, + 0.021222324252627222, + 0.014692378328741922, + 0.0016324864809712653, + -0.01795735129068475, + -0.04407713498622608, + -0.0767268646056525, + -0.11590654014896447, + -0.16161616161616177, + -0.21385572900724448, + -0.27262524232221197, + -0.33792470156106524, + -0.40975410672380386, + -0.4881134578104278, + -0.5730027548209372, + -0.664421997755331, + -0.7623711866136111, + -0.8668503213957763, + -0.9778594021018269, + -1.0953984287317622, + -1.2194674012855833, + -1.3500663197632898, + -1.4871951841648818, + -1.630853994490358, + -1.7810427507397204, + -1.937761452912968, + -2.1010101010101017, + -2.2707886950311185, + -2.4470972349760243, + -2.629935720844812, + -2.8193041526374847, + -3.0152025303540464, + -3.2176308539944896, + -3.4265891235588226, + -3.6420773390470362, + -3.8640955004591353, + -4.092643607795124, + -4.327721661054994, + -4.569329660238749, + -4.817467605346393, + -5.072135496377919, + -5.333333333333335, + -5.601061116212631, + -5.875318845015812, + -6.156106519742885, + -6.443424140393837, + -6.737271706968679, + -7.0376492194674025 + ], + [ + -9.63656769717376, + -9.283950617283951, + -8.937863483318027, + -8.598306295275995, + -8.265279053157842, + -7.938781756963576, + -7.618814406693195, + -7.3053770023467015, + -6.99846954392409, + -6.698092031425365, + -6.4042444648505255, + -6.116926844199572, + -5.836139169472504, + -5.561881440669321, + -5.294153657790022, + -5.0329558208346095, + -4.778287929803083, + -4.5301499846954405, + -4.288541985511682, + -4.053463932251812, + -3.8249158249158253, + -3.6028976635037244, + -3.387409448015509, + -3.178451178451179, + -2.9760228548107337, + -2.7801244770941747, + -2.5907560453014997, + -2.4079175594327116, + -2.2316090194878075, + -2.0618304254667894, + -1.8985817773696565, + -1.741863075196409, + -1.5916743189470464, + -1.4480155086215691, + -1.3108866442199778, + -1.1802877257422713, + -1.0562187531884504, + -0.9386797265585146, + -0.8276706458524643, + -0.7231915110702989, + -0.6252423222120191, + -0.5338230792776253, + -0.4489337822671159, + -0.3705744311804919, + -0.2987450260177532, + -0.23344556677890044, + -0.17467605346393245, + -0.12243648607284978, + -0.07672686460565245, + -0.037547189062340475, + -0.004897459442914093, + 0.021222324252627253, + 0.04081216202428327, + 0.05387205387205392, + 0.060401999795939194, + 0.060401999795939236, + 0.053872053872053925, + 0.04081216202428328, + 0.021222324252627434, + -0.004897459442913865, + -0.03754718906234042, + -0.07672686460565248, + -0.12243648607284935, + -0.17467605346393206, + -0.23344556677889988, + -0.2987450260177532, + -0.37057443118049194, + -0.4489337822671152, + -0.5338230792776246, + -0.6252423222120191, + -0.7231915110702991, + -0.8276706458524635, + -0.9386797265585141, + -1.0562187531884502, + -1.1802877257422713, + -1.310886644219977, + -1.4480155086215687, + -1.5916743189470457, + -1.7418630751964086, + -1.8985817773696552, + -2.06183042546679, + -2.2316090194878067, + -2.407917559432709, + -2.5907560453015, + -2.780124477094173, + -2.9760228548107346, + -3.1784511784511777, + -3.3874094480155064, + -3.602897663503725, + -3.8249158249158235, + -4.053463932251808, + -4.288541985511682, + -4.530149984695436, + -4.778287929803082, + -5.032955820834608, + -5.294153657790019, + -5.561881440669319, + -5.836139169472501, + -6.116926844199573, + -6.404244464850525 + ], + [ + -10.302622181410062, + -9.936945209672484, + -9.577798183858791, + -9.225181103968985, + -8.879093970003064, + -8.539536781961026, + -8.206509539842875, + -7.880012243648611, + -7.560044893378229, + -7.246607489031733, + -6.939700030609123, + -6.639322518110399, + -6.34547495153556, + -6.0581573308846055, + -5.7773696561575365, + -5.503111927354354, + -5.235384144475056, + -4.974186307519642, + -4.719518416488114, + -4.471380471380472, + -4.229772472196715, + -3.9946944189368447, + -3.766146311600858, + -3.5441281501887576, + -3.3286399347005418, + -3.1196816651362123, + -2.9172533414957664, + -2.7213549637792074, + -2.531986531986533, + -2.3491480461177443, + -2.1728395061728403, + -2.003060912151822, + -1.839812264054689, + -1.683093561881441, + -1.532904805632079, + -1.3892459953066019, + -1.2521171309050103, + -1.1215182124273038, + -0.9974492398734829, + -0.8799102132435469, + -0.7689011325374964, + -0.6644219977553318, + -0.5664728088970519, + -0.4750535659626572, + -0.39016426895214784, + -0.31180491786552456, + -0.2399755127027858, + -0.17467605346393245, + -0.11590654014896443, + -0.06366697275788176, + -0.017957351290684813, + 0.021222324252627225, + 0.05387205387205393, + 0.07999183756759526, + 0.09958167533925112, + 0.11264156718702184, + 0.11917151311090722, + 0.11917151311090726, + 0.112641567187022, + 0.09958167533925141, + 0.07999183756759551, + 0.05387205387205418, + 0.021222324252627878, + -0.017957351290684154, + -0.06366697275788125, + -0.11590654014896401, + -0.17467605346393195, + -0.2399755127027846, + -0.31180491786552333, + -0.3901642689521473, + -0.47505356596265647, + -0.5664728088970504, + -0.6644219977553302, + -0.7689011325374954, + -0.879910213243546, + -0.997449239873481, + -1.1215182124273024, + -1.2521171309050088, + -1.3892459953066005, + -1.5329048056320764, + -1.6830935618814404, + -1.839812264054687, + -2.0030609121518186, + -2.1728395061728385, + -2.349148046117741, + -2.5319865319865325, + -2.7213549637792047, + -2.917253341495763, + -3.119681665136211, + -3.328639934700539, + -3.5441281501887527, + -3.7661463116008553, + -3.9946944189368394, + -4.229772472196714, + -4.471380471380469, + -4.719518416488109, + -4.97418630751964, + -5.23538414447505, + -5.503111927354352, + -5.777369656157533 + ], + [ + -10.975206611570245, + -10.596469747984896, + -10.224262830323433, + -9.858585858585856, + -9.499438832772164, + -9.146821752882357, + -8.800734618916433, + -8.4611774308744, + -8.128150188756248, + -7.801652892561982, + -7.481685542291601, + -7.168248137945106, + -6.861340679522496, + -6.560963167023772, + -6.267115600448932, + -5.979797979797978, + -5.69901030507091, + -5.424752576267727, + -5.157024793388428, + -4.895826956433016, + -4.641159065401488, + -4.393021120293846, + -4.151413121110089, + -3.916335067850218, + -3.6877869605142317, + -3.4657687991021318, + -3.2502805836139155, + -3.041322314049586, + -2.838893990409141, + -2.642995612692582, + -2.4536271808999075, + -2.2707886950311185, + -2.094480155086215, + -1.924701561065196, + -1.7614529129680636, + -1.604734210794816, + -1.4545454545454537, + -1.3108866442199767, + -1.1737577798183854, + -1.0431588613406788, + -0.9190898887868576, + -0.8015508621569227, + -0.6905417814508721, + -0.5860626466687069, + -0.48811345781042703, + -0.3966942148760331, + -0.3118049178655239, + -0.2334455667788999, + -0.16161616161616132, + -0.09631670237730809, + -0.037547189062340676, + 0.014692378328741934, + 0.06040199979593921, + 0.09958167533925111, + 0.13223140495867744, + 0.15835118865421874, + 0.1779410264258747, + 0.19100091827364532, + 0.19753086419753046, + 0.19753086419753052, + 0.1910009182736451, + 0.17794102642587445, + 0.15835118865421857, + 0.13223140495867713, + 0.0995816753392505, + 0.06040199979593858, + 0.014692378328741151, + -0.03754718906234111, + -0.09631670237730916, + -0.16161616161616255, + -0.23344556677890116, + -0.3118049178655248, + -0.39669421487603407, + -0.48811345781042836, + -0.5860626466687088, + -0.6905417814508734, + -0.8015508621569236, + -0.9190898887868595, + -1.043158861340681, + -1.173757779818387, + -1.31088664421998, + -1.4545454545454555, + -1.6047342107948166, + -1.7614529129680663, + -1.924701561065198, + -2.0944801550862184, + -2.270788695031121, + -2.453627180899909, + -2.642995612692585, + -2.8388939904091437, + -3.041322314049587, + -3.250280583613919, + -3.465768799102133, + -3.687786960514236, + -3.916335067850221, + -4.151413121110091, + -4.3930211202938505, + -4.6411590654014905, + -4.895826956433022, + -5.157024793388432 + ], + [ + -11.654320987654321, + -11.2625242322212, + -10.877257422711967, + -10.49852055912662, + -10.126313641465156, + -9.760636669727578, + -9.401489643913884, + -9.04887256402408, + -8.702785430058157, + -8.36322824201612, + -8.030200999897968, + -7.703703703703702, + -7.3837363534333225, + -7.070298949086827, + -6.763391490664216, + -6.463013978165493, + -6.169166411590654, + -5.8818487909397, + -5.60106111621263, + -5.326803387409447, + -5.059075604530149, + -4.797877767574736, + -4.543209876543209, + -4.295071931435567, + -4.05346393225181, + -3.818385878991939, + -3.589837771655953, + -3.3678196102438527, + -3.152331394755637, + -2.9433731251913073, + -2.740944801550862, + -2.545046423834303, + -2.355677992041628, + -2.1728395061728385, + -1.9965309662279354, + -1.826752372206917, + -1.6635037241097845, + -1.5067850219365366, + -1.3565962656871746, + -1.2129374553616974, + -1.0758085909601056, + -0.9452096724824001, + -0.8211406999285787, + -0.7036016732986428, + -0.5925925925925922, + -0.48811345781042786, + -0.39016426895214784, + -0.2987450260177532, + -0.21385572900724392, + -0.13549637792062003, + -0.06366697275788202, + 0.0016324864809712653, + 0.06040199979593924, + 0.11264156718702183, + 0.1583511886542187, + 0.19753086419753071, + 0.23018059381695738, + 0.2563003775124987, + 0.27589021528415447, + 0.28895010713192515, + 0.2954800530558105, + 0.2954800530558104, + 0.28895010713192515, + 0.27589021528415436, + 0.25630037751249846, + 0.2301805938169571, + 0.1975308641975304, + 0.1583511886542187, + 0.11264156718702134, + 0.06040199979593863, + 0.0016324864809706963, + -0.06366697275788225, + -0.13549637792062064, + -0.2138557290072447, + -0.2987450260177542, + -0.3901642689521483, + -0.4881134578104276, + -0.5925925925925928, + -0.7036016732986439, + -0.8211406999285786, + -0.9452096724824015, + -1.0758085909601063, + -1.2129374553616967, + -1.3565962656871755, + -1.506785021936537, + -1.6635037241097868, + -1.8267523722069186, + -1.9965309662279356, + -2.172839506172841, + -2.355677992041629, + -2.545046423834302, + -2.740944801550863, + -2.9433731251913064, + -3.152331394755639, + -3.3678196102438527, + -3.589837771655952, + -3.8183858789919416, + -4.053463932251811, + -4.2950719314355705, + -4.543209876543212 + ], + [ + -12.33996530966228, + -11.935108662381388, + -11.536781961024385, + -11.144985205591269, + -10.759718396082032, + -10.380981532496683, + -10.00877461483522, + -9.643097643097644, + -9.283950617283951, + -8.931333537394144, + -8.585246403428222, + -8.245689215386186, + -7.912661973268035, + -7.586164677073769, + -7.266197326803387, + -6.9527599224568934, + -6.6458524640342835, + -6.345474951535559, + -6.051627384960718, + -5.764309764309765, + -5.483522089582696, + -5.209264360779512, + -4.941536577900214, + -4.680338740944801, + -4.425670849913274, + -4.177532904805632, + -3.9359249056218752, + -3.7008468523620044, + -3.472298745026018, + -3.2502805836139177, + -3.034792368125702, + -2.825834098561372, + -2.6234057749209265, + -2.4275073972043666, + -2.2381389654116925, + -2.0553004795429035, + -1.8789919395980004, + -1.7092133455769818, + -1.545964697479849, + -1.3892459953066014, + -1.2390572390572387, + -1.0953984287317629, + -0.9582695643301706, + -0.8276706458524641, + -0.7036016732986428, + -0.5860626466687078, + -0.47505356596265713, + -0.3705744311804919, + -0.2726252423222119, + -0.18120599938781728, + -0.09631670237730873, + -0.01795735129068475, + 0.05387205387205392, + 0.11917151311090718, + 0.17794102642587467, + 0.23018059381695735, + 0.2758902152841547, + 0.31506989082746667, + 0.347719620446893, + 0.3738394041424344, + 0.39342924191409046, + 0.4064891337618611, + 0.4130190796857463, + 0.41301907968574625, + 0.406489133761861, + 0.3934292419140904, + 0.3738394041424344, + 0.3477196204468933, + 0.3150698908274666, + 0.2758902152841546, + 0.23018059381695744, + 0.17794102642587484, + 0.11917151311090712, + 0.05387205387205385, + -0.017957351290684764, + -0.09631670237730838, + -0.18120599938781723, + -0.2726252423222115, + -0.37057443118049216, + -0.47505356596265647, + -0.586062646668708, + -0.7036016732986425, + -0.8276706458524623, + -0.9582695643301706, + -1.095398428731761, + -1.2390572390572399, + -1.3892459953066014, + -1.5459646974798478, + -1.709213345576983, + -1.878991939598, + -2.055300479542902, + -2.238138965411693, + -2.4275073972043653, + -2.623405774920927, + -2.8258340985613706, + -3.034792368125699, + -3.2502805836139173, + -3.472298745026017, + -3.7008468523620057, + -3.9359249056218757 + ], + [ + -13.032139577594126, + -12.614223038465463, + -12.202836445260688, + -11.797979797979801, + -11.399653096622796, + -11.007856341189676, + -10.622589531680442, + -10.243852668095094, + -9.87164575043363, + -9.505968778696053, + -9.14682175288236, + -8.794204672992553, + -8.448117539026631, + -8.108560350984595, + -7.775533108866444, + -7.449035812672178, + -7.129068462401798, + -6.815631058055303, + -6.508723599632691, + -6.208346087133966, + -5.9144985205591265, + -5.627180899908174, + -5.346393225181105, + -5.072135496377922, + -4.804407713498623, + -4.543209876543211, + -4.288541985511683, + -4.0404040404040416, + -3.7987960412202844, + -3.5637179879604135, + -3.335169880624427, + -3.1131517192123264, + -2.89766350372411, + -2.6887052341597797, + -2.486276910519335, + -2.2903785328027757, + -2.1010101010101017, + -1.9181716151413124, + -1.741863075196409, + -1.5720844811753907, + -1.4088358330782573, + -1.2521171309050108, + -1.101928374655648, + -0.9582695643301706, + -0.8211406999285789, + -0.6905417814508732, + -0.5664728088970519, + -0.44893378226711583, + -0.3379247015610652, + -0.2334455667788999, + -0.13549637792062075, + -0.044077134986226084, + 0.04081216202428327, + 0.11917151311090722, + 0.19100091827364526, + 0.2563003775124987, + 0.31506989082746667, + 0.3673094582185494, + 0.41301907968574625, + 0.4521987552290584, + 0.48484848484848503, + 0.5109682685440264, + 0.5305581063156822, + 0.5436179981634529, + 0.5501479440873385, + 0.5501479440873384, + 0.543617998163453, + 0.5305581063156826, + 0.5109682685440264, + 0.4848484848484853, + 0.4521987552290586, + 0.4130190796857469, + 0.36730945821854977, + 0.31506989082746706, + 0.25630037751249923, + 0.1910009182736463, + 0.1191715131109079, + 0.04081216202428406, + -0.044077134986225674, + -0.1354963779206193, + -0.23344556677890016, + -0.33792470156106424, + -0.44893378226711356, + -0.5664728088970508, + -0.690541781450871, + -0.8211406999285789, + -0.9582695643301693, + -1.1019283746556456, + -1.2521171309050096, + -1.408835833078256, + -1.5720844811753882, + -1.7418630751964073, + -1.9181716151413095, + -2.1010101010101008, + -2.290378532802774, + -2.4862769105193316, + -2.6887052341597797, + -2.897663503724108, + -3.1131517192123255, + -3.3351698806244254 + ], + [ + -13.730843791449848, + -13.299867360473415, + -12.875420875420872, + -12.457504336292214, + -12.046117743087438, + -11.641261095806547, + -11.242934394449543, + -10.851137639016425, + -10.46587082950719, + -10.087133965921842, + -9.714927048260378, + -9.3492500765228, + -8.99010305070911, + -8.637485970819302, + -8.291398836853379, + -7.951841648811344, + -7.618814406693193, + -7.292317110498927, + -6.972349760228545, + -6.658912355882051, + -6.352004897459441, + -6.0516273849607165, + -5.7577798183858775, + -5.470462197734923, + -5.189674523007854, + -4.915416794204671, + -4.647689011325373, + -4.3864911743699615, + -4.131823283338433, + -3.8836853382307917, + -3.6420773390470345, + -3.406999285787164, + -3.1784511784511773, + -2.956433017039076, + -2.740944801550861, + -2.531986531986531, + -2.3295582083460866, + -2.1336598306295267, + -1.944291398836853, + -1.7614529129680636, + -1.5851443730231596, + -1.4153657790021428, + -1.2521171309050094, + -1.0953984287317615, + -0.945209672482399, + -0.801550862156923, + -0.664421997755331, + -0.5338230792776245, + -0.40975410672380325, + -0.2922150800938673, + -0.18120599938781773, + -0.07672686460565248, + 0.02122232425262744, + 0.112641567187022, + 0.19753086419753046, + 0.27589021528415447, + 0.3477196204468931, + 0.4130190796857463, + 0.47178859300071363, + 0.5240281603917963, + 0.5697377818589936, + 0.6089174574023055, + 0.6415671870217318, + 0.667686970717273, + 0.6872768084889291, + 0.7003367003366997, + 0.706866646260585, + 0.7068666462605848, + 0.7003367003366993, + 0.6872768084889289, + 0.667686970717273, + 0.6415671870217313, + 0.608917457402305, + 0.5697377818589928, + 0.5240281603917953, + 0.4717885930007131, + 0.41301907968574514, + 0.347719620446892, + 0.27589021528415314, + 0.19753086419752997, + 0.11264156718701956, + 0.021222324252625713, + -0.07672686460565314, + -0.18120599938781945, + -0.29221508009386943, + -0.40975410672380663, + -0.5338230792776266, + -0.6644219977553325, + -0.8015508621569256, + -0.945209672482402, + -1.0953984287317633, + -1.2521171309050119, + -1.4153657790021432, + -1.5851443730231645, + -1.7614529129680667, + -1.944291398836854, + -2.1336598306295307, + -2.329558208346089, + -2.531986531986536, + -2.7409448015508655 + ], + [ + -14.436077951229464, + -13.99204162840526, + -13.554535251504946, + -13.123558820528517, + -12.69911233547597, + -12.281195796347308, + -11.869809203142534, + -11.464952555861647, + -11.066625854504641, + -10.674829099071522, + -10.289562289562287, + -9.91082542597694, + -9.538618508315476, + -9.172941536577898, + -8.813794510764206, + -8.4611774308744, + -8.115090296908479, + -7.7755331088664414, + -7.44250586674829, + -7.116008570554024, + -6.796041220283643, + -6.482603815937148, + -6.175696357514537, + -5.875318845015814, + -5.581471278440974, + -5.294153657790021, + -5.013365983062952, + -4.73910825425977, + -4.471380471380471, + -4.210182634425059, + -3.9555147433935307, + -3.707376798285889, + -3.4657687991021318, + -3.23069074584226, + -3.0021426385062746, + -2.7801244770941733, + -2.5646362616059584, + -2.3556779920416275, + -2.1532496684011835, + -1.9573512906846235, + -1.767982858891949, + -1.5851443730231614, + -1.4088358330782573, + -1.2390572390572387, + -1.0758085909601054, + -0.9190898887868588, + -0.7689011325374963, + -0.625242322212019, + -0.4881134578104271, + -0.3575145393327206, + -0.23344556677890038, + -0.11590654014896445, + -0.0048974594429138235, + 0.0995816753392514, + 0.19753086419753046, + 0.28895010713192515, + 0.37383940414243444, + 0.4521987552290584, + 0.5240281603917962, + 0.5893276196306496, + 0.6480971329456178, + 0.7003367003367001, + 0.7460463218038971, + 0.7852259973472089, + 0.8178757269666357, + 0.8439955106621769, + 0.8635853484338329, + 0.8766452402816035, + 0.8831751862054886, + 0.8831751862054886, + 0.8766452402816033, + 0.8635853484338326, + 0.8439955106621769, + 0.8178757269666354, + 0.7852259973472087, + 0.7460463218038967, + 0.7003367003366998, + 0.6480971329456173, + 0.589327619630649, + 0.5240281603917967, + 0.4521987552290574, + 0.3738394041424342, + 0.2889501071319258, + 0.19753086419752997, + 0.09958167533925089, + -0.0048974594429158635, + -0.1159065401489654, + -0.23344556677890038, + -0.35751453933272304, + -0.48811345781042803, + -0.6252423222120189, + -0.768901132537497, + -0.9190898887868579, + -1.0758085909601078, + -1.2390572390572396, + -1.4088358330782569, + -1.5851443730231631, + -1.7679828588919504, + -1.957351290684627, + -2.1532496684011853 + ], + [ + -15.147842056932967, + -14.690745842260993, + -14.240179573512904, + -13.796143250688708, + -13.35863687378839, + -12.927660442811959, + -12.50321395775941, + -12.085297418630752, + -11.673910825425978, + -11.269054178145087, + -10.870727476788081, + -10.478930721354963, + -10.09366391184573, + -9.714927048260382, + -9.342720130598916, + -8.977043158861342, + -8.61789613304765, + -8.26527905315784, + -7.919191919191918, + -7.579634731149882, + -7.24660748903173, + -6.920110192837465, + -6.6001428425670845, + -6.28670543822059, + -5.979797979797979, + -5.679420467299256, + -5.385572900724416, + -5.098255280073461, + -4.817467605346393, + -4.5432098765432105, + -4.275482093663912, + -4.0142842567085, + -3.7596163656769717, + -3.511478420569329, + -3.2698704213855727, + -3.034792368125701, + -2.8062442607897156, + -2.5842260993776143, + -2.3687378838893993, + -2.1597796143250685, + -1.9573512906846235, + -1.7614529129680654, + -1.5720844811753905, + -1.3892459953066014, + -1.2129374553616974, + -1.0431588613406801, + -0.879910213243547, + -0.723191511070299, + -0.5730027548209363, + -0.4293439444954591, + -0.2922150800938684, + -0.16161616161616174, + -0.03754718906234042, + 0.07999183756759548, + 0.19100091827364513, + 0.2954800530558105, + 0.39342924191409046, + 0.4848484848484851, + 0.5697377818589936, + 0.6480971329456175, + 0.7199265381083563, + 0.7852259973472095, + 0.843995510662177, + 0.8962350780532595, + 0.941944699520457, + 0.981124375063769, + 1.0137741046831956, + 1.0398938883787368, + 1.0594837261503924, + 1.0725436179981633, + 1.0790735639220486, + 1.0790735639220486, + 1.0725436179981633, + 1.0594837261503927, + 1.0398938883787368, + 1.0137741046831954, + 0.9811243750637691, + 0.9419446995204572, + 0.8962350780532597, + 0.8439955106621779, + 0.7852259973472089, + 0.7199265381083564, + 0.6480971329456187, + 0.5697377818589939, + 0.48484848484848486, + 0.39342924191408946, + 0.2954800530558104, + 0.1910009182736463, + 0.07999183756759409, + -0.03754718906234089, + -0.16161616161616088, + -0.2922150800938681, + -0.42934394449545854, + -0.573002754820938, + -0.7231915110702993, + -0.8799102132435452, + -1.0431588613406801, + -1.2129374553616974, + -1.3892459953066036, + -1.572084481175391 + ], + [ + -15.866136108560353, + -15.39598000204061, + -14.932353841444751, + -14.47525762677278, + -14.024691358024693, + -13.58065503520049, + -13.143148658300174, + -12.712172227323745, + -12.2877257422712, + -11.869809203142538, + -11.458422609937763, + -11.053565962656872, + -10.655239261299869, + -10.263442505866749, + -9.878175696357514, + -9.499438832772167, + -9.127231915110706, + -8.761554943373127, + -8.402407917559433, + -8.049790837669626, + -7.703703703703704, + -7.364146515661668, + -7.031119273543517, + -6.704621977349252, + -6.38465462707887, + -6.0712172227323755, + -5.764309764309765, + -5.463932251811041, + -5.170084685236201, + -4.882767064585247, + -4.601979389858178, + -4.327721661054996, + -4.059993878175698, + -3.7987960412202835, + -3.544128150188757, + -3.2959902050811145, + -3.054382205897358, + -2.8193041526374865, + -2.590756045301501, + -2.3687378838893993, + -2.153249668401183, + -1.9442913988368549, + -1.7418630751964095, + -1.5459646974798493, + -1.3565962656871746, + -1.173757779818387, + -0.9974492398734829, + -0.8276706458524643, + -0.6644219977553311, + -0.507703295582083, + -0.35751453933272176, + -0.21385572900724442, + -0.07672686460565245, + 0.053872053872054154, + 0.17794102642587437, + 0.2954800530558104, + 0.4064891337618611, + 0.5109682685440264, + 0.6089174574023055, + 0.7003367003367001, + 0.7852259973472095, + 0.8635853484338336, + 0.9354147535965716, + 1.0007142128354247, + 1.059483726150393, + 1.1117232935414756, + 1.1574329150086728, + 1.1966125905519844, + 1.229262320171411, + 1.2553821038669526, + 1.2749719416386087, + 1.2880318334863787, + 1.2945617794102648, + 1.2945617794102646, + 1.2880318334863792, + 1.2749719416386083, + 1.2553821038669528, + 1.2292623201714115, + 1.1966125905519844, + 1.1574329150086735, + 1.1117232935414758, + 1.0594837261503935, + 1.0007142128354263, + 0.9354147535965724, + 0.863585348433834, + 0.7852259973472093, + 0.7003367003367007, + 0.6089174574023066, + 0.5109682685440258, + 0.4064891337618617, + 0.2954800530558117, + 0.1779410264258754, + 0.0538720538720554, + -0.0767268646056527, + -0.2138557290072436, + -0.35751453933271904, + -0.5077032955820839, + -0.6644219977553298, + -0.8276706458524643, + -0.9974492398734824 + ], + [ + -16.59096010611162, + -16.107744107744104, + -15.631058055300475, + -15.160901948780733, + -14.697275788184877, + -14.240179573512904, + -13.789613304764815, + -13.345576981940617, + -12.908070605040297, + -12.477094174063868, + -12.052647689011321, + -11.634731149882661, + -11.223344556677887, + -10.818487909396998, + -10.420161208039993, + -10.028364452606874, + -9.643097643097642, + -9.264360779512293, + -8.89215386185083, + -8.526476890113251, + -8.167329864299557, + -7.8147127844097515, + -7.46862565044383, + -7.1290684624017935, + -6.796041220283643, + -6.469543924089377, + -6.149576573818996, + -5.836139169472501, + -5.52923171104989, + -5.228854198551167, + -4.935006631976327, + -4.647689011325374, + -4.366901336598305, + -4.092643607795121, + -3.8249158249158235, + -3.563717987960411, + -3.3090500969288836, + -3.060912151821241, + -2.8193041526374856, + -2.584226099377613, + -2.3556779920416266, + -2.1336598306295276, + -1.9181716151413117, + -1.7092133455769811, + -1.5067850219365357, + -1.3108866442199778, + -1.121518212427303, + -0.938679726558514, + -0.7623711866136101, + -0.5925925925925916, + -0.4293439444954598, + -0.2726252423222119, + -0.12243648607284938, + 0.021222324252627822, + 0.15835118865421852, + 0.28895010713192515, + 0.41301907968574636, + 0.5305581063156823, + 0.6415671870217318, + 0.7460463218038971, + 0.843995510662177, + 0.9354147535965716, + 1.0203040506070802, + 1.0986634016937038, + 1.1704928068564426, + 1.2357922660952958, + 1.2945617794102637, + 1.3468013468013456, + 1.3925109682685428, + 1.431690643811855, + 1.4643403734312819, + 1.4904601571268223, + 1.5100499948984787, + 1.5231098867462491, + 1.5296398326701341, + 1.5296398326701341, + 1.5231098867462491, + 1.5100499948984782, + 1.4904601571268221, + 1.464340373431281, + 1.431690643811854, + 1.3925109682685421, + 1.3468013468013456, + 1.2945617794102624, + 1.2357922660952945, + 1.1704928068564406, + 1.0986634016937025, + 1.0203040506070788, + 0.9354147535965684, + 0.8439955106621748, + 0.7460463218038953, + 0.6415671870217299, + 0.5305581063156808, + 0.4130190796857427, + 0.28895010713192226, + 0.15835118865421727, + 0.021222324252622826, + -0.12243648607285262, + -0.2726252423222162, + -0.4293439444954634 + ], + [ + -17.322314049586772, + -16.82603815937149, + -16.336292215080093, + -15.853076216712576, + -15.376390164268951, + -14.906234057749208, + -14.442607897153348, + -13.985511682481377, + -13.53494541373329, + -13.090909090909088, + -12.653402714008772, + -12.222426283032341, + -11.797979797979796, + -11.380063258851136, + -10.96867666564636, + -10.563820018365472, + -10.165493317008469, + -9.773696561575349, + -9.388429752066113, + -9.009692888480766, + -8.637485970819302, + -8.271808999081726, + -7.9126619732680314, + -7.560044893378225, + -7.213957759412303, + -6.874400571370268, + -6.5413733292521155, + -6.214876033057851, + -5.894908682787469, + -5.581471278440975, + -5.274563820018365, + -4.97418630751964, + -4.680338740944801, + -4.393021120293846, + -4.112233445566778, + -3.8379757167635944, + -3.570247933884297, + -3.3090500969288836, + -3.0543822058973573, + -2.8062442607897142, + -2.5646362616059575, + -2.3295582083460875, + -2.1010101010101008, + -1.878991939598, + -1.6635037241097839, + -1.454545454545455, + -1.2521171309050099, + -1.05621875318845, + -0.8668503213957754, + -0.6840118355269862, + -0.5077032955820838, + -0.33792470156106524, + -0.17467605346393203, + -0.017957351290684126, + 0.13223140495867716, + 0.27589021528415447, + 0.41301907968574636, + 0.5436179981634529, + 0.667686970717273, + 0.7852259973472091, + 0.8962350780532597, + 1.000714212835425, + 1.0986634016937038, + 1.1900826446280983, + 1.2749719416386078, + 1.3533312927252317, + 1.4251606978879705, + 1.490460157126823, + 1.5492296704417907, + 1.6014692378328736, + 1.6471788593000707, + 1.6863585348433823, + 1.719008264462809, + 1.7451280481583504, + 1.7647178859300063, + 1.7777777777777763, + 1.7843077237016622, + 1.7843077237016622, + 1.7777777777777768, + 1.7647178859300063, + 1.74512804815835, + 1.7190082644628093, + 1.6863585348433832, + 1.64717885930007, + 1.6014692378328732, + 1.5492296704417896, + 1.4904601571268223, + 1.4251606978879696, + 1.3533312927252297, + 1.2749719416386065, + 1.1900826446280983, + 1.098663401693703, + 1.0007142128354247, + 0.8962350780532571, + 0.7852259973472075, + 0.6676869707172726, + 0.5436179981634499, + 0.4130190796857445, + 0.2758902152841518, + 0.13223140495867547 + ], + [ + -18.060197938985816, + -17.550862156922758, + -17.04805632078359, + -16.55178043056831, + -16.062034486276907, + -15.578818487909395, + -15.102132435465768, + -14.631976328946028, + -14.168350168350168, + -13.711253953678195, + -13.260687684930108, + -12.816651362105906, + -12.379144985205592, + -11.94816855422916, + -11.523722069176614, + -11.105805530047952, + -10.69441893684318, + -10.289562289562289, + -9.891235588205284, + -9.499438832772167, + -9.114172023262931, + -8.735435159677582, + -8.36322824201612, + -7.997551270278542, + -7.63840424446485, + -7.2857871645750425, + -6.939700030609121, + -6.6001428425670845, + -6.267115600448934, + -5.940618304254668, + -5.6206509539842875, + -5.307213549637792, + -5.000306091215181, + -4.699928578716457, + -4.406081012141618, + -4.118763391490663, + -3.8379757167635953, + -3.5637179879604117, + -3.2959902050811145, + -3.034792368125701, + -2.7801244770941733, + -2.531986531986533, + -2.2903785328027757, + -2.0553004795429035, + -1.8267523722069172, + -1.6047342107948177, + -1.3892459953066016, + -1.1802877257422713, + -0.9778594021018259, + -0.781961024385266, + -0.592592592592593, + -0.40975410672380386, + -0.2334455667788999, + -0.06366697275788136, + 0.09958167533925047, + 0.2563003775124984, + 0.4064891337618611, + 0.5501479440873384, + 0.6872768084889289, + 0.8178757269666357, + 0.941944699520457, + 1.0594837261503929, + 1.1704928068564426, + 1.2749719416386078, + 1.3729211304968878, + 1.4643403734312825, + 1.5492296704417918, + 1.627589021528415, + 1.6994184266911536, + 1.764717885930007, + 1.823487399244975, + 1.8757269666360568, + 1.9214365881032545, + 1.9606162636465665, + 1.9932659932659933, + 2.019385776961534, + 2.0389756147331903, + 2.052035506580961, + 2.0585654525048462, + 2.0585654525048462, + 2.0520355065809612, + 2.0389756147331903, + 2.019385776961535, + 1.9932659932659929, + 1.9606162636465665, + 1.9214365881032538, + 1.8757269666360572, + 1.8234873992449745, + 1.7647178859300063, + 1.6994184266911536, + 1.627589021528415, + 1.5492296704417914, + 1.4643403734312836, + 1.3729211304968865, + 1.2749719416386078, + 1.1704928068564437, + 1.059483726150391, + 0.941944699520457, + 0.8178757269666335, + 0.687276808488928 + ], + [ + -18.804611774308743, + -18.282216100397918, + -17.766350372410976, + -17.257014590347925, + -16.754208754208754, + -16.257932863993467, + -15.768186919702071, + -15.28497092133456, + -14.808284868890931, + -14.338128762371188, + -13.87450260177533, + -13.417406387103357, + -12.966840118355272, + -12.522803795531068, + -12.085297418630752, + -11.654320987654323, + -11.229874502601778, + -10.811957963473116, + -10.40057137026834, + -9.99571472298745, + -9.597388021630445, + -9.205591266197327, + -8.820324456688093, + -8.441587593102746, + -8.06938067544128, + -7.703703703703705, + -7.3445566778900115, + -6.991939598000205, + -6.645852464034283, + -6.306295275992246, + -5.973268033874095, + -5.64677073767983, + -5.3268033874094485, + -5.013365983062952, + -4.706458524640343, + -4.406081012141618, + -4.11223344556678, + -3.824915824915825, + -3.544128150188757, + -3.2698704213855727, + -3.0021426385062746, + -2.7409448015508637, + -2.4862769105193356, + -2.238138965411693, + -1.9965309662279354, + -1.7614529129680658, + -1.5329048056320789, + -1.3108866442199778, + -1.095398428731762, + -0.8864401591674312, + -0.6840118355269879, + -0.4881134578104278, + -0.2987450260177531, + -0.1159065401489639, + 0.060401999795938494, + 0.2301805938169572, + 0.39342924191409046, + 0.5501479440873385, + 0.7003367003366997, + 0.843995510662177, + 0.9811243750637693, + 1.1117232935414758, + 1.235792266095296, + 1.3533312927252317, + 1.4643403734312825, + 1.5688195082134477, + 1.6667686970717281, + 1.7581879400061218, + 1.8430772370166308, + 1.9214365881032553, + 1.993265993265994, + 2.0585654525048462, + 2.117334965819815, + 2.1695745332108975, + 2.215284154678095, + 2.2544638302214057, + 2.287113559840833, + 2.3132333435363743, + 2.3328231813080302, + 2.345883073155801, + 2.3524130190796866, + 2.3524130190796866, + 2.345883073155801, + 2.3328231813080302, + 2.3132333435363743, + 2.2871135598408325, + 2.2544638302214066, + 2.215284154678095, + 2.1695745332108967, + 2.117334965819815, + 2.058565452504847, + 1.993265993265994, + 1.9214365881032567, + 1.8430772370166308, + 1.7581879400061227, + 1.6667686970717295, + 1.5688195082134473, + 1.4643403734312836, + 1.353331292725232, + 1.235792266095297 + ], + [ + -19.555555555555557, + -19.02009998979696, + -18.49117436996225, + -17.968778696051427, + -17.45291296806449, + -16.94357718600143, + -16.44077134986226, + -15.94449545964698, + -15.454749515355578, + -14.971533516988064, + -14.494847464544435, + -14.024691358024693, + -13.561065197428837, + -13.103968982756864, + -12.653402714008774, + -12.209366391184576, + -11.77186001428426, + -11.340883583307829, + -10.916437098255281, + -10.498520559126622, + -10.087133965921847, + -9.682277318640958, + -9.283950617283953, + -8.892153861850833, + -8.506887052341598, + -8.128150188756251, + -7.755943271094788, + -7.39026629935721, + -7.031119273543518, + -6.67850219365371, + -6.332415059687788, + -5.992857871645752, + -5.659830629527601, + -5.333333333333334, + -5.013365983062954, + -4.699928578716459, + -4.393021120293849, + -4.092643607795123, + -3.7987960412202852, + -3.511478420569331, + -3.230690745842261, + -2.9564330170390796, + -2.6887052341597806, + -2.4275073972043675, + -2.1728395061728394, + -1.924701561065199, + -1.683093561881442, + -1.4480155086215698, + -1.219467401285583, + -0.9974492398734819, + -0.7819610243852679, + -0.5730027548209371, + -0.3705744311804918, + -0.1746760534639319, + 0.01469237832874104, + 0.1975308641975304, + 0.37383940414243444, + 0.5436179981634531, + 0.7068666462605849, + 0.8635853484338329, + 1.0137741046831956, + 1.157432915008673, + 1.2945617794102637, + 1.4251606978879703, + 1.5492296704417918, + 1.6667686970717277, + 1.7777777777777786, + 1.882256912559943, + 1.9802061014182228, + 2.0716253443526176, + 2.156514641363127, + 2.2348739924497503, + 2.306703397612489, + 2.3720028568513425, + 2.43077237016631, + 2.4830119375573925, + 2.52872155902459, + 2.5679012345679024, + 2.600550964187329, + 2.62667074788287, + 2.6462605856545265, + 2.6593204775022965, + 2.665850423426182, + 2.665850423426183, + 2.6593204775022965, + 2.6462605856545265, + 2.626670747882871, + 2.600550964187329, + 2.567901234567903, + 2.528721559024592, + 2.4830119375573934, + 2.4307723701663115, + 2.3720028568513443, + 2.3067033976124898, + 2.2348739924497525, + 2.1565146413631293, + 2.071625344352619, + 1.9802061014182253, + 1.882256912559943, + 1.777777777777779 + ], + [ + -20.313029282726248, + -19.76451382511988, + -19.2225283134374, + -18.68707274767881, + -18.158147127844096, + -17.635751453933267, + -17.11988572594633, + -16.610549943883278, + -16.107744107744107, + -15.61146821752882, + -15.121722273237424, + -14.638506274869908, + -14.161820222426282, + -13.691664115906539, + -13.22803795531068, + -12.770941740638708, + -12.320375471890625, + -11.876339149066421, + -11.438832772166101, + -11.007856341189672, + -10.583409856137125, + -10.165493317008467, + -9.754106723803691, + -9.349250076522802, + -8.950923375165797, + -8.55912661973268, + -8.173859810223444, + -7.795122946638098, + -7.422916028976633, + -7.057239057239057, + -6.698092031425363, + -6.345474951535557, + -5.999387817569635, + -5.6598306295275975, + -5.326803387409447, + -5.00030609121518, + -4.680338740944801, + -4.366901336598305, + -4.059993878175696, + -3.7596163656769703, + -3.465768799102131, + -3.1784511784511786, + -2.897663503724109, + -2.6234057749209256, + -2.3556779920416275, + -2.094480155086216, + -1.8398122640546886, + -1.5916743189470457, + -1.3500663197632887, + -1.1149882665034168, + -0.8864401591674322, + -0.664421997755331, + -0.4489337822671151, + -0.23997551270278455, + -0.03754718906234117, + 0.1583511886542188, + 0.34771962044689336, + 0.5305581063156826, + 0.7068666462605849, + 0.8766452402816036, + 1.0398938883787368, + 1.1966125905519847, + 1.346801346801346, + 1.490460157126823, + 1.627589021528415, + 1.7581879400061218, + 1.882256912559943, + 1.9997959391898779, + 2.1108050198959285, + 2.215284154678094, + 2.3132333435363734, + 2.404652586470767, + 2.4895418834812766, + 2.5679012345679006, + 2.6397306397306393, + 2.705030098969491, + 2.7637996122844597, + 2.816039179675543, + 2.8617488011427397, + 2.9009284766860515, + 2.9335782063054783, + 2.9596979900010196, + 2.979287827772676, + 2.9923477196204455, + 2.9988776655443314, + 2.9988776655443306, + 2.9923477196204455, + 2.979287827772675, + 2.959697990001018, + 2.933578206305478, + 2.9009284766860515, + 2.861748801142739, + 2.8160391796755424, + 2.7637996122844584, + 2.705030098969491, + 2.6397306397306393, + 2.567901234567899, + 2.4895418834812757, + 2.404652586470766, + 2.313233343536371 + ], + [ + -21.077032955820833, + -20.515457606366695, + -19.960412202836444, + -19.41189674523008, + -18.869911233547597, + -18.334455667789, + -17.805530047954285, + -17.283134374043467, + -16.76726864605652, + -16.257932863993467, + -15.755127027854297, + -15.258851137639017, + -14.769105193347617, + -14.285889194980104, + -13.809203142536473, + -13.339047036016733, + -12.875420875420875, + -12.418324660748903, + -11.967758392000814, + -11.523722069176614, + -11.086215692276296, + -10.655239261299867, + -10.23079277624732, + -9.812876237118662, + -9.401489643913886, + -8.996632996632997, + -8.598306295275993, + -8.206509539842873, + -7.821242730333639, + -7.4425058667482915, + -7.070298949086828, + -6.70462197734925, + -6.345474951535557, + -5.99285787164575, + -5.646770737679828, + -5.307213549637791, + -4.974186307519641, + -4.647689011325375, + -4.327721661054994, + -4.014284256708499, + -3.707376798285888, + -3.4069992857871654, + -3.1131517192123255, + -2.8258340985613715, + -2.545046423834302, + -2.2707886950311202, + -2.0030609121518217, + -1.7418630751964084, + -1.4871951841648807, + -1.239057239057238, + -0.9974492398734831, + -0.7623711866136111, + -0.5338230792776244, + -0.3118049178655232, + -0.09631670237730927, + 0.1126415671870214, + 0.3150698908274667, + 0.5109682685440265, + 0.7003367003366994, + 0.8831751862054888, + 1.0594837261503929, + 1.2292623201714115, + 1.3925109682685433, + 1.549229670441791, + 1.6994184266911538, + 1.8430772370166308, + 1.980206101418223, + 2.1108050198959285, + 2.2348739924497494, + 2.3524130190796857, + 2.463422099785736, + 2.5679012345679006, + 2.6658504234261806, + 2.757269666360575, + 2.8421589633710846, + 2.9205183144577074, + 2.9923477196204464, + 3.0576471788593, + 3.1164166921742678, + 3.16865625956535, + 3.214365881032548, + 3.2535455565758595, + 3.2861952861952863, + 3.3123150698908277, + 3.331904907662483, + 3.3449647995102536, + 3.3514947454341395, + 3.351494745434138, + 3.3449647995102536, + 3.3319049076624827, + 3.3123150698908272, + 3.286195286195286, + 3.2535455565758604, + 3.2143658810325464, + 3.1686562595653505, + 3.116416692174268, + 3.057647178859299, + 2.9923477196204464, + 2.9205183144577065, + 2.8421589633710833 + ], + [ + -21.847566574839302, + -21.272931333537393, + -20.704826038159368, + -20.143250688705237, + -19.588205285174983, + -19.039689827568615, + -18.497704315886132, + -17.962248750127543, + -17.433323130292827, + -16.910927456382, + -16.395061728395063, + -15.885725946332007, + -15.382920110192838, + -14.886644219977555, + -14.396898275686155, + -13.913682277318642, + -13.436996224875015, + -12.96684011835527, + -12.50321395775941, + -12.046117743087441, + -11.595551474339352, + -11.151515151515152, + -10.714008774614836, + -10.283032343638403, + -9.858585858585858, + -9.4406693194572, + -9.029282726252424, + -8.624426078971535, + -8.22609937761453, + -7.834302622181411, + -7.449035812672176, + -7.07029894908683, + -6.698092031425365, + -6.332415059687786, + -5.973268033874095, + -5.6206509539842875, + -5.274563820018366, + -4.9350066319763295, + -4.601979389858179, + -4.275482093663912, + -3.9555147433935307, + -3.6420773390470376, + -3.335169880624427, + -3.034792368125702, + -2.7409448015508615, + -2.4536271808999093, + -2.1728395061728403, + -1.8985817773696565, + -1.630853994490358, + -1.3696561575349446, + -1.114988266503419, + -0.8668503213957764, + -0.625242322212019, + -0.39016426895214723, + -0.16161616161616266, + 0.06040199979593869, + 0.27589021528415464, + 0.4848484848484853, + 0.6872768084889287, + 0.8831751862054887, + 1.0725436179981633, + 1.2553821038669528, + 1.431690643811855, + 1.6014692378328734, + 1.764717885930007, + 1.921436588103255, + 2.0716253443526176, + 2.2152841546780935, + 2.3524130190796853, + 2.483011937557392, + 2.607080910111214, + 2.724619936741148, + 2.835629017447199, + 2.9401081522293646, + 3.038057341087644, + 3.1294765840220378, + 3.2143658810325473, + 3.292725232119172, + 3.3645546372819104, + 3.429854096520763, + 3.4886236098357317, + 3.540863177226814, + 3.586572798694011, + 3.625752474237323, + 3.658402203856749, + 3.6845219875522908, + 3.704111825323947, + 3.717171717171717, + 3.7237016630956017, + 3.7237016630956026, + 3.717171717171717, + 3.704111825323947, + 3.6845219875522917, + 3.6584022038567485, + 3.625752474237323, + 3.5865727986940117, + 3.540863177226813, + 3.4886236098357317, + 3.4298540965207622, + 3.364554637281909 + ], + [ + -22.624630139781658, + -22.03693500663198, + -21.455769819406182, + -20.881134578104277, + -20.313029282726255, + -19.751453933272117, + -19.196408529741866, + -18.647893072135503, + -18.10590756045302, + -17.570451994694423, + -17.041526374859707, + -16.519130700948885, + -16.003264972961947, + -15.49392919089889, + -14.991123354759718, + -14.494847464544435, + -14.005101520253039, + -13.521885521885523, + -13.045199469441895, + -12.575043362922154, + -12.111417202326294, + -11.654320987654323, + -11.203754718906236, + -10.759718396082034, + -10.322212019181716, + -9.891235588205287, + -9.466789103152742, + -9.04887256402408, + -8.637485970819306, + -8.232629323538415, + -7.834302622181411, + -7.442505866748293, + -7.057239057239058, + -6.67850219365371, + -6.306295275992246, + -5.940618304254668, + -5.581471278440977, + -5.2288541985511685, + -4.882767064585248, + -4.5432098765432105, + -4.210182634425058, + -3.8836853382307948, + -3.5637179879604135, + -3.2502805836139177, + -2.943373125191307, + -2.642995612692584, + -2.3491480461177443, + -2.06183042546679, + -1.7810427507397204, + -1.5067850219365364, + -1.23905723905724, + -0.977859402101827, + -0.7231915110702989, + -0.4750535659626564, + -0.23344556677890121, + 0.0016324864809708073, + 0.2301805938169575, + 0.45219875522905884, + 0.6676869707172728, + 0.8766452402816035, + 1.0790735639220488, + 1.2749719416386087, + 1.4643403734312819, + 1.647178859300071, + 1.823487399244975, + 1.9932659932659935, + 2.156514641363127, + 2.3132333435363734, + 2.463422099785736, + 2.607080910111214, + 2.7442097745128056, + 2.8748086929905106, + 2.9988776655443328, + 3.116416692174268, + 3.227425772880319, + 3.3319049076624827, + 3.429854096520764, + 3.5212733394551585, + 3.606162636465667, + 3.684521987552291, + 3.7563513927150303, + 3.821650851953883, + 3.880420365268851, + 3.9326599326599343, + 3.97836955412713, + 4.017549229670443, + 4.050198959289871, + 4.07631874298541, + 4.095908580757067, + 4.108968472604838, + 4.115498418528722, + 4.115498418528723, + 4.108968472604839, + 4.095908580757067, + 4.0763187429854115, + 4.050198959289871, + 4.0175492296704425, + 3.9783695541271316, + 3.9326599326599334, + 3.8804203652688516 + ], + [ + -23.40822365064789, + -22.80746862565044, + -22.213243546576876, + -21.625548413427204, + -21.044383226201408, + -20.4697479848995, + -19.901642689521474, + -19.34006734006734, + -18.785021936537085, + -18.23650647893072, + -17.694520967248238, + -17.15906540148964, + -16.630139781654933, + -16.107744107744107, + -15.591878379757166, + -15.082542597694111, + -14.579736761554944, + -14.083460871339659, + -13.593714927048257, + -13.110498928680745, + -12.633812876237116, + -12.163656769717374, + -11.700030609121516, + -11.242934394449545, + -10.792368125701458, + -10.348331802877256, + -9.910825425976938, + -9.47984899500051, + -9.055402509947964, + -8.637485970819304, + -8.226099377614528, + -7.82124273033364, + -7.422916028976635, + -7.0311192735435135, + -6.645852464034281, + -6.267115600448932, + -5.89490868278747, + -5.529231711049891, + -5.1700846852362, + -4.817467605346392, + -4.47138047138047, + -4.131823283338436, + -3.7987960412202835, + -3.4722987450260168, + -3.152331394755636, + -2.838893990409143, + -2.531986531986532, + -2.231609019487807, + -1.9377614529129672, + -1.6504438322620125, + -1.369656157534946, + -1.095398428731762, + -0.8276706458524635, + -0.5664728088970503, + -0.3118049178655247, + -0.06366697275788208, + 0.17794102642587517, + 0.4130190796857471, + 0.6415671870217315, + 0.8635853484338327, + 1.0790735639220488, + 1.2880318334863792, + 1.4904601571268226, + 1.6863585348433823, + 1.8757269666360572, + 2.0585654525048462, + 2.2348739924497503, + 2.4046525864707675, + 2.5679012345679, + 2.7246199367411483, + 2.874808692990511, + 3.0184675033159865, + 3.155596367717579, + 3.2861952861952854, + 3.4102642587491068, + 3.5278032853790413, + 3.638812366085092, + 3.7432915008672576, + 3.841240689725537, + 3.9326599326599316, + 4.017549229670442, + 4.095908580757064, + 4.1677379859198025, + 4.233037445158657, + 4.291806958473623, + 4.344046525864706, + 4.389756147331904, + 4.428935822875215, + 4.461585552494642, + 4.487705336190183, + 4.507295173961838, + 4.5203550658096106, + 4.526885011733496, + 4.526885011733495, + 4.52035506580961, + 4.50729517396184, + 4.487705336190182, + 4.4615855524946415, + 4.428935822875214, + 4.3897561473319024 + ], + [ + -24.198347107438018, + -23.584532190592796, + -22.97724721967146, + -22.376492194674015, + -21.782267115600447, + -21.194571982450768, + -20.613406795224975, + -20.03877155392307, + -19.470666258545045, + -18.909090909090907, + -18.354045505560656, + -17.80553004795429, + -17.26354453627181, + -16.728088970513213, + -16.199163350678504, + -15.676767676767676, + -15.160901948780737, + -14.65156616671768, + -14.14876033057851, + -13.652484440363228, + -13.162738496071828, + -12.679522497704315, + -12.202836445260687, + -11.732680338740945, + -11.269054178145087, + -10.811957963473116, + -10.361391694725029, + -9.917355371900825, + -9.47984899500051, + -9.04887256402408, + -8.624426078971533, + -8.206509539842873, + -7.795122946638097, + -7.390266299357208, + -6.9919395980002035, + -6.600142842567084, + -6.214876033057851, + -5.836139169472502, + -5.463932251811039, + -5.098255280073461, + -4.739108254259769, + -4.386491174369963, + -4.040404040404041, + -3.700846852362004, + -3.367819610243852, + -3.041322314049588, + -2.7213549637792065, + -2.407917559432711, + -2.1010101010101003, + -1.800632588511375, + -1.5067850219365377, + -1.2194674012855833, + -0.938679726558514, + -0.6644219977553301, + -0.39669421487603385, + -0.13549637792062053, + 0.11917151311090735, + 0.36730945821855, + 0.6089174574023049, + 0.8439955106621769, + 1.0725436179981636, + 1.2945617794102648, + 1.5100499948984787, + 1.719008264462809, + 1.921436588103255, + 2.1173349658198144, + 2.3067033976124893, + 2.489541883481277, + 2.6658504234261806, + 2.835629017447199, + 2.9988776655443323, + 3.155596367717579, + 3.305785123966942, + 3.4494439342924186, + 3.5865727986940112, + 3.7171717171717162, + 3.8412406897255384, + 3.9587797163554743, + 4.069788797061524, + 4.17426793184369, + 4.27221712070197, + 4.363636363636363, + 4.448525660646872, + 4.526885011733497, + 4.598714416896235, + 4.664013876135089, + 4.722783389450056, + 4.775022956841139, + 4.820732578308336, + 4.859912253851648, + 4.892561983471074, + 4.918681767166616, + 4.938271604938272, + 4.951331496786041, + 4.957861442709928, + 4.957861442709929, + 4.951331496786041, + 4.938271604938271, + 4.918681767166615, + 4.892561983471074 + ], + [ + -24.995000510152025, + -24.368125701459032, + -23.747780838689927, + -23.133965921844712, + -22.526680950923378, + -21.925925925925924, + -21.331700846852364, + -20.744005713702684, + -20.16284052647689, + -19.588205285174983, + -19.02009998979696, + -18.458524640342823, + -17.903479236812572, + -17.3549637792062, + -16.81297826752372, + -16.27752270176513, + -15.748597081930416, + -15.226201408019591, + -14.71033568003265, + -14.200999897969595, + -13.698194061830424, + -13.20191817161514, + -12.712172227323741, + -12.228956228956228, + -11.7522701765126, + -11.282114069992858, + -10.818487909397, + -10.361391694725029, + -9.910825425976942, + -9.466789103152742, + -9.029282726252424, + -8.598306295275993, + -8.173859810223448, + -7.755943271094786, + -7.3445566778900115, + -6.939700030609122, + -6.541373329252117, + -6.149576573818998, + -5.764309764309766, + -5.385572900724416, + -5.013365983062952, + -4.647689011325377, + -4.288541985511683, + -3.9359249056218752, + -3.5898377716559526, + -3.250280583613918, + -2.9172533414957664, + -2.5907560453015, + -2.270788695031119, + -1.9573512906846229, + -1.650443832262015, + -1.3500663197632898, + -1.0562187531884497, + -0.7689011325374953, + -0.4881134578104286, + -0.2138557290072446, + 0.05387205387205396, + 0.31506989082746734, + 0.5697377818589928, + 0.8178757269666355, + 1.0594837261503929, + 1.2945617794102646, + 1.5231098867462494, + 1.7451280481583504, + 1.9606162636465667, + 2.169574533210897, + 2.372002856851343, + 2.5679012345679006, + 2.7572696663605747, + 2.9401081522293646, + 3.116416692174268, + 3.2861952861952854, + 3.449443934292419, + 3.6061626364656667, + 3.75635139271503, + 3.900010203040505, + 4.037139067442098, + 4.167737985919804, + 4.291806958473625, + 4.409345985103561, + 4.520355065809612, + 4.624834200591776, + 4.722783389450056, + 4.814202632384451, + 4.8990919293949595, + 4.977451280481584, + 5.049280685644323, + 5.114580144883175, + 5.173349658198143, + 5.225589225589226, + 5.271298847056422, + 5.310478522599736, + 5.343128252219163, + 5.369248035914703, + 5.388837873686359, + 5.40189776553413, + 5.408427711458014, + 5.408427711458015, + 5.401897765534129, + 5.388837873686358 + ], + [ + -25.79818385878992, + -25.15824915824916, + -24.52484440363228, + -23.897969594939294, + -23.27762473217019, + -22.663809815324967, + -22.056524844403633, + -21.45576981940619, + -20.861544740332622, + -20.273849607182942, + -19.692684419957146, + -19.11804917865524, + -18.549943883277223, + -17.98836853382308, + -17.433323130292827, + -16.884807672686463, + -16.342822161003983, + -15.807366595245384, + -15.278440975410673, + -14.75604530149985, + -14.240179573512908, + -13.730843791449855, + -13.228037955310683, + -12.7317620650954, + -12.242016120804, + -11.758800122436488, + -11.282114069992858, + -10.811957963473116, + -10.348331802877258, + -9.891235588205287, + -9.4406693194572, + -8.996632996633, + -8.559126619732682, + -8.12815018875625, + -7.703703703703706, + -7.285787164575044, + -6.87440057137027, + -6.469543924089379, + -6.0712172227323755, + -5.679420467299256, + -5.294153657790021, + -4.915416794204676, + -4.543209876543211, + -4.177532904805632, + -3.8183858789919394, + -3.465768799102135, + -3.119681665136212, + -2.7801244770941747, + -2.4470972349760225, + -2.1205999387817562, + -1.800632588511378, + -1.487195184164882, + -1.1802877257422715, + -0.8799102132435462, + -0.5860626466687087, + -0.2987450260177541, + -0.017957351290684764, + 0.2563003775124993, + 0.5240281603917953, + 0.7852259973472087, + 1.0398938883787368, + 1.2880318334863794, + 1.5296398326701344, + 1.7647178859300061, + 1.9932659932659933, + 2.2152841546780944, + 2.43077237016631, + 2.6397306397306393, + 2.842158963371084, + 3.0380573410876446, + 3.227425772880319, + 3.4102642587491063, + 3.5865727986940112, + 3.75635139271503, + 3.9196000408121625, + 4.076318742985409, + 4.226507499234772, + 4.37016630956025, + 4.507295173961841, + 4.637894092439547, + 4.7619630649933695, + 4.879502091623304, + 4.990511172329354, + 5.09499030711152, + 5.192939495969799, + 5.284358738904195, + 5.369248035914703, + 5.447607387001326, + 5.519436792164066, + 5.584736251402918, + 5.643505764717886, + 5.695745332108969, + 5.7414549535761665, + 5.780634629119478, + 5.813284358738905, + 5.8394041424344465, + 5.858993980206102, + 5.872053872053873, + 5.878583817977757, + 5.878583817977757 + ], + [ + -26.607897153351693, + -25.95490256096316, + -25.308437914498516, + -24.668503213957756, + -24.03509845934088, + -23.40822365064789, + -22.787878787878782, + -22.174063871033567, + -21.566778900112233, + -20.96602387511478, + -20.37179879604122, + -19.78410366289154, + -19.202938475665746, + -18.628303234363838, + -18.060197938985816, + -17.498622589531678, + -16.943577186001427, + -16.39506172839506, + -15.853076216712576, + -15.317620650953984, + -14.78869503111927, + -14.266299357208446, + -13.750433629221504, + -13.24109784715845, + -12.738292011019281, + -12.242016120804, + -11.752270176512598, + -11.269054178145087, + -10.792368125701458, + -10.322212019181714, + -9.858585858585858, + -9.401489643913886, + -8.950923375165798, + -8.506887052341595, + -8.06938067544128, + -7.638404244464848, + -7.213957759412304, + -6.796041220283643, + -6.384654627078869, + -5.979797979797978, + -5.581471278440973, + -5.189674523007858, + -4.804407713498622, + -4.425670849913272, + -4.05346393225181, + -3.687786960514234, + -3.328639934700541, + -2.976022854810733, + -2.62993572084481, + -2.290378532802773, + -1.9573512906846247, + -1.630853994490358, + -1.3108866442199767, + -0.9974492398734811, + -0.6905417814508732, + -0.39016426895214795, + -0.09631670237730794, + 0.19100091827364662, + 0.4717885930007132, + 0.7460463218038971, + 1.0137741046831958, + 1.274971941638609, + 1.5296398326701346, + 1.7777777777777768, + 2.0193857769615344, + 2.2544638302214057, + 2.483011937557393, + 2.705030098969492, + 2.9205183144577074, + 3.129476584022038, + 3.331904907662483, + 3.5278032853790413, + 3.7171717171717162, + 3.9000102030405057, + 4.076318742985409, + 4.246097337006425, + 4.40934598510356, + 4.566064687276808, + 4.71625344352617, + 4.859912253851646, + 4.9970411182532395, + 5.127640036730944, + 5.251709009284765, + 5.369248035914702, + 5.480257116620751, + 5.584736251402917, + 5.682685440261197, + 5.774104683195589, + 5.858993980206099, + 5.937353331292724, + 6.009182736455461, + 6.074482195694316, + 6.133251709009283, + 6.185491276400365, + 6.231200897867563, + 6.270380573410875, + 6.3030303030303, + 6.329150086725842, + 6.348739924497497, + 6.361799816345268 + ], + [ + -27.424140393837362, + -26.758085909601057, + -26.09856137128864, + -25.445566778900115, + -24.799102132435465, + -24.1591674318947, + -23.525762677277825, + -22.89888786858484, + -22.278543005815735, + -21.664728088970513, + -21.057443118049175, + -20.456688093051728, + -19.862463013978164, + -19.274767880828485, + -18.693602693602692, + -18.118967452300787, + -17.550862156922765, + -16.989286807468623, + -16.434241403938373, + -15.885725946332006, + -15.343740434649522, + -14.80828486889093, + -14.279359249056217, + -13.756963575145392, + -13.241097847158452, + -12.731762065095399, + -12.228956228956228, + -11.732680338740945, + -11.242934394449545, + -10.759718396082032, + -10.283032343638403, + -9.812876237118662, + -9.349250076522804, + -8.89215386185083, + -8.441587593102746, + -7.9975512702785405, + -7.560044893378227, + -7.129068462401795, + -6.70462197734925, + -6.286705438220588, + -5.875318845015813, + -5.470462197734926, + -5.07213549637792, + -4.680338740944801, + -4.295071931435567, + -3.9163350678502207, + -3.544128150188757, + -3.1784511784511786, + -2.819304152637485, + -2.4666870727476775, + -2.1205999387817576, + -1.7810427507397204, + -1.4480155086215687, + -1.1215182124273022, + -0.8015508621569237, + -0.48811345781042803, + -0.18120599938781734, + 0.1191715131109079, + 0.41301907968574497, + 0.7003367003366996, + 0.981124375063769, + 1.255382103866953, + 1.523109886746249, + 1.784307723701662, + 2.0389756147331903, + 2.2871135598408325, + 2.52872155902459, + 2.7637996122844597, + 2.992347719620446, + 3.2143658810325473, + 3.4298540965207636, + 3.6388123660850917, + 3.841240689725537, + 4.037139067442097, + 4.226507499234772, + 4.409345985103559, + 4.585654525048463, + 4.755433119069482, + 4.918681767166616, + 5.075400469339862, + 5.225589225589227, + 5.369248035914702, + 5.506376900316293, + 5.636975818794, + 5.76104479134782, + 5.8785838179777565, + 5.989592898683807, + 6.094072033465971, + 6.192021222324252, + 6.2834404652586455, + 6.368329762269155, + 6.446689113355778, + 6.518518518518517, + 6.58381797775737, + 6.642587491072338, + 6.694827058463421, + 6.740536679930617, + 6.779716355473929, + 6.812366085093358, + 6.838485868788896 + ], + [ + -28.246913580246915, + -27.56779920416284, + -26.89521477400265, + -26.229160289766355, + -25.569635751453937, + -24.9166411590654, + -24.270176512600752, + -23.630241812059996, + -22.996837057443116, + -22.369962248750127, + -21.749617385981022, + -21.1358024691358, + -20.52851749821447, + -19.92776247321702, + -19.333537394143452, + -18.745842260993776, + -18.164677073767983, + -17.590041832466078, + -17.021936537088052, + -16.460361187633914, + -15.90531578410366, + -15.356800326497297, + -14.814814814814813, + -14.279359249056217, + -13.750433629221508, + -13.228037955310683, + -12.712172227323743, + -12.202836445260688, + -11.700030609121518, + -11.203754718906236, + -10.714008774614834, + -10.230792776247323, + -9.754106723803694, + -9.28395061728395, + -8.820324456688093, + -8.36322824201612, + -7.912661973268034, + -7.4686256504438315, + -7.031119273543517, + -6.6001428425670845, + -6.175696357514537, + -5.757779818385881, + -5.346393225181105, + -4.941536577900214, + -4.543209876543209, + -4.151413121110092, + -3.766146311600858, + -3.387409448015508, + -3.015202530354045, + -2.649525558616466, + -2.2903785328027766, + -1.9377614529129683, + -1.5916743189470457, + -1.2521171309050083, + -0.9190898887868596, + -0.592592592592593, + -0.27262524232221175, + 0.04081216202428417, + 0.3477196204468921, + 0.6480971329456171, + 0.9419446995204571, + 1.229262320171412, + 1.5100499948984785, + 1.784307723701662, + 2.0520355065809612, + 2.313233343536374, + 2.567901234567902, + 2.816039179675543, + 3.0576471788592996, + 3.292725232119172, + 3.521273339455158, + 3.743291500867257, + 3.9587797163554734, + 4.167737985919804, + 4.37016630956025, + 4.566064687276807, + 4.755433119069482, + 4.938271604938272, + 5.114580144883175, + 5.284358738904193, + 5.4476073870013275, + 5.604326089174574, + 5.754514845423936, + 5.898173655749415, + 6.035302520151005, + 6.165901438628712, + 6.289970411182533, + 6.407509437812466, + 6.518518518518519, + 6.622997653300684, + 6.720946842158962, + 6.812366085093358, + 6.897255382103867, + 6.975614733190491, + 7.047444138353229, + 7.1127435975920825, + 7.17151311090705, + 7.2237526782981325, + 7.269462299765329, + 7.308641975308641 + ], + [ + -29.076216712580347, + -28.384042444648504, + -27.698398122640548, + -27.019283746556475, + -26.34669931639629, + -25.680644832159985, + -25.021120293847567, + -24.368125701459036, + -23.72166105499439, + -23.08172635445363, + -22.448321599836753, + -21.821446791143764, + -21.20110192837466, + -20.58728701152944, + -19.9800020406081, + -19.37924701561065, + -18.785021936537092, + -18.197326803387412, + -17.616161616161616, + -17.04152637485971, + -16.473421079481685, + -15.91184573002755, + -15.356800326497297, + -14.808284868890931, + -14.266299357208448, + -13.730843791449853, + -13.201918171615143, + -12.679522497704319, + -12.163656769717377, + -11.654320987654321, + -11.151515151515152, + -10.655239261299869, + -10.16549331700847, + -9.682277318640955, + -9.205591266197327, + -8.735435159677584, + -8.271808999081728, + -7.814712784409754, + -7.36414651566167, + -6.920110192837465, + -6.482603815937148, + -6.051627384960721, + -5.627180899908174, + -5.209264360779512, + -4.797877767574737, + -4.3930211202938505, + -3.9946944189368443, + -3.6028976635037244, + -3.2176308539944904, + -2.8388939904091406, + -2.46668707274768, + -2.1010101010101017, + -1.7418630751964086, + -1.3892459953066008, + -1.043158861340681, + -0.7036016732986438, + -0.3705744311804918, + -0.04407713498622512, + 0.27589021528415303, + 0.5893276196306492, + 0.8962350780532597, + 1.196612590551985, + 1.4904601571268223, + 1.7777777777777768, + 2.0585654525048462, + 2.3328231813080302, + 2.600550964187329, + 2.8617488011427397, + 3.1164166921742673, + 3.3645546372819104, + 3.606162636465667, + 3.841240689725537, + 4.069788797061524, + 4.291806958473625, + 4.507295173961841, + 4.716253443526169, + 4.918681767166616, + 5.114580144883175, + 5.303948576675849, + 5.4867870625446375, + 5.663095602489543, + 5.83287419651056, + 5.996122844607692, + 6.152841546780942, + 6.303030303030303, + 6.446689113355782, + 6.583817977757373, + 6.714416896235077, + 6.838485868788899, + 6.956024895418835, + 7.0670339761248835, + 7.171513110907051, + 7.269462299765331, + 7.360881542699724, + 7.445770839710234, + 7.524130190796858, + 7.595959595959596, + 7.661259055198449, + 7.720028568513419, + 7.772268135904499 + ], + [ + -29.912049790837667, + -29.20681563105805, + -28.50811141720232, + -27.81593714927048, + -27.130292827262522, + -26.451178451178446, + -25.778594021018257, + -25.11253953678196, + -24.45301499846954, + -23.800020406081007, + -23.15355575961636, + -22.513621059075597, + -21.880216304458727, + -21.25334149576574, + -20.63299663299663, + -20.019181716151408, + -19.411896745230077, + -18.811141720232627, + -18.216916641159063, + -17.629221508009387, + -17.04805632078359, + -16.47342107948168, + -15.90531578410366, + -15.343740434649522, + -14.78869503111927, + -14.240179573512906, + -13.69819406183042, + -13.162738496071828, + -12.633812876237116, + -12.11141720232629, + -11.595551474339352, + -11.086215692276298, + -10.583409856137127, + -10.087133965921842, + -9.597388021630444, + -9.114172023262931, + -8.637485970819302, + -8.167329864299559, + -7.703703703703702, + -7.24660748903173, + -6.796041220283641, + -6.352004897459444, + -5.914498520559126, + -5.483522089582694, + -5.059075604530147, + -4.6411590654014905, + -4.229772472196714, + -3.824915824915824, + -3.426589123558819, + -3.034792368125699, + -2.649525558616468, + -2.2707886950311185, + -1.898581777369655, + -1.5329048056320769, + -1.1737577798183865, + -0.8211406999285789, + -0.47505356596265613, + -0.13549637792061897, + 0.19753086419752985, + 0.5240281603917963, + 0.8439955106621777, + 1.1574329150086737, + 1.4643403734312814, + 1.764717885930006, + 2.0585654525048462, + 2.3458830731558007, + 2.62667074788287, + 2.900928476686051, + 3.1686562595653496, + 3.429854096520763, + 3.6845219875522908, + 3.9326599326599307, + 4.174267931843689, + 4.40934598510356, + 4.637894092439547, + 4.859912253851645, + 5.075400469339862, + 5.284358738904192, + 5.4867870625446375, + 5.682685440261196, + 5.872053872053872, + 6.054892357922659, + 6.231200897867563, + 6.400979491888583, + 6.564228139985714, + 6.720946842158963, + 6.871135598408324, + 7.014794408733799, + 7.1519232731353926, + 7.282522191613099, + 7.406591164166918, + 7.524130190796856, + 7.635139271502906, + 7.739618406285071, + 7.8375675951433506, + 7.928986838077745, + 8.013876135088253, + 8.092235486174877, + 8.164064891337617, + 8.229364350576468 + ], + [ + -30.75441281501888, + -30.036118763391492, + -29.32435465768799, + -28.619120497908384, + -27.920416284052656, + -27.22824201612081, + -26.54259769411285, + -25.863483318028784, + -25.19089888786859, + -24.524844403632287, + -23.86531986531987, + -23.212325272931338, + -22.565860626466694, + -21.92592592592593, + -21.292521171309055, + -20.665646362616066, + -20.04530149984696, + -19.43148658300174, + -18.8242016120804, + -18.223446587082954, + -17.629221508009387, + -17.041526374859714, + -16.460361187633918, + -15.885725946332009, + -15.317620650953987, + -14.756045301499853, + -14.200999897969597, + -13.652484440363231, + -13.110498928680748, + -12.575043362922155, + -12.046117743087443, + -11.523722069176618, + -11.007856341189678, + -10.498520559126622, + -9.995714722987453, + -9.499438832772167, + -9.009692888480771, + -8.526476890113257, + -8.049790837669628, + -7.579634731149885, + -7.116008570554026, + -6.658912355882056, + -6.208346087133968, + -5.7643097643097665, + -5.3268033874094485, + -4.89582695643302, + -4.471380471380474, + -4.053463932251813, + -3.6420773390470362, + -3.237220691766146, + -2.8388939904091446, + -2.4470972349760247, + -2.06183042546679, + -1.6830935618814409, + -1.31088664421998, + -0.9452096724824013, + -0.5860626466687079, + -0.23344556677889994, + 0.11264156718701945, + 0.45219875522905684, + 0.785225997347209, + 1.1117232935414756, + 1.4316906438118537, + 1.7451280481583495, + 2.052035506580961, + 2.3524130190796857, + 2.646260585654526, + 2.9335782063054783, + 3.2143658810325473, + 3.4886236098357317, + 3.75635139271503, + 4.017549229670441, + 4.272217120701969, + 4.520355065809611, + 4.7619630649933695, + 4.997041118253239, + 5.225589225589227, + 5.4476073870013275, + 5.663095602489543, + 5.872053872053873, + 6.074482195694319, + 6.270380573410878, + 6.459749005203551, + 6.642587491072343, + 6.8188960310172435, + 6.988674625038264, + 7.151923273135397, + 7.3086419753086425, + 7.458830731558006, + 7.602489541883483, + 7.739618406285073, + 7.870217324762782, + 7.994286297316603, + 8.111825323946539, + 8.22283440465259, + 8.327313539434753, + 8.425262728293033, + 8.516681971227428, + 8.601571268237937, + 8.67993061932456 + ], + [ + -31.603305785123965, + -30.87195184164881, + -30.14712784409754, + -29.428833792470154, + -28.717069686766656, + -28.011835526987042, + -27.31313131313131, + -26.62095704519947, + -25.935312723191515, + -25.256198347107436, + -24.583613916947247, + -23.917559432710945, + -23.25803489439853, + -22.605040302009996, + -21.958575655545353, + -21.318640955004593, + -20.685236200387717, + -20.058361391694724, + -19.438016528925615, + -18.8242016120804, + -18.216916641159067, + -17.616161616161616, + -17.021936537088052, + -16.434241403938373, + -15.85307621671258, + -15.278440975410673, + -14.71033568003265, + -14.148760330578511, + -13.593714927048259, + -13.045199469441894, + -12.50321395775941, + -11.967758392000817, + -11.438832772166105, + -10.91643709825528, + -10.400571370268338, + -9.891235588205284, + -9.388429752066116, + -8.89215386185083, + -8.402407917559433, + -7.919191919191919, + -7.442505866748289, + -6.97234976022855, + -6.508723599632691, + -6.051627384960718, + -5.601061116212629, + -5.157024793388431, + -4.719518416488114, + -4.2885419855116815, + -3.8640955004591357, + -3.4461789613304745, + -3.0347923681257023, + -2.629935720844812, + -2.2316090194878067, + -1.8398122640546868, + -1.4545454545454557, + -1.0758085909601065, + -0.7036016732986424, + -0.3379247015610639, + 0.021222324252625935, + 0.3738394041424339, + 0.7199265381083565, + 1.059483726150394, + 1.3925109682685428, + 1.7190082644628089, + 2.0389756147331908, + 2.3524130190796866, + 2.659320477502297, + 2.959697990001019, + 3.253545556575859, + 3.540863177226814, + 3.8216508519538834, + 4.095908580757064, + 4.363636363636363, + 4.624834200591776, + 4.879502091623304, + 5.127640036730944, + 5.369248035914702, + 5.604326089174574, + 5.832874196510561, + 6.05489235792266, + 6.270380573410878, + 6.479338842975206, + 6.68176716661565, + 6.877665544332212, + 7.067033976124884, + 7.249872461993675, + 7.426181001938579, + 7.595959595959594, + 7.75920824405673, + 7.915926946229976, + 8.066115702479337, + 8.209774512804817, + 8.346903377206408, + 8.477502295684115, + 8.601571268237935, + 8.719110294867871, + 8.830119375573922, + 8.934598510356086, + 9.032547699214366, + 9.123966942148758 + ], + [ + -32.458728701152936, + -31.714314865830005, + -30.97643097643097, + -30.245077032955813, + -29.520253035404544, + -28.80195898377716, + -28.09019487807366, + -27.384960718294046, + -26.68625650443832, + -25.994082236506472, + -25.308437914498516, + -24.62932353841444, + -23.956739108254254, + -23.290684624017953, + -22.631160085705535, + -21.978165493317004, + -21.331700846852357, + -20.691766146311593, + -20.058361391694717, + -19.43148658300173, + -18.811141720232623, + -18.197326803387405, + -17.59004183246607, + -16.98928680746862, + -16.395061728395056, + -15.80736659524538, + -15.226201408019584, + -14.651566166717679, + -14.083460871339655, + -13.521885521885517, + -12.966840118355268, + -12.418324660748901, + -11.87633914906642, + -11.340883583307821, + -10.811957963473112, + -10.289562289562285, + -9.773696561575345, + -9.264360779512291, + -8.761554943373122, + -8.265279053157837, + -7.775533108866439, + -7.292317110498928, + -6.815631058055299, + -6.3454749515355555, + -5.881848790939697, + -5.424752576267727, + -4.9741863075196395, + -4.530149984695437, + -4.09264360779512, + -3.661667176818689, + -3.2372206917661455, + -2.8193041526374847, + -2.4079175594327085, + -2.0030609121518186, + -1.604734210794817, + -1.212937455361697, + -0.8276706458524626, + -0.44893378226711356, + -0.07672686460565337, + 0.28895010713192526, + 0.6480971329456187, + 1.0007142128354263, + 1.3468013468013456, + 1.6863585348433825, + 2.019385776961535, + 2.3458830731558007, + 2.6658504234261824, + 2.979287827772675, + 3.2861952861952854, + 3.586572798694011, + 3.8804203652688507, + 4.1677379859198025, + 4.4485256606468715, + 4.722783389450055, + 4.990511172329354, + 5.251709009284764, + 5.506376900316293, + 5.754514845423936, + 5.996122844607692, + 6.231200897867563, + 6.459749005203551, + 6.68176716661565, + 6.8972553821038645, + 7.106213651668197, + 7.308641975308639, + 7.504540353025201, + 7.693908784817875, + 7.876747270686661, + 8.053055810631566, + 8.222834404652584, + 8.386083052749715, + 8.542801754922966, + 8.692990511172328, + 8.836649321497804, + 8.973778185899395, + 9.104377104377102, + 9.228446076930922, + 9.345985103560857, + 9.45699418426691, + 9.561473319049071 + ], + [ + -33.32068156310581, + -32.56320783593511, + -31.812264054688292, + -31.067850219365376, + -30.329966329966332, + -29.598612386491176, + -28.873788388939907, + -28.155494337312525, + -27.44373023160902, + -26.73849607182941, + -26.039791857973675, + -25.347617590041835, + -24.661973268033876, + -23.982858891949803, + -23.31027446178961, + -22.644219977553313, + -21.984695439240898, + -21.331700846852364, + -20.685236200387717, + -20.045301499846957, + -19.41189674523008, + -18.785021936537092, + -18.164677073767983, + -17.550862156922765, + -16.943577186001427, + -16.34282216100398, + -15.748597081930416, + -15.160901948780738, + -14.579736761554944, + -14.005101520253039, + -13.436996224875015, + -12.875420875420879, + -12.320375471890625, + -11.771860014284258, + -11.229874502601776, + -10.694418936843181, + -10.16549331700847, + -9.643097643097644, + -9.127231915110706, + -8.617896133047648, + -8.115090296908479, + -7.618814406693198, + -7.129068462401797, + -6.6458524640342835, + -6.169166411590654, + -5.699010305070914, + -5.235384144475056, + -4.778287929803083, + -4.327721661054994, + -3.883685338230792, + -3.4461789613304785, + -3.0152025303540464, + -2.5907560453014997, + -2.1728395061728385, + -1.7614529129680665, + -1.3565962656871762, + -0.9582695643301706, + -0.5664728088970505, + -0.18120599938781967, + 0.19753086419752952, + 0.5697377818589938, + 0.9354147535965726, + 1.2945617794102624, + 1.6471788593000698, + 1.993265993265993, + 2.3328231813080302, + 2.665850423426182, + 2.9923477196204455, + 3.3123150698908264, + 3.6257524742373226, + 3.9326599326599334, + 4.233037445158656, + 4.526885011733496, + 4.8142026323844505, + 5.09499030711152, + 5.369248035914701, + 5.636975818794001, + 5.898173655749414, + 6.152841546780941, + 6.400979491888583, + 6.642587491072343, + 6.877665544332212, + 7.106213651668196, + 7.3282318130803, + 7.543720028568513, + 7.752678298132846, + 7.9551066217732895, + 8.151004999489846, + 8.340373431282524, + 8.523211917151313, + 8.699520457096213, + 8.869299051117235, + 9.032547699214367, + 9.189266401387615, + 9.339455157636978, + 9.483113967962455, + 9.620242832364045, + 9.75084175084175, + 9.874910723395574, + 9.992449750025509 + ], + [ + -34.18916437098255, + -33.41863075196408, + -32.654627078869495, + -31.897153351698805, + -31.146209570451994, + -30.401795735129063, + -29.66391184573002, + -28.93255790225487, + -28.207733904703602, + -27.489439853076213, + -26.77767574737271, + -26.072441587593097, + -25.373737373737374, + -24.68156310580553, + -23.995918783797567, + -23.316804407713498, + -22.644219977553313, + -21.978165493317007, + -21.31864095500459, + -20.66564636261606, + -20.019181716151408, + -19.379247015610648, + -18.745842260993772, + -18.118967452300783, + -17.498622589531678, + -16.88480767268646, + -16.277522701765122, + -15.676767676767676, + -15.082542597694111, + -14.494847464544435, + -13.913682277318639, + -13.339047036016732, + -12.77094174063871, + -12.20936639118457, + -11.65432098765432, + -11.10580553004795, + -10.563820018365472, + -10.028364452606874, + -9.499438832772164, + -8.977043158861338, + -8.461177430874397, + -7.951841648811347, + -7.449035812672176, + -6.952759922456891, + -6.463013978165491, + -5.979797979797981, + -5.503111927354352, + -5.032955820834608, + -4.56932966023875, + -4.112233445566776, + -3.661667176818692, + -3.21763085399449, + -2.780124477094173, + -2.3491480461177408, + -1.924701561065198, + -1.506785021936537, + -1.095398428731761, + -0.6905417814508708, + -0.29221508009386943, + 0.09958167533925044, + 0.4848484848484851, + 0.8635853484338342, + 1.2357922660952945, + 1.601469237832873, + 1.9606162636465667, + 2.313233343536374, + 2.659320477502297, + 2.998877665544331, + 3.3319049076624827, + 3.658402203856749, + 3.9783695541271302, + 4.291806958473623, + 4.598714416896234, + 4.8990919293949595, + 5.192939495969799, + 5.48025711662075, + 5.761044791347821, + 6.035302520151005, + 6.303030303030303, + 6.5642281399857145, + 6.818896031017244, + 7.067033976124884, + 7.308641975308641, + 7.543720028568514, + 7.772268135904498, + 7.9942862973166005, + 8.209774512804815, + 8.418732782369144, + 8.62116110600959, + 8.817059483726148, + 9.006427915518822, + 9.189266401387611, + 9.365574941332516, + 9.535353535353533, + 9.698602183450665, + 9.855320885623913, + 10.005509641873276, + 10.149168452198753, + 10.286297316600347, + 10.416896235078049 + ], + [ + -35.064177124783185, + -34.280583613916946, + -33.5035200489746, + -32.732986429956135, + -31.96898275686155, + -31.211509029690852, + -30.46056524844404, + -29.716151413121118, + -28.978267523722074, + -28.24691358024692, + -27.52208958269565, + -26.80379553106826, + -26.092031425364766, + -25.38679726558515, + -24.688093051729417, + -23.995918783797578, + -23.310274461789618, + -22.631160085705545, + -21.958575655545356, + -21.292521171309055, + -20.632996632996637, + -19.980002040608106, + -19.333537394143455, + -18.6936026936027, + -18.060197938985823, + -17.433323130292834, + -16.812978267523725, + -16.199163350678507, + -15.591878379757173, + -14.991123354759722, + -14.396898275686159, + -13.809203142536479, + -13.228037955310686, + -12.653402714008777, + -12.085297418630756, + -11.523722069176618, + -10.968676665646365, + -10.42016120804, + -9.878175696357518, + -9.34272013059892, + -8.81379451076421, + -8.291398836853388, + -7.775533108866446, + -7.26619732680339, + -6.763391490664219, + -6.267115600448938, + -5.777369656157538, + -5.294153657790023, + -4.817467605346394, + -4.347311498826651, + -3.8836853382307956, + -3.4265891235588226, + -2.9760228548107346, + -2.531986531986532, + -2.094480155086219, + -1.6635037241097872, + -1.2390572390572403, + -0.8211406999285786, + -0.40975410672380663, + -0.004897459442916086, + 0.39342924191408946, + 0.7852259973472095, + 1.1704928068564406, + 1.5492296704417894, + 1.921436588103254, + 2.2871135598408325, + 2.646260585654526, + 2.9988776655443306, + 3.3449647995102527, + 3.6845219875522908, + 4.0175492296704425, + 4.344046525864706, + 4.664013876135089, + 4.977451280481583, + 5.284358738904195, + 5.584736251402917, + 5.878583817977757, + 6.165901438628712, + 6.446689113355781, + 6.720946842158963, + 6.988674625038264, + 7.249872461993674, + 7.5045403530252015, + 7.752678298132846, + 7.9942862973166005, + 8.229364350576475, + 8.45791245791246, + 8.679930619324558, + 8.895418834812777, + 9.104377104377106, + 9.306805428017547, + 9.50270380573411, + 9.692072237526785, + 9.874910723395574, + 10.051219263340478, + 10.220997857361496, + 10.384246505458629, + 10.540965207631876, + 10.69115396388124, + 10.834812774206716 + ], + [ + -35.945719824507705, + -35.14906642179369, + -34.35894296500357, + -33.57534945413733, + -32.79828588919498, + -32.02775227017651, + -31.26374859708193, + -30.506274869911234, + -29.75533108866442, + -29.010917253341496, + -28.273033363942456, + -27.541679420467297, + -26.81685542291603, + -26.098561371288646, + -25.386797265585145, + -24.68156310580553, + -23.982858891949803, + -23.290684624017956, + -22.605040302009996, + -21.925925925925927, + -21.25334149576574, + -20.587287011529437, + -19.92776247321702, + -19.274767880828488, + -18.62830323436384, + -17.98836853382308, + -17.3549637792062, + -16.728088970513213, + -16.107744107744107, + -15.49392919089889, + -14.886644219977555, + -14.285889194980104, + -13.69166411590654, + -13.10396898275686, + -12.522803795531068, + -11.94816855422916, + -11.38006325885114, + -10.818487909397, + -10.263442505866749, + -9.714927048260382, + -9.172941536577898, + -8.637485970819307, + -8.108560350984595, + -7.586164677073768, + -7.070298949086826, + -6.560963167023775, + -6.058157330884605, + -5.561881440669319, + -5.07213549637792, + -4.588919498010406, + -4.112233445566781, + -3.6420773390470367, + -3.178451178451178, + -2.7213549637792047, + -2.270788695031121, + -1.826752372206919, + -1.3892459953066014, + -0.9582695643301697, + -0.5338230792776271, + -0.11590654014896562, + 0.2954800530558104, + 0.7003367003367007, + 1.0986634016937025, + 1.490460157126822, + 1.875726966636057, + 2.2544638302214057, + 2.62667074788287, + 2.992347719620445, + 3.3514947454341386, + 3.7041118253239462, + 4.050198959289869, + 4.3897561473319024, + 4.722783389450056, + 5.049280685644321, + 5.369248035914703, + 5.682685440261196, + 5.9895928986838065, + 6.289970411182532, + 6.583817977757372, + 6.871135598408324, + 7.151923273135395, + 7.426181001938577, + 7.693908784817875, + 7.9551066217732895, + 8.209774512804813, + 8.457912457912458, + 8.699520457096215, + 8.934598510356084, + 9.163146617692073, + 9.385164779104173, + 9.600652994592386, + 9.809611264156718, + 10.012039587797162, + 10.207937965513722, + 10.397306397306398, + 10.580144883175185, + 10.756453423120089, + 10.926232017141107, + 11.089480665238241, + 11.246199367411487 + ], + [ + -36.8337924701561, + -36.02407917559432, + -35.22089582695642, + -34.42424242424242, + -33.634118967452295, + -32.850525456586055, + -32.0734618916437, + -31.30292827262524, + -30.538924599530656, + -29.781450872359954, + -29.030507091113144, + -28.28609325579022, + -27.548209366391177, + -26.816855422916028, + -26.092031425364752, + -25.37373737373737, + -24.661973268033872, + -23.956739108254254, + -23.258034894398527, + -22.565860626466684, + -21.88021630445872, + -21.20110192837465, + -20.528517498214462, + -19.86246301397816, + -19.202938475665743, + -18.549943883277216, + -17.903479236812565, + -17.26354453627181, + -16.63013978165493, + -16.00326497296194, + -15.382920110192835, + -14.769105193347615, + -14.161820222426282, + -13.56106519742883, + -12.966840118355266, + -12.379144985205588, + -11.797979797979794, + -11.223344556677889, + -10.655239261299865, + -10.093663911845727, + -9.538618508315475, + -8.990103050709111, + -8.44811753902663, + -7.912661973268032, + -7.383736353433319, + -6.861340679522498, + -6.345474951535557, + -5.836139169472501, + -5.333333333333331, + -4.837057443118047, + -4.347311498826651, + -3.8640955004591357, + -3.3874094480155073, + -2.917253341495763, + -2.453627180899909, + -1.9965309662279358, + -1.545964697479848, + -1.1019283746556454, + -0.6644219977553323, + -0.2334455667789006, + 0.19100091827364585, + 0.6089174574023073, + 1.0203040506070793, + 1.4251606978879694, + 1.823487399244975, + 2.2152841546780944, + 2.6005509641873292, + 2.979287827772675, + 3.351494745434138, + 3.717171717171717, + 4.076318742985411, + 4.428935822875214, + 4.775022956841138, + 5.114580144883174, + 5.447607387001327, + 5.7741046831955884, + 6.094072033465972, + 6.407509437812466, + 6.714416896235077, + 7.014794408733801, + 7.3086419753086425, + 7.595959595959594, + 7.876747270686662, + 8.151004999489848, + 8.418732782369144, + 8.679930619324558, + 8.934598510356086, + 9.182736455463726, + 9.424344454647484, + 9.659422507907355, + 9.887970615243336, + 10.109988776655442, + 10.325476992143656, + 10.534435261707987, + 10.73686358534843, + 10.93276196306499, + 11.122130394857665, + 11.304968880726454, + 11.481277420671358, + 11.651056014692374 + ], + [ + -37.7283950617284, + -36.90562187531884, + -36.08937863483318, + -35.27966534027141, + -34.47648199163351, + -33.6798285889195, + -32.88970513212938, + -32.106111621263146, + -31.329048056320786, + -30.55851443730232, + -29.794510764207736, + -29.03703703703704, + -28.286093255790234, + -27.5416794204673, + -26.803795531068257, + -26.072441587593104, + -25.347617590041835, + -24.62932353841445, + -23.917559432710952, + -23.212325272931338, + -22.513621059075604, + -21.821446791143764, + -21.135802469135804, + -20.456688093051735, + -19.784103662891543, + -19.118049178655244, + -18.458524640342823, + -17.805530047954292, + -17.15906540148965, + -16.519130700948885, + -15.885725946332009, + -15.25885113763902, + -14.638506274869913, + -14.024691358024693, + -13.417406387103359, + -12.81665136210591, + -12.222426283032346, + -11.634731149882667, + -11.053565962656876, + -10.478930721354965, + -9.910825425976942, + -9.349250076522809, + -8.794204672992555, + -8.245689215386188, + -7.703703703703705, + -7.1682481379451115, + -6.6393225181104, + -6.116926844199574, + -5.601061116212632, + -5.091725334149577, + -4.5889194980104095, + -4.092643607795125, + -3.6028976635037244, + -3.1196816651362105, + -2.6429956126925855, + -2.1728395061728416, + -1.709213345576983, + -1.2521171309050096, + -0.8015508621569261, + -0.35751453933272326, + 0.07999183756759409, + 0.510968268544026, + 0.9354147535965687, + 1.3533312927252297, + 1.7647178859300063, + 2.169574533210896, + 2.567901234567902, + 2.9596979900010183, + 3.3449647995102527, + 3.7237016630956026, + 4.095908580757066, + 4.461585552494641, + 4.820732578308336, + 5.173349658198143, + 5.519436792164065, + 5.858993980206098, + 6.192021222324252, + 6.518518518518519, + 6.838485868788899, + 7.151923273135393, + 7.458830731558007, + 7.759208244056729, + 8.053055810631566, + 8.340373431282524, + 8.62116110600959, + 8.895418834812777, + 9.163146617692075, + 9.424344454647484, + 9.679012345679013, + 9.927150290786654, + 10.168758289970409, + 10.403836343230285, + 10.63238445056627, + 10.854402611978372, + 11.069890827466587, + 11.278849097030916, + 11.481277420671361, + 11.677175798387921, + 11.866544230180594, + 12.049382716049383 + ], + [ + -38.629527599224566, + -37.79369452096724, + -36.964391388633814, + -36.141618202224265, + -35.325374961738596, + -34.515661667176815, + -33.71247831853892, + -32.91582491582491, + -32.125701459034794, + -31.342107948168554, + -30.5650443832262, + -29.79451076420773, + -29.03050709111315, + -28.273033363942453, + -27.522089582695642, + -26.77767574737272, + -26.039791857973675, + -25.30843791449852, + -24.583613916947247, + -23.865319865319865, + -23.15355575961636, + -22.448321599836753, + -21.749617385981022, + -21.05744311804918, + -20.37179879604122, + -19.69268441995715, + -19.020099989796957, + -18.35404550556066, + -17.694520967248238, + -17.041526374859707, + -16.395061728395063, + -15.755127027854302, + -15.121722273237424, + -14.494847464544431, + -13.87450260177533, + -13.260687684930106, + -12.653402714008775, + -12.052647689011325, + -11.458422609937761, + -10.870727476788083, + -10.289562289562287, + -9.714927048260384, + -9.146821752882358, + -8.585246403428222, + -8.030200999897968, + -7.481685542291605, + -6.9397000306091225, + -6.4042444648505255, + -5.875318845015814, + -5.352923171104988, + -4.83705744311805, + -4.327721661054994, + -3.824915824915824, + -3.328639934700539, + -2.8388939904091437, + -2.3556779920416293, + -1.878991939598, + -1.408835833078256, + -0.9452096724824017, + -0.4881134578104287, + -0.03754718906234045, + 0.4064891337618619, + 0.843995510662175, + 1.2749719416386065, + 1.699418426691154, + 2.1173349658198144, + 2.528721559024591, + 2.9335782063054774, + 3.3319049076624827, + 3.7237016630956026, + 4.108968472604837, + 4.4877053361901815, + 4.859912253851647, + 5.225589225589225, + 5.584736251402919, + 5.937353331292722, + 6.283440465258646, + 6.622997653300684, + 6.956024895418835, + 7.2825221916131, + 7.602489541883484, + 7.915926946229976, + 8.222834404652584, + 8.523211917151311, + 8.81705948372615, + 9.104377104377106, + 9.385164779104173, + 9.659422507907353, + 9.927150290786654, + 10.188348127742067, + 10.44301601877359, + 10.691153963881236, + 10.932761963064992, + 11.167840016324863, + 11.396388123660849, + 11.618406285072949, + 11.833894500561165, + 12.042852770125494, + 12.245281093765945, + 12.4411794714825 + ], + [ + -39.53719008264462, + -38.68829711253953, + -37.84593408835832, + -37.01010101010101, + -36.18079787776757, + -35.35802469135802, + -34.54178145087235, + -33.732068156310575, + -32.92888480767268, + -32.132231404958674, + -31.342107948168547, + -30.55851443730231, + -29.78145087235996, + -29.01091725334149, + -28.246913580246904, + -27.48943985307621, + -26.738496071829402, + -25.994082236506472, + -25.256198347107432, + -24.52484440363228, + -23.800020406081003, + -23.08172635445362, + -22.36996224875012, + -21.66472808897051, + -20.966023875114775, + -20.27384960718294, + -19.58820528517498, + -18.909090909090903, + -18.236506478930718, + -17.570451994694416, + -16.910927456381998, + -16.257932863993467, + -15.611468217528818, + -14.971533516988059, + -14.338128762371182, + -13.711253953678192, + -13.090909090909086, + -12.477094174063868, + -11.869809203142534, + -11.269054178145083, + -10.674829099071518, + -10.087133965921844, + -9.50596877869605, + -8.93133353739414, + -8.363228242016117, + -7.801652892561983, + -7.246607489031731, + -6.698092031425363, + -6.15610651974288, + -5.620650953984283, + -5.091725334149576, + -4.56932966023875, + -4.053463932251808, + -3.5441281501887527, + -3.0413223140495873, + -2.545046423834302, + -2.055300479542902, + -1.5720844811753878, + -1.095398428731763, + -0.6252423222120194, + -0.16161616161616066, + 0.2954800530558124, + 0.7460463218038962, + 1.1900826446280979, + 1.627589021528416, + 2.058565452504847, + 2.483011937557394, + 2.900928476686051, + 3.3123150698908264, + 3.7171717171717176, + 4.1154984185287224, + 4.507295173961838, + 4.892561983471073, + 5.271298847056422, + 5.643505764717887, + 6.009182736455461, + 6.3683297622691555, + 6.720946842158963, + 7.067033976124884, + 7.406591164166919, + 7.739618406285074, + 8.066115702479337, + 8.386083052749717, + 8.699520457096215, + 9.006427915518822, + 9.306805428017551, + 9.600652994592387, + 9.887970615243338, + 10.168758289970409, + 10.44301601877359, + 10.710743801652887, + 10.971941638608305, + 11.22660952963983, + 11.474747474747474, + 11.71635547393123, + 11.951433527191101, + 12.179981634527087, + 12.401999795939187, + 12.617488011427403, + 12.826446280991732 + ], + [ + -40.45138251198857, + -39.58942965003571, + -38.734006734006726, + -37.88511376390164, + -37.04275073972044, + -36.206917661463116, + -35.37761452912968, + -34.55484134272014, + -33.73859810223446, + -32.92888480767269, + -32.125701459034794, + -31.329048056320786, + -30.538924599530667, + -29.755331088664423, + -28.978267523722067, + -28.207733904703602, + -27.443730231609024, + -26.686256504438326, + -25.93531272319151, + -25.190898887868588, + -24.45301499846954, + -23.721661054994392, + -22.996837057443116, + -22.278543005815735, + -21.566778900112233, + -20.86154474033262, + -20.16284052647689, + -19.470666258545048, + -18.785021936537092, + -18.105907560453016, + -17.433323130292827, + -16.76726864605653, + -16.107744107744107, + -15.454749515355577, + -14.80828486889093, + -14.16835016835017, + -13.534945413733293, + -12.908070605040303, + -12.2877257422712, + -11.673910825425978, + -11.06662585450464, + -10.465870829507198, + -9.871645750433629, + -9.283950617283951, + -8.702785430058157, + -8.128150188756251, + -7.560044893378229, + -6.99846954392409, + -6.443424140393836, + -5.89490868278747, + -5.352923171104991, + -4.817467605346394, + -4.2885419855116815, + -3.7661463116008553, + -3.250280583613919, + -2.740944801550863, + -2.238138965411692, + -1.7418630751964068, + -1.2521171309050119, + -0.7689011325374973, + -0.2922150800938679, + 0.17794102642587606, + 0.6415671870217301, + 1.098663401693703, + 1.5492296704417918, + 1.9932659932659935, + 2.4307723701663115, + 2.861748801142739, + 3.2861952861952863, + 3.704111825323947, + 4.115498418528723, + 4.52035506580961, + 4.918681767166616, + 5.310478522599736, + 5.69574533210897, + 6.074482195694315, + 6.446689113355781, + 6.812366085093359, + 7.171513110907052, + 7.524130190796857, + 7.870217324762783, + 8.209774512804817, + 8.542801754922966, + 8.869299051117235, + 9.189266401387613, + 9.50270380573411, + 9.80961126415672, + 10.109988776655442, + 10.403836343230285, + 10.691153963881238, + 10.971941638608303, + 11.246199367411492, + 11.513927150290789, + 11.775124987246203, + 12.029792878277728, + 12.277930823385372, + 12.519538822569128, + 12.754616875828999, + 12.983164983164984, + 13.205183144577084 + ], + [ + -41.3721048872564, + -40.497092133455766, + -39.62860932557901, + -38.76665646362616, + -37.91123354759718, + -37.06234057749209, + -36.219977553310876, + -35.38414447505356, + -34.554841342720124, + -33.732068156310575, + -32.915824915824906, + -32.10611162126313, + -31.302928272625238, + -30.50627486991123, + -29.716151413121104, + -28.93255790225487, + -28.15549433731252, + -27.384960718294046, + -26.62095704519946, + -25.86348331802877, + -25.112539536781952, + -24.368125701459032, + -23.630241812059992, + -22.898887868584833, + -22.174063871033564, + -21.455769819406182, + -20.744005713702677, + -20.038771553923066, + -19.340067340067336, + -18.647893072135496, + -17.962248750127536, + -17.283134374043463, + -16.610549943883278, + -15.944495459646971, + -15.284970921334557, + -14.63197632894602, + -13.985511682481377, + -13.345576981940614, + -12.71217222732374, + -12.085297418630748, + -11.464952555861643, + -10.851137639016425, + -10.24385266809509, + -9.643097643097642, + -9.048872564024077, + -8.4611774308744, + -7.880012243648607, + -7.305377002346698, + -6.737271706968674, + -6.1756963575145365, + -5.6206509539842875, + -5.0721354963779195, + -4.530149984695436, + -3.99469441893684, + -3.465768799102133, + -2.943373125191307, + -2.4275073972043653, + -1.9181716151413097, + -1.4153657790021439, + -0.9190898887868586, + -0.42934394449545876, + 0.053872053872055625, + 0.5305581063156806, + 1.0007142128354238, + 1.4643403734312828, + 1.9214365881032553, + 2.372002856851344, + 2.816039179675542, + 3.253545556575859, + 3.684521987552291, + 4.108968472604837, + 4.526885011733494, + 4.938271604938271, + 5.343128252219161, + 5.7414549535761665, + 6.133251709009281, + 6.518518518518517, + 6.897255382103866, + 7.26946229976533, + 7.635139271502906, + 7.994286297316603, + 8.346903377206406, + 8.692990511172326, + 9.032547699214367, + 9.365574941332515, + 9.692072237526784, + 10.012039587797164, + 10.325476992143654, + 10.632384450566269, + 10.932761963064992, + 11.226609529639827, + 11.513927150290787, + 11.794714825017852, + 12.068972553821038, + 12.336700336700334, + 12.597898173655745, + 12.852566064687274, + 13.100704009794914, + 13.342312008978677, + 13.577390062238543 + ], + [ + -42.29935720844812, + -41.411284562799715, + -40.5297418630752, + -39.65472910927457, + -38.786246301397824, + -37.92429343944496, + -37.06887052341598, + -36.2199775533109, + -35.37761452912969, + -34.541781450872364, + -33.71247831853893, + -32.88970513212938, + -32.07346189164372, + -31.263748597081936, + -30.46056524844404, + -29.66391184573003, + -28.87378838893991, + -28.09019487807367, + -27.313131313131315, + -26.54259769411285, + -25.778594021018264, + -25.021120293847574, + -24.270176512600756, + -23.525762677277832, + -22.787878787878793, + -22.05652484440364, + -21.331700846852364, + -20.613406795224982, + -19.90164268952148, + -19.196408529741866, + -18.49770431588614, + -17.805530047954296, + -17.119885725946336, + -16.44077134986226, + -15.768186919702075, + -15.102132435465771, + -14.442607897153355, + -13.789613304764822, + -13.143148658300177, + -12.503213957759415, + -11.869809203142536, + -11.24293439444955, + -10.622589531680447, + -10.008774614835223, + -9.401489643913887, + -8.800734618916442, + -8.206509539842877, + -7.618814406693196, + -7.037649219467402, + -6.463013978165494, + -5.894908682787474, + -5.333333333333336, + -4.778287929803082, + -4.229772472196714, + -3.6877869605142366, + -3.152331394755639, + -2.6234057749209274, + -2.1010101010101003, + -1.5851443730231642, + -1.075808590960108, + -0.5730027548209373, + -0.07672686460565226, + 0.41301907968574314, + 0.8962350780532575, + 1.3729211304968876, + 1.8430772370166308, + 2.30670339761249, + 2.7637996122844593, + 3.214365881032547, + 3.65840220385675, + 4.095908580757067, + 4.526885011733494, + 4.951331496786042, + 5.369248035914703, + 5.780634629119479, + 6.185491276400365, + 6.583817977757372, + 6.975614733190492, + 7.360881542699726, + 7.7396184062850715, + 8.11182532394654, + 8.477502295684115, + 8.836649321497806, + 9.189266401387616, + 9.535353535353535, + 9.874910723395576, + 10.207937965513725, + 10.534435261707989, + 10.854402611978372, + 11.167840016324867, + 11.474747474747472, + 11.775124987246201, + 12.068972553821041, + 12.356290174471996, + 12.637077849199065, + 12.911335578002245, + 13.179063360881544, + 13.440261197836957, + 13.694929088868488, + 13.943067033976126 + ], + [ + -43.23313947556372, + -42.332006938067536, + -41.43740434649525, + -40.54933170084686, + -39.66778900112233, + -38.7927762473217, + -37.92429343944495, + -37.062340577492094, + -36.20691766146311, + -35.358024691358025, + -34.51566166717682, + -33.6798285889195, + -32.85052545658606, + -32.027752270176514, + -31.21150902969085, + -30.401795735129063, + -29.598612386491176, + -28.80195898377717, + -28.011835526987042, + -27.228242016120802, + -26.451178451178446, + -25.680644832159985, + -24.9166411590654, + -24.1591674318947, + -23.40822365064789, + -22.663809815324967, + -21.925925925925924, + -21.19457198245077, + -20.4697479848995, + -19.751453933272117, + -19.039689827568615, + -18.334455667789, + -17.635751453933274, + -16.943577186001427, + -16.257932863993467, + -15.578818487909396, + -14.90623405774921, + -14.240179573512904, + -13.58065503520049, + -12.927660442811957, + -12.28119579634731, + -11.641261095806552, + -11.007856341189676, + -10.380981532496683, + -9.760636669727576, + -9.14682175288236, + -8.539536781961026, + -7.938781756963574, + -7.34455667789001, + -6.756861544740331, + -6.17569635751454, + -5.601061116212632, + -5.032955820834609, + -4.471380471380469, + -3.9163350678502216, + -3.367819610243853, + -2.825834098561371, + -2.290378532802774, + -1.761452912968067, + -1.23905723905724, + -0.7231915110702989, + -0.21385572900724314, + 0.2889501071319225, + 0.7852259973472078, + 1.274971941638608, + 1.7581879400061218, + 2.2348739924497516, + 2.705030098969491, + 3.1686562595653496, + 3.625752474237323, + 4.076318742985411, + 4.520355065809609, + 4.957861442709927, + 5.388837873686358, + 5.813284358738905, + 6.231200897867561, + 6.642587491072339, + 7.047444138353229, + 7.445770839710233, + 7.8375675951433506, + 8.22283440465259, + 8.601571268237935, + 8.973778185899395, + 9.339455157636978, + 9.698602183450665, + 10.051219263340476, + 10.397306397306398, + 10.73686358534843, + 11.069890827466585, + 11.396388123660849, + 11.716355473931227, + 12.029792878277728, + 12.336700336700336, + 12.637077849199061, + 12.930925415773899, + 13.218243036424852, + 13.499030711151923, + 13.773288439955104, + 14.041016222834406, + 14.302214059789815 + ], + [ + -44.173451688603194, + -43.25925925925925, + -42.351596775839184, + -41.45046423834302, + -40.55586164677074, + -39.66778900112233, + -38.7862463013978, + -37.911233547597185, + -37.04275073972043, + -36.18079787776757, + -35.32537496173859, + -34.476481991633506, + -33.634118967452295, + -32.79828588919497, + -31.968982756861536, + -31.146209570451987, + -30.329966329966325, + -29.520253035404544, + -28.71706968676665, + -27.920416284052642, + -27.130292827262515, + -26.346699316396283, + -25.56963575145393, + -24.799102132435458, + -24.03509845934088, + -23.277624732170185, + -22.52668095092337, + -21.782267115600447, + -21.044383226201404, + -20.313029282726248, + -19.58820528517498, + -18.869911233547594, + -18.158147127844096, + -17.452912968064474, + -16.75420875420875, + -16.062034486276907, + -15.376390164268948, + -14.697275788184875, + -14.02469135802469, + -13.358636873788384, + -12.699112335475967, + -12.04611774308744, + -11.399653096622792, + -10.759718396082029, + -10.126313641465153, + -9.499438832772165, + -8.879093970003058, + -8.265279053157839, + -7.6579940822365025, + -7.057239057239053, + -6.463013978165492, + -5.875318845015813, + -5.2941536577900195, + -4.71951841648811, + -4.151413121110091, + -3.5898377716559526, + -3.0347923681256996, + -2.486276910519331, + -1.9442913988368544, + -1.4088358330782569, + -0.8799102132435452, + -0.3575145393327186, + 0.1583511886542177, + 0.667686970717273, + 1.1704928068564442, + 1.6667686970717286, + 2.1565146413631293, + 2.639730639730639, + 3.1164166921742678, + 3.586572798694012, + 4.050198959289871, + 4.507295173961839, + 4.957861442709927, + 5.401897765534129, + 5.8394041424344465, + 6.270380573410874, + 6.694827058463422, + 7.1127435975920825, + 7.524130190796857, + 7.928986838077745, + 8.327313539434755, + 8.71911029486787, + 9.104377104377102, + 9.483113967962455, + 9.855320885623913, + 10.220997857361496, + 10.580144883175187, + 10.932761963064989, + 11.278849097030914, + 11.61840628507295, + 11.9514335271911, + 12.277930823385368, + 12.597898173655746, + 12.911335578002245, + 13.218243036424852, + 13.518620548923575, + 13.812468115498415, + 14.099785736149368, + 14.380573410876442, + 14.65483113967962 + ], + [ + -45.12029384756657, + -44.193041526374856, + -43.27231915110703, + -42.358126721763085, + -41.45046423834303, + -40.54933170084685, + -39.65472910927456, + -38.76665646362617, + -37.88511376390164, + -37.01010101010101, + -36.141618202224265, + -35.2796653402714, + -34.42424242424243, + -33.57534945413734, + -32.73298642995613, + -31.897153351698808, + -31.067850219365376, + -30.24507703295582, + -29.428833792470158, + -28.61912049790838, + -27.815937149270482, + -27.01928374655648, + -26.229160289766348, + -25.445566778900115, + -24.668503213957756, + -23.897969594939294, + -23.133965921844712, + -22.376492194674015, + -21.625548413427204, + -20.88113457810428, + -20.143250688705237, + -19.411896745230084, + -18.687072747678812, + -17.968778696051423, + -17.257014590347925, + -16.55178043056831, + -15.853076216712584, + -15.160901948780737, + -14.475257626772784, + -13.796143250688706, + -13.123558820528517, + -12.457504336292219, + -11.7979797979798, + -11.144985205591269, + -10.49852055912662, + -9.858585858585862, + -9.225181103968985, + -8.598306295275995, + -7.977961432506888, + -7.364146515661666, + -6.756861544740335, + -6.156106519742885, + -5.561881440669319, + -4.97418630751964, + -4.3930211202938505, + -3.8183858789919407, + -3.250280583613918, + -2.6887052341597792, + -2.133659830629531, + -1.5851443730231631, + -1.0431588613406806, + -0.507703295582083, + 0.021222324252623714, + 0.5436179981634499, + 1.0594837261503918, + 1.568819508213447, + 2.0716253443526185, + 2.567901234567899, + 3.0576471788592983, + 3.5408631772268135, + 4.0175492296704425, + 4.4877053361901815, + 4.951331496786041, + 5.408427711458014, + 5.858993980206102, + 6.303030303030299, + 6.740536679930618, + 7.17151311090705, + 7.595959595959595, + 8.013876135088253, + 8.425262728293035, + 8.83011937557392, + 9.228446076930922, + 9.620242832364045, + 10.005509641873276, + 10.384246505458629, + 10.75645342312009, + 11.122130394857665, + 11.481277420671361, + 11.833894500561167, + 12.179981634527085, + 12.519538822569126, + 12.852566064687275, + 13.179063360881544, + 13.499030711151924, + 13.812468115498419, + 14.11937557392103, + 14.419753086419753, + 14.713600652994593, + 15.000918273645546 + ], + [ + -46.07366595245383, + -45.13335373941434, + -44.19957147229874, + -43.27231915110703, + -42.3515967758392, + -41.437404346495256, + -40.52974186307519, + -39.62860932557902, + -38.73400673400673, + -37.84593408835833, + -36.964391388633814, + -36.089378634833174, + -35.22089582695643, + -34.35894296500357, + -33.50352004897459, + -32.6546270788695, + -31.8122640546883, + -30.976430976430976, + -30.14712784409754, + -29.32435465768799, + -28.508111417202322, + -27.698398122640548, + -26.895214774002653, + -26.09856137128864, + -25.30843791449852, + -24.524844403632283, + -23.747780838689927, + -22.977247219671465, + -22.213243546576876, + -21.455769819406182, + -20.70482603815937, + -19.960412202836444, + -19.222528313437405, + -18.491174369962245, + -17.766350372410976, + -17.04805632078359, + -16.336292215080093, + -15.631058055300477, + -14.93235384144475, + -14.240179573512904, + -13.554535251504944, + -12.875420875420875, + -12.202836445260687, + -11.536781961024385, + -10.877257422711967, + -10.224262830323436, + -9.577798183858791, + -8.93786348331803, + -8.304458728701151, + -7.67758392000816, + -7.057239057239058, + -6.443424140393837, + -5.836139169472501, + -5.23538414447505, + -4.641159065401491, + -4.053463932251811, + -3.4722987450260163, + -2.897663503724108, + -2.3295582083460893, + -1.7679828588919504, + -1.212937455361697, + -0.6644219977553298, + -0.12243648607285218, + 0.4130190796857445, + 0.9419446995204572, + 1.4643403734312832, + 1.9802061014182248, + 2.4895418834812757, + 2.992347719620446, + 3.4886236098357317, + 3.978369554127131, + 4.461585552494641, + 4.938271604938271, + 5.408427711458014, + 5.872053872053873, + 6.329150086725841, + 6.77971635547393, + 7.223752678298133, + 7.66125905519845, + 8.092235486174879, + 8.516681971227428, + 8.934598510356086, + 9.345985103560858, + 9.750841750841753, + 10.149168452198753, + 10.540965207631876, + 10.926232017141107, + 11.304968880726452, + 11.677175798387921, + 12.042852770125496, + 12.401999795939187, + 12.754616875828997, + 13.100704009794917, + 13.440261197836955, + 13.773288439955104, + 14.099785736149368, + 14.419753086419751, + 14.733190490766244, + 15.04009794918886, + 15.34047546168758 + ], + [ + -47.033568003264975, + -46.080195898377724, + -45.133353739414346, + -44.19304152637487, + -43.25925925925927, + -42.33200693806755, + -41.41128456279972, + -40.49709213345578, + -39.58942965003572, + -38.688297112539544, + -37.79369452096726, + -36.90562187531886, + -36.02407917559434, + -35.149066421793705, + -34.280583613916946, + -33.418630751964095, + -32.56320783593512, + -31.71431486583002, + -30.871951841648816, + -30.036118763391492, + -29.20681563105806, + -28.384042444648514, + -27.567799204162846, + -26.758085909601068, + -25.95490256096317, + -25.158249158249163, + -24.368125701459036, + -23.584532190592803, + -22.807468625650447, + -22.036935006631982, + -21.2729313335374, + -20.515457606366702, + -19.76451382511989, + -19.02009998979696, + -18.28221610039792, + -17.550862156922765, + -16.826038159371496, + -16.10774410774411, + -15.395980002040613, + -14.690745842260998, + -13.992041628405266, + -13.299867360473428, + -12.614223038465468, + -11.935108662381392, + -11.262524232221203, + -10.596469747984905, + -9.936945209672487, + -9.283950617283953, + -8.637485970819306, + -7.997551270278544, + -7.364146515661671, + -6.73727170696868, + -6.116926844199574, + -5.503111927354352, + -4.895826956433022, + -4.295071931435572, + -3.7008468523620057, + -3.1131517192123255, + -2.5319865319865373, + -1.9573512906846273, + -1.3892459953066032, + -0.8276706458524647, + -0.27262524232221663, + 0.2758902152841509, + 0.8178757269666339, + 1.3533312927252308, + 1.8822569125599433, + 2.4046525864707653, + 2.920518314457706, + 3.4298540965207622, + 3.932659932659933, + 4.4289358228752125, + 4.918681767166614, + 5.4018977655341285, + 5.878583817977757, + 6.348739924497496, + 6.812366085093356, + 7.26946229976533, + 7.720028568513417, + 8.164064891337617, + 8.601571268237937, + 9.032547699214366, + 9.45699418426691, + 9.874910723395574, + 10.286297316600345, + 10.691153963881238, + 11.089480665238241, + 11.481277420671358, + 11.866544230180594, + 12.245281093765943, + 12.617488011427401, + 12.983164983164983, + 13.342312008978675, + 13.694929088868484, + 14.041016222834404, + 14.38057341087644, + 14.713600652994593, + 15.040097949188858, + 15.360065299459242, + 15.673502703805735 + ], + [ + -48, + -47.033568003264975, + -46.07366595245383, + -45.12029384756658, + -44.17345168860321, + -43.23313947556372, + -42.299357208448114, + -41.372104887256405, + -40.45138251198858, + -39.53719008264463, + -38.629527599224566, + -37.72839506172839, + -36.83379247015611, + -35.945719824507705, + -35.06417712478318, + -34.18916437098256, + -33.32068156310581, + -32.45872870115294, + -31.603305785123965, + -30.754412815018878, + -29.912049790837667, + -29.07621671258035, + -28.24691358024691, + -27.424140393837362, + -26.6078971533517, + -25.79818385878992, + -24.995000510152025, + -24.19834710743802, + -23.408223650647894, + -22.624630139781658, + -21.847566574839302, + -21.077032955820837, + -20.313029282726255, + -19.555555555555557, + -18.804611774308746, + -18.060197938985816, + -17.32231404958678, + -16.59096010611162, + -15.866136108560353, + -15.147842056932967, + -14.436077951229466, + -13.730843791449855, + -13.032139577594126, + -12.339965309662281, + -11.65432098765432, + -10.97520661157025, + -10.302622181410062, + -9.636567697173758, + -8.97704315886134, + -8.324048566472806, + -7.677583920008165, + -7.0376492194674025, + -6.404244464850526, + -5.777369656157533, + -5.157024793388432, + -4.543209876543212, + -3.9359249056218752, + -3.335169880624425, + -2.740944801550865, + -2.153249668401185, + -1.5720844811753905, + -0.9974492398734816, + -0.429343944495463, + 0.13223140495867503, + 0.6872768084889289, + 1.235792266095296, + 1.7777777777777792, + 2.3132333435363717, + 2.8421589633710833, + 3.36455463728191, + 3.8804203652688507, + 4.389756147331902, + 4.892561983471073, + 5.388837873686358, + 5.878583817977757, + 6.361799816345267, + 6.838485868788898, + 7.3086419753086425, + 7.7722681359045, + 8.22936435057647, + 8.679930619324562, + 9.123966942148758, + 9.561473319049075, + 9.99244975002551, + 10.416896235078053, + 10.834812774206716, + 11.246199367411489, + 11.651056014692376, + 12.049382716049383, + 12.441179471482503, + 12.826446280991732, + 13.205183144577084, + 13.577390062238546, + 13.943067033976126, + 14.302214059789817, + 14.654831139679622, + 15.000918273645546, + 15.340475461687582, + 15.673502703805735, + 16 + ] + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + }, + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + }, + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "autotypenumbers": "strict", + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "trace = go.Surface(x=mx, y=my, z=mz)\n", + "fig = go.Figure(data=[trace])\n", + "py.iplot(fig, show_link=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We have a superb saddle point.\n", + "\n", + "Of course with another random seed we would have something else. Imagine what you could have if all\n", + "values ​​of A are positive." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Let's optimize\n", + "\n", + "If we have to do this calculation many times in high dimension, it would be nice to find the solution\n", + "optimal. While Einstein's notation helps here, it's not always the fastest. So let's compare with\n", + "other methods.\n", + "\n", + "### Using a J function and a loop" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def J(x):\n", + " return x @ A @ x\n", + "\n", + "mz2 = np.array([J(x) for line in M for x in line]).reshape([M.shape[0], M.shape[1]])\n", + "\n", + "np.max(np.square(mz2 - mz)) # pour vérifier qu'on obtient la même chose" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "143 µs ± 1.99 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "# comparons les temps calculs :\n", + "\n", + "%timeit np.einsum(\"ijk, ijk -> ij\", np.einsum(\"ijk, ka -> ija\", M, A), M)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "19.7 ms ± 494 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "%timeit np.array([J(x) for line in M for x in line]).reshape([M.shape[0], M.shape[1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We are more than 100 times faster with Einstein's summation." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Note that with `apply_along_axis` it is worse:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "34.6 ms ± 989 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "%timeit np.array([np.apply_along_axis(J, 1, line) for line in M]).reshape([M.shape[0], M.shape[1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Using `np.tensordot`\n", + "\n", + "A tensor is an N-dimensional matrix so here is a function that should be able to be used since our set of points is in 3 dimensions." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100 µs ± 1.15 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit # pour calculer le temps d'execution de toute la cellule %%\n", + "\n", + "MA = np.tensordot(M, A, axes=(2,1)) # on somme sur l'axe 2 de M (les points) et l'axe 1 de A (les colonnes)\n", + "np.einsum(\"ijk, ijk -> ij\", MA, M) # je n'arrive pas à faire cette opération autrement" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "We have a gain of 30% compared to `einsum`.\n", + "\n", + "To have good measurements it would be necessary to use cases bigger than 100x100 and to launch the tests\n", + "on a machine that does just that, so in single user mode under Linux.\n", + "\n", + "### Conclusion\n", + "\n", + "Roughly we have:\n", + "\n", + "| Method | Time |\n", + "| --- | --: |\n", + "|`einsum` | 140 µs|\n", + "|`tensordot` | 100 µs|\n", + "| `for` loop | 20,000 µs|" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma52 M\303\251thode du gradiant pour syst\303\250me matriciel.ipynb" "b/PVCM/cama/en/ma52 M\303\251thode du gradiant pour syst\303\250me matriciel.ipynb" new file mode 100644 index 0000000..c2d26ae --- /dev/null +++ "b/PVCM/cama/en/ma52 M\303\251thode du gradiant pour syst\303\250me matriciel.ipynb" @@ -0,0 +1,31856 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gradient et dérivée\n", + "\n", + "Le gradient est composé des dérivées partielles suivant chaque direction de la base. On peut rérouler les calculs et calculer $\\nabla J$ facilement (mais c'est long). Faisons le pour une matrice sur la partie compliquée :\n", + "\n", + "$$ \n", + "\\begin{align}\n", + "\\frac{1}{2} {\\bf x}^T A {\\bf x} &= \\frac{1}{2} \\begin{pmatrix} x_1 & x_2 \\end{pmatrix} \\begin{pmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\end{pmatrix} \\begin{pmatrix} x_1 \\\\ x_2 \\end{pmatrix} \\\\\n", + "&= \\frac{1}{2} \\left( x_1 a_{11} x_1 + x_1 a_{12} x_2 + x_2 a_{21} x_1 + x_2 a_{22} x_2 \\right) \\\\\n", + "& = \\frac{1}{2} \\left( a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2 \\right)\n", + "\\end{align}\n", + "$$\n", + "\n", + "Calcul des dérivées partielles de $ \\frac{1}{2} x^T A x $ :\n", + "\n", + "$$\n", + "\\frac{\\partial}{\\partial x_1} \\left( \\frac{1}{2} (a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2) \\right)\n", + " = \\frac{1}{2} (2 a_{11} x_1 + (a_{12} + a_{21}) x_2) = a_{11} x_1 + \\frac{a_{12} + a_{21}}{2} x_2\n", + "$$\n", + "\n", + "$$\n", + " \\frac{\\partial}{\\partial x_2} \\left( \\frac{1}{2} (a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2) \\right)\n", + " = \\frac{1}{2} ((a_{12} + a_{21}) x_1 + 2 a_{22} x_2) = \\frac{a_{12} + a_{21}}{2} x_1 + a_{22} x_2\n", + "$$\n", + "\n", + "\n", + "Donc le gradient de $\\frac{1}{2} {\\bf x}^T A {\\bf x}$ est :\n", + "\n", + "$$\n", + "\\nabla \\left( \\frac{1}{2} x^T A x \\right) = \\begin{pmatrix} a_{11} x_1 + \\frac{a_{12} + a_{21}}{2} x_2 \\\\ \\frac{a_{12} + a_{21}}{2} x_1 + a_{22} x_2 \\end{pmatrix} = \\frac{1}{2} (A + A^T) \\, {\\bf x}\n", + "$$\n", + "\n", + "Il faut faire le calcul pour une matrice $n \\times n$ mais on arrive au même résultat\n", + "et donc\n", + "\n", + "$$\n", + "J'({\\bf x}) = \\nabla J({\\bf x})\n", + "$$\n", + "\n", + "Ainsi on peut aussi calculer la dérivée suivant la direction $\\bf h$ avec le gradient :\n", + "\n", + "$$\n", + "J'({\\bf x})({\\bf h}) = \\nabla J({\\bf x}) \\, . \\, {\\bf h}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# A x = b seen as an optimization problem\n", + "\n", + "To solve $A {\\bf x} = {\\bf b}$ we will seek the minimum of the functional\n", + "\n", + "$$\n", + "J({\\bf x}) = \\frac{1}{2} \\, {\\bf x}^T \\, A \\, {\\bf x} - {\\bf b}\\, . {\\bf x}\n", + "$$\n", + "\n", + "At this point the derivative vanishes and in a precise case the derivative is precisely $A {\\bf x} - {\\bf b}$.\n", + "\n", + "## Calculation of derivative\n", + "\n", + "The notion of derivative in dimension greater than 1 must be handled with care because there are different\n", + "types of derivatives, partial derivatives and the total derivative.\n", + "\n", + "What interests us is the derivative in one direction which corresponds to the partial derivative in $y$ if we\n", + "goes in the direction of the axis $y$.\n", + "\n", + "### Definition\n", + "\n", + "We say that $f : \\Omega \\subset X \\rightarrow Y$ (open $\\Omega$) is differentiable in ${\\bf p} \\in \\Omega$ if\n", + "\n", + "$$\n", + "\\exists \\; f'({\\bf p}) \\in L(X,Y) \\textrm{ tel que} \\\\\n", + "f ({\\bf p} + {\\bf h}) = f({\\bf p}) + f'({\\bf p}) ( {\\bf h} ) + {\\bf h} \\; \\varepsilon({\\bf h}) \\quad\n", + "\\textrm{ avec } \\lim_{\\bf h \\rightarrow 0} \\varepsilon({\\bf h}) = {\\bf 0}\n", + "$$\n", + "\n", + "where $L(X,Y)$ represents the space of continuous linear maps of $X$ in $Y$. Be careful it is\n", + "$f'(p) \\in L(X,Y)$ and not $f'$.\n", + "\n", + "\n", + "We note that if $f$ is differentiable in ${\\bf p}$ then $\\forall \\; {\\bf h} \\in X$\n", + "\n", + "$$\n", + "f'({\\bf p}) ({\\bf h})= \\lim_{\\theta \\rightarrow 0} \\frac{f({\\bf p} + \\theta \\, {\\bf h}) - f({\\bf p})}{\\theta}\n", + "$$\n", + "\n", + "Pay attention to the type of each term. To visualize well I considered that $f$ is a\n", + "scalar function therefore $Y = ℝ$. On the other hand $X = ℝ^n$ with $n > 1$.\n", + "\n", + "#### Other notation\n", + "\n", + "I find the notation with the gradient clearer. We can see better where the vectors and the scalars are:\n", + "\n", + "$$\n", + "f ({\\bf p} + {\\bf h}) = f({\\bf p}) + \\nabla \\!f \\, ({\\bf p})^T \\; {\\bf h} + {\\bf h}^T \\; \\varepsilon({\\bf h}) \\quad\n", + "$$\n", + "\n", + "As I took $Y = ℝ$ the $f$ map is scalar. $\\nabla \\! f \\, ({\\bf p})$ is a vector whose\n", + "dot product with ${\\bf h}$ gives a real.\n", + "\n", + "### Calculate the derivative of J along a direction\n", + "\n", + "We calculate the derivative of $J({\\bf x})$ at the point ${\\bf p}$ following the direction given by the vector $\\bf h$:\n", + "\n", + "$$\n", + "\\begin{align}\n", + "J'({\\bf p}) ({\\bf h}) &= \\lim_{\\theta \\rightarrow 0} \\; \\frac{J({\\bf p} + \\theta \\, {\\bf h}) - J({\\bf p})}{\\theta} \\\\\n", + " &= \\lim_{\\theta \\rightarrow 0} \\; \\frac{1}{\\theta} \\; \n", + " \\left( \\frac{1}{2} \\; ({\\bf p} + \\theta {\\bf h})^T \\, A \\; ({\\bf p} + \\theta {\\bf h})\n", + " - {\\bf b}^T \\, ({\\bf p} + \\theta {\\bf h})\n", + " - \\frac{1}{2} \\; {\\bf p}^T \\, A \\; {\\bf p} + {\\bf b}^T \\, {\\bf p}\n", + " \\right) \\\\\n", + " &= \\lim_{\\theta \\rightarrow 0} \\; \\frac{1}{\\theta} \\; \n", + " \\left( \\frac{1}{2} \\left( \\theta \\, {\\bf p}^T \\, A \\; {\\bf h} \n", + " + \\theta \\, {\\bf h}^T \\, A \\; {\\bf p} \n", + " + \\theta^2 \\, {\\bf h}^T \\, A \\; {\\bf h} \\right) \n", + " - \\theta \\, {\\bf b}^T \\, {\\bf h}\n", + " \\right) \\\\\n", + " &= \\frac{1}{2} \\left( {\\bf p}^T \\, A \\; {\\bf h} +{\\bf h}^T \\, A \\; {\\bf p} \\right) - {\\bf b}^T \\, {\\bf h} \\\\\n", + " &= \\frac{1}{2} \\left( {\\bf p}^T \\, A \\; {\\bf h} +{\\bf p}^T \\, A^T \\; {\\bf h} \\right) - {\\bf b}^T \\, {\\bf h} \\\\\n", + " &= \\frac{1}{2} \\left( {\\bf p}^T \\, ( A + A^T ) - {\\bf b}^T \\right) \\, {\\bf h} \\\\\n", + " &= \\frac{1}{2} \\left( ( A + A^T ) \\, {\\bf p} - {\\bf b} \\right) \\, . \\, {\\bf h}\n", + "\\end{align}\n", + "$$\n", + "\n", + "SO\n", + "\n", + "$$\n", + "\\begin{align}\n", + "J' : \\; & {\\bf x} \\in \\Omega \\subset ℝ^n \\longrightarrow \\;L(ℝ^n, ℝ) \\\\\n", + " & {\\bf x} \\; \\longmapsto \\; \\frac{1}{2} ( A + A^T ) \\, {\\bf x}^T - {\\bf b}\n", + "\\end{align}\n", + "$$\n", + "\n", + "### A symmetrical\n", + "\n", + "If A is symmetric, we have\n", + "\n", + "$$\n", + "J'({\\bf x}) = A \\; {\\bf x} - {\\bf b}\n", + "$$\n", + "\n", + "We note that if the derivative vanishes then we have solved our matrix system!\n", + "\n", + "It is therefore necessary that\n", + "\n", + "* A is symmetric\n", + "* There is a minimum (for some, we saw a case of saddle point)\n", + "\n", + "and in this case we can use a gradient method to find the minimum which will be the solution of\n", + "our matrix system.\n", + "\n", + "#### Property\n", + "\n", + "If A is symmetric and positive definite then $J$ is strictly convex and coervice (i.e.\n", + "$\\lim_{||{\\bf p}|| \\rightarrow \\infty} J({\\bf p}) = + \\infty$) which guarantees that it has a minimum." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Gradient and derivative\n", + "\n", + "The gradient is composed of the partial derivatives with respect to each direction of the basis. We can go through the calculations and compute $\\nabla J $ easily (though it is lengthy). Let's do it for a 2x2 matrix on the complicated part. :\n", + "\n", + "$$ \n", + "\\begin{align}\n", + "\\frac{1}{2} {\\bf x}^T A {\\bf x} &= \\frac{1}{2} \\begin{pmatrix} x_1 & x_2 \\end{pmatrix} \\begin{pmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\end{pmatrix} \\begin{pmatrix} x_1 \\\\ x_2 \\end{pmatrix} \\\\\n", + "&= \\frac{1}{2} \\left( x_1 a_{11} x_1 + x_1 a_{12} x_2 + x_2 a_{21} x_1 + x_2 a_{22} x_2 \\right) \\\\\n", + "& = \\frac{1}{2} \\left( a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2 \\right)\n", + "\\end{align}\n", + "$$\n", + "\n", + "Lets evaluate partial derivatives of $ \\frac{1}{2} x^T A x $ :\n", + "\n", + "$$\n", + "\\frac{\\partial}{\\partial x_1} \\left( \\frac{1}{2} (a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2) \\right)\n", + " = \\frac{1}{2} (2 a_{11} x_1 + (a_{12} + a_{21}) x_2) = a_{11} x_1 + \\frac{a_{12} + a_{21}}{2} x_2\n", + "$$\n", + "\n", + "$$\n", + " \\frac{\\partial}{\\partial x_2} \\left( \\frac{1}{2} (a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2) \\right)\n", + " = \\frac{1}{2} ((a_{12} + a_{21}) x_1 + 2 a_{22} x_2) = \\frac{a_{12} + a_{21}}{2} x_1 + a_{22} x_2\n", + "$$\n", + "\n", + "\n", + "Therefore the gradient of $\\frac{1}{2} {\\bf x}^T A {\\bf x}$ is :\n", + "\n", + "$$\n", + "\\nabla \\left( \\frac{1}{2} x^T A x \\right) = \\begin{pmatrix} a_{11} x_1 + \\frac{a_{12} + a_{21}}{2} x_2 \\\\ \\frac{a_{12} + a_{21}}{2} x_1 + a_{22} x_2 \\end{pmatrix} = \\frac{1}{2} (A + A^T) \\, {\\bf x}\n", + "$$\n", + "\n", + "We should do computations for an $n \\times n$ matrix, but it gives the same result, so\n", + "\n", + "$$\n", + "J'({\\bf x}) = \\nabla J({\\bf x})\n", + "$$\n", + "\n", + "We can also compute derivative of J in the direction $\\bf h$ with its gradient :\n", + "\n", + "$$\n", + "J'({\\bf x})({\\bf h}) = \\nabla J({\\bf x}) \\, . \\, {\\bf h}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import plotly.offline as py\n", + "import plotly.graph_objects as go\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([[2,1], [1,2]])\n", + "b = np.array([-1, 0.5])\n", + "\n", + "# lets make the mesh\n", + "x = np.linspace(-20,20,100)\n", + "y = np.linspace(-20,20,100)\n", + "mx, my = np.meshgrid(x,y) \n", + "M = np.array(np.meshgrid(x,y)).swapaxes(0,2)\n", + "\n", + "# and compute 0.5 x.T A x - b x on each node of the mesh\n", + "MA = np.einsum(\"ijk, ka -> ija\", M, A)\n", + "mz = 0.5 * np.einsum(\"ijk, ijk -> ij\", MA, M) - M @ b" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "linkText": "Export to plot.ly", + "plotlyServerURL": "https://plot.ly", + "showLink": false + }, + "data": [ + { + "type": "surface", + "x": [ + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ] + ], + "y": [ + [ + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20 + ], + [ + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595 + ], + [ + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919 + ], + [ + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879 + ], + [ + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384 + ], + [ + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798 + ], + [ + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574 + ], + [ + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173 + ], + [ + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768 + ], + [ + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363 + ], + [ + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958 + ], + [ + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555 + ], + [ + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152 + ], + [ + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747 + ], + [ + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343 + ], + [ + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394 + ], + [ + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536 + ], + [ + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131 + ], + [ + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727 + ], + [ + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324 + ], + [ + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919 + ], + [ + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516 + ], + [ + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111 + ], + [ + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708 + ], + [ + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303 + ], + [ + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899 + ], + [ + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495 + ], + [ + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092 + ], + [ + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687 + ], + [ + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284 + ], + [ + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879 + ], + [ + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476 + ], + [ + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071 + ], + [ + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666 + ], + [ + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263 + ], + [ + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858 + ], + [ + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455 + ], + [ + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505 + ], + [ + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647 + ], + [ + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242 + ], + [ + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373 + ], + [ + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436 + ], + [ + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031 + ], + [ + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263 + ], + [ + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214 + ], + [ + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201 + ], + [ + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153 + ], + [ + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104 + ], + [ + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055 + ], + [ + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066 + ], + [ + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066 + ], + [ + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055 + ], + [ + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104 + ], + [ + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153 + ], + [ + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166 + ], + [ + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214 + ], + [ + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263 + ], + [ + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031 + ], + [ + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325 + ], + [ + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373 + ], + [ + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242 + ], + [ + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647 + ], + [ + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048 + ], + [ + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453 + ], + [ + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858 + ], + [ + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263 + ], + [ + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668 + ], + [ + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069 + ], + [ + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474 + ], + [ + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879 + ], + [ + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284 + ], + [ + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685 + ], + [ + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909 + ], + [ + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495 + ], + [ + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899 + ], + [ + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301 + ], + [ + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706 + ], + [ + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111 + ], + [ + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516 + ], + [ + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917 + ], + [ + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325 + ], + [ + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727 + ], + [ + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128 + ], + [ + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536 + ], + [ + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938 + ], + [ + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346 + ], + [ + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747 + ], + [ + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149 + ], + [ + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557 + ], + [ + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958 + ], + [ + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636 + ], + [ + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768 + ], + [ + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717 + ], + [ + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578 + ], + [ + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798 + ], + [ + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838 + ], + [ + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879 + ], + [ + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919 + ], + [ + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596 + ], + [ + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20 + ] + ], + "z": [ + [ + 1190, + 1165.7188042036528, + 1141.7641057034996, + 1118.135904499541, + 1094.8342005917764, + 1071.8589939802062, + 1049.21028466483, + 1026.8880726456487, + 1004.892357922661, + 983.2231404958677, + 961.8804203652687, + 940.8641975308642, + 920.1744719926538, + 899.8112437506377, + 879.7745128048158, + 860.0642791551882, + 840.680542801755, + 821.623303744516, + 802.8925619834711, + 784.4883175186205, + 766.4105703499642, + 748.6593204775023, + 731.2345679012345, + 714.1363126211611, + 697.3645546372819, + 680.919293949597, + 664.8005305581063, + 649.00826446281, + 633.5424956637077, + 618.4032241607999, + 603.5904499540864, + 589.104173043567, + 574.944393429242, + 561.1111111111111, + 547.6043260891746, + 534.4240383634323, + 521.5702479338843, + 509.04295480053054, + 496.84215896337116, + 484.9678604224059, + 473.42005917763487, + 462.19875522905824, + 451.30394857667585, + 440.73563922048777, + 430.4938271604938, + 420.5785123966943, + 410.98969492908884, + 401.7273747576778, + 392.791551882461, + 384.1822263034384, + 375.89939802061014, + 367.94306703397604, + 360.31323334353635, + 353.0098969492909, + 346.03305785123973, + 339.38271604938274, + 333.05887154372, + 327.0615243342516, + 321.3906744209775, + 316.0463218038976, + 311.0284664830119, + 306.3371084583205, + 301.97224772982344, + 297.9338842975207, + 294.22201816141217, + 290.8366493214978, + 287.7777777777777, + 285.04540353025203, + 282.63952657892054, + 280.56014692378335, + 278.8072645648403, + 277.38087950209166, + 276.2809917355372, + 275.507601265177, + 275.06070809101107, + 274.94031221303953, + 275.14641363126213, + 275.67901234567904, + 276.5381083562902, + 277.7237016630956, + 279.2357922660953, + 281.07438016528926, + 283.2394653606774, + 285.73104785225996, + 288.54912764003666, + 291.6937047240078, + 295.1647791041731, + 298.9623507805326, + 303.08641975308643, + 307.5369860218345, + 312.3140495867768, + 317.4176104479135, + 322.8476686052443, + 328.6042240587695, + 334.68727680848895, + 341.0968268544026, + 347.8328741965106, + 354.89541883481274, + 362.2844607693093, + 370 + ], + [ + 1166.3248648097133, + 1142.2069176614627, + 1118.4154678094071, + 1094.9505152535457, + 1071.8120599938782, + 1049.000102030405, + 1026.514641363126, + 1004.3556779920416, + 982.5232119171512, + 961.0172431384552, + 939.8377716559532, + 918.9847974696457, + 898.4583205795326, + 878.2583409856137, + 858.384858687889, + 838.8378736863585, + 819.6173859810225, + 800.7233955718802, + 782.1559024589327, + 763.9149066421794, + 746.0004081216201, + 728.4124068972554, + 711.1509029690847, + 694.2158963371085, + 677.6073870013264, + 661.3253749617386, + 645.369860218345, + 629.7408427711458, + 614.4383226201406, + 599.46229976533, + 584.8127742067135, + 570.4897459442914, + 556.4932149780635, + 542.8231813080298, + 529.4796449341904, + 516.4626058565453, + 503.7720640750943, + 491.4080195898378, + 479.3704724007754, + 467.6594225079074, + 456.2748699112335, + 445.21681461075406, + 434.48525660646874, + 424.0801958983776, + 414.0016324864809, + 404.2495663707785, + 394.8239975512703, + 385.7249260279563, + 376.9523518008366, + 368.5062748699112, + 360.38669523518007, + 352.59361289664326, + 345.12702785430054, + 337.9869401081521, + 331.1733496581981, + 324.6862565044383, + 318.5256606468728, + 312.69156208550146, + 307.1839608203245, + 302.0028568513417, + 297.1482501785532, + 292.62014080195894, + 288.418528721559, + 284.5434139373533, + 280.99479644934183, + 277.77267625752467, + 274.87705336190186, + 272.30792776247324, + 270.0652994592389, + 268.14916845219875, + 266.55953474135293, + 265.2963983267013, + 264.35975920824404, + 263.74961738598097, + 263.4659728599122, + 263.50882563003773, + 263.8781756963575, + 264.57402305887155, + 265.5963677175799, + 266.94520967248235, + 268.6205489235792, + 270.6223854708703, + 272.95071931435564, + 275.60555045403527, + 278.58687888990914, + 281.8947046219773, + 285.52902765023975, + 289.48984797469643, + 293.7771655953474, + 298.3909805121926, + 303.33129272523206, + 308.5981022344659, + 314.1914090398938, + 320.1112131415162, + 326.3575145393327, + 332.93031323334344, + 339.8296092235487, + 347.05540250994795, + 354.6076930925416, + 362.48648097132946 + ], + [ + 1142.9762269156208, + 1119.0215284154676, + 1095.393327211509, + 1072.0916233037444, + 1049.1164166921742, + 1026.4677073767982, + 1004.1454953576164, + 982.1497806346291, + 960.480563207836, + 939.1378430772369, + 918.1216202428323, + 897.4318947046219, + 877.0686664626057, + 857.0319355167838, + 837.3217018671563, + 817.937965513723, + 798.880726456484, + 780.1499846954392, + 761.7457402305887, + 743.6679930619324, + 725.9167431894704, + 708.4919906132027, + 691.3937353331293, + 674.6219773492501, + 658.176716661565, + 642.0579532700744, + 626.265687174778, + 610.7999183756759, + 595.660646872768, + 580.8478726660544, + 566.361595755535, + 552.20181614121, + 538.3685338230791, + 524.8617488011425, + 511.68146107540036, + 498.8276706458524, + 486.30037751249864, + 474.0995816753392, + 462.22528313437397, + 450.6774818896031, + 439.4561779410263, + 428.56137128864395, + 417.9930619324558, + 407.751249872462, + 397.83593510866234, + 388.247117641057, + 378.9847974696459, + 370.04897459442907, + 361.43964901540653, + 353.15682073257824, + 345.20048974594425, + 337.57065605550446, + 330.26731966125897, + 323.29048056320784, + 316.64013876135084, + 310.31629425568815, + 304.31894704621965, + 298.6480971329455, + 293.3037445158657, + 288.2858891949801, + 283.59453117028875, + 279.22967044179154, + 275.19130700948875, + 271.4794408733802, + 268.094072033466, + 265.03520048974593, + 262.30282624222014, + 259.8969492908886, + 257.8175696357514, + 256.06468727680846, + 254.63830221405973, + 253.53841444750532, + 252.76502397714512, + 252.31813080297923, + 252.19773492500758, + 252.40383634323024, + 252.93643505764717, + 253.79553106825833, + 254.98112437506373, + 256.4932149780634, + 258.3318028772574, + 260.4968880726456, + 262.98847056422807, + 265.8065503520049, + 268.9511274359759, + 272.4222018161412, + 276.21977349250074, + 280.3438424650545, + 284.7944087338027, + 289.571472298745, + 294.6750331598816, + 300.1050913172125, + 305.86164677073765, + 311.9446995204571, + 318.3542495663707, + 325.09029690847865, + 332.1528415467809, + 339.54188348127735, + 347.25742271196816, + 355.29945923885316 + ], + [ + 1119.9540863177228, + 1096.1626364656668, + 1072.6976839098052, + 1049.5592286501378, + 1026.7472706866647, + 1004.2618100193858, + 982.1028466483012, + 960.2703805734111, + 938.764411794715, + 917.584940312213, + 896.7319661259055, + 876.2054892357922, + 856.0055096418733, + 836.1320273441486, + 816.5850423426181, + 797.3645546372819, + 778.4705642281401, + 759.9030711151925, + 741.6620752984389, + 723.7475767778799, + 706.159575553515, + 688.8980716253444, + 671.9630649933681, + 655.354555657586, + 639.0725436179982, + 623.1170288746047, + 607.4880114274054, + 592.1854912764004, + 577.2094684215897, + 562.5599428629732, + 548.2369146005509, + 534.240383634323, + 520.5703499642893, + 507.22681359045004, + 494.20977451280487, + 481.51923273135395, + 469.1551882460974, + 457.11764105703503, + 445.40659116416697, + 434.02203856749315, + 422.96398326701353, + 412.2324252627284, + 401.82736455463737, + 391.7488011427406, + 381.9967350270381, + 372.57116620753, + 363.4720946842159, + 354.69952045709624, + 346.2534435261709, + 338.13386389143966, + 330.3407815529028, + 322.8741965105602, + 315.73410876441187, + 308.9205183144578, + 302.433425160698, + 296.27282930313237, + 290.438730741761, + 284.93112947658403, + 279.7500255076013, + 274.89541883481286, + 270.36730945821853, + 266.16569737781856, + 262.2905825936129, + 258.74196510560154, + 255.51984491378437, + 252.62422201816145, + 250.05509641873277, + 247.81246811549846, + 245.89633710845834, + 244.3067033976125, + 243.04356698296098, + 242.10692786450366, + 241.4967860422406, + 241.21314151617185, + 241.25599428629738, + 241.6253443526171, + 242.32119171513114, + 243.3435363738394, + 244.692378328742, + 246.3677175798388, + 248.36955412712993, + 250.69788797061526, + 253.35271911029488, + 256.3340475461688, + 259.6418732782369, + 263.2761963064994, + 267.2370166309561, + 271.52433425160694, + 276.13814916845223, + 281.0784613814917, + 286.3452708907254, + 291.9385776961535, + 297.85838179777573, + 304.1046831955924, + 310.67748188960314, + 317.57677787980816, + 324.80257116620754, + 332.3548617488011, + 340.23364962758905, + 348.43893480257117 + ], + [ + 1097.2584430160189, + 1073.63024181206, + 1050.3285379042954, + 1027.3533312927252, + 1004.7046219773493, + 982.3824099581675, + 960.38669523518, + 938.717477808387, + 917.374757677788, + 896.3585348433834, + 875.6688093051728, + 855.3055810631569, + 835.268850117335, + 815.5586164677073, + 796.174880114274, + 777.117641057035, + 758.3868992959901, + 739.9826548311396, + 721.9049076624833, + 704.1536577900215, + 686.7289052137537, + 669.6306499336803, + 652.8588919498011, + 636.4136312621162, + 620.2948678706255, + 604.5026017753291, + 589.036832976227, + 573.8975614733191, + 559.0847872666054, + 544.5985103560861, + 530.4387307417611, + 516.6054484236303, + 503.09866340169367, + 489.91837567595144, + 477.0645852464035, + 464.5372921130498, + 452.3364962758902, + 440.46219773492504, + 428.91439649015405, + 417.69309254157736, + 406.798285889195, + 396.2299765330069, + 385.988164473013, + 376.0728497092133, + 366.484032241608, + 357.221712070197, + 348.2858891949802, + 339.67656361595755, + 331.39373533312926, + 323.43740434649527, + 315.8075706560555, + 308.50423426181004, + 301.5273951637588, + 294.87705336190174, + 288.55320885623917, + 282.5558616467708, + 276.88501173349664, + 271.5406591164167, + 266.5228037955311, + 261.8314457708397, + 257.4665850423426, + 253.4282216100398, + 249.71635547393126, + 246.33098663401697, + 243.27211509029692, + 240.53974084277115, + 238.13386389143966, + 236.05448423630241, + 234.30160187735942, + 232.87521681461078, + 231.77532904805634, + 231.0019385776962, + 230.55504540353027, + 230.43464952555863, + 230.64075094378126, + 231.17334965819816, + 232.03244566880932, + 233.21803897561472, + 234.73012957861442, + 236.56871747780838, + 238.73380267319664, + 241.2253851647791, + 244.0434649525558, + 247.18804203652692, + 250.65911641669217, + 254.45668809305175, + 258.58075706560555, + 263.0313233343536, + 267.808386899296, + 272.91194776043255, + 278.34200591776346, + 284.0985613712886, + 290.181614121008, + 296.5911641669218, + 303.3272115090297, + 310.38975614733187, + 317.77879808182837, + 325.4943373125191, + 333.5363738394042, + 341.9049076624834 + ], + [ + 1074.8892970105092, + 1051.4243444546473, + 1028.28588919498, + 1005.4739312315071, + 982.9884705642281, + 960.8295071931435, + 938.9970411182533, + 917.4910723395573, + 896.3116008570555, + 875.4586266707478, + 854.9321497806345, + 834.7321701867156, + 814.858687888991, + 795.3117028874605, + 776.0912151821242, + 757.1972247729822, + 738.6297316600346, + 720.3887358432813, + 702.474237322722, + 684.8862360983572, + 667.6247321701867, + 650.6897255382105, + 634.0812162024283, + 617.7992041628405, + 601.8436894194471, + 586.2146719722477, + 570.9121518212427, + 555.9361289664321, + 541.2866034078155, + 526.9635751453934, + 512.9670441791653, + 499.2970105091317, + 485.9534741352923, + 472.93643505764715, + 460.2458932761963, + 447.8818487909396, + 435.84430160187736, + 424.1332517090093, + 412.74869911233554, + 401.6906438118559, + 390.95908580757055, + 380.5540250994796, + 370.4754616875829, + 360.7233955718804, + 351.29782675237215, + 342.1987552290583, + 333.4261810019386, + 324.98010407101316, + 316.86052443628205, + 309.06744209774513, + 301.60085705540246, + 294.4607693092541, + 287.6471788593, + 281.1600857055402, + 274.9994898479747, + 269.16539128660344, + 263.65779002142637, + 258.4766860524436, + 253.62207937965513, + 249.09397000306097, + 244.89235792266095, + 241.01724313845523, + 237.4686256504438, + 234.24650545862667, + 231.35088256300375, + 228.78175696357513, + 226.53912866034077, + 224.62299765330067, + 223.03336394245486, + 221.77022752780329, + 220.83358840934596, + 220.22344658708292, + 219.93980206101418, + 219.98265483113968, + 220.35200489745944, + 221.04785225997344, + 222.07019691868175, + 223.41903887358433, + 225.09437812468116, + 227.09621467197223, + 229.4245485154576, + 232.0793796551372, + 235.0607080910111, + 238.36853382307928, + 242.00285685134165, + 245.96367717579838, + 250.2509947964493, + 254.86480971329456, + 259.80512192633404, + 265.07193143556776, + 270.66523824099573, + 276.58504234261807, + 282.8313437404346, + 289.4041424344455, + 296.3034384246505, + 303.5292317110498, + 311.08152229364356, + 318.9603101724313, + 327.16559534741356, + 335.6973778185899 + ], + [ + 1052.8466483011937, + 1029.544944393429, + 1006.5697377818587, + 983.9210284664831, + 961.5988164473013, + 939.6031017243139, + 917.9338842975205, + 896.5911641669217, + 875.574941332517, + 854.8852157943066, + 834.5219875522905, + 814.4852566064686, + 794.775022956841, + 775.3912866034078, + 756.3340475461687, + 737.6033057851239, + 719.1990613202735, + 701.121314151617, + 683.370064279155, + 665.9453117028874, + 648.8470564228138, + 632.0752984389347, + 615.6300377512498, + 599.5112743597592, + 583.7190082644628, + 568.2532394653607, + 553.1139679624528, + 538.3011937557392, + 523.8149168452198, + 509.65513723089475, + 495.82185491276397, + 482.31506989082743, + 469.1347821650852, + 456.2809917355371, + 443.7536986021834, + 431.55290276502393, + 419.67860422405863, + 408.1308029792878, + 396.9094990307111, + 386.0146923783287, + 375.44638302214054, + 365.20457096214676, + 355.2892561983471, + 345.7004387307417, + 336.4381185593306, + 327.5022956841138, + 318.8929701050913, + 310.610141822263, + 302.653810835629, + 295.02397714518924, + 287.72064075094374, + 280.74380165289256, + 274.09345985103556, + 267.7696153453728, + 261.7722681359044, + 256.1014182226303, + 250.75706560555042, + 245.73921028466478, + 241.04785225997344, + 236.68299153147632, + 232.64462809917353, + 228.93276196306493, + 225.54739312315067, + 222.4885215794306, + 219.75614733190486, + 217.35027038057336, + 215.27089072543615, + 213.51800836649318, + 212.09162330374448, + 210.99173553719004, + 210.21834506682987, + 209.77145189266398, + 209.65105601469233, + 209.85715743291496, + 210.38975614733187, + 211.24885215794302, + 212.43444546474845, + 213.94653606774816, + 215.7851239669421, + 217.95020916233034, + 220.44179165391284, + 223.2598714416896, + 226.4044485256606, + 229.8755229058259, + 233.67309458218543, + 237.79716355473929, + 242.2477298234874, + 247.02479338842969, + 252.12835424956634, + 257.5584124068972, + 263.3149678604223, + 269.39802061014177, + 275.8075706560554, + 282.5436179981634, + 289.60616263646557, + 296.9952045709621, + 304.71074380165294, + 312.7527803285379, + 321.12131415161724, + 329.81634527089074 + ], + [ + 1031.130496888073, + 1007.9920416284052, + 985.1800836649321, + 962.6946229976535, + 940.5356596265688, + 918.7031935516785, + 897.1972247729823, + 876.0177532904806, + 855.1647791041732, + 834.6383022140599, + 814.4383226201409, + 794.5648403224162, + 775.0178553208857, + 755.7973676155495, + 736.9033772064075, + 718.3358840934599, + 700.0948882767066, + 682.1803897561473, + 664.5923885317825, + 647.3308846036119, + 630.3958779716355, + 613.7873686358536, + 597.5053565962656, + 581.5498418528722, + 565.9208244056729, + 550.618304254668, + 535.6422813998573, + 520.9927558412409, + 506.6697275788186, + 492.6731966125907, + 479.00316294255697, + 465.65962656871756, + 452.6425874910724, + 439.9520457096215, + 427.5880012243649, + 415.55045403530255, + 403.8394041424345, + 392.4548515457607, + 381.3967962452811, + 370.6652382409959, + 360.2601775329049, + 350.1816141210082, + 340.42954800530566, + 331.0039791857974, + 321.9049076624835, + 313.1323334353638, + 304.6862565044384, + 296.56667686970724, + 288.77359453117026, + 281.3070094888277, + 274.16692174267945, + 267.35333129272533, + 260.86623813896546, + 254.7056422813999, + 248.87154372002863, + 243.3639424548516, + 238.18283848586884, + 233.32823181308032, + 228.8001224364861, + 224.59851035608617, + 220.72339557188045, + 217.17477808386906, + 213.95265789205192, + 211.05703499642897, + 208.48790939700032, + 206.24528109376595, + 204.32915008672586, + 202.73951637588004, + 201.47637996122847, + 200.53974084277118, + 199.92959902050814, + 199.64595449443937, + 199.6888072645649, + 200.05815733088465, + 200.75400469339868, + 201.77634935210696, + 203.12519130700952, + 204.80053055810635, + 206.80236710539745, + 209.13070094888278, + 211.7855320885624, + 214.7668605244363, + 218.07468625650444, + 221.70900928476692, + 225.66982960922354, + 229.95714722987455, + 234.57096214671975, + 239.5112743597592, + 244.77808386899304, + 250.371390674421, + 256.29119477604326, + 262.53749617385984, + 269.1102948678706, + 276.00959085807574, + 283.23538414447506, + 290.78767472706863, + 298.66646260585657, + 306.87174778083863, + 315.4035302520152, + 324.2618100193858 + ], + [ + 1009.7408427711458, + 986.7656361595755, + 964.1169268441996, + 941.794714825018, + 919.7990001020304, + 898.1297826752373, + 876.7870625446382, + 855.7708397102339, + 835.0811141720234, + 814.7178859300071, + 794.6811549841852, + 774.9709213345577, + 755.5871849811244, + 736.5299459238853, + 717.7992041628405, + 699.39495969799, + 681.3172125293338, + 663.5659626568718, + 646.141210080604, + 629.0429548005305, + 612.2711968166514, + 595.8259361289664, + 579.7071727374757, + 563.9149066421794, + 548.4491378430772, + 533.3098663401694, + 518.4970921334557, + 504.0108152229365, + 489.8510356086114, + 476.0177532904806, + 462.510968268544, + 449.3306805428018, + 436.47689011325383, + 423.94959697990004, + 411.7488011427406, + 399.8745026017753, + 388.32670135700437, + 377.10539740842773, + 366.21059075604535, + 355.64228139985715, + 345.4004693398632, + 335.48515457606374, + 325.89633710845834, + 316.6340169370473, + 307.6981940618304, + 299.088868482808, + 290.80604019997963, + 282.8497092133456, + 275.21987552290585, + 267.9165391286603, + 260.9397000306092, + 254.28935822875215, + 247.96551372308951, + 241.9681665136211, + 236.29731660034693, + 230.95296398326704, + 225.93510866238142, + 221.24375063769003, + 216.878889909193, + 212.84052647689015, + 209.12866034078155, + 205.7432915008673, + 202.68441995714727, + 199.95204570962147, + 197.54616875829, + 195.46678910315276, + 193.7139067442098, + 192.28752168146107, + 191.18763391490666, + 190.41424344454649, + 189.9673502703806, + 189.84695439240895, + 190.05305581063158, + 190.58565452504848, + 191.44475053565967, + 192.63034384246507, + 194.14243444546474, + 195.9810223446587, + 198.14610754004696, + 200.63769003162943, + 203.4557698194062, + 206.6003469033772, + 210.07142128354243, + 213.86899295990207, + 217.99306193245587, + 222.443628201204, + 227.22069176614633, + 232.32425262728287, + 237.75431078461384, + 243.51086623813896, + 249.59391898785836, + 256.0034690337721, + 262.73951637588, + 269.8020610141823, + 277.1911029486787, + 284.9066421793694, + 292.9486787062545, + 301.3172125293337, + 310.01224364860735, + 319.0337720640751 + ], + [ + 988.6776859504132, + 965.8657279869401, + 943.3802673196611, + 921.2213039485766, + 899.3888378736864, + 877.8828690949902, + 856.7033976124884, + 835.850423426181, + 815.3239465360678, + 795.1239669421489, + 775.250484644424, + 755.7034996428937, + 736.4830119375574, + 717.5890215284154, + 699.0215284154679, + 680.7805325987144, + 662.8660340781553, + 645.2780328537905, + 628.0165289256197, + 611.0815222936435, + 594.4730129578613, + 578.1910009182736, + 562.2354861748801, + 546.6064687276809, + 531.3039485766758, + 516.3279257218652, + 501.6784001632487, + 487.35537190082647, + 473.3588409345985, + 459.6888072645648, + 446.3452708907255, + 433.3282318130803, + 420.6376900316294, + 408.2736455463728, + 396.2360983573105, + 384.5250484644424, + 373.14049586776855, + 362.08244056728904, + 351.3508825630038, + 340.94582185491277, + 330.867258443016, + 321.1151923273136, + 311.6896235078053, + 302.59055198449136, + 293.8179777573717, + 285.3719008264463, + 277.2523211917152, + 269.45923885317825, + 261.9926538108356, + 254.8525660646872, + 248.0389756147332, + 241.55188246097342, + 235.3912866034078, + 229.5571880420365, + 224.0495867768595, + 218.86848280787677, + 214.01387613508825, + 209.485766758494, + 205.28415467809407, + 201.40903989388838, + 197.86042240587693, + 194.6383022140598, + 191.7426793184369, + 189.17355371900828, + 186.93092541577388, + 185.0147944087338, + 183.42516069788795, + 182.1620242832364, + 181.22538516477908, + 180.61524334251604, + 180.3315988164473, + 180.3744515865728, + 180.74380165289256, + 181.4396490154066, + 182.46199367411486, + 183.81083562901745, + 185.48617488011428, + 187.48801142740535, + 189.8163452708907, + 192.4711764105703, + 195.45250484644424, + 198.7603305785124, + 202.3946536067748, + 206.3554739312315, + 210.64279155188242, + 215.25660646872768, + 220.1969186817672, + 225.46372819100088, + 231.05703499642897, + 236.9768390980512, + 243.22314049586768, + 249.79593918987857, + 256.6952351800836, + 263.92102846648305, + 271.4733190490766, + 279.35210692786444, + 287.5573921028467, + 296.08917457402305, + 304.9474543413938, + 314.1322314049587 + ], + [ + 967.9410264258748, + 945.2923171104987, + 922.9701050913171, + 900.9743903683298, + 879.3051729415364, + 857.9624528109375, + 836.9462299765329, + 816.2565044383226, + 795.8932761963064, + 775.8565452504845, + 756.146311600857, + 736.7625752474238, + 717.7053361901848, + 698.9745944291399, + 680.5703499642893, + 662.4926027956329, + 644.7413529231711, + 627.3166003469033, + 610.2183450668299, + 593.4465870829507, + 577.0013263952657, + 560.8825630037751, + 545.0902969084786, + 529.6245281093765, + 514.4852566064686, + 499.6724823997551, + 485.18620548923576, + 471.0264258749108, + 457.19314355677983, + 443.68635853484335, + 430.50607080910106, + 417.6522803795531, + 405.12498724619934, + 392.9241914090398, + 381.0498928680746, + 369.5020916233037, + 358.28078767472704, + 347.38598102234465, + 336.8176716661565, + 326.5758596061626, + 316.6605448423629, + 307.07172737475764, + 297.80940720334655, + 288.8735843281297, + 280.26425874910717, + 271.981430466279, + 264.0250994796449, + 256.39526578920515, + 249.09192939495966, + 242.11509029690842, + 235.4647484950515, + 229.1409039893888, + 223.1435567799204, + 217.47270686664623, + 212.12835424956634, + 207.11049892868073, + 202.41914090398933, + 198.05428017549224, + 194.01591674318945, + 190.3040506070809, + 186.9186817671666, + 183.85981022344654, + 181.12743597592083, + 178.7215590245893, + 176.6421793694521, + 174.8892970105091, + 173.46291194776038, + 172.36302418120596, + 171.58963371084582, + 171.14274053667992, + 171.02234465870825, + 171.2284460769309, + 171.76104479134779, + 172.62014080195897, + 173.8057341087644, + 175.31782471176408, + 177.15641261095803, + 179.32149780634626, + 181.8130802979288, + 184.63116008570552, + 187.77573716967655, + 191.24681154984182, + 195.04438322620135, + 199.16845219875523, + 203.61901846750325, + 208.3960820324457, + 213.49964289358226, + 218.9297010509131, + 224.68625650443835, + 230.7693092541577, + 237.17885930007134, + 243.91490664217935, + 250.97745128048152, + 258.3664932149781, + 266.0820324456688, + 274.1240689725538, + 282.49260279563316, + 291.1876339149066, + 300.2091623303745, + 309.5571880420365 + ], + [ + 947.5308641975308, + 925.0454035302519, + 902.8864401591674, + 881.0539740842771, + 859.5480053055811, + 838.3685338230792, + 817.5155596367716, + 796.9890827466586, + 776.7891031527395, + 756.9156208550148, + 737.3686358534843, + 718.148148148148, + 699.2541577390064, + 680.6866646260586, + 662.4456688093052, + 644.531170288746, + 626.9431690643813, + 609.6816651362107, + 592.7466585042342, + 576.1381491684522, + 559.8561371288645, + 543.9006223854709, + 528.2716049382716, + 512.9690847872666, + 497.9930619324558, + 483.3435363738394, + 469.02050811141714, + 455.0239771451893, + 441.35394347515563, + 428.01040710131616, + 414.9933680236711, + 402.3028262422202, + 389.9387817569636, + 377.9012345679012, + 366.19018467503315, + 354.80563207835934, + 343.7475767778798, + 333.0160187735945, + 322.61095806550355, + 312.53239465360673, + 302.78032853790427, + 293.3547597183961, + 284.25568819508214, + 275.4831139679624, + 267.037037037037, + 258.9174574023059, + 251.124375063769, + 243.6577900214264, + 236.51770227527803, + 229.7041118253239, + 223.21701867156415, + 217.05642281399858, + 211.22232425262726, + 205.71472298745024, + 200.5336190184675, + 195.67901234567904, + 191.15090296908477, + 186.94929088868483, + 183.07417610447914, + 179.52555861646772, + 176.30343842465055, + 173.40781552902763, + 170.83868992959904, + 168.59606162636464, + 166.67993061932458, + 165.0902969084787, + 163.82716049382717, + 162.89052137536987, + 162.2803795531068, + 161.99673502703808, + 162.03958779716356, + 162.40893786348332, + 163.10478522599732, + 164.12712988470562, + 165.47597183960823, + 167.151311090705, + 169.1531476379961, + 171.48148148148147, + 174.1363126211611, + 177.11764105703497, + 180.42546678910318, + 184.05978981736558, + 188.0206101418222, + 192.30792776247324, + 196.9217426793184, + 201.86205489235797, + 207.12886440159167, + 212.72217120701964, + 218.641975308642, + 224.8882767064585, + 231.46107540046927, + 238.3603713906744, + 245.58616467707367, + 253.1384552596674, + 261.01724313845517, + 269.2225283134373, + 277.75431078461384, + 286.61259055198445, + 295.7973676155495, + 305.30864197530866 + ], + [ + 927.4471992653811, + 905.1249872461992, + 883.1292725232119, + 861.4600550964188, + 840.1173349658199, + 819.1011121314152, + 798.4113865932046, + 778.0481583511887, + 758.0114274053668, + 738.3011937557392, + 718.9174574023059, + 699.8602183450669, + 681.129476584022, + 662.7252321191716, + 644.6474849505151, + 626.8962350780533, + 609.4714825017857, + 592.3732272217121, + 575.6014692378329, + 559.1562085501481, + 543.0374451586573, + 527.245179063361, + 511.7794102642588, + 496.6401387613509, + 481.82736455463737, + 467.34108764411803, + 453.1813080297929, + 439.3480257116621, + 425.8412406897255, + 412.6609529639834, + 399.80716253443535, + 387.27986940108156, + 375.0790735639221, + 363.2047750229568, + 351.6569737781859, + 340.43566982960925, + 329.5408631772268, + 318.9725538210387, + 308.7307417610448, + 298.81542699724514, + 289.2266095296399, + 279.9642893582289, + 271.028466483012, + 262.4191409039894, + 254.1363126211611, + 246.17998163452717, + 238.55014794408737, + 231.24681154984188, + 224.26997245179066, + 217.6196306499337, + 211.295786144271, + 205.2984389348026, + 199.62758902152845, + 194.28323640444856, + 189.26538108356294, + 184.57402305887157, + 180.20916233037445, + 176.17079889807167, + 172.4589327619631, + 169.0735639220488, + 166.01469237832876, + 163.282318130803, + 160.87644117947153, + 158.79706152433428, + 157.0441791653913, + 155.6177941026426, + 154.51790633608817, + 153.74451586572803, + 153.2976226915621, + 153.17722681359047, + 153.3833282318131, + 153.91592694623, + 154.77502295684118, + 155.96061626364659, + 157.47270686664626, + 159.31129476584022, + 161.47637996122842, + 163.96796245281095, + 166.7860422405877, + 169.9306193245587, + 173.401693704724, + 177.1992653810836, + 181.3233343536374, + 185.7739006223855, + 190.55096418732782, + 195.65452504846448, + 201.08458320579535, + 206.84113865932045, + 212.92419140903993, + 219.33374145495355, + 226.06978879706148, + 233.13233343536376, + 240.5213753698602, + 248.23691460055102, + 256.27895112743596, + 264.6474849505152, + 273.3425160697888, + 282.36404448525656, + 291.7120701969187, + 301.38659320477507 + ], + [ + 907.6900316294256, + 885.531068258341, + 863.6986021834506, + 842.1926334047547, + 821.0131619222528, + 800.1601877359453, + 779.6337108458321, + 759.4337312519132, + 739.5602489541883, + 720.0132639526578, + 700.7927762473216, + 681.8987858381797, + 663.3312927252322, + 645.0902969084786, + 627.1757983879195, + 609.5877971635547, + 592.3262932353841, + 575.3912866034078, + 558.7827772676258, + 542.500765228038, + 526.5452504846444, + 510.9162330374452, + 495.61371288644017, + 480.6376900316295, + 465.98816447301294, + 451.66513621059073, + 437.66860524436277, + 423.99857157432916, + 410.6550352004897, + 397.6379961228446, + 384.9474543413937, + 372.5834098561371, + 360.54586266707486, + 348.8348127742067, + 337.4502601775329, + 326.3922048770533, + 315.6606468727681, + 305.2555861646771, + 295.1770227527804, + 285.42495663707786, + 275.9993878175696, + 266.90031629425573, + 258.12774206713607, + 249.68166513621057, + 241.56208550147943, + 233.7690031629426, + 226.30241812059995, + 219.16233037445159, + 212.34873992449747, + 205.86164677073768, + 199.70105091317214, + 193.86695235180085, + 188.3593510866238, + 183.17824711764104, + 178.32364044485257, + 173.79553106825836, + 169.59391898785836, + 165.71880420365267, + 162.17018671564125, + 158.9480665238241, + 156.05244362820122, + 153.48331802877257, + 151.24068972553823, + 149.3245587184981, + 147.73492500765227, + 146.4717885930007, + 145.5351494745434, + 144.92500765228036, + 144.64136312621162, + 144.68421589633712, + 145.05356596265688, + 145.7494133251709, + 146.77175798387918, + 148.12059993878177, + 149.7959391898786, + 151.79777573716967, + 154.12610958065503, + 156.78094072033463, + 159.76226915620856, + 163.0700948882767, + 166.70441791653914, + 170.66523824099582, + 174.95255586164672, + 179.566370778492, + 184.50668299153148, + 189.77349250076526, + 195.36679930619323, + 201.28660340781548, + 207.53290480563209, + 214.10570349964289, + 221.0049994898479, + 228.23079277624734, + 235.78308335884086, + 243.66187123762887, + 251.86715641261094, + 260.39893888378725, + 269.2572186511581, + 278.44199571472296, + 287.95327007448225, + 297.79104173043567 + ], + [ + 888.2593612896643, + 866.2636465666769, + 844.5944291398836, + 823.2517090092848, + 802.2354861748801, + 781.5457606366697, + 761.1825323946535, + 741.1458014488318, + 721.4355677992041, + 702.0518314457709, + 682.9945923885317, + 664.2638506274869, + 645.8596061626364, + 627.7818589939801, + 610.0306091215182, + 592.6058565452504, + 575.507601265177, + 558.7358432812978, + 542.2905825936127, + 526.1718192021223, + 510.37955310682577, + 494.9137843077237, + 479.77451280481574, + 464.9617385981022, + 450.4754616875829, + 436.3156820732579, + 422.48239975512695, + 408.9756147331905, + 395.7953270074481, + 382.94153657790025, + 370.41424344454646, + 358.21344760738697, + 346.3391490664217, + 334.7913478216508, + 323.5700438730742, + 312.67523722069177, + 302.1069278645036, + 291.86511580450974, + 281.9498010407101, + 272.36098357310476, + 263.09866340169367, + 254.1628405264769, + 245.55351494745432, + 237.27068666462603, + 229.314355677992, + 221.68452198755233, + 214.3811855933068, + 207.40434649525557, + 200.7540046933986, + 194.4301601877359, + 188.43281297826752, + 182.76196306499335, + 177.41761044791346, + 172.39975512702782, + 167.70839710233648, + 163.34353637383936, + 159.30517294153657, + 155.59330680542797, + 152.2079379655137, + 149.14906642179366, + 146.41669217426795, + 144.01081522293643, + 141.9314355677992, + 140.17855320885621, + 138.75216814610752, + 137.65228037955308, + 136.87888990919294, + 136.431996735027, + 136.31160085705537, + 136.517702275278, + 137.0503009896949, + 137.90939700030606, + 139.0949903071115, + 140.6070809101112, + 142.44566880930518, + 144.61075400469338, + 147.10233649627588, + 149.92041628405264, + 153.06499336802366, + 156.5360677481889, + 160.3336394245485, + 164.45770839710232, + 168.90827466585037, + 173.68533823079278, + 178.78889909192935, + 184.2189572492603, + 189.97551270278544, + 196.0585654525048, + 202.4681154984185, + 209.20416284052646, + 216.26670747882864, + 223.6557494133252, + 231.37128864401583, + 239.413325170901, + 247.7818589939802, + 256.47689011325366, + 265.4984185287216, + 274.8464442403836, + 284.52096724824, + 294.52198755229057 + ], + [ + 869.1551882460972, + 847.322722171207, + 825.8167533925109, + 804.6372819100093, + 783.7843077237018, + 763.2578308335883, + 743.0578512396694, + 723.1843689419447, + 703.6373839404142, + 684.4168962350781, + 665.5229058259359, + 646.9554127129884, + 628.7144168962351, + 610.7999183756759, + 593.211917151311, + 575.9504132231405, + 559.0154065911642, + 542.4068972553821, + 526.1248852157943, + 510.1693704724008, + 494.54035302520145, + 479.2378328741965, + 464.2618100193858, + 449.61228446076933, + 435.2892561983471, + 421.2927252321192, + 407.6226915620855, + 394.27915518824614, + 381.262116110601, + 368.57157432915017, + 356.2075298438935, + 344.1699826548312, + 332.45893276196307, + 321.07438016528926, + 310.01632486480975, + 299.2847668605244, + 288.87970615243347, + 278.8011427405367, + 269.04907662483424, + 259.623507805326, + 250.524436282012, + 241.75186205489237, + 233.30578512396696, + 225.18620548923582, + 217.3931231506989, + 209.9265381083563, + 202.78645036220797, + 195.97285991225385, + 189.48576675849404, + 183.32517090092847, + 177.4910723395572, + 171.9834710743802, + 166.8023671053974, + 161.9477604326089, + 157.41965105601471, + 153.21803897561475, + 149.34292419140903, + 145.79430670339758, + 142.57218651158047, + 139.67656361595755, + 137.10743801652893, + 134.86480971329456, + 132.9486787062545, + 131.35904499540865, + 130.09590858075708, + 129.15926946229976, + 128.54912764003672, + 128.26548311396795, + 128.30833588409345, + 128.67768595041323, + 129.37353331292726, + 130.39587797163554, + 131.7447199265381, + 133.42005917763493, + 135.42189572492603, + 137.75022956841138, + 140.40506070809099, + 143.3863891439649, + 146.69421487603307, + 150.32853790429544, + 154.28935822875218, + 158.5766758494031, + 163.19049076624827, + 168.13080297928784, + 173.39761248852156, + 178.99091929394964, + 184.91072339557186, + 191.15702479338842, + 197.7298234873993, + 204.62911947760432, + 211.85491276400361, + 219.40720334659733, + 227.2859912253851, + 235.4912764003674, + 244.02305887154372, + 252.8813386389143, + 262.0661157024794, + 271.5773900622385, + 281.4151617181921, + 291.5794306703398 + ], + [ + 850.3775124987246, + 828.7082950719315, + 807.3655749413324, + 786.349352106928, + 765.6596265687175, + 745.2963983267014, + 725.2596673808796, + 705.5494337312521, + 686.1656973778187, + 667.1084583205795, + 648.3777165595347, + 629.9734720946843, + 611.895724926028, + 594.144475053566, + 576.7197224772982, + 559.6214671972248, + 542.8497092133456, + 526.4044485256607, + 510.28568513417, + 494.4934190388737, + 479.02765023977145, + 463.8883787368637, + 449.07560453015, + 434.5893276196307, + 420.42954800530566, + 406.5962656871748, + 393.0894806652382, + 379.90919293949605, + 367.055402509948, + 354.52810937659433, + 342.3273135394348, + 330.4530149984696, + 318.90521375369866, + 307.6839098051219, + 296.7891031527396, + 286.22079379655133, + 275.9789817365575, + 266.0636669727579, + 256.4748495051526, + 247.21252933374146, + 238.27670645852467, + 229.66738087950216, + 221.38455259667387, + 213.42822161003983, + 205.79838791960003, + 198.49505152535463, + 191.51821242730338, + 184.86787062544641, + 178.54402611978372, + 172.54667891031525, + 166.8758289970412, + 161.53147637996128, + 156.5136210590756, + 151.82226303438426, + 147.45740230588717, + 143.41903887358436, + 139.70717273747582, + 136.3218038975615, + 133.26293235384145, + 130.5305581063157, + 128.12468115498422, + 126.045301499847, + 124.29241914090403, + 122.86603407815531, + 121.76614631160088, + 120.99275584124071, + 120.54586266707483, + 120.42546678910318, + 120.63156820732578, + 121.1641669217427, + 122.02326293235386, + 123.20885623915927, + 124.72094684215898, + 126.55953474135293, + 128.7246199367412, + 131.21620242832367, + 134.0342822161004, + 137.17885930007142, + 140.64993368023673, + 144.44750535659625, + 148.57157432915014, + 153.0221405978982, + 157.7992041628405, + 162.90276502397717, + 168.33282318130802, + 174.08937863483325, + 180.1724313845526, + 186.58198143046624, + 193.31802877257425, + 200.38057341087642, + 207.76961534537287, + 215.48515457606368, + 223.52719110294862, + 231.89572492602798, + 240.59075604530148, + 249.61228446076925, + 258.9603101724314, + 268.6348331802877, + 278.63585348433844, + 288.96337108458323 + ], + [ + 831.9263340475462, + 810.4203652688499, + 789.2408937863482, + 768.3879196000408, + 747.8614427099275, + 727.6614631160087, + 707.7879808182837, + 688.2409958167534, + 669.0205081114173, + 650.1265177022754, + 631.5590245893276, + 613.3180287725743, + 595.4035302520151, + 577.8155290276502, + 560.5540250994796, + 543.6190184675033, + 527.0105091317213, + 510.72849709213335, + 494.7729823487399, + 479.1439649015407, + 463.8414447505357, + 448.865421895725, + 434.2158963371084, + 419.8928680746863, + 405.89633710845834, + 392.2263034384247, + 378.88276706458527, + 365.86572798694016, + 353.1751862054892, + 340.8111417202326, + 328.7735945311704, + 317.06254463830226, + 305.67799204162844, + 294.6199367411489, + 283.8883787368636, + 273.4833180287726, + 263.40475461687583, + 253.6526885011734, + 244.22711968166516, + 235.1280481583512, + 226.35547393123147, + 217.90939700030614, + 209.78981736557498, + 201.99673502703808, + 194.5301499846954, + 187.39006223854713, + 180.576471788593, + 174.0893786348332, + 167.92878277726763, + 162.0946842158963, + 156.58708295071935, + 151.40597898173655, + 146.5513723089481, + 142.02326293235382, + 137.8216508519539, + 133.94653606774818, + 130.39791857973677, + 127.17579838791958, + 124.28017549229673, + 121.71104989286806, + 119.46842158963372, + 117.55229058259361, + 115.9626568717478, + 114.69952045709624, + 113.76288133863892, + 113.15273951637587, + 112.86909499030712, + 112.91194776043261, + 113.2812978267524, + 113.9771451892664, + 114.9994898479747, + 116.34833180287727, + 118.02367105397408, + 120.02550760126519, + 122.35384144475054, + 125.00867258443014, + 127.99000102030404, + 131.2978267523722, + 134.93214978063466, + 138.89297010509128, + 143.1802877257423, + 147.79410264258752, + 152.73441485562694, + 158.00122436486075, + 163.59453117028872, + 169.51433527191108, + 175.76063666972755, + 182.33343536373835, + 189.2327313539435, + 196.4585246403428, + 204.01081522293634, + 211.88960310172433, + 220.09488827670643, + 228.6266707478829, + 237.48495051525356, + 246.66972757881837, + 256.1810019385777, + 266.0187735945311, + 276.18304254667896, + 286.673808795021 + ], + [ + 813.801652892562, + 792.458932761963, + 771.4427099275583, + 750.752984389348, + 730.3897561473318, + 710.3530252015099, + 690.6427915518823, + 671.2590551984492, + 652.2018161412101, + 633.4710743801652, + 615.0668299153148, + 596.9890827466585, + 579.2378328741966, + 561.8130802979288, + 544.7148250178552, + 527.9430670339761, + 511.4978063462912, + 495.3790429548005, + 479.5867768595041, + 464.12100806040195, + 448.98173655749406, + 434.1689623507805, + 419.6826854402612, + 405.5229058259361, + 391.68962350780527, + 378.1828384858688, + 365.00255076012644, + 352.1487603305785, + 339.6214671972247, + 327.4206713600653, + 315.5463728191, + 303.99857157432916, + 292.77726762575253, + 281.88246097337003, + 271.3141516171819, + 261.072339557188, + 251.15702479338842, + 241.56820732578305, + 232.305887154372, + 223.37006427915517, + 214.76073870013258, + 206.47791041730437, + 198.52157943067033, + 190.89174574023056, + 183.58840934598507, + 176.6115702479339, + 169.96122844607692, + 163.63738394041422, + 157.64003673094578, + 151.96918681767164, + 146.62483420059178, + 141.60697887970613, + 136.91562085501477, + 132.55076012651767, + 128.51239669421489, + 124.80053055810632, + 121.41516171819202, + 118.35629017447195, + 115.62391592694622, + 113.21803897561473, + 111.13865932047749, + 109.38577696153452, + 107.95939189878584, + 106.8595041322314, + 106.08611366187122, + 105.63922048770533, + 105.5188246097337, + 105.72492602795631, + 106.2575247423732, + 107.11662075298437, + 108.3022140597898, + 109.81430466278948, + 111.65289256198346, + 113.81797775737168, + 116.3095602489542, + 119.12764003673092, + 122.27221712070195, + 125.74329150086723, + 129.5408631772268, + 133.6649321497806, + 138.11549841852874, + 142.89256198347107, + 147.99612284460764, + 153.42618100193857, + 159.18273645546373, + 165.26578920518318, + 171.67533925109683, + 178.41138659320472, + 185.47393123150698, + 192.86297316600346, + 200.57851239669415, + 208.6205489235792, + 216.98908274665845, + 225.6841138659321, + 234.70564228139983, + 244.05366799306182, + 253.7281910009183, + 263.7292113049688, + 274.0567289052138, + 284.7107438016529 + ], + [ + 796.003469033772, + 774.8239975512703, + 753.9710233649627, + 733.4445464748495, + 713.2445668809305, + 693.3710845832057, + 673.8240995816752, + 654.6036118763392, + 635.7096214671972, + 617.1421283542496, + 598.9011325374962, + 580.986634016937, + 563.3986327925724, + 546.1371288644016, + 529.2021222324253, + 512.5936128966432, + 496.3116008570555, + 480.35608611366195, + 464.72706866646257, + 449.4245485154576, + 434.44852566064685, + 419.79900010203045, + 405.4759718396082, + 391.47944087338027, + 377.8094072033466, + 364.46587082950725, + 351.4488317518621, + 338.7582899704112, + 326.3942454851546, + 314.35669829609225, + 302.6456484032242, + 291.2610958065504, + 280.2030405060708, + 269.47148250178554, + 259.0664217936946, + 248.98785838179774, + 239.23579226609533, + 229.81022344658706, + 220.71115192327318, + 211.93857769615346, + 203.49250076522802, + 195.37292113049696, + 187.57983879196001, + 180.1132537496174, + 172.973166003469, + 166.15957555351497, + 159.67248239975515, + 153.5118865421896, + 147.6777879808183, + 142.17018671564125, + 136.9890827466585, + 132.13447607387002, + 127.6063666972758, + 123.40475461687583, + 119.52963983267017, + 115.98102234465874, + 112.75890215284156, + 109.86327925721865, + 107.29415365779003, + 105.05152535455568, + 103.13539434751557, + 101.54576063666973, + 100.28262422201817, + 99.34598510356086, + 98.73584328129783, + 98.45219875522908, + 98.49505152535455, + 98.86440159167432, + 99.56024895418835, + 100.58259361289663, + 101.93143556779921, + 103.60677481889604, + 105.60861136618712, + 107.93694520967247, + 110.5917763493521, + 113.573104785226, + 116.88093051729416, + 120.51525354555656, + 124.47607387001327, + 128.76339149066416, + 133.37720640750945, + 138.31751862054892, + 143.58432812978262, + 149.1776349352107, + 155.09743903683292, + 161.3437404346496, + 167.91653912866033, + 174.81583511886535, + 182.0416284052648, + 189.59391898785833, + 197.47270686664615, + 205.6779920416284, + 214.20977451280478, + 223.06805428017552, + 232.25283134374038, + 241.76410570349958, + 251.60187735945317, + 261.7661463116008, + 272.2569125599429, + 283.0741761044791 + ], + [ + 778.5317824711764, + 757.5155596367716, + 736.8258340985612, + 716.4626058565452, + 696.4258749107233, + 676.7156412610957, + 657.3319049076623, + 638.2746658504234, + 619.5439240893786, + 601.139679624528, + 583.0619324558717, + 565.31068258341, + 547.8859300071422, + 530.7876747270686, + 514.0159167431895, + 497.57065605550446, + 481.4518926640139, + 465.6596265687175, + 450.1938577696153, + 435.0545862667075, + 420.2418120599939, + 405.7555351494745, + 391.59575553514946, + 377.7624732170187, + 364.2556881950821, + 351.0754004693398, + 338.22161003979187, + 325.69431690643813, + 313.49352106927864, + 301.6192225283135, + 290.07142128354246, + 278.8501173349659, + 267.9553106825834, + 257.38700132639525, + 247.1451892664014, + 237.22987450260175, + 227.64105703499644, + 218.37873686358532, + 209.44291398836853, + 200.83358840934596, + 192.55076012651767, + 184.5944291398837, + 176.96459544944392, + 169.66125905519843, + 162.68441995714718, + 156.0340781552903, + 149.71023364962758, + 143.71288644015914, + 138.042036526885, + 132.6976839098051, + 127.67982858891949, + 122.98847056422812, + 118.62360983573105, + 114.5852464034282, + 110.87338026731966, + 107.48801142740537, + 104.42913988368531, + 101.69676563615955, + 99.29088868482808, + 97.21150902969084, + 95.45862667074786, + 94.03224160799917, + 92.93235384144474, + 92.15896337108457, + 91.71207019691869, + 91.59167431894704, + 91.79777573716967, + 92.33037445158656, + 93.18947046219772, + 94.37506376900316, + 95.88715437200285, + 97.7257422711968, + 99.89082746658504, + 102.38240995816753, + 105.20048974594428, + 108.34506682991528, + 111.81614121008059, + 115.61371288644015, + 119.737781858994, + 124.18834812774202, + 128.96541169268443, + 134.06897255382103, + 139.49903071115187, + 145.2555861646771, + 151.33863891439645, + 157.74818896031022, + 164.4842363024181, + 171.54678094072028, + 178.93582287521684, + 186.65136210590754, + 194.69339863279248, + 203.06193245587184, + 211.75696357514533, + 220.77849199061328, + 230.1265177022753, + 239.80104071013156, + 249.80206101418227, + 260.1295786144271, + 270.78359351086635, + 281.76410570349964 + ], + [ + 761.3865932047751, + 740.5336190184676, + 720.0071421283542, + 699.8071625344353, + 679.9336802367105, + 660.3866952351801, + 641.1662075298439, + 622.2722171207021, + 603.7047240077543, + 585.4637281910009, + 567.5492296704417, + 549.9612284460769, + 532.6997245179064, + 515.76471788593, + 499.15620855014794, + 482.8741965105601, + 466.9186817671667, + 451.28966431996736, + 435.98714416896235, + 421.0111213141517, + 406.3615957555351, + 392.03856749311296, + 378.042036526885, + 364.37200285685134, + 351.0284664830119, + 338.0114274053668, + 325.3208856239159, + 312.95684113865934, + 300.91929394959703, + 289.208244056729, + 277.82369146005516, + 266.7656361595756, + 256.0340781552903, + 245.62901744719926, + 235.55045403530255, + 225.79838791960006, + 216.37281910009185, + 207.27374757677788, + 198.50117334965822, + 190.0550964187328, + 181.93551678400163, + 174.1424344454648, + 166.67584940312216, + 159.53576165697376, + 152.7221712070197, + 146.23507805325994, + 140.07448219569434, + 134.24038363432305, + 128.73278236914598, + 123.55167840016325, + 118.69707172737479, + 114.16896235078056, + 109.96735027038058, + 106.09223548617489, + 102.54361799816348, + 99.3214978063463, + 96.42587491072342, + 93.85674931129476, + 91.61412100806041, + 89.69799000102032, + 88.10835629017448, + 86.84521987552291, + 85.90858075706561, + 85.29843893480259, + 85.0147944087338, + 85.05764717885931, + 85.42699724517907, + 86.1228446076931, + 87.14518926640139, + 88.49403122130396, + 90.16937047240079, + 92.17120701969188, + 94.49954086317723, + 97.15437200285686, + 100.13570043873075, + 103.44352617079889, + 107.07784919906132, + 111.038669523518, + 115.32598714416898, + 119.93980206101416, + 124.8801142740537, + 130.1469237832874, + 135.74023058871538, + 141.66003469033774, + 147.90633608815426, + 154.47913478216515, + 161.37843077237017, + 168.60422405876946, + 176.15651464136317, + 184.035302520151, + 192.2405876951331, + 200.77237016630957, + 209.6306499336802, + 218.81542699724523, + 228.32670135700437, + 238.1644730129578, + 248.32874196510565, + 258.8195082134476, + 269.636771757984, + 280.78053259871444 + ], + [ + 744.5679012345679, + 723.8781756963574, + 703.5149474543414, + 683.4782165085196, + 663.767982858892, + 644.3842465054586, + 625.3270074482194, + 606.5962656871748, + 588.1920212223242, + 570.1142740536679, + 552.3630241812059, + 534.9382716049382, + 517.8400163248648, + 501.0682583409856, + 484.6229976533006, + 468.50423426181004, + 452.7119681665136, + 437.2461993674114, + 422.1069278645036, + 407.29415365779, + 392.8078767472707, + 378.6480971329456, + 364.8148148148148, + 351.3080297928783, + 338.127742067136, + 325.273951637588, + 312.74665850423423, + 300.5458626670748, + 288.67156412610956, + 277.1237628813386, + 265.902458932762, + 255.00765228037957, + 244.43934292419144, + 234.1975308641975, + 224.2822161003979, + 214.69339863279254, + 205.43107846138145, + 196.49525558616466, + 187.88593000714215, + 179.60310172431383, + 171.64677073767982, + 164.01693704724008, + 156.71360065299461, + 149.73676155494337, + 143.0864197530864, + 136.76257524742374, + 130.76522803795532, + 125.09437812468114, + 119.75002550760126, + 114.73217018671562, + 110.04081216202428, + 105.67595143352719, + 101.63758800122436, + 97.92572186511579, + 94.54035302520151, + 91.4814814814815, + 88.74910723395571, + 86.3432302826242, + 84.26385062748699, + 82.51096826854402, + 81.08458320579533, + 79.9846954392409, + 79.21130496888071, + 78.76441179471482, + 78.64401591674319, + 78.85011733496583, + 79.38271604938272, + 80.24181205999386, + 81.4274053667993, + 82.93949596979898, + 84.77808386899295, + 86.94316906438117, + 89.43475155596366, + 92.25283134374044, + 95.39740842771145, + 98.86848280787672, + 102.66605448423628, + 106.79012345679013, + 111.2406897255382, + 116.01775329048053, + 121.12131415161721, + 126.55137230894805, + 132.30792776247318, + 138.39098051219264, + 144.8005305581063, + 151.5365779002143, + 158.59912253851644, + 165.98816447301292, + 173.70370370370372, + 181.74574023058867, + 190.1142740536679, + 198.80930517294155, + 207.8308335884093, + 217.17885930007148, + 226.85338230792775, + 236.8544026119783, + 247.18192021222325, + 257.83593510866234, + 268.81644730129585, + 280.1234567901235 + ], + [ + 728.0757065605551, + 707.5492296704418, + 687.3492500765228, + 667.4757677787982, + 647.9287827772677, + 628.7082950719314, + 609.8143046627895, + 591.2468115498419, + 573.0058157330885, + 555.0913172125294, + 537.5033159881643, + 520.2418120599939, + 503.3068054280176, + 486.6982960922356, + 470.4162840526477, + 454.4607693092542, + 438.83175186205494, + 423.52923171104993, + 408.5532088562391, + 393.9036832976227, + 379.5806550352005, + 365.5841240689725, + 351.9140903989389, + 338.57055402509957, + 325.55351494745435, + 312.8629731660035, + 300.49892868074687, + 288.46138149168456, + 276.75033159881644, + 265.36577900214263, + 254.3077237016631, + 243.5761656973779, + 233.17110498928682, + 223.09254157739005, + 213.34047546168762, + 203.91490664217937, + 194.81583511886546, + 186.04326089174572, + 177.59718396082033, + 169.4776043260892, + 161.6845219875523, + 154.21793694520971, + 147.07784919906132, + 140.26425874910723, + 133.7771655953474, + 127.6165697377819, + 121.78247117641061, + 116.27486991123357, + 111.0937659422508, + 106.23915926946229, + 101.7110498928681, + 97.50943781246814, + 93.63432302826243, + 90.085705540251, + 86.86358534843386, + 83.96796245281097, + 81.39883685338232, + 79.15620855014794, + 77.24007754310787, + 75.65044383226203, + 74.38730741761046, + 73.45066829915315, + 72.84052647689012, + 72.55688195082136, + 72.59973472094684, + 72.96908478726661, + 73.66493214978064, + 74.68727680848895, + 76.0361187633915, + 77.71145801448831, + 79.71329456177942, + 82.04162840526476, + 84.69645954494439, + 87.67778798081828, + 90.98561371288646, + 94.61993674114885, + 98.58075706560555, + 102.8680746862565, + 107.48188960310173, + 112.42220181614118, + 117.68901132537499, + 123.28231813080296, + 129.2021222324252, + 135.44842363024185, + 142.02122232425262, + 148.92051831445778, + 156.14631160085708, + 163.69860218345062, + 171.57739006223858, + 179.7826752372207, + 188.31445770839704, + 197.1727374757678, + 206.35751453933267, + 215.868788899092, + 225.70656055504543, + 235.8708295071931, + 246.36159575553518, + 257.1788593000714, + 268.32262014080203, + 279.7928782777268 + ], + [ + 711.9100091827365, + 691.5467809407204, + 671.5100499948984, + 651.799816345271, + 632.4160799918376, + 613.3588409345986, + 594.6280991735537, + 576.2238547087032, + 558.146107540047, + 540.3948576675849, + 522.9701050913171, + 505.8718498112437, + 489.1000918273646, + 472.6548311396796, + 456.53606774818894, + 440.7438016528926, + 425.27803285379053, + 410.1387613508826, + 395.3259871441689, + 380.8397102336496, + 366.6799306193245, + 352.84664830119374, + 339.3398632792572, + 326.1595755535149, + 313.3057851239669, + 300.77849199061325, + 288.57769615345376, + 276.7033976124885, + 265.1555963677176, + 253.9342924191409, + 243.0394857667585, + 232.4711764105704, + 222.22936435057645, + 212.31404958677686, + 202.72523211917152, + 193.4629119477604, + 184.52708907254365, + 175.91776349352105, + 167.6349352106928, + 159.67860422405874, + 152.04877053361898, + 144.74543413937357, + 137.76859504132233, + 131.11825323946536, + 124.79440873380267, + 118.79706152433427, + 113.1262116110601, + 107.78185899398021, + 102.76400367309458, + 98.0726456484032, + 93.70778491990615, + 89.6694214876033, + 85.95755535149473, + 82.57218651158044, + 79.51331496786042, + 76.78094072033466, + 74.37506376900316, + 72.29568411386593, + 70.54280175492298, + 69.11641669217425, + 68.01652892561984, + 67.24313845525965, + 66.79624528109376, + 66.67584940312213, + 66.88195082134476, + 67.41454953576167, + 68.2736455463728, + 69.45923885317825, + 70.97132945617793, + 72.80991735537191, + 74.97500255076012, + 77.4665850423426, + 80.28466483011937, + 83.4292419140904, + 86.9003162942557, + 90.69788797061521, + 94.82195694316904, + 99.27252321191716, + 104.0495867768595, + 109.15314763799608, + 114.58320579532703, + 120.33976124885217, + 126.42281399857151, + 132.83236404448527, + 139.56841138659314, + 146.63095602489545, + 154.01999795939187, + 161.7355371900826, + 169.77757371696768, + 178.14610754004687, + 186.8411386593204, + 195.8626670747883, + 205.2106927864503, + 214.88521579430673, + 224.88623609835727, + 235.2137536986021, + 245.86776859504135, + 256.84828078767464, + 268.15529027650246, + 279.7887970615243 + ], + [ + 696.0708091011121, + 675.8708295071932, + 655.9973472094684, + 636.450362207938, + 617.2298745026019, + 598.3358840934599, + 579.7683909805122, + 561.5273951637589, + 543.6128966431997, + 526.024895418835, + 508.76339149066416, + 491.8283848586879, + 475.2198755229059, + 458.937863483318, + 442.98234873992453, + 427.3533312927252, + 412.0508111417203, + 397.07478828690955, + 382.42526272829303, + 368.1022344658709, + 354.10570349964286, + 340.43566982960925, + 327.09213345576984, + 314.0750943781247, + 301.3845525966738, + 289.0205081114172, + 276.9829609223549, + 265.2719110294869, + 253.88735843281302, + 242.8293031323335, + 232.0977451280482, + 221.69268441995717, + 211.6141210080604, + 201.86205489235792, + 192.43648607284976, + 183.33741454953577, + 174.5648403224161, + 166.11876339149066, + 157.99918375675955, + 150.20610141822266, + 142.73951637588002, + 135.5994286297317, + 128.78583817977758, + 122.29874502601776, + 116.1381491684522, + 110.30405060708095, + 104.79644934190391, + 99.61534537292115, + 94.76073870013265, + 90.23262932353842, + 86.03101724313849, + 82.15590245893277, + 78.60728497092134, + 75.38516477910417, + 72.48954188348131, + 69.92041628405266, + 67.6777879808183, + 65.7616569737782, + 64.17202326293237, + 62.908886848280794, + 61.97224772982349, + 61.36210590756047, + 61.07846138149169, + 61.121314151617185, + 61.49066421793696, + 62.186511580451, + 63.20885623915928, + 64.55769819406183, + 66.23303744515866, + 68.23487399244976, + 70.56320783593512, + 73.21803897561472, + 76.19936741148862, + 79.50719314355678, + 83.14151617181922, + 87.10233649627588, + 91.38965411692683, + 96.00346903377206, + 100.94378124681155, + 106.21059075604528, + 111.80389756147335, + 117.7237016630956, + 123.9700030609121, + 130.542801754923, + 137.44209774512802, + 144.66789103152743, + 152.220181614121, + 160.09896949290885, + 168.30425466789106, + 176.83603713906743, + 185.69431690643802, + 194.87909397000308, + 204.39036832976223, + 214.2281399857158, + 224.39240893786348, + 234.88317518620542, + 245.7004387307418, + 256.84419957147225, + 268.3144577083972, + 280.11121314151615 + ], + [ + 680.558106315682, + 660.5213753698602, + 640.8111417202325, + 621.4274053667993, + 602.3701663095603, + 583.6394245485154, + 565.2351800836649, + 547.1574329150088, + 529.4061830425467, + 511.981430466279, + 494.88317518620545, + 478.11141720232627, + 461.6661565146414, + 445.54739312315064, + 429.7551270278542, + 414.2893582287521, + 399.1500867258443, + 384.3373125191307, + 369.8510356086113, + 355.69125599428634, + 341.8579736761555, + 328.35118865421896, + 315.17090092847667, + 302.3171104989287, + 289.78981736557495, + 277.58902152841546, + 265.7147229874502, + 254.16692174267936, + 242.94561779410262, + 232.05081114172023, + 221.4825017855321, + 211.24068972553823, + 201.32537496173862, + 191.73655749413322, + 182.47423732272216, + 173.53841444750535, + 164.9290888684828, + 156.64626058565452, + 148.6899295990205, + 141.06009590858073, + 133.75675951433527, + 126.77992041628409, + 120.12957861442712, + 113.8057341087644, + 107.80838689929597, + 102.13753698602186, + 96.79318436894197, + 91.77532904805632, + 87.08397102336495, + 82.71911029486785, + 78.68074686256506, + 74.96888072645649, + 71.58351188654218, + 68.52464034282214, + 65.79226609529641, + 63.386389143964905, + 61.30700948882767, + 59.554127129884705, + 58.127742067136005, + 57.02785430058158, + 56.25446383022141, + 55.807570656055496, + 55.68717477808386, + 55.893276196306495, + 56.425874910723394, + 57.28497092133456, + 58.470564228139985, + 59.98265483113967, + 61.82124273033363, + 63.98632792572187, + 66.47791041730436, + 69.2959902050811, + 72.44056728905213, + 75.91164166921743, + 79.70921334557698, + 83.83328231813077, + 88.28384858687888, + 93.06091215182124, + 98.16447301295787, + 103.59453117028872, + 109.35108662381393, + 115.4341393735333, + 121.84368941944695, + 128.57973676155495, + 135.6422813998571, + 143.0313233343537, + 150.74686256504438, + 158.78889909192932, + 167.1574329150087, + 175.8524640342822, + 184.87399244974995, + 194.22201816141214, + 203.89654116926837, + 213.89756147331912, + 224.2250790735639, + 234.87909397000297, + 245.85960616263648, + 257.1666156514641, + 268.80012243648616, + 280.7601265177023 + ], + [ + 665.3719008264463, + 645.4984185287216, + 625.951433527191, + 606.7309458218549, + 587.836955412713, + 569.2694622997655, + 551.0284664830119, + 533.113967962453, + 515.5259667380881, + 498.26446280991735, + 481.3294561779411, + 464.72094684215904, + 448.4389348025712, + 432.48342005917766, + 416.8544026119784, + 401.5518824609734, + 386.5758596061627, + 371.9263340475462, + 357.60330578512395, + 343.60677481889604, + 329.9367411488624, + 316.593204775023, + 303.57616569737786, + 290.885623915927, + 278.52157943067033, + 266.4840322416081, + 254.77298234873996, + 243.38842975206614, + 232.3303744515866, + 221.59881644730135, + 211.19375573921033, + 201.11519232731357, + 191.36312621161107, + 181.93755739210286, + 172.83848586878895, + 164.06591164166923, + 155.61983471074382, + 147.50025507601268, + 139.70717273747582, + 132.24058769513317, + 125.10049994898478, + 118.28690949903076, + 111.79981634527091, + 105.63922048770536, + 99.80512192633405, + 94.29752066115707, + 89.1164166921743, + 84.26181001938579, + 79.73370064279155, + 75.53208856239159, + 71.65697377818591, + 68.1083562901745, + 64.88623609835732, + 61.990613202734416, + 59.42148760330582, + 57.178859300071444, + 55.262728293031344, + 53.6730945821855, + 52.409958167533944, + 51.473319049076636, + 50.8631772268136, + 50.579532700744835, + 50.62238547087033, + 50.99173553719009, + 51.68758289970412, + 52.70992755841241, + 54.058769513314985, + 55.7341087644118, + 57.735945311702885, + 60.06427915518826, + 62.71911029486788, + 65.70043873074177, + 69.00826446280992, + 72.64258749107235, + 76.60340781552904, + 80.89072543617996, + 85.50454035302519, + 90.44485256606468, + 95.71166207529845, + 101.30496888072642, + 107.22477298234877, + 113.47107438016526, + 120.04387307417603, + 126.94316906438121, + 134.1689623507805, + 141.72125293337416, + 149.60004081216204, + 157.8053259871441, + 166.3371084583206, + 175.1953882256912, + 184.38016528925607, + 193.8914396490154, + 203.72921130496883, + 213.89348025711666, + 224.38424650545858, + 235.2015100499948, + 246.34527089072543, + 257.81552902765014, + 269.6122844607694, + 281.7355371900826 + ], + [ + 650.5121926334047, + 630.801958983777, + 611.4182226303437, + 592.3609835731048, + 573.6302418120599, + 555.2259973472094, + 537.1482501785531, + 519.3970003060914, + 501.97224772982355, + 484.87399244975, + 468.1022344658707, + 451.6569737781859, + 435.53821038669525, + 419.7459442913988, + 404.2801754922966, + 389.1409039893889, + 374.32812978267526, + 359.84185287215587, + 345.6820732578308, + 331.84879093970005, + 318.34200591776346, + 305.1617181920212, + 292.30792776247324, + 279.7806346291195, + 267.57983879196, + 255.70554025099483, + 244.15773900622384, + 232.9364350576472, + 222.04162840526476, + 211.47331904907665, + 201.23150698908276, + 191.31619222528317, + 181.72737475767778, + 172.4650545862667, + 163.52923171104993, + 154.91990613202734, + 146.63707784919907, + 138.68074686256503, + 131.0509131721253, + 123.74757677787979, + 116.77073767982858, + 110.12039587797167, + 103.79655137230895, + 97.79920416284052, + 92.12835424956636, + 86.78400163248651, + 81.76614631160088, + 77.0747882869095, + 72.70992755841242, + 68.67156412610956, + 64.95969799000103, + 61.574329150086726, + 58.5154576063667, + 55.78308335884094, + 53.37720640750945, + 51.29782675237222, + 49.54494439342923, + 48.11855933068054, + 47.018671564126116, + 46.24528109376594, + 45.79838791960004, + 45.67799204162841, + 45.88409345985103, + 46.416692174267936, + 47.27578818487909, + 48.46138149168452, + 49.973472094684226, + 51.81205999387817, + 53.977145189266395, + 56.468727680848886, + 59.28680746862566, + 62.431384552596654, + 65.90245893276196, + 69.70003060912153, + 73.82409958167534, + 78.2746658504234, + 83.05172941536577, + 88.1552902765024, + 93.58534843383329, + 99.3419038873584, + 105.42495663707788, + 111.83450668299153, + 118.57055402509944, + 125.63309866340173, + 133.0221405978982, + 140.73767982858897, + 148.77971635547397, + 157.14825017855316, + 165.84328129782682, + 174.86480971329456, + 184.21283542495655, + 193.887358432813, + 203.88837873686353, + 214.21589633710852, + 224.8699112335476, + 235.85042342618095, + 247.1574329150087, + 258.79093970003055, + 270.75094378124686, + 283.0374451586573 + ], + [ + 635.9789817365576, + 616.431996735027, + 597.2115090296908, + 578.317518620549, + 559.7500255076012, + 541.5090296908479, + 523.5945311702886, + 506.006529945924, + 488.74502601775333, + 471.8100193857769, + 455.20151004999485, + 438.91949801040704, + 422.96398326701365, + 407.3349658198143, + 392.0324456688094, + 377.05642281399867, + 362.4068972553822, + 348.08386899295994, + 334.08733802673197, + 320.4173043566983, + 307.07376798285895, + 294.0567289052138, + 281.36618712376287, + 269.00214263850626, + 256.96459544944395, + 245.25354555657592, + 233.86899295990207, + 222.81093765942256, + 212.07937965513725, + 201.67431894704626, + 191.5957555351495, + 181.84368941944703, + 172.41812059993882, + 163.31904907662485, + 154.5464748495052, + 146.10039791857974, + 137.98081828384863, + 130.18773594531172, + 122.72115090296913, + 115.58106315682075, + 108.76747270686666, + 102.28037955310687, + 96.11978369554129, + 90.28568513417, + 84.77808386899295, + 79.59697990001025, + 74.74237322722175, + 70.2142638506275, + 66.01265177022754, + 62.13753698602183, + 58.588919498010426, + 55.366799306193265, + 52.471176410570365, + 49.90205081114173, + 47.65942250790738, + 45.74329150086727, + 44.15365779002144, + 42.890521375369865, + 41.95388225691258, + 41.34374043464954, + 41.06009590858076, + 41.10294867870626, + 41.47229874502602, + 42.16814610754005, + 43.19049076624835, + 44.53933272115091, + 46.21467197224774, + 48.21650851953881, + 50.54484236302419, + 53.19967350270381, + 56.18100193857771, + 59.48882767064585, + 63.12315069890827, + 67.08397102336497, + 71.37128864401592, + 75.98510356086112, + 80.92541577390061, + 86.19222528313438, + 91.7855320885624, + 97.70533619018465, + 103.95163758800126, + 110.52443628201202, + 117.42373227221705, + 124.64952555861649, + 132.20181614121003, + 140.080604019998, + 148.28588919498011, + 156.81767166615646, + 165.67595143352722, + 174.86072849709208, + 184.37200285685122, + 194.20977451280484, + 204.3740434649525, + 214.86480971329462, + 225.6820732578308, + 236.8258340985613, + 248.29609223548624, + 260.0928476686052, + 272.2161003979187, + 284.66585042342615 + ], + [ + 621.7722681359045, + 602.3885317824711, + 583.331292725232, + 564.6005509641873, + 546.1963064993369, + 528.1185593306805, + 510.36730945821853, + 492.9425568819509, + 475.84430160187736, + 459.07254361799824, + 442.6272829303132, + 426.5085195388226, + 410.7162534435262, + 395.25048464442403, + 380.11121314151615, + 365.29843893480256, + 350.8121620242833, + 336.65238240995825, + 322.8191000918273, + 309.3123150698909, + 296.1320273441485, + 283.2782369146006, + 270.7509437812468, + 258.5501479440873, + 246.67584940312216, + 235.12804815835122, + 223.9067442097745, + 213.01193755739214, + 202.44362820120398, + 192.20181614121012, + 182.28650137741047, + 172.69768390980516, + 163.43536373839405, + 154.49954086317723, + 145.8902152841547, + 137.6073870013264, + 129.6510560146924, + 122.02122232425263, + 114.71788593000716, + 107.74104683195591, + 101.09070503009896, + 94.7668605244363, + 88.76951331496788, + 83.0986634016937, + 77.7543107846138, + 72.7364554637282, + 68.04509743903684, + 63.680236710539745, + 59.641873278236915, + 55.930007142128346, + 52.544638302214075, + 49.48576675849404, + 46.75339251096827, + 44.34751555963677, + 42.26813590449955, + 40.51525354555658, + 39.08886848280788, + 37.98898071625345, + 37.21559024589328, + 36.768697071727374, + 36.64830119375574, + 36.85440261197837, + 37.387001326395264, + 38.24609733700643, + 39.431690643811855, + 40.943781246811554, + 42.78236914600552, + 44.94745434139373, + 47.43903683297623, + 50.25711662075298, + 53.40169370472401, + 56.87276808488928, + 60.67033976124884, + 64.79440873380267, + 69.24497500255077, + 74.02203856749308, + 79.12559942862973, + 84.5556575859606, + 90.31221303948577, + 96.39526578920514, + 102.8048158351189, + 109.54086317722681, + 116.60340781552897, + 123.99244975002553, + 131.7079889807162, + 139.75002550760132, + 148.11855933068054, + 156.813590449954, + 165.83511886542192, + 175.18314457708397, + 184.85766758494023, + 194.85868788899091, + 205.1862054892357, + 215.840220385675, + 226.82073257830834, + 238.12774206713593, + 249.76124885215793, + 261.7212529333741, + 274.0077543107847, + 286.6207529843894 + ], + [ + 607.8920518314458, + 588.6715641261096, + 569.7775737169676, + 551.21008060402, + 532.9690847872666, + 515.0545862667075, + 497.46658504234256, + 480.20508111417206, + 463.27007448219575, + 446.6615651464137, + 430.3795531068258, + 414.4240383634323, + 398.79502091623306, + 383.49250076522804, + 368.5164779104173, + 353.8669523518009, + 339.54392408937866, + 325.5473931231507, + 311.87735945311704, + 298.5338230792777, + 285.5167840016326, + 272.82624222018165, + 260.46219773492504, + 248.42465054586273, + 236.71360065299461, + 225.3290480563208, + 214.27099275584126, + 203.539434751556, + 193.134374043465, + 183.05581063156822, + 173.3037445158658, + 163.87817569635757, + 154.7791041730436, + 146.0065299459239, + 137.56045301499847, + 129.4408733802673, + 121.64779104173046, + 114.18120599938783, + 107.04111825323949, + 100.22752780328541, + 93.74043464952557, + 87.57983879196004, + 81.74574023058875, + 76.23813896541171, + 71.05703499642895, + 66.20242832364048, + 61.67431894704625, + 57.47270686664628, + 53.59759208244057, + 50.04897459442914, + 46.826854402612, + 43.9312315069891, + 41.36210590756047, + 39.11947760432609, + 37.203346597286014, + 35.61371288644017, + 34.35057647178861, + 33.413937353331306, + 32.803795531068275, + 32.520151004999505, + 32.56300377512499, + 32.93235384144476, + 33.62820120395878, + 34.65054586266708, + 35.99938781756964, + 37.67472706866647, + 39.67656361595757, + 42.004897459442915, + 44.65972859912254, + 47.641057034996436, + 50.9488827670646, + 54.583205795327, + 58.544026119783695, + 62.831343740434654, + 67.44515865727989, + 72.38547087031934, + 77.6522803795531, + 83.24558718498112, + 89.16539128660341, + 95.41169268441993, + 101.98449137843082, + 108.88378736863586, + 116.10958065503516, + 123.66187123762884, + 131.54065911641666, + 139.7459442913989, + 148.27772676257527, + 157.13600652994586, + 166.32078359351092, + 175.83205795327004, + 185.66982960922346, + 195.83409856137132, + 206.32486480971323, + 217.14212835424965, + 228.2858891949801, + 239.75614733190483, + 251.55290276502402, + 263.6761554943373, + 276.12590551984505, + 288.9021528415468 + ], + [ + 594.3383328231814, + 575.2810937659423, + 556.5503520048974, + 538.146107540047, + 520.0683603713907, + 502.3171104989287, + 484.89235792266095, + 467.7941026425875, + 451.02234465870833, + 434.57708397102334, + 418.4583205795327, + 402.6660544842363, + 387.20028568513425, + 372.06101418222636, + 357.24823997551266, + 342.7619630649934, + 328.60218345066835, + 314.7689011325375, + 301.26211611060097, + 288.0818283848587, + 275.2280379553107, + 262.70074482195696, + 250.49994898479747, + 238.62565044383228, + 227.0778491990613, + 215.85654525048466, + 204.96173859810224, + 194.3934292419141, + 184.15161718192022, + 174.23630241812063, + 164.64748495051526, + 155.3851647791042, + 146.44934190388736, + 137.8400163248648, + 129.55718804203656, + 121.60085705540251, + 113.97102336496279, + 106.66768697071726, + 99.69084787266607, + 93.0405060708091, + 86.7166615651464, + 80.71931435567802, + 75.04846444240384, + 69.70411182532396, + 64.68625650443832, + 59.994898479746986, + 55.63003775124989, + 51.59167431894705, + 47.87980818283848, + 44.49443934292418, + 41.43556779920417, + 38.70319355167841, + 36.2973166003469, + 34.217936945209665, + 32.46505458626672, + 31.038669523518017, + 29.938781756963575, + 29.16539128660341, + 28.71849811243751, + 28.59810223446587, + 28.8042036526885, + 29.336802367105403, + 30.195898377716556, + 31.381491684521983, + 32.89358228752168, + 34.73217018671564, + 36.89725538210388, + 39.38883787368634, + 42.206917661463116, + 45.35149474543414, + 48.822569125599436, + 52.62014080195897, + 56.7442097745128, + 61.194776043260894, + 65.97183960820325, + 71.07540046933983, + 76.50545862667073, + 82.2620140801959, + 88.34506682991534, + 94.75461687582896, + 101.49066421793697, + 108.55320885623914, + 115.94225079073557, + 123.6577900214264, + 131.69982654831136, + 140.0683603713907, + 148.7633914906642, + 157.78491990613196, + 167.13294561779412, + 176.80746862565042, + 186.80848892970093, + 197.13600652994592, + 207.79002142638498, + 218.77053361901852, + 230.07754310784608, + 241.71104989286795, + 253.67105397408432, + 265.9575553514947, + 278.5705540250995, + 291.5100499948985 + ], + [ + 581.1111111111111, + 562.2171207019692, + 543.6496275890214, + 525.4086317722682, + 507.494133251709, + 489.90613202734414, + 472.6446280991735, + 455.7096214671972, + 439.10111213141516, + 422.8191000918273, + 406.86358534843373, + 391.2345679012345, + 375.9320477502296, + 360.9560248954188, + 346.30649933680235, + 331.9834710743802, + 317.9869401081522, + 304.31690643811856, + 290.9733700642791, + 277.956330986634, + 265.2657892051831, + 252.90174471992654, + 240.86419753086415, + 229.1531476379961, + 217.76859504132233, + 206.71053974084276, + 195.97898173655747, + 185.5739210284665, + 175.49535761656972, + 165.7432915008673, + 156.31772268135904, + 147.2186511580451, + 138.4460769309254, + 129.99999999999997, + 121.88042036526885, + 114.08733802673194, + 106.62075298438936, + 99.48066523824097, + 92.66707478828691, + 86.17998163452707, + 80.01938577696151, + 74.18528721559026, + 68.67768595041322, + 63.49658198143047, + 58.64197530864196, + 54.113865932047766, + 49.9122538516478, + 46.0371390674421, + 42.48852157943065, + 39.26640138761349, + 36.37077849199061, + 33.801652892561975, + 31.559024589327613, + 29.642893582287517, + 28.053259871441686, + 26.79012345679012, + 25.85348433833282, + 25.24334251606978, + 24.95969799000102, + 25.002550760126514, + 25.37190082644627, + 26.06774818896031, + 27.090092847668593, + 28.438934802571154, + 30.114274053667987, + 32.11611060095908, + 34.44444444444444, + 37.09927558412405, + 40.08060401999795, + 43.388429752066116, + 47.02275278032854, + 50.9835731047852, + 55.27089072543617, + 59.8847056422814, + 64.8250178553209, + 70.09182736455462, + 75.68513416998263, + 81.60493827160494, + 87.8512396694215, + 94.42403836343227, + 101.32333435363743, + 108.54912764003673, + 116.1014182226303, + 123.98020610141823, + 132.18549127640034, + 140.71727374757685, + 149.57555351494747, + 158.76033057851234, + 168.27160493827165, + 178.10937659422507, + 188.27364554637273, + 198.76441179471485, + 209.58167533925103, + 220.7254361799817, + 232.1956943169064, + 243.99244975002546, + 256.1157024793389, + 268.5654525048464, + 281.3416998265484, + 294.44444444444446 + ], + [ + 568.2103866952352, + 549.4796449341904, + 531.0754004693398, + 512.9976533006836, + 495.2464034282217, + 477.8216508519539, + 460.7233955718804, + 443.9516375880013, + 427.50637690031635, + 411.3876135088256, + 395.59534741352917, + 380.1295786144271, + 364.9903071115192, + 350.1775329048056, + 335.69125599428634, + 321.5314763799613, + 307.6981940618305, + 294.1914090398939, + 281.0111213141516, + 268.15733088460365, + 255.63003775124986, + 243.42924191409043, + 231.55494337312518, + 220.00714212835427, + 208.78583817977758, + 197.8910315273952, + 187.32272217120703, + 177.0809101112132, + 167.16559534741356, + 157.57677787980822, + 148.3144577083971, + 139.3786348331803, + 130.76930925415778, + 122.48648097132946, + 114.53014998469546, + 106.90031629425569, + 99.59697990001021, + 92.62014080195898, + 85.96979900010206, + 79.64595449443934, + 73.64860728497092, + 67.9777573716968, + 62.6334047546169, + 57.61554943373126, + 52.92419140903989, + 48.55933068054283, + 44.52096724823999, + 40.80910111213142, + 37.42373227221712, + 34.36486072849709, + 31.63248648097134, + 29.226609529639838, + 27.147229874502607, + 25.394347515559637, + 23.967962452810944, + 22.86807468625651, + 22.094684215896343, + 21.64779104173044, + 21.5273951637588, + 21.733496581981434, + 22.26609529639833, + 23.125191307009494, + 24.31078461381491, + 25.82287521681461, + 27.66146311600857, + 29.826548311396802, + 32.3181308029793, + 35.13621059075603, + 38.280787674727065, + 41.751862054892364, + 45.54943373125192, + 49.67350270380571, + 54.12406897255381, + 58.90113253749618, + 64.00469339863281, + 69.43475155596364, + 75.19130700948881, + 81.27435975920825, + 87.68390980512194, + 94.41995714722984, + 101.48250178553212, + 108.87154372002855, + 116.58708295071926, + 124.62911947760435, + 132.99765330068357, + 141.6926844199572, + 150.71421283542495, + 160.06223854708696, + 169.7367615549434, + 179.73778185899394, + 190.06529945923876, + 200.71931435567802, + 211.69982654831134, + 223.00683603713912, + 234.640342822161, + 246.6003469033771, + 258.8868482807877, + 271.4998469543924, + 284.43934292419146, + 297.70533619018465 + ], + [ + 555.6361595755534, + 537.068666462606, + 518.8276706458524, + 500.91317212529333, + 483.3251709009285, + 466.06366697275774, + 449.12866034078155, + 432.52015100499955, + 416.2381389654117, + 400.28262422201817, + 384.65360677481885, + 369.3510866238139, + 354.3750637690032, + 339.7255382103866, + 325.40250994796446, + 311.4059789817365, + 297.7359453117029, + 284.39240893786354, + 271.3753698602183, + 258.68482807876745, + 246.32078359351084, + 234.28323640444853, + 222.5721865115804, + 211.18763391490666, + 200.1295786144271, + 189.39802061014183, + 178.99295990205079, + 168.91439649015408, + 159.16233037445159, + 149.7367615549434, + 140.63769003162943, + 131.86511580450974, + 123.41903887358434, + 115.29945923885315, + 107.5063769003163, + 100.03979185797367, + 92.89970411182532, + 86.08611366187124, + 79.59902050811142, + 73.43842465054584, + 67.60432608917455, + 62.09672482399757, + 56.91562085501481, + 52.061014182226295, + 47.532904805632064, + 43.33129272523213, + 39.45617794102643, + 35.907560453014995, + 32.685440261197826, + 29.789817365574926, + 27.220691766146317, + 24.978063462911948, + 23.061932455871844, + 21.47229874502601, + 20.209162330374454, + 19.27252321191715, + 18.662381389654115, + 18.378736863585345, + 18.42158963371084, + 18.790939700030606, + 19.486787062544636, + 20.509131721252935, + 21.85797367615548, + 23.533312927252314, + 25.53514947454341, + 27.86348331802877, + 30.518314457708406, + 33.499642893582276, + 36.80746862565044, + 40.441791653912865, + 44.40261197836956, + 48.68992959902049, + 53.303744515865716, + 58.24405672890521, + 63.51086623813898, + 69.10417304356696, + 75.02397714518926, + 81.27027854300582, + 87.84307723701663, + 94.74237322722168, + 101.96816651362109, + 109.52045709621467, + 117.39924497500247, + 125.60453014998471, + 134.13631262116107, + 142.99459238853186, + 152.1793694520967, + 161.69064381185586, + 171.52841546780948, + 181.69268441995715, + 192.18345066829903, + 203.00071421283545, + 214.14447505356588, + 225.61473319049085, + 237.4114886236098, + 249.53474135292308, + 261.98449137843085, + 274.76073870013266, + 287.8634833180289, + 301.2927252321192 + ], + [ + 543.388429752066, + 524.9841852872155, + 506.90643811855927, + 489.1551882460974, + 471.7304356698296, + 454.6321803897561, + 437.8604224058768, + 421.41516171819205, + 405.29639832670136, + 389.5041322314049, + 374.0383634323028, + 358.89909192939496, + 344.0863177226814, + 329.60004081216204, + 315.4402611978369, + 301.60697887970616, + 288.1001938577696, + 274.91990613202734, + 262.06611570247935, + 249.5388225691256, + 237.33802673196612, + 225.46372819100094, + 213.91592694622994, + 202.69462299765334, + 191.7998163452709, + 181.2315069890828, + 170.98969492908887, + 161.07438016528928, + 151.48556269768392, + 142.22324252627286, + 133.28741965105604, + 124.67809407203349, + 116.39526578920521, + 108.43893480257117, + 100.80910111213143, + 93.50576471788592, + 86.52892561983472, + 79.87858381797776, + 73.55473931231508, + 67.55739210284666, + 61.88654218957248, + 56.54218957249263, + 51.524334251607, + 46.83297622691563, + 42.46811549841853, + 38.429752066115725, + 34.71788593000716, + 31.332517090092857, + 28.273645546372823, + 25.54127129884705, + 23.13539434751557, + 21.056014692378337, + 19.30313233343537, + 17.876747270686668, + 16.776859504132236, + 16.00346903377207, + 15.556575859606166, + 15.43617998163453, + 15.64228139985716, + 16.174880114274057, + 17.03397612488522, + 18.21956943169065, + 19.73166003469033, + 21.570247933884296, + 23.735333129272522, + 26.226915620855017, + 29.044995408631785, + 32.189572492602785, + 35.660646872768076, + 39.45821854912765, + 43.582287521681465, + 48.03285379042953, + 52.80991735537189, + 57.913478216508516, + 63.34353637383941, + 69.10009182736452, + 75.18314457708397, + 81.59269462299766, + 88.32874196510562, + 95.39128660340779, + 102.78032853790435, + 110.49586776859505, + 118.53790429547999, + 126.90643811855935, + 135.60146923783284, + 144.62299765330076, + 153.97102336496275, + 163.64554637281904, + 173.64656667686975, + 183.97408427711454, + 194.62809917355364, + 205.60861136618718, + 216.91562085501477, + 228.54912764003677, + 240.5091317212529, + 252.79563309866333, + 265.40863177226817, + 278.3481277420671, + 291.6141210080606, + 305.206611570248 + ], + [ + 531.4671972247729, + 513.2262014080196, + 495.31170288746046, + 477.72370166309565, + 460.46219773492504, + 443.5271911029487, + 426.91868176716656, + 410.63666972757886, + 394.6811549841853, + 379.052137536986, + 363.749617385981, + 348.77359453117026, + 334.12406897255386, + 319.80104071013164, + 305.8045097439037, + 292.13447607387, + 278.79093970003066, + 265.7739006223855, + 253.08335884093458, + 240.71931435567797, + 228.68176716661563, + 216.97071727374757, + 205.58616467707373, + 194.52810937659422, + 183.79655137230893, + 173.39149066421794, + 163.31292725232117, + 153.56086113661874, + 144.1352923171105, + 135.03622079379656, + 126.26364656667687, + 117.81756963575147, + 109.69799000102029, + 101.9049076624834, + 94.43832262014081, + 87.29823487399244, + 80.48464442403836, + 73.99755127027854, + 67.836955412713, + 62.002856851341704, + 56.49525558616466, + 51.314151617181935, + 46.45954494439343, + 41.931435567799205, + 37.72982348739924, + 33.854708703193566, + 30.306091215182132, + 27.08397102336496, + 24.18834812774206, + 21.61922252831343, + 19.376594225079074, + 17.460463218038974, + 15.870829507193141, + 14.60769309254157, + 13.671053974084277, + 13.06091215182124, + 12.777267625752472, + 12.82012039587797, + 13.18947046219773, + 13.885317824711759, + 14.907662483420056, + 16.25650443832262, + 17.931843689419434, + 19.93368023671053, + 22.262014080195897, + 24.916845219875526, + 27.89817365574942, + 31.20599938781756, + 34.84032241607998, + 38.80114274053668, + 43.08846036118765, + 47.70227527803283, + 52.64258749107232, + 57.90939700030609, + 63.50270380573413, + 69.42250790735636, + 75.66880930517291, + 82.24160799918374, + 89.14090398938885, + 96.36669727578813, + 103.91898785838181, + 111.79777573716966, + 120.00306091215172, + 128.53484338332825, + 137.39312315069887, + 146.5779002142639, + 156.08917457402305, + 165.92694622997647, + 176.09121518212433, + 186.58198143046624, + 197.39924497500243, + 208.5430058157331, + 220.01326395265784, + 231.81001938577705, + 243.93327211509023, + 256.3830221405978, + 269.15926946229973, + 282.2620140801958, + 295.69125599428634, + 309.44699520457095 + ], + [ + 519.8724619936742, + 501.79471482501776, + 484.04346495255584, + 466.6187123762882, + 449.52045709621467, + 432.74869911233554, + 416.3034384246505, + 400.1846750331599, + 384.39240893786354, + 368.92664013876134, + 353.78736863585345, + 338.97459442913987, + 324.4883175186206, + 310.32853790429556, + 296.49525558616466, + 282.9884705642282, + 269.8081828384859, + 256.9543924089379, + 244.4270992755841, + 232.22630343842468, + 220.35200489745944, + 208.80420365268853, + 197.58289970411184, + 186.68809305172942, + 176.11978369554126, + 165.87797163554742, + 155.96265687174778, + 146.37383940414247, + 137.11151923273135, + 128.1756963575146, + 119.566370778492, + 111.28354249566374, + 103.3272115090297, + 95.69737781858994, + 88.39404142434448, + 81.41720232629324, + 74.7668605244363, + 68.44301601877359, + 62.44566880930518, + 56.77481889603102, + 51.43046627895112, + 46.41261095806553, + 41.72125293337416, + 37.35639220487706, + 33.31802877257422, + 29.60616263646569, + 26.220793796551384, + 23.16192225283135, + 20.429548005305584, + 18.02367105397408, + 15.944291398836864, + 14.191409039893896, + 12.765023977145194, + 11.665136210590758, + 10.891745740230595, + 10.444852566064693, + 10.324456688093056, + 10.530558106315684, + 11.063156820732576, + 11.922252831343739, + 13.10784613814917, + 14.619936741148868, + 16.458524640342816, + 18.623609835731042, + 21.115192327313537, + 23.9332721150903, + 27.077849199061333, + 30.548923579226603, + 34.34649525558616, + 38.470564228139985, + 42.92113049688808, + 47.6981940618304, + 52.80175492296703, + 58.231813080297925, + 63.98836853382309, + 70.07142128354246, + 76.48097132945615, + 83.21701867156412, + 90.27956330986635, + 97.66860524436278, + 105.3841444750536, + 113.42618100193856, + 121.79471482501779, + 130.48974594429143, + 139.51127435975917, + 148.85930007142136, + 158.53382307927762, + 168.53484338332814, + 178.86236098357313, + 189.51637588001222, + 200.49688807264553, + 211.80389756147335, + 223.43740434649519, + 235.3974084277115, + 247.6839098051219, + 260.2969084787265, + 273.23640444852566, + 286.5023977145188, + 300.09488827670646, + 314.01387613508814 + ], + [ + 508.60422405876955, + 490.6897255382104, + 473.10172431384547, + 455.84022038567497, + 438.9052137536986, + 422.29670441791654, + 406.0146923783287, + 390.0591776349353, + 374.43016018773596, + 359.12764003673095, + 344.1516171819202, + 329.50209162330367, + 315.1790633608815, + 301.1825323946536, + 287.51249872461995, + 274.1689623507806, + 261.1519232731354, + 248.46138149168453, + 236.0973370064279, + 224.05978981736558, + 212.34873992449747, + 200.9641873278237, + 189.90613202734414, + 179.17457402305888, + 168.76951331496784, + 158.69094990307113, + 148.93888378736864, + 139.51331496786045, + 130.41424344454646, + 121.64166921742681, + 113.19559228650137, + 105.07601265177026, + 97.28293031323334, + 89.81634527089071, + 82.67625752474237, + 75.86266707478828, + 69.37557392102848, + 63.214978063462915, + 57.38087950209163, + 51.8732782369146, + 46.692174267931826, + 41.83756759514337, + 37.30945821854913, + 33.10784613814917, + 29.232731353943468, + 25.684113865932062, + 22.461993674114893, + 19.56637077849199, + 16.997245179063356, + 14.754616875828987, + 12.838485868788904, + 11.248852157943066, + 9.985715743291498, + 9.049076624834196, + 8.438934802571167, + 8.155290276502397, + 8.198143046627894, + 8.567493112947659, + 9.263340475461682, + 10.285685134169979, + 11.634527089072542, + 13.309866340169373, + 15.31170288746045, + 17.640036730945816, + 20.294867870625446, + 23.27619630649934, + 26.584022038567504, + 30.218345066829897, + 34.179165391286595, + 38.46648301193756, + 43.080297928782784, + 48.020610141822246, + 53.287419651056, + 58.88072645648404, + 64.80053055810632, + 71.04683195592284, + 77.61963064993367, + 84.51892664013876, + 91.74471992653812, + 99.2970105091317, + 107.17579838791966, + 115.38108356290172, + 123.91286603407809, + 132.77114580144885, + 141.95592286501372, + 151.46719722477303, + 161.30496888072648, + 171.46923783287411, + 181.96000408121623, + 192.77726762575244, + 203.92102846648288, + 215.39128660340782, + 227.1880420365268, + 239.3112947658403, + 251.7610447913478, + 264.5372921130496, + 277.64003673094584, + 291.0692786450362, + 304.825017855321, + 318.9072543617998 + ], + [ + 497.6624834200591, + 479.91123354759713, + 462.4864809713293, + 445.38822569125597, + 428.6164677073768, + 412.17120701969174, + 396.05244362820116, + 380.2601775329049, + 364.79440873380264, + 349.6551372308948, + 334.8423630241811, + 320.35608611366183, + 306.19630649933686, + 292.36302418120596, + 278.8562391592694, + 265.67595143352713, + 252.8221610039792, + 240.2948678706254, + 228.09407203346592, + 216.21977349250076, + 204.6719722477298, + 193.45066829915314, + 182.55586164677072, + 171.9875522905826, + 161.7457402305887, + 151.8304254667891, + 142.24160799918374, + 132.97928782777265, + 124.04346495255585, + 115.43413937353333, + 107.15131109070502, + 99.19498010407102, + 91.56514641363125, + 84.26181001938575, + 77.28497092133455, + 70.63462911947758, + 64.3107846138149, + 58.31343740434647, + 52.642587491072334, + 47.298234873992435, + 42.280379553106805, + 37.58902152841548, + 33.22416079991838, + 29.185797367615542, + 25.473931231506974, + 22.088562391592703, + 19.029690847872665, + 16.2973166003469, + 13.891439649015398, + 11.812059993878163, + 10.059177634935208, + 8.632792572186506, + 7.5329048056320715, + 6.759514335271904, + 6.312621161106005, + 6.19222528313437, + 6.398326701357, + 6.930925415773899, + 7.790021426385055, + 8.975614733190485, + 10.487705336190182, + 12.326293235384144, + 14.491378430772356, + 16.982960922354852, + 19.801040710131616, + 22.945617794102645, + 26.416692174267943, + 30.214263850627475, + 34.338332823181304, + 38.788899091929395, + 43.56596265687176, + 48.66952351800835, + 54.09958167533924, + 59.856137128864404, + 65.93918987858383, + 72.34873992449747, + 79.08478726660542, + 86.14733190490766, + 93.53637383940415, + 101.25191307009486, + 109.29394959697993, + 117.66248342005917, + 126.35751453933266, + 135.37904295480058, + 144.72706866646257, + 154.40159167431904, + 164.40261197836955, + 174.73012957861437, + 185.38414447505363, + 196.36465666768697, + 207.67166615651453, + 219.3051729415366, + 231.2651770227527, + 243.5516784001633, + 256.164677073768, + 269.10417304356696, + 282.3701663095604, + 295.96265687174775, + 309.8816447301297, + 324.1271298847057 + ], + [ + 487.0472400775431, + 469.4592388531783, + 452.1977349250076, + 435.2627282930314, + 418.6542189572493, + 402.3722069176614, + 386.41669217426795, + 370.78767472706875, + 355.4851545760637, + 340.509131721253, + 325.85960616263645, + 311.5365779002143, + 297.54004693398645, + 283.87001326395267, + 270.52647689011326, + 257.50943781246815, + 244.81889603101732, + 232.4548515457607, + 220.4173043566983, + 208.70625446383028, + 197.3217018671564, + 186.26364656667693, + 175.5320885623916, + 165.12702785430062, + 155.04846444240385, + 145.2963983267014, + 135.87082950719318, + 126.77175798387924, + 117.99918375675955, + 109.55310682583413, + 101.43352719110297, + 93.64044485256609, + 86.17385981022348, + 79.03377206407511, + 72.22018161412103, + 65.7330884603612, + 59.57249260279566, + 53.73839404142435, + 48.23079277624734, + 43.04968880726458, + 38.19508213447608, + 33.66697275788189, + 29.465360677481915, + 25.59024589327621, + 22.041628405264774, + 18.819508213447634, + 15.923885317824732, + 13.354759718396096, + 11.112131415161727, + 9.196000408121625, + 7.606366697275803, + 6.3432302826242335, + 5.4065911641669295, + 4.7964493419038945, + 4.512804815835127, + 4.555657585960622, + 4.925007652280385, + 5.620855014794415, + 6.6431996735027035, + 7.992041628405262, + 9.667380879502094, + 11.669217426793187, + 13.99755127027853, + 16.65238240995816, + 19.633710845832056, + 22.941536577900216, + 26.575859606162645, + 30.536679930619307, + 34.82399755127027, + 39.437812468115496, + 44.378124681154986, + 49.6449341903887, + 55.23824099581673, + 61.158045097439015, + 67.4043464952556, + 73.97714518926635, + 80.87644117947144, + 88.10223446587082, + 95.65452504846444, + 103.53331292725227, + 111.7385981022345, + 120.27038057341085, + 129.12866034078147, + 138.3134374043465, + 147.82471176410564, + 157.66248342005923, + 167.8267523722069, + 178.31751862054884, + 189.1347821650852, + 200.27854300581566, + 211.7488011427404, + 223.5455565758596, + 235.66880930517286, + 248.11855933068063, + 260.8948066523824, + 273.99755127027845, + 287.426793184369, + 301.18253239465355, + 315.26476890113264, + 329.6735027038058 + ], + [ + 476.7584940312213, + 459.3337414549536, + 442.23548617488007, + 425.463728191001, + 409.01846750331606, + 392.8997041118253, + 377.10743801652893, + 361.64166921742685, + 346.5023977145189, + 331.6896235078053, + 317.203346597286, + 303.04356698296095, + 289.21028466483017, + 275.70349964289363, + 262.5232119171513, + 249.66942148760333, + 237.14212835424962, + 224.9413325170901, + 213.0670339761249, + 201.51923273135395, + 190.29792878277726, + 179.40312213039488, + 168.8348127742067, + 158.59300071421285, + 148.67768595041323, + 139.0888684828079, + 129.8265483113968, + 120.89072543618, + 112.28139985715744, + 103.99857157432918, + 96.04224058769515, + 88.41240689725542, + 81.1090705030099, + 74.13223140495867, + 67.48188960310175, + 61.15804509743904, + 55.160697887970635, + 49.48984797469646, + 44.14549535761659, + 39.12764003673095, + 34.436282012039584, + 30.07142128354252, + 26.033057851239686, + 22.321191715131114, + 18.935822875216815, + 15.876951331496805, + 13.144577083971035, + 10.738700132639533, + 8.659320477502298, + 6.906438118559329, + 5.4800530558106395, + 4.380165289256204, + 3.6067748188960334, + 3.159881644730132, + 3.0394857667584967, + 3.245587184981126, + 3.7781858993980233, + 4.637281910009186, + 5.822875216814605, + 7.334965819814302, + 9.173553719008265, + 11.338638914396492, + 13.83022140597897, + 16.64830119375573, + 19.792878277726757, + 23.263952657892055, + 27.061524334251615, + 31.18559330680541, + 35.636159575553506, + 40.41322314049587, + 45.51678400163249, + 50.946842158963335, + 56.7033976124885, + 62.78645036220794, + 69.19600040812163, + 75.93204775022953, + 82.99459238853176, + 90.38363432302825, + 98.099173553719, + 106.14121008060397, + 114.50974390368333, + 123.20477502295681, + 132.22630343842457, + 141.57432915008675, + 151.24885215794302, + 161.24987246199373, + 171.57739006223852, + 182.23140495867762, + 193.21191715131116, + 204.51892664013872, + 216.15243342516055, + 228.1124375063769, + 240.39893888378728, + 253.01193755739217, + 265.95143352719106, + 279.21742679318425, + 292.8099173553719, + 306.7289052137536, + 320.97439036832986, + 335.54637281910004 + ], + [ + 466.79624528109383, + 449.53474135292305, + 432.5997347209468, + 415.99122538516485, + 399.709213345577, + 383.7536986021835, + 368.12468115498416, + 352.8221610039792, + 337.8461381491685, + 323.1966125905519, + 308.8735843281297, + 294.8770533619018, + 281.2070196918682, + 267.8634833180288, + 254.8464442403836, + 242.1559024589328, + 229.7918579736762, + 217.75431078461384, + 206.04326089174572, + 194.65870829507193, + 183.60065299459237, + 172.8690949903071, + 162.4640342822161, + 152.38547087031935, + 142.63340475461686, + 133.20783593510868, + 124.10876441179471, + 115.33619018467505, + 106.89011325374962, + 98.77053361901848, + 90.97745128048157, + 83.51086623813899, + 76.37077849199062, + 69.55718804203653, + 63.070094888276714, + 56.909499030711146, + 51.075400469339876, + 45.56779920416284, + 40.38669523518009, + 35.53208856239159, + 31.003979185797355, + 26.80236710539743, + 22.927252321191723, + 19.378634833180286, + 16.15651464136312, + 13.260891745740244, + 10.691766146311608, + 8.449137843077239, + 6.533006836037137, + 4.943373125191303, + 3.680236710539744, + 2.743597592082442, + 2.133455769819406, + 1.8498112437506373, + 1.8926640138761348, + 2.262014080195897, + 2.9578614427099277, + 3.9802061014182257, + 5.329048056320778, + 7.0043873074176055, + 9.006223854708702, + 11.334557698194066, + 13.98938883787367, + 16.970717273747564, + 20.278543005815727, + 23.91286603407816, + 27.873686358534854, + 32.161003979185786, + 36.77481889603101, + 41.715131109070505, + 46.98194061830427, + 52.57524742373224, + 58.49505152535453, + 64.7413529231711, + 71.31415161718193, + 78.21344760738697, + 85.43924089378633, + 92.99153147637995, + 100.87031935516787, + 109.07560453014993, + 117.60738700132643, + 126.46566676869708, + 135.65044383226194, + 145.16171819202125, + 154.99948984797467, + 165.1637588001225, + 175.65452504846442, + 186.4717885930006, + 197.61554943373127, + 209.08580757065602, + 220.882563003775, + 233.0058157330885, + 245.455565758596, + 258.23181308029797, + 271.33455769819403, + 284.7637996122843, + 298.5195388225691, + 312.60177532904794, + 327.0105091317213, + 341.74574023058864 + ], + [ + 457.1604938271605, + 440.06223854708696, + 423.2904805632078, + 406.8452198755229, + 390.72645648403227, + 374.93419038873583, + 359.46842158963364, + 344.3291500867259, + 329.5163758800122, + 315.0300989694929, + 300.8703193551678, + 287.037037037037, + 273.5302520151005, + 260.3499642893582, + 247.4961738598102, + 234.96888072645646, + 222.76808488929703, + 210.8937863483318, + 199.34598510356082, + 188.12468115498416, + 177.22987450260172, + 166.66156514641364, + 156.41975308641975, + 146.50443832262013, + 136.9156208550148, + 127.65330068360372, + 118.71747780838687, + 110.10815222936435, + 101.82532394653606, + 93.86899295990204, + 86.23915926946229, + 78.93582287521683, + 71.95898377716559, + 65.30864197530863, + 58.984797469645954, + 52.98745026017752, + 47.31660034690338, + 41.97224772982348, + 36.95439240893786, + 32.263034384246495, + 27.898173655749396, + 23.859810223446594, + 20.14794408733803, + 16.762575247423726, + 13.703703703703694, + 10.971329456177948, + 8.565452504846446, + 6.4860728497092115, + 4.733190490766243, + 3.306805428017542, + 2.206917661463117, + 1.4335271911029475, + 0.9866340169370451, + 0.8662381389654104, + 1.0723395571880392, + 1.6049382716049356, + 2.464034282216099, + 3.649627589021531, + 5.161718192021214, + 7.000306091215178, + 9.165391286603407, + 11.656973778185906, + 14.475053565962645, + 17.61963064993367, + 21.090705030098967, + 24.88827670645853, + 29.012345679012356, + 33.46291194776042, + 38.239975512702784, + 43.34353637383941, + 48.7735945311703, + 54.53014998469541, + 60.61320273441485, + 67.02275278032855, + 73.7588001224365, + 80.82134476073868, + 88.21038669523516, + 95.92592592592594, + 103.96796245281095, + 112.33649627589017, + 121.03152739516382, + 130.05305581063158, + 139.40108152229357, + 149.07560453015, + 159.07662483420054, + 169.40414243444553, + 180.05815733088463, + 191.03866952351794, + 202.34567901234576, + 213.9791857973676, + 225.9391898785837, + 238.22569125599432, + 250.83868992959893, + 263.77818589939807, + 277.0441791653913, + 290.63666972757875, + 304.55565758596066, + 318.80114274053665, + 333.3731251913071, + 348.2716049382716 + ], + [ + 447.85123966942155, + 430.9162330374452, + 414.30772370166306, + 398.0257116620754, + 382.0701969186818, + 366.4411794714825, + 351.1386593204774, + 336.1626364656669, + 321.5131109070504, + 307.1900826446281, + 293.1935516784002, + 279.5235180083665, + 266.17998163452717, + 253.16294255688197, + 240.4724007754311, + 228.1083562901745, + 216.0708091011122, + 204.3597592082441, + 192.97520661157026, + 181.91715131109075, + 171.18559330680546, + 160.78053259871447, + 150.70196918681768, + 140.94990307111522, + 131.524334251607, + 122.42526272829308, + 113.65268850117337, + 105.20661157024797, + 97.0870319355168, + 89.29394959697994, + 81.8273645546373, + 74.68727680848896, + 67.87368635853485, + 61.38659320477504, + 55.225997347209486, + 49.39189878583819, + 43.88429752066118, + 38.70319355167841, + 33.84858687888993, + 29.320477502295695, + 25.118865421895727, + 21.243750637690056, + 17.69513314967862, + 14.473012957861453, + 11.57739006223855, + 9.008264462809937, + 6.765636159575568, + 4.849505152535464, + 3.2598714416896275, + 1.996735027038059, + 1.0600959085807644, + 0.44995408631772715, + 0.16630956024895704, + 0.20916233037445453, + 0.5785123966942143, + 1.2743597592082434, + 2.2967044179165397, + 3.645546372819103, + 5.320885623915917, + 7.322722171207012, + 9.651056014692374, + 12.305887154372003, + 15.287215590245873, + 18.595041322314035, + 22.22936435057646, + 26.190184675033155, + 30.47750229568412, + 35.091317212529304, + 40.0316294255688, + 45.29843893480257, + 50.89174574023059, + 56.81154984185284, + 63.05785123966938, + 69.63064993368022, + 76.52994592388531, + 83.75573921028462, + 91.30802979287824, + 99.18681767166613, + 107.39210284664829, + 115.92388531782464, + 124.7821650851954, + 133.9669421487603, + 143.47821650851944, + 153.31598816447303, + 163.4802571166207, + 173.9710233649628, + 184.788286909499, + 195.93204775022946, + 207.4023058871544, + 219.1990613202734, + 231.32231404958662, + 243.77206407509436, + 256.5483113967961, + 269.6510560146924, + 283.0802979287827, + 296.83603713906734, + 310.9182736455464, + 325.3270074482195, + 340.0622385470871, + 355.12396694214874 + ], + [ + 438.8684828078767, + 422.0967248239976, + 405.6514641363126, + 389.53270074482197, + 373.74043464952564, + 358.2746658504234, + 343.1353943475155, + 328.32262014080203, + 313.83634323028264, + 299.67656361595766, + 285.8432812978267, + 272.3364962758902, + 259.156208550148, + 246.30241812059995, + 233.7751249872462, + 221.57432915008675, + 209.70003060912157, + 198.1522293643506, + 186.93092541577388, + 176.0361187633915, + 165.46780940720333, + 155.2259973472095, + 145.31068258340989, + 135.72186511580455, + 126.45954494439343, + 117.52372206917664, + 108.91439649015408, + 100.63156820732581, + 92.67523722069178, + 85.04540353025206, + 77.74206713600654, + 70.76522803795534, + 64.11488623609837, + 57.79104173043567, + 51.793694520967264, + 46.1228446076931, + 40.77849199061322, + 35.76063666972758, + 31.069278645036235, + 26.704417916539132, + 22.666054484236298, + 18.954188348127765, + 15.568819508213458, + 12.509947964493424, + 9.777573716967655, + 7.371696765636175, + 5.292317110498938, + 3.5394347515559677, + 2.1130496888072656, + 1.0131619222528303, + 0.2397714518926679, + -0.20712172227323555, + -0.3275176002448721, + -0.12141618202224125, + 0.4111825323946512, + 1.2702785430058134, + 2.455871849811243, + 3.96796245281094, + 5.806550352004887, + 7.971635547393115, + 10.46321803897561, + 13.281297826752374, + 16.425874910723373, + 19.89694929088867, + 23.69452096724823, + 27.81858993980206, + 32.26915620855016, + 37.046219773492474, + 42.14978063462911, + 47.57983879196, + 53.33639424548516, + 59.419446995204545, + 65.82899704111823, + 72.56504438322618, + 79.62758902152842, + 87.01663095602484, + 94.73217018671562, + 102.77420671360063, + 111.14274053667994, + 119.83777165595342, + 128.85930007142133, + 138.20732578308335, + 147.8818487909396, + 157.88286909499033, + 168.2103866952351, + 178.86440159167438, + 189.84491378430772, + 201.1519232731353, + 212.78543005815735, + 224.7454341393735, + 237.03193551678388, + 249.64493419038877, + 262.5844301601877, + 275.8504234261811, + 289.4429139883685, + 303.3619018467502, + 317.60738700132646, + 332.1793694520967, + 347.07784919906146, + 362.30282624222025 + ], + [ + 430.2122232425263, + 413.6037139067442, + 397.3217018671564, + 381.3661871237629, + 365.7371696765636, + 350.4346495255586, + 335.45862667074783, + 320.8091011121315, + 306.4860728497092, + 292.48954188348125, + 278.81950821344753, + 265.47597183960823, + 252.45893276196307, + 239.7683909805122, + 227.40434649525557, + 215.36679930619326, + 203.6557494133252, + 192.27119681665135, + 181.21314151617182, + 170.48158351188656, + 160.0765228037955, + 149.9979593918988, + 140.24589327619628, + 130.82032445668813, + 121.72125293337415, + 112.94867870625448, + 104.50260177532905, + 96.38302214059792, + 88.58993980206101, + 81.12335475971842, + 73.98326701357004, + 67.16967656361598, + 60.68258340985614, + 54.52198755229058, + 48.687888990919305, + 43.18028772574226, + 37.99918375675952, + 33.14457708397102, + 28.616467707376806, + 24.414855626976838, + 20.53974084277114, + 16.991123354759736, + 13.769003162942564, + 10.873380267319662, + 8.304254667891028, + 6.061626364656679, + 4.145495357616575, + 2.5558616467707393, + 1.2927252321191705, + 0.35608611366186915, + -0.25405570860116145, + -0.5377002346699313, + -0.49484746454443407, + -0.12549739822466965, + 0.5703499642893544, + 1.5926946229976506, + 2.941536577900214, + 4.616875828997044, + 6.618712376288123, + 8.947046219773485, + 11.601877359453114, + 14.583205795327013, + 17.891031527395143, + 21.52535455565757, + 25.48617488011427, + 29.773492500765233, + 34.38730741761046, + 39.32761963064991, + 44.59442913988367, + 50.18773594531171, + 56.107540046934005, + 62.353841444750515, + 68.92664013876133, + 75.82593612896642, + 83.05172941536578, + 90.60401999795934, + 98.48280787674724, + 106.68809305172941, + 115.21987552290582, + 124.07815529027644, + 133.2629323538415, + 142.77420671360062, + 152.61197836955407, + 162.77624732170187, + 173.26701357004382, + 184.08427711458023, + 195.22803795531067, + 206.6982960922354, + 218.4950515253546, + 230.61830425466786, + 243.06805428017535, + 255.8443016018774, + 268.9470462197734, + 282.37628813386397, + 296.1320273441485, + 310.2142638506274, + 324.62299765330073, + 339.35822875216803, + 354.4199571472299, + 369.8081828384859 + ], + [ + 421.8824609733701, + 405.43720028568504, + 389.3184368941944, + 373.5261707988982, + 358.06040199979594, + 342.9211304968881, + 328.1083562901744, + 313.62207937965513, + 299.4622997653301, + 285.6290174471992, + 272.12223242526267, + 258.94194469952043, + 246.08815426997248, + 233.56086113661868, + 221.3600652994592, + 209.48576675849404, + 197.93796551372313, + 186.7166615651464, + 175.82185491276397, + 165.25354555657586, + 155.01173349658197, + 145.09641873278235, + 135.50760126517702, + 126.24528109376595, + 117.30945821854912, + 108.70013263952659, + 100.4173043566983, + 92.46097337006428, + 84.83113967962454, + 77.52780328537905, + 70.55096418732782, + 63.90062238547088, + 57.576777879808176, + 51.57943067033975, + 45.90858075706561, + 40.56422813998571, + 35.5463728191001, + 30.855014794408728, + 26.490154065911646, + 22.45179063360881, + 18.739924497500247, + 15.354555657585973, + 12.295684113865937, + 9.563309866340168, + 7.157432915008667, + 5.078053259871449, + 3.3251709009284802, + 1.8987858381797778, + 0.7988980716253427, + 0.025507601265174706, + -0.4213855729007235, + -0.5417814508723597, + -0.3356800326497289, + 0.1969186817671693, + 1.0560146923783256, + 2.2416079991837554, + 3.7536986021834524, + 5.592286501377417, + 7.757371696765627, + 10.248954188348122, + 13.067033976124884, + 16.21161106009592, + 19.68268544026118, + 23.48025711662074, + 27.60432608917457, + 32.05489235792267, + 36.831955922865035, + 41.935516784001614, + 47.36557494133251, + 53.12213039485767, + 59.205183144577106, + 65.61473319049074, + 72.3507805325987, + 79.41332517090093, + 86.80236710539742, + 94.51790633608812, + 102.55994286297314, + 110.92847668605243, + 119.62350780532601, + 128.64503622079377, + 137.99306193245593, + 147.6675849403122, + 157.66860524436274, + 167.99612284460773, + 178.65013774104682, + 189.63064993368033, + 200.93765942250792, + 212.57116620752976, + 224.5311702887461, + 236.81767166615649, + 249.43067033976112, + 262.3701663095602, + 275.63615957555345, + 289.2286501377411, + 303.1476379961228, + 317.3931231506988, + 331.96510560146925, + 346.86358534843373, + 362.0885623915928, + 377.6400367309457 + ], + [ + 413.8791960004081, + 397.59718396082025, + 381.6416692174267, + 366.01265177022754, + 350.7101316192226, + 335.7341087644118, + 321.0845832057953, + 306.7615549433732, + 292.7650239771452, + 279.09499030711146, + 265.75145393327205, + 252.73441485562694, + 240.04387307417613, + 227.6798285889195, + 215.64228139985713, + 203.93123150698906, + 192.54667891031528, + 181.4886236098357, + 170.75706560555042, + 160.35200489745944, + 150.27344148556267, + 140.5213753698602, + 131.095806550352, + 121.99673502703806, + 113.22416079991835, + 104.77808386899297, + 96.65850423426178, + 88.86542189572492, + 81.39883685338229, + 74.25874910723395, + 67.44515865727986, + 60.958065503520054, + 54.797469645954486, + 48.963371084583194, + 43.455769819406186, + 38.27466585042341, + 33.42005917763493, + 28.891949801040703, + 24.69033772064075, + 20.81522293643505, + 17.26660544842362, + 14.044485256606478, + 11.148862360983575, + 8.57973676155494, + 6.337108458320573, + 4.420977451280488, + 2.831343740434652, + 1.5682073257830837, + 0.631568207325782, + 0.02142638506274773, + -0.2622181410060183, + -0.21936537088052105, + 0.14998469543924342, + 0.8458320579532752, + 1.868176716661564, + 3.2170186715641274, + 4.892357922660957, + 6.894194469952055, + 9.222528313437397, + 11.877359453117027, + 14.858687888990925, + 18.16651362105909, + 21.800836649321482, + 25.76165697377818, + 30.048974594429147, + 34.66278951127437, + 39.60310172431387, + 44.86991123354758, + 50.46321803897562, + 56.383022140597916, + 62.62932353841447, + 69.20212223242524, + 76.10141822263034, + 83.32721150902971, + 90.87950209162334, + 98.75828997041117, + 106.9635751453933, + 115.49535761656975, + 124.35363738394045, + 133.53841444750532, + 143.04968880726463, + 152.88746046321805, + 163.0517294153657, + 173.54249566370785, + 184.35975920824404, + 195.50352004897468, + 206.97377818589942, + 218.7705336190184, + 230.89378634833187, + 243.34353637383938, + 256.1197836955412, + 269.22252831343746, + 282.6517702275278, + 296.40750943781256, + 310.48974594429137, + 324.8984797469645, + 339.6337108458321, + 354.69543924089373, + 370.0836649321499, + 385.79838791960003 + ], + [ + 406.20242832364045, + 390.08366493214976, + 374.2913988368533, + 358.8256300377513, + 343.68635853484335, + 328.8735843281297, + 314.3873074176104, + 300.2275278032855, + 286.39424548515467, + 272.8874604632181, + 259.70717273747573, + 246.85338230792777, + 234.32608917457404, + 222.12529333741455, + 210.25099479644936, + 198.70319355167842, + 187.4818896031018, + 176.58708295071935, + 166.01877359453115, + 155.77696153453732, + 145.86164677073768, + 136.27282930313237, + 127.01050913172125, + 118.07468625650446, + 109.4653606774819, + 101.18253239465365, + 93.2262014080196, + 85.59636771757985, + 78.29303132333436, + 71.31619222528315, + 64.66585042342619, + 58.342005917763515, + 52.34465870829508, + 46.67380879502092, + 41.32945617794104, + 36.3116008570554, + 31.620242832364056, + 27.255382103866953, + 23.217018671564134, + 19.50515253545557, + 16.119783695541265, + 13.060912151821258, + 10.328537904295487, + 7.922660952963985, + 5.84328129782675, + 4.090398938883796, + 2.6640138761350918, + 1.5641261095806551, + 0.7907356392204858, + 0.34384246505458366, + 0.2234465870829484, + 0.4295480053055778, + 0.9621467197224747, + 1.8212427303336383, + 3.006836037139058, + 4.518926640138753, + 6.357514539332716, + 8.522599734720945, + 11.014182226303419, + 13.832262014080182, + 16.976839098051208, + 20.447913478216506, + 24.24548515457603, + 28.369554127129863, + 32.82012039587796, + 37.59718396082032, + 42.700744821956945, + 48.13080297928779, + 53.88735843281295, + 59.97041118253239, + 66.37996122844608, + 73.11600857055397, + 80.17855320885621, + 87.56759514335269, + 95.28313437404346, + 103.32517090092843, + 111.69370472400772, + 120.38873584328128, + 129.41026425874912, + 138.7582899704111, + 148.43281297826755, + 158.4338332823181, + 168.76135088256288, + 179.41536577900212, + 190.39587797163549, + 201.70288746046327, + 213.33639424548514, + 225.29639832670125, + 237.58289970411187, + 250.1958983777165, + 263.1353943475154, + 276.4013876135088, + 289.9938781756963, + 303.9128660340782, + 318.1583511886542, + 332.73033363942443, + 347.6288133863892, + 362.8537904295479, + 378.40526476890125, + 394.28323640444853 + ], + [ + 398.85215794306697, + 382.8966431996736, + 367.26762575247415, + 351.96510560146925, + 336.98908274665854, + 322.33955718804197, + 308.0165289256198, + 294.01999795939196, + 280.34996428935824, + 267.0064279155189, + 253.98938883787363, + 241.29884705642283, + 228.93480257116624, + 216.89725538210388, + 205.18620548923576, + 193.801652892562, + 182.7435975920825, + 172.01203958779718, + 161.60697887970613, + 151.5284154678094, + 141.7763493521069, + 132.35078053259875, + 123.25170900928477, + 114.4791347821651, + 106.03305785123966, + 97.91347821650854, + 90.12039587797163, + 82.65381083562905, + 75.51372308948066, + 68.7001326395266, + 62.213039485766764, + 56.052443628201225, + 50.21834506682992, + 44.71074380165288, + 39.52963983267014, + 34.67503315988164, + 30.146923783287427, + 25.94531170288746, + 22.070196918681773, + 18.521579430670336, + 15.29945923885317, + 12.403836343230296, + 9.834710743801658, + 7.59208244056729, + 5.675951433527188, + 4.086317722681366, + 2.8231813080297954, + 1.8865421895724925, + 1.2764003673094568, + 0.9927558412406883, + 1.035608611366185, + 1.4049586776859482, + 2.1008060401999784, + 3.123150698908276, + 4.471992653810828, + 6.147331904907657, + 8.149168452198753, + 10.477502295684117, + 13.132333435363723, + 16.113661871237618, + 19.421487603305778, + 23.055810631568214, + 27.01663095602487, + 31.303948576675833, + 35.91776349352106, + 40.858075706560555, + 46.124885215794315, + 51.71819202122229, + 57.637996122844584, + 63.88429752066116, + 70.45709621467198, + 77.35639220487701, + 84.58218549127638, + 92.13447607387, + 100.01326395265791, + 108.21854912763997, + 116.75033159881642, + 125.60861136618712, + 134.79338842975204, + 144.3046627895112, + 154.1424344454648, + 164.30670339761247, + 174.79746964595438, + 185.6147331904908, + 196.75849403122123, + 208.22875216814617, + 220.02550760126516, + 232.14876033057843, + 244.59851035608617, + 257.37475767778795, + 270.477502295684, + 283.90674420977456, + 297.6624834200591, + 311.7447199265382, + 326.1534537292113, + 340.8886848280787, + 355.9504132231406, + 371.3386389143965, + 387.0533619018469, + 403.09458218549133 + ], + [ + 391.82838485868785, + 376.03611876339147, + 360.5703499642893, + 345.43107846138156, + 330.6183042546679, + 316.1320273441485, + 301.97224772982344, + 288.1389654116927, + 274.6321803897562, + 261.4518926640138, + 248.59810223446584, + 236.0708091011121, + 223.87001326395267, + 211.99571472298746, + 200.4479134782165, + 189.22660952963983, + 178.33180287725742, + 167.76349352106928, + 157.5216814610754, + 147.6063666972758, + 138.01754922967044, + 128.75522905825937, + 119.81940618304255, + 111.21008060402, + 102.9272523211917, + 94.9709213345577, + 87.34108764411795, + 80.03775124987247, + 73.06091215182124, + 66.4105703499643, + 60.086725844301604, + 54.089378634833196, + 48.41852872155903, + 43.07417610447913, + 38.05632078359352, + 33.364962758902145, + 29.000102030405067, + 24.961738598102233, + 21.249872461993682, + 17.864503622079376, + 14.805632078359343, + 12.0732578308336, + 9.667380879502096, + 7.588001224364861, + 5.835118865421893, + 4.408733802673202, + 3.3088460361187666, + 2.535455565758597, + 2.0885623915926947, + 1.96816651362106, + 2.1742679318436893, + 2.7068666462605857, + 3.5659626568717497, + 4.7515559636771805, + 6.263646566676864, + 8.102234465870827, + 10.267319661259057, + 12.758902152841554, + 15.576981940618293, + 18.721559024589325, + 22.192633404754616, + 25.990205081114176, + 30.11427405366797, + 34.56484032241607, + 39.34190388735843, + 44.445464748495056, + 49.87552290582595, + 55.63207835935106, + 61.715131109070505, + 68.12468115498419, + 74.86072849709215, + 81.92327313539431, + 89.31231506989081, + 97.02785430058157, + 105.06989082746661, + 113.43842465054583, + 122.13345576981938, + 131.15498418528722, + 140.50300989694932, + 150.1775329048056, + 160.17855320885627, + 170.5060708091011, + 181.16008570554018, + 192.1405978981737, + 203.44760738700128, + 215.08111417202332, + 227.04111825323946, + 239.32761963064985, + 251.94061830425474, + 264.88011427405365, + 278.14610754004684, + 291.7385981022345, + 305.65758596061625, + 319.9030711151924, + 334.47505356596264, + 349.3735333129271, + 364.59851035608614, + 380.1499846954392, + 396.02795633098674, + 412.23242526272827 + ], + [ + 385.13110907050304, + 369.5020916233036, + 354.19957147229877, + 339.2235486174881, + 324.5740230588715, + 310.25099479644933, + 296.2544638302213, + 282.58443016018776, + 269.24089378634835, + 256.2238547087032, + 243.5333129272523, + 231.1692684419957, + 219.1317212529334, + 207.42067136006528, + 196.03611876339144, + 184.97806346291193, + 174.2465054586267, + 163.84144475053563, + 153.7628813386389, + 144.01081522293643, + 134.58524640342821, + 125.48617488011429, + 116.71360065299457, + 108.26752372206919, + 100.14794408733802, + 92.35486174880114, + 84.88827670645851, + 77.74818896031017, + 70.9345985103561, + 64.44750535659628, + 58.28690949903071, + 52.452810937659436, + 46.94520967248239, + 41.76410570349964, + 36.90949903071115, + 32.381389654116916, + 28.179777573716972, + 24.30466278951127, + 20.756045301499853, + 17.533925109682684, + 14.638302214059783, + 12.069176614631171, + 9.826548311396802, + 7.9104173043567, + 6.320783593510866, + 5.057647178859307, + 4.121008060402005, + 3.510866238138969, + 3.2272217120702003, + 3.270074482195699, + 3.63942454851546, + 4.335271911029491, + 5.357616569737788, + 6.706458524640353, + 8.38179777573717, + 10.383634323028264, + 12.711968166513628, + 15.366799306193258, + 18.348127742067128, + 21.655953474135288, + 25.29027650239772, + 29.251096826854415, + 33.538414447505346, + 38.152229364350575, + 43.092541577390065, + 48.35935108662383, + 53.95265789205186, + 59.87246199367411, + 66.11876339149067, + 72.69156208550149, + 79.59085807570659, + 86.81665136210589, + 94.36894194469951, + 102.24772982348742, + 110.45301499846957, + 118.98479746964593, + 127.84307723701662, + 137.0278543005816, + 146.5391286603408, + 156.37690031629424, + 166.54116926844208, + 177.031935516784, + 187.8491990613202, + 198.99295990205084, + 210.4632180389756, + 222.25997347209477, + 234.38322620140804, + 246.83297622691555, + 259.60922354861754, + 272.71196816651354, + 286.1412100806039, + 299.89694929088876, + 313.97918579736756, + 328.38791960004085, + 343.12315069890826, + 358.18487909396987, + 373.573104785226, + 389.2878277726762, + 405.32904805632086, + 421.6967656361595 + ], + [ + 378.7603305785125, + 363.29456177941023, + 348.15529027650234, + 333.34251606978887, + 318.8562391592694, + 304.69645954494445, + 290.86317722681355, + 277.3563922048771, + 264.1761044791348, + 251.3223140495868, + 238.795020916233, + 226.59422507907357, + 214.7199265381084, + 203.17212529333742, + 191.95082134476073, + 181.05601469237834, + 170.4877053361902, + 160.24589327619634, + 150.3305785123967, + 140.7417610447914, + 131.47944087338027, + 122.54361799816348, + 113.9342924191409, + 105.65146413631265, + 97.69513314967861, + 90.06529945923887, + 82.76196306499338, + 75.78512396694218, + 69.13478216508521, + 62.81093765942253, + 56.8135904499541, + 51.14274053667995, + 45.798387919600046, + 40.78053259871441, + 36.08917457402306, + 31.724313845525963, + 27.685950413223143, + 23.974084277114578, + 20.588715437200293, + 17.529843893480255, + 14.797469645954486, + 12.391592694623005, + 10.31221303948577, + 8.5593306805428, + 7.132945617794096, + 6.033057851239669, + 5.259667380879499, + 4.812774206713595, + 4.692378328741959, + 4.89847974696459, + 5.431078461381482, + 6.2901744719926445, + 7.475767778798073, + 8.987858381797771, + 10.826446280991718, + 12.991531476379945, + 15.483113967962442, + 18.301193755739202, + 21.445770839710203, + 24.916845219875498, + 28.71441689623506, + 32.838485868788894, + 37.28905213753695, + 42.06611570247931, + 47.16967656361594, + 52.599734720946834, + 58.356290174471994, + 64.43934292419137, + 70.84889297010506, + 77.584940312213, + 84.64748495051526, + 92.03652688501168, + 99.75206611570243, + 107.79410264258746, + 116.16263646566676, + 124.85766758494024, + 133.87919600040806, + 143.22722171207016, + 152.90174471992654, + 162.90276502397705, + 173.23028262422204, + 183.8842975206611, + 194.86480971329445, + 206.17181920212224, + 217.8053259871441, + 229.7653300683604, + 242.0518314457708, + 254.66483011937544, + 267.60432608917455, + 280.87031935516774, + 294.4628099173551, + 308.3817977757371, + 322.6272829303131, + 337.1992653810836, + 352.0977451280481, + 367.3227221712068, + 382.8741965105601, + 398.7521681461074, + 414.9566370778492, + 431.48760330578506 + ], + [ + 372.71604938271605, + 357.41352923171104, + 342.4375063769003, + 327.78798081828387, + 313.46495255586166, + 299.4684215896337, + 285.7983879196, + 272.45485154576073, + 259.4378124681155, + 246.74727068666465, + 234.383226201408, + 222.3456790123457, + 210.63462911947764, + 199.2500765228038, + 188.19202122232423, + 177.460463218039, + 167.05540250994798, + 156.97683909805122, + 147.22477298234872, + 137.79920416284057, + 128.70013263952657, + 119.92755841240691, + 111.48148148148148, + 103.36190184675036, + 95.56881950821344, + 88.10223446587085, + 80.96214671972248, + 74.1485562697684, + 67.66146311600858, + 61.50086725844304, + 55.66676869707173, + 50.159167431894716, + 44.978063462911955, + 40.123456790123456, + 35.59534741352924, + 31.39373533312927, + 27.518620548923582, + 23.97000306091215, + 20.747882869094994, + 17.852259973472094, + 15.283134374043458, + 13.040506070809109, + 11.124375063769005, + 9.534741352923168, + 8.2716049382716, + 7.334965819814306, + 6.724823997551269, + 6.441179471482498, + 6.484032241607996, + 6.8533823079277605, + 7.549229670441784, + 8.571574329150081, + 9.920416284052644, + 11.595755535149474, + 13.597592082440553, + 15.925925925925915, + 18.580757065605546, + 21.56208550147944, + 24.869911233547576, + 28.504234261810005, + 32.4650545862667, + 36.752372206917656, + 41.36618712376285, + 46.30649933680235, + 51.573308846036106, + 57.16661565146413, + 63.08641975308643, + 69.33272115090294, + 75.90551984491377, + 82.80481583511884, + 90.03060912151821, + 97.58289970411178, + 105.46168758289969, + 113.66697275788182, + 122.19875522905825, + 131.05703499642888, + 140.24181205999383, + 149.75308641975306, + 159.5908580757066, + 169.75512702785426, + 180.24589327619634, + 191.06315682073253, + 202.206917661463, + 213.6771757983879, + 225.47393123150692, + 237.5971839608204, + 250.0469339863279, + 262.8231813080297, + 275.925925925926, + 289.3551678400163, + 303.11090705030085, + 317.1931435567799, + 331.601877359453, + 346.33710845832064, + 361.39883685338225, + 376.78706254463816, + 392.5017855320886, + 408.54300581573307, + 424.91072339557195, + 441.60493827160496 + ], + [ + 366.9982654831139, + 351.8589939802061, + 337.0462197734924, + 322.5599428629731, + 308.40016324864814, + 294.56688093051724, + 281.0600959085807, + 267.87980818283853, + 255.02601775329052, + 242.49872461993672, + 230.2979287827772, + 218.42363024181205, + 206.87582899704114, + 195.65452504846442, + 184.759718396082, + 174.19140903989387, + 163.94959697990006, + 154.03428221610042, + 144.44546474849506, + 135.183144577084, + 126.24732170186714, + 117.63799612284463, + 109.35516784001632, + 101.39883685338232, + 93.76900316294255, + 86.46566676869709, + 79.48882767064585, + 72.83848586878892, + 66.5146413631262, + 60.51729415365781, + 54.84644424038364, + 49.50209162330376, + 44.48423630241812, + 39.79287827772676, + 35.42801754922968, + 31.38965411692684, + 27.677787980818287, + 24.292419140903988, + 21.233547597183964, + 18.501173349658195, + 16.095296398326695, + 14.015916743189479, + 12.26303438424651, + 10.836649321497806, + 9.73676155494337, + 8.963371084583208, + 8.516477910417304, + 8.396082032445669, + 8.6021834506683, + 9.134782165085198, + 9.993878175696356, + 11.179471482501784, + 12.69156208550148, + 14.530149984695445, + 16.695235180083657, + 19.18681767166615, + 22.004897459442915, + 25.149474543413945, + 28.62054892357921, + 32.418120599938774, + 36.5421895724926, + 40.9927558412407, + 45.76981940618302, + 50.87338026731965, + 56.30343842465054, + 62.0599938781757, + 68.14304662789513, + 74.55259667380878, + 81.28864401591673, + 88.35118865421896, + 95.74023058871545, + 103.45576981940616, + 111.49780634629117, + 119.86634016937046, + 128.561371288644, + 137.58289970411178, + 146.93092541577388, + 156.60544842363024, + 166.60646872768083, + 176.93398632792565, + 187.58800122436492, + 198.56851341699826, + 209.87552290582582, + 221.5090296908479, + 233.46903377206402, + 245.7555351494746, + 258.36853382307925, + 271.3080297928782, + 284.57402305887166, + 298.16651362105904, + 312.0855014794408, + 326.330986634017, + 340.90296908478723, + 355.801448831752, + 371.02642587491073, + 386.57790021426376, + 402.4558718498113, + 418.6603407815529, + 435.191307009489, + 452.0487705336191 + ], + [ + 361.60697887970616, + 346.6309560248954, + 331.9814304662789, + 317.6584022038568, + 303.6618712376288, + 289.9918375675951, + 276.6483011937557, + 263.63126211611063, + 250.94072033465974, + 238.5766758494031, + 226.53912866034074, + 214.8280787674727, + 203.44352617079892, + 192.38547087031935, + 181.65391286603403, + 171.24885215794305, + 161.17028874604634, + 151.41822263034382, + 141.9926538108356, + 132.89358228752167, + 124.12100806040198, + 115.67493112947659, + 107.55535149474542, + 99.76226915620855, + 92.29568411386593, + 85.15559636771759, + 78.34200591776349, + 71.85491276400369, + 65.69431690643812, + 59.86021834506684, + 54.35261707988981, + 49.171513110907064, + 44.316906438118565, + 39.78879706152433, + 35.58718498112438, + 31.71207019691868, + 28.163452708907258, + 24.941332517090093, + 22.045709621467203, + 19.47658402203857, + 17.233955718804204, + 15.317824711764116, + 13.72819100091828, + 12.465054586266712, + 11.52841546780941, + 10.91827364554638, + 10.634629119477609, + 10.677481889603106, + 11.046831955922872, + 11.742679318436902, + 12.76502397714519, + 14.113865932047755, + 15.789205183144585, + 17.79104173043568, + 20.119375573921026, + 22.774206713600655, + 25.755535149474554, + 29.063360881542717, + 32.697683909805114, + 36.65850423426181, + 40.945821854912765, + 45.559636771758, + 50.49994898479745, + 55.766758494031215, + 61.36006529945925, + 67.27986940108154, + 73.52617079889811, + 80.09896949290886, + 86.99826548311395, + 94.22405876951333, + 101.77634935210695, + 109.6551372308948, + 117.86042240587695, + 126.39220487705339, + 135.25048464442406, + 144.43526170798896, + 153.94653606774816, + 163.7843077237017, + 173.94857667584944, + 184.43934292419138, + 195.25660646872774, + 206.4003673094582, + 217.87062544638297, + 229.66738087950216, + 241.7906336088154, + 254.2403836343231, + 267.0166309560249, + 280.11937557392093, + 293.54861748801153, + 307.30435669829603, + 321.38659320477495, + 335.79532700744824, + 350.53055810631565, + 365.59228650137754, + 380.9805121926334, + 396.69523518008356, + 412.73645546372825, + 429.1041730435669, + 445.7983879196002, + 462.8191000918274 + ], + [ + 356.54218957249265, + 341.729415365779, + 327.2431384552596, + 313.0833588409347, + 299.25007652280385, + 285.74329150086726, + 272.56300377512497, + 259.709213345577, + 247.18192021222328, + 234.98112437506376, + 223.10682583409852, + 211.55902458932763, + 200.33772064075097, + 189.44291398836853, + 178.87460463218036, + 168.63279257218653, + 158.71747780838692, + 149.12866034078158, + 139.86634016937046, + 130.93051729415367, + 122.3211917151311, + 114.03836343230284, + 106.0820324456688, + 98.45219875522908, + 91.14886236098359, + 84.17202326293237, + 77.52168146107539, + 71.19783695541273, + 65.2004897459443, + 59.529639832670156, + 54.18528721559025, + 49.167431894704634, + 44.476073870013266, + 40.11121314151617, + 36.072849709213344, + 32.360983573104775, + 28.97561473319049, + 25.916743189470456, + 23.184368941944697, + 20.778491990613194, + 18.69911233547596, + 16.946229976533004, + 15.5198449137843, + 14.419957147229866, + 13.646566676869694, + 13.199673502703796, + 13.079277624732159, + 13.285379042954787, + 13.817977757371684, + 14.677073767982847, + 15.862667074788266, + 17.37475767778796, + 19.213345576981926, + 21.37843077237015, + 23.87001326395263, + 26.688093051729393, + 29.83267013570042, + 33.303744515865716, + 37.10131619222524, + 41.22538516477907, + 45.67595143352716, + 50.45301499846953, + 55.55657585960611, + 60.986634016937, + 66.74318947046217, + 72.82624222018158, + 79.2357922660953, + 85.97183960820318, + 93.0343842465054, + 100.4234261810019, + 108.13896541169267, + 116.18100193857762, + 124.54953576165691, + 133.24456688093048, + 142.26609529639828, + 151.61412100806032, + 161.2886440159167, + 171.2896643199673, + 181.61718192021218, + 192.27119681665124, + 203.25170900928478, + 214.55871849811237, + 226.1922252831342, + 238.15222936435055, + 250.438730741761, + 263.05172941536586, + 275.99122538516474, + 289.2572186511579, + 302.84970921334553, + 316.7686970717273, + 331.01418222630326, + 345.58616467707367, + 360.48464442403827, + 375.7096214671973, + 391.2610958065503, + 407.13906744209754, + 423.3435363738394, + 439.87450260177525, + 456.73196612590556, + 473.9159269462299 + ], + [ + 351.8038975614734, + 337.1543720028568, + 322.8313437404346, + 308.8348127742068, + 295.164779104173, + 281.8212427303337, + 268.80420365268844, + 256.1136618712377, + 243.74961738598105, + 231.7120701969187, + 220.0010203040506, + 208.61646770737678, + 197.5584124068973, + 186.82685440261199, + 176.42179369452094, + 166.3432302826242, + 156.59116416692177, + 147.16559534741353, + 138.0665238240996, + 129.29394959697993, + 120.84787266605447, + 112.72829303132335, + 104.93521069278644, + 97.46862565044384, + 90.32853790429547, + 83.5149474543414, + 77.02785430058158, + 70.86725844301603, + 65.03315988164474, + 59.52555861646772, + 54.34445464748495, + 49.489847974696474, + 44.96173859810223, + 40.76012651770227, + 36.88501173349658, + 33.336394245485145, + 30.114274053667994, + 27.21865115804509, + 24.649525558616467, + 22.4068972553821, + 20.490766248342, + 18.901132537496174, + 17.637996122844605, + 16.7013570043873, + 16.091215182124266, + 15.807570656055498, + 15.850423426180994, + 16.219773492500757, + 16.915620855014787, + 17.937965513723086, + 19.28680746862564, + 20.96214671972247, + 22.963983267013564, + 25.29231711049892, + 27.94714825017853, + 30.928476686052427, + 34.23630241812059, + 37.870625446383016, + 41.83144577083968, + 46.11876339149064, + 50.73257830833587, + 55.672890521375365, + 60.93970003060908, + 66.5330068360371, + 72.4528109376594, + 78.69911233547597, + 85.27191102948679, + 92.17120701969182, + 99.3970003060912, + 106.94929088868481, + 114.8280787674727, + 123.03336394245478, + 131.56514641363125, + 140.42342618100193, + 149.60820324456688, + 159.11947760432602, + 168.95724926027953, + 179.1215182124273, + 189.6122844607693, + 200.4295480053055, + 211.57330884603613, + 223.04356698296084, + 234.84032241607989, + 246.96357514539335, + 259.41332517090086, + 272.18957249260285, + 285.2923171104989, + 298.7215590245892, + 312.477298234874, + 326.5595347413528, + 340.96826854402593, + 355.7034996428935, + 370.7652280379552, + 386.1534537292113, + 401.8681767166615, + 417.90939700030594, + 434.2771145801449, + 450.9713294561778, + 467.9920416284053, + 485.3392510968268 + ], + [ + 347.3921028466483, + 332.90582593612896, + 318.7460463218039, + 304.9127640036731, + 291.40597898173655, + 278.22569125599426, + 265.3719008264462, + 252.84460769309257, + 240.64381185593305, + 228.76951331496787, + 217.2217120701969, + 206.00040812162024, + 195.10560146923785, + 184.5372921130497, + 174.29548005305583, + 164.3801652892562, + 154.79134782165087, + 145.52902765023978, + 136.59320477502294, + 127.98387919600042, + 119.70105091317211, + 111.74471992653812, + 104.11488623609834, + 96.81154984185288, + 89.83471074380165, + 83.18436894194471, + 76.86052443628202, + 70.8631772268136, + 65.19232731353944, + 59.84797469645956, + 54.83011937557392, + 50.13876135088257, + 45.77390062238547, + 41.73553719008264, + 38.023671053974084, + 34.638302214059784, + 31.579430670339764, + 28.847056422813996, + 26.441179471482506, + 24.36179981634527, + 22.6089174574023, + 21.182532394653613, + 20.082644628099175, + 19.309254157739005, + 18.862360983573105, + 18.741965105601466, + 18.948066523824096, + 19.480665238240995, + 20.339761248852156, + 21.52535455565759, + 23.03744515865727, + 24.87603305785123, + 27.041118253239464, + 29.53270074482196, + 32.3507805325987, + 35.495357616569734, + 38.966431996735025, + 42.764003673094585, + 46.88807264564838, + 51.338638914396476, + 56.115702479338836, + 61.219263340475464, + 66.64932149780633, + 72.40587695133148, + 78.48892970105089, + 84.8984797469646, + 91.63452708907255, + 98.69707172737473, + 106.08611366187122, + 113.80165289256196, + 121.84368941944702, + 130.21222324252622, + 138.90725436179977, + 147.9287827772676, + 157.27680848892973, + 166.95133149678597, + 176.95235180083662, + 187.2798694010815, + 197.9338842975207, + 208.91439649015402, + 220.2214059789818, + 231.85491276400364, + 243.81491684521976, + 256.10141822263034, + 268.714416896235, + 281.65391286603415, + 294.9199061320274, + 308.5123966942148, + 322.43138455259674, + 336.6768697071727, + 351.24885215794296, + 366.1473319049077, + 381.3723089480664, + 396.92378328741967, + 412.801754922967, + 429.00622385470854, + 445.5371900826447, + 462.3946536067748, + 479.5786144270994, + 497.08907254361804 + ], + [ + 343.30680542801747, + 328.9837771655953, + 314.9872461993673, + 301.31721252933374, + 287.97367615549433, + 274.95663707784917, + 262.26609529639825, + 249.90205081114178, + 237.8645036220794, + 226.1534537292113, + 214.76890113253745, + 203.71084583205794, + 192.97928782777268, + 182.57422711968167, + 172.4956637077849, + 162.74359759208244, + 153.31802877257428, + 144.21895724926028, + 135.4463830221406, + 127.00030609121518, + 118.88072645648403, + 111.08764411794715, + 103.62105907560453, + 96.48097132945618, + 89.66738087950208, + 83.18028772574229, + 77.01969186817671, + 71.18559330680544, + 65.67799204162841, + 60.49688807264566, + 55.64228139985716, + 51.11417202326294, + 46.912559942862984, + 43.03744515865728, + 39.48882767064586, + 36.26670747882869, + 33.37108458320581, + 30.801958983777165, + 28.559330680542807, + 26.643199673502707, + 25.05356596265687, + 23.790429548005314, + 22.85379042954801, + 22.243648607284975, + 21.96000408121621, + 22.002856851341704, + 22.372206917661465, + 23.0680542801755, + 24.090398938883794, + 25.43924089378636, + 27.114580144883174, + 29.116416692174276, + 31.444750535659633, + 34.099581675339266, + 37.080910111213136, + 40.388735843281296, + 44.02305887154373, + 47.98387919600043, + 52.271196816651354, + 56.885011733496576, + 61.82532394653607, + 67.09213345576983, + 72.68544026119781, + 78.60524436282012, + 84.85154576063668, + 91.42434445464751, + 98.32364044485259, + 105.5494337312519, + 113.10172431384552, + 120.98051219263343, + 129.18579736761558, + 137.71757983879195, + 146.57585960616262, + 155.76063666972757, + 165.2719110294868, + 175.10968268544025, + 185.273951637588, + 195.76471788593003, + 206.5819814304663, + 217.72574227119674, + 229.19600040812173, + 240.9927558412407, + 253.11600857055396, + 265.56575859606164, + 278.34200591776346, + 291.44475053565975, + 304.87399244975006, + 318.6297316600346, + 332.7119681665137, + 347.1207019691868, + 361.8559330680542, + 376.9176614631161, + 392.305887154372, + 408.02061014182243, + 424.06183042546684, + 440.42954800530543, + 457.1237628813387, + 474.1444750535659, + 491.49168452198774, + 509.1653912866035 + ], + [ + 339.548005305581, + 325.388225691256, + 311.5549433731251, + 298.04815835118865, + 284.8678706254464, + 272.0140801958984, + 259.48678706254464, + 247.28599122538523, + 235.41169268442002, + 223.86389143964902, + 212.64258749107233, + 201.74778083868995, + 191.1794714825018, + 180.93765942250792, + 171.0223446587083, + 161.43352719110297, + 152.1712070196919, + 143.23538414447506, + 134.6260585654525, + 126.34323028262423, + 118.38689929599019, + 110.75706560555045, + 103.45372921130496, + 96.47689011325376, + 89.82654831139678, + 83.50270380573411, + 77.50535659626567, + 71.83450668299153, + 66.49015406591164, + 61.47229874502602, + 56.780940720334655, + 52.41607999183756, + 48.37771655953473, + 44.665850423426164, + 41.28048158351188, + 38.22161003979184, + 35.489235792266086, + 33.08335884093458, + 31.003979185797355, + 29.251096826854386, + 27.824711764105686, + 26.724823997551255, + 25.95143352719109, + 25.504540353025185, + 25.38414447505355, + 25.590245893276176, + 26.122844607693068, + 26.981940618304233, + 28.16753392510966, + 29.679624528109358, + 31.518212427303304, + 33.68329762269153, + 36.17488011427403, + 38.99295990205079, + 42.13753698602179, + 45.60861136618709, + 49.40618304254665, + 53.53025201510047, + 57.980818283848535, + 62.757881848790895, + 67.86144270992753, + 73.2915008672584, + 79.04805632078353, + 85.13110907050294, + 91.54065911641666, + 98.27670645852461, + 105.33925109682684, + 112.72829303132328, + 120.44383226201403, + 128.48586878889907, + 136.85440261197834, + 145.54943373125184, + 154.57096214671964, + 163.91898785838177, + 173.59351086623812, + 183.59453117028863, + 193.92204877053354, + 204.5760636669727, + 215.5565758596061, + 226.86358534843373, + 238.49709213345577, + 250.45709621467188, + 262.7435975920823, + 275.3565962656872, + 288.2960922354861, + 301.5620855014795, + 315.1545760636669, + 329.0735639220486, + 343.3190490766248, + 357.89103152739506, + 372.7895112743596, + 388.0144883175186, + 403.56596265687165, + 419.4439342924192, + 435.64840322416075, + 452.1793694520966, + 469.0368329762269, + 486.2207937965513, + 503.73125191307014, + 521.5682073257831 + ], + [ + 336.1157024793389, + 322.11917151311087, + 308.44913784307715, + 295.1056014692379, + 282.08856239159275, + 269.3980206101418, + 257.03397612488516, + 244.9964289358229, + 233.28537904295482, + 221.900826446281, + 210.8427711458014, + 200.11121314151617, + 189.7061524334252, + 179.6275890215284, + 169.8755229058259, + 160.44995408631775, + 151.3508825630038, + 142.57830833588412, + 134.13223140495867, + 126.01265177022754, + 118.21956943169063, + 110.75298438934803, + 103.61289664319966, + 96.7993061932456, + 90.31221303948577, + 84.15161718192022, + 78.31751862054892, + 72.80991735537191, + 67.62881338638914, + 62.77420671360066, + 58.246097337006425, + 54.04448525660647, + 50.16937047240077, + 46.62075298438933, + 43.39863279257219, + 40.50300989694928, + 37.933884297520656, + 35.69125599428629, + 33.775124987246194, + 32.185491276400356, + 30.922354861748786, + 29.985715743291493, + 29.375573921028458, + 29.091929394959685, + 29.13478216508518, + 29.504132231404945, + 30.199979593918975, + 31.222324252627267, + 32.57116620752983, + 34.24650545862666, + 36.24834200591774, + 38.5766758494031, + 41.23150698908273, + 44.21283542495663, + 47.52066115702476, + 51.15498418528719, + 55.11580450974389, + 59.40312213039485, + 64.01693704724003, + 68.95724926027953, + 74.22405876951329, + 79.81736557494133, + 85.73716967656355, + 91.98347107438013, + 98.55626976839095, + 105.45556575859605, + 112.68135904499542, + 120.23364962758896, + 128.11243750637686, + 136.31772268135902, + 144.84950515253544, + 153.70778491990606, + 162.892561983471, + 172.40383634323027, + 182.24160799918374, + 192.40587695133144, + 202.89664319967343, + 213.71390674420974, + 224.8576675849403, + 236.32792572186503, + 248.12468115498422, + 260.2479338842974, + 272.69768390980505, + 285.473931231507, + 298.57667584940305, + 312.0059177634936, + 325.76165697377814, + 339.84389348025695, + 354.25262728293035, + 368.9878583817977, + 384.0495867768593, + 399.43781246811545, + 415.15253545556567, + 431.19375573921036, + 447.561473319049, + 464.255688195082, + 481.27640036730946, + 498.6236098357309, + 516.297316600347, + 534.297520661157 + ], + [ + 333.0098969492909, + 319.17661463116, + 305.66982960922354, + 292.4895418834813, + 279.63575145393327, + 267.10845832057953, + 254.90766248342, + 243.03336394245488, + 231.48556269768395, + 220.26425874910723, + 209.3694520967248, + 198.80114274053668, + 188.55933068054284, + 178.64401591674317, + 169.05519844913783, + 159.79287827772677, + 150.85705540250996, + 142.24772982348742, + 133.9649015406591, + 126.00857055402511, + 118.37873686358535, + 111.07540046933987, + 104.09856137128864, + 97.4482195694317, + 91.124375063769, + 85.1270278543006, + 79.45617794102643, + 74.11182532394655, + 69.09397000306092, + 64.40261197836956, + 60.037751249872464, + 55.99938781756964, + 52.28752168146107, + 48.90215284154677, + 45.84328129782675, + 43.11090705030099, + 40.70503009896949, + 38.62565044383226, + 36.872768084889294, + 35.446383022140594, + 34.346495255586156, + 33.57310478522599, + 33.12621161106009, + 33.005815733088454, + 33.211917151311084, + 33.744515865727976, + 34.60361187633914, + 35.789205183144574, + 37.301295786144266, + 39.13988368533823, + 41.30496888072644, + 43.79655137230894, + 46.61463116008569, + 49.75920824405673, + 53.230282624222, + 57.02785430058156, + 61.15192327313539, + 65.60248954188349, + 70.37955310682581, + 75.48311396796242, + 80.91317212529333, + 86.6697275788185, + 92.75278032853787, + 99.16233037445156, + 105.89837771655952, + 112.96092235486174, + 120.34996428935825, + 128.06550352004894, + 136.10754004693396, + 144.47607387001327, + 153.17110498928682, + 162.1926334047546, + 171.54065911641666, + 181.215182124273, + 191.21620242832364, + 201.54372002856846, + 212.19773492500758, + 223.17824711764104, + 234.48525660646874, + 246.11876339149057, + 258.0787674727069, + 270.3652688501173, + 282.9782675237219, + 295.917763493521, + 309.18375675951427, + 322.77624732170193, + 336.6952351800836, + 350.9407203346596, + 365.51270278543006, + 380.4111825323946, + 395.63615957555334, + 411.1876339149066, + 427.0656055504539, + 443.2700744821957, + 459.80104071013153, + 476.65850423426167, + 493.8424650545863, + 511.3529231711049, + 529.189878583818, + 547.3533312927252 + ], + [ + 330.2305887154372, + 316.5605550454035, + 303.2170186715641, + 290.199979593919, + 277.5094378124681, + 265.1453933272115, + 253.1078461381491, + 241.3967962452811, + 230.0122436486073, + 218.95418834812773, + 208.22263034384244, + 197.81756963575143, + 187.73900622385472, + 177.9869401081522, + 168.561371288644, + 159.46229976533007, + 150.6897255382104, + 142.24364860728497, + 134.1240689725538, + 126.33098663401695, + 118.86440159167432, + 111.72431384552598, + 104.91072339557188, + 98.42363024181206, + 92.26303438424651, + 86.42893582287525, + 80.9213345576982, + 75.74023058871543, + 70.88562391592694, + 66.35751453933274, + 62.155902458932765, + 58.28078767472708, + 54.73217018671564, + 51.51004999489848, + 48.61442709927559, + 46.04530149984695, + 43.802673196612595, + 41.886542189572495, + 40.296908478726664, + 39.033772064075094, + 38.097132945617794, + 37.48699112335476, + 37.203346597286, + 37.24619936741149, + 37.61554943373126, + 38.311396796245276, + 39.333741454953575, + 40.68258340985614, + 42.35792266095297, + 44.35975920824407, + 46.68809305172941, + 49.34292419140904, + 52.32425262728294, + 55.632078359351105, + 59.266401387613506, + 63.22722171207019, + 67.51453933272116, + 72.1283542495664, + 77.06866646260583, + 82.3354759718396, + 87.92878277726763, + 93.84858687888993, + 100.09488827670644, + 106.66768697071727, + 113.56698296092235, + 120.79277624732173, + 128.34506682991534, + 136.22385470870316, + 144.42913988368537, + 152.96092235486176, + 161.81920212223247, + 171.00397918579733, + 180.51525354555656, + 190.35302520151004, + 200.51729415365784, + 211.00806040199976, + 221.82532394653603, + 232.96908478726658, + 244.43934292419146, + 256.2360983573104, + 268.35935108662386, + 280.8091011121314, + 293.5853484338332, + 306.6880930517295, + 320.11733496581974, + 333.8730741761046, + 347.95531068258344, + 362.3640444852565, + 377.09927558412414, + 392.16100397918575, + 407.54922967044166, + 423.2639526578921, + 439.3051729415365, + 455.67289052137545, + 472.3671053974084, + 489.38781756963556, + 506.7350270380574, + 524.408733802673, + 542.4089378634834, + 560.7356392204877 + ], + [ + 327.7777777777777, + 314.2709927558413, + 301.09070503009895, + 288.23691460055096, + 275.7096214671972, + 263.50882563003773, + 251.63452708907252, + 240.08672584430164, + 228.86542189572495, + 217.97061524334248, + 207.4023058871543, + 197.1604938271605, + 187.2451790633609, + 177.65636159575553, + 168.39404142434444, + 159.45821854912762, + 150.84889297010514, + 142.56606468727682, + 134.60973370064278, + 126.97990001020304, + 119.67656361595755, + 112.69972451790633, + 106.0493827160494, + 99.7255382103867, + 93.72819100091826, + 88.05734108764413, + 82.71298847056423, + 77.69513314967863, + 73.00377512498726, + 68.63891439649018, + 64.60055096418733, + 60.88868482807878, + 57.50331598816449, + 54.44444444444444, + 51.712070196918695, + 49.306193245587195, + 47.226813590449964, + 45.473931231506995, + 44.0475461687583, + 42.94765840220387, + 42.1742679318437, + 41.7273747576778, + 41.60697887970616, + 41.81308029792879, + 42.34567901234569, + 43.20477502295685, + 44.39036832976228, + 45.902458932761974, + 47.74104683195594, + 49.90613202734418, + 52.39771451892665, + 55.21579430670341, + 58.360371390674445, + 61.831445770839736, + 65.62901744719927, + 69.7530864197531, + 74.2036526885012, + 78.98071625344356, + 84.08427711458015, + 89.51433527191104, + 95.27089072543619, + 101.35394347515562, + 107.76349352106928, + 114.49954086317723, + 121.56208550147947, + 128.95112743597593, + 136.6666666666667, + 144.70870319355166, + 153.07723701663096, + 161.7722681359045, + 170.7937965513724, + 180.14182226303438, + 189.81634527089074, + 199.81736557494133, + 210.14488317518624, + 220.7988980716253, + 231.77941026425876, + 243.08641975308646, + 254.71992653810838, + 266.6799306193245, + 278.96643199673514, + 291.57943067033983, + 304.5189266401387, + 317.78491990613213, + 331.37741046831957, + 345.29639832670154, + 359.54188348127747, + 374.1138659320477, + 389.01234567901247, + 404.23732272217126, + 419.7887970615243, + 435.6667686970718, + 451.87123762881333, + 468.40220385674945, + 485.25966738087953, + 502.44362820120386, + 519.9540863177228, + 537.7910417304356, + 555.9544944393431, + 574.4444444444445 + ], + [ + 325.6514641363126, + 312.30792776247324, + 299.290888684828, + 286.6003469033773, + 274.2363024181206, + 262.19875522905824, + 250.48770533619015, + 239.1031527395164, + 228.04509743903685, + 217.31353943475156, + 206.90847872666052, + 196.8299153147638, + 187.07784919906135, + 177.65228037955308, + 168.55320885623914, + 159.78063462911948, + 151.3345576981941, + 143.2149780634629, + 135.421895724926, + 127.95531068258342, + 120.81522293643505, + 114.00163248648097, + 107.51453933272114, + 101.3539434751556, + 95.51984491378431, + 90.01224364860728, + 84.83113967962451, + 79.97653300683605, + 75.4484236302418, + 71.24681154984185, + 67.37169676563614, + 63.82307927762473, + 60.60095908580756, + 57.70533619018465, + 55.13621059075603, + 52.89358228752167, + 50.977451280481574, + 49.38781756963574, + 48.124681154984174, + 47.188042036526866, + 46.577900214263835, + 46.294255688195065, + 46.33710845832056, + 46.706458524640325, + 47.402305887154355, + 48.42465054586264, + 49.7734925007652, + 51.44883175186203, + 53.45066829915312, + 55.77900214263849, + 58.4338332823181, + 61.41516171819199, + 64.72298745026015, + 68.35731047852259, + 72.31813080297925, + 76.60544842363021, + 81.21926334047544, + 86.15957555351493, + 91.42638506274864, + 97.01969186817668, + 102.93949596979897, + 109.18579736761552, + 115.7585960616263, + 122.65789205183138, + 129.88368533823075, + 137.43597592082438, + 145.31476379961225, + 153.52004897459435, + 162.0518314457708, + 170.9101112131415, + 180.09488827670646, + 189.6061626364656, + 199.44393429241907, + 209.60820324456685, + 220.09896949290885, + 230.91623303744507, + 242.05999387817562, + 253.53025201510044, + 265.32700744821955, + 277.45026017753275, + 289.90001020304055, + 302.67625752474237, + 315.7790021426384, + 329.2082440567289, + 342.9639832670135, + 357.04621977349257, + 371.4549535761657, + 386.190184675033, + 401.25191307009493, + 416.6401387613508, + 432.354861748801, + 448.3960820324457, + 464.76379961228434, + 481.4580144883176, + 498.4787266605448, + 515.8259361289663, + 533.4996428935823, + 551.4998469543923, + 569.8265483113969, + 588.4797469645954 + ], + [ + 323.8516477910417, + 310.67136006529944, + 297.81756963575134, + 285.2902765023978, + 273.0894806652382, + 261.21518212427304, + 249.66738087950208, + 238.44607693092544, + 227.551270278543, + 216.98296092235483, + 206.74114886236094, + 196.82583409856136, + 187.23701663095605, + 177.97469645954493, + 169.0388735843281, + 160.42954800530555, + 152.14671972247731, + 144.1903887358433, + 136.5605550454035, + 129.25721865115804, + 122.28037955310681, + 115.63003775124989, + 109.30619324558718, + 103.30884603611877, + 97.6379961228446, + 92.29364350576472, + 87.27578818487908, + 82.58443016018774, + 78.21956943169063, + 74.18120599938783, + 70.46933986327926, + 67.08397102336497, + 64.02509947964494, + 61.29272523211915, + 58.886848280787675, + 56.807468625650436, + 55.05458626670747, + 53.62820120395877, + 52.52831343740434, + 51.754922967044166, + 51.308029792878266, + 51.187633914906634, + 51.393735333129264, + 51.92633404754616, + 52.78543005815733, + 53.97102336496275, + 55.48311396796244, + 57.3217018671564, + 59.48678706254463, + 61.97836955412713, + 64.79644934190387, + 67.9410264258749, + 71.4121008060402, + 75.20967248239975, + 79.33374145495354, + 83.78430772370164, + 88.56137128864401, + 93.66493214978063, + 99.09499030711146, + 104.85154576063665, + 110.93459851035607, + 117.34414855626977, + 124.08019589837767, + 131.1427405366799, + 138.53178247117637, + 146.24732170186718, + 154.28935822875218, + 162.6578920518314, + 171.35292317110495, + 180.37445158657277, + 189.72247729823488, + 199.39700030609114, + 209.3980206101418, + 219.72553821038667, + 230.3795531068258, + 241.36006529945917, + 252.66707478828684, + 264.3005815733088, + 276.260585654525, + 288.5470870319354, + 301.16008570554027, + 314.0995816753392, + 327.36557494133245, + 340.95806550352006, + 354.8770533619018, + 369.122538516478, + 383.6945209672482, + 398.5930007142127, + 413.8179777573717, + 429.36945209672473, + 445.247423732272, + 461.4518926640139, + 477.9828588919497, + 494.8403224160801, + 512.0242832364045, + 529.534741352923, + 547.3716967656362, + 565.5351494745433, + 584.025099479645, + 602.8415467809407 + ], + [ + 322.37832874196516, + 309.36128966431994, + 296.670747882869, + 284.30670339761247, + 272.26915620855016, + 260.5581063156821, + 249.17355371900823, + 238.11549841852877, + 227.38394041424345, + 216.9788797061524, + 206.90031629425567, + 197.1482501785532, + 187.72268135904503, + 178.62360983573106, + 169.85103560861134, + 161.40495867768595, + 153.28537904295482, + 145.49229670441792, + 138.02571166207528, + 130.88562391592694, + 124.07203346597285, + 117.58494031221305, + 111.42434445464747, + 105.5902458932762, + 100.08264462809917, + 94.90154065911642, + 90.04693398632793, + 85.51882460973371, + 81.31721252933374, + 77.44209774512805, + 73.89348025711662, + 70.67136006529947, + 67.77573716967656, + 65.20661157024793, + 62.963983267013575, + 61.047852259973475, + 59.45821854912765, + 58.19508213447608, + 57.258443016018774, + 56.64830119375574, + 56.36465666768697, + 56.40750943781247, + 56.77685950413223, + 57.47270686664626, + 58.49505152535456, + 59.843893480257115, + 61.519232731353945, + 63.521069278645044, + 65.8494031221304, + 68.50423426181004, + 71.4855626976839, + 74.79338842975207, + 78.42771145801449, + 82.38853178247119, + 86.6758494031221, + 91.28966431996733, + 96.22997653300683, + 101.4967860422406, + 107.09009284766857, + 113.00989694929088, + 119.25619834710741, + 125.82899704111827, + 132.72829303132332, + 139.95408631772267, + 147.5063769003163, + 155.38516477910417, + 163.59044995408632, + 172.12223242526272, + 180.9805121926334, + 190.16528925619835, + 199.67656361595758, + 209.51433527191097, + 219.67860422405877, + 230.16937047240077, + 240.98663401693707, + 252.1303948576675, + 263.6006529945924, + 275.39740842771147, + 287.52066115702485, + 299.9704111825323, + 312.7466585042343, + 325.8494031221303, + 339.2786450362206, + 353.03438424650545, + 367.1166207529843, + 381.52535455565766, + 396.2605856545251, + 411.3223140495867, + 426.7105397408428, + 442.425262728293, + 458.4664830119373, + 474.8342005917763, + 491.5284154678092, + 508.5491276400367, + 525.8963371084583, + 543.570043873074, + 561.5702479338843, + 579.8969492908885, + 598.5501479440875, + 617.5298438934802 + ], + [ + 321.23150698908273, + 308.37771655953475, + 295.85042342618095, + 283.6496275890216, + 271.77532904805634, + 260.22752780328534, + 249.00622385470865, + 238.11141720232632, + 227.54310784613816, + 217.30129578614424, + 207.38598102234462, + 197.7971635547393, + 188.53484338332825, + 179.5990205081114, + 170.98969492908887, + 162.7068666462606, + 154.7505356596266, + 147.12070196918683, + 139.8173655749413, + 132.84052647689012, + 126.19018467503315, + 119.86634016937049, + 113.86899295990204, + 108.1981430466279, + 102.853790429548, + 97.8359351086624, + 93.14457708397103, + 88.77971635547394, + 84.74135292317112, + 81.02948678706255, + 77.64411794714826, + 74.58524640342824, + 71.85287215590247, + 69.44699520457097, + 67.36761554943375, + 65.61473319049078, + 64.18834812774207, + 63.08846036118765, + 62.31506989082748, + 61.86817671666158, + 61.74778083868994, + 61.953882256912564, + 62.48648097132946, + 63.34557698194064, + 64.53117028874607, + 66.04326089174575, + 67.88184879093971, + 70.04693398632794, + 72.53851647791043, + 75.35659626568719, + 78.5011733496582, + 81.9722477298235, + 85.76981940618307, + 89.8938883787369, + 94.34445464748495, + 99.1215182124273, + 104.22507907356393, + 109.65513723089484, + 115.41169268441995, + 121.49474543413938, + 127.90429548005308, + 134.64034282216105, + 141.7028874604632, + 149.09192939495966, + 156.80746862565047, + 164.8495051525355, + 173.2180389756148, + 181.91307009488827, + 190.93459851035607, + 200.2826242220182, + 209.95714722987455, + 219.9581675339251, + 230.28568513416997, + 240.93970003060912, + 251.9202122232426, + 263.22722171207016, + 274.86072849709217, + 286.82073257830837, + 299.10723395571887, + 311.7202326293235, + 324.6597285991226, + 337.9257218651158, + 351.51821242730324, + 365.4372002856852, + 379.68268544026114, + 394.25466789103166, + 409.15314763799614, + 424.37812468115493, + 439.9295990205082, + 455.8075706560555, + 472.012039587797, + 488.5430058157331, + 505.4004693398632, + 522.5844301601879, + 540.0948882767066, + 557.9318436894195, + 576.0952963983268, + 594.5852464034282, + 613.4016937047242, + 632.5446383022141 + ], + [ + 320.4111825323947, + 307.72064075094374, + 295.35659626568713, + 283.3190490766249, + 271.60799918375676, + 260.22344658708295, + 249.16539128660338, + 238.43383328231818, + 228.02877257422713, + 217.95020916233037, + 208.19814304662788, + 198.77257422711966, + 189.67350270380575, + 180.90092847668606, + 172.4548515457606, + 164.33527191102948, + 156.5421895724926, + 149.07560453015, + 141.9355167840016, + 135.12192633404754, + 128.6348331802877, + 122.47423732272217, + 116.64013876135085, + 111.13253749617385, + 105.95143352719109, + 101.09682685440261, + 96.56871747780836, + 92.36710539740844, + 88.49199061320272, + 84.9433731251913, + 81.72125293337413, + 78.82563003775124, + 76.2565044383226, + 74.01387613508822, + 72.09774512804813, + 70.5081114172023, + 69.24497500255075, + 68.30833588409342, + 67.69819406183039, + 67.41454953576164, + 67.45740230588713, + 67.82675237220688, + 68.52259973472091, + 69.5449443934292, + 70.89378634833177, + 72.5691255994286, + 74.5709621467197, + 76.89929599020505, + 79.55412712988468, + 82.53545556575857, + 85.8432812978267, + 89.47760432608914, + 93.43842465054581, + 97.7257422711968, + 102.33955718804198, + 107.27986940108148, + 112.54667891031524, + 118.13998571574328, + 124.0597898173655, + 130.30609121518205, + 136.87888990919288, + 143.778185899398, + 151.0039791857973, + 158.5562697683909, + 166.4350576471788, + 174.64034282216096, + 183.17212529333742, + 192.03040506070803, + 201.21518212427296, + 210.72645648403218, + 220.5642281399857, + 230.72849709213338, + 241.21926334047538, + 252.03652688501165, + 263.18028772574223, + 274.65054586266695, + 286.447301295786, + 298.5705540250994, + 311.020304050607, + 323.79655137230884, + 336.89929599020513, + 350.32853790429544, + 364.08427711458, + 378.16651362105904, + 392.57524742373215, + 407.31047852259974, + 422.3722069176614, + 437.76043260891726, + 453.4751555963677, + 469.51637588001216, + 485.8840934598508, + 502.57830833588406, + 519.5990205081113, + 536.946229976533, + 554.6199367411489, + 572.6201408019589, + 590.9468421589634, + 609.6000408121619, + 628.5797367615551, + 647.8859300071421 + ], + [ + 319.91735537190084, + 307.3900622385471, + 295.18926640138756, + 283.3149678604224, + 271.7671666156515, + 260.5458626670748, + 249.65105601469233, + 239.08274665850428, + 228.8409345985104, + 218.92561983471074, + 209.33680236710538, + 200.0744821956943, + 191.13865932047753, + 182.52933374145493, + 174.24650545862664, + 166.29017447199266, + 158.66034078155292, + 151.3570043873074, + 144.38016528925618, + 137.72982348739924, + 131.40597898173655, + 125.40863177226814, + 119.73778185899397, + 114.39342924191409, + 109.37557392102846, + 104.68421589633711, + 100.31935516784, + 96.2809917355372, + 92.56912559942862, + 89.18375675951432, + 86.1248852157943, + 83.39251096826854, + 80.98663401693705, + 78.9072543617998, + 77.15437200285683, + 75.72798694010814, + 74.62809917355371, + 73.85470870319354, + 73.40781552902763, + 73.287419651056, + 73.49352106927863, + 74.02611978369552, + 74.88521579430669, + 76.0708091011121, + 77.58289970411181, + 79.42148760330575, + 81.58657279869398, + 84.07815529027648, + 86.89623507805325, + 90.04081216202428, + 93.51188654218954, + 97.3094582185491, + 101.43352719110294, + 105.88409345985103, + 110.66115702479335, + 115.76471788592998, + 121.19477604326086, + 126.95133149678604, + 133.0343842465054, + 139.44393429241913, + 146.17998163452705, + 153.24252627282928, + 160.6315682073257, + 168.34710743801648, + 176.3891439649015, + 184.7576777879808, + 193.45270890725436, + 202.4742373227221, + 211.82226303438424, + 221.4967860422406, + 231.49780634629118, + 241.82532394653597, + 252.47933884297515, + 263.45985103560855, + 274.76686052443625, + 286.4003673094581, + 298.36037139067435, + 310.64687276808485, + 323.2598714416896, + 336.1993674114885, + 349.46536067748195, + 363.0578512396694, + 376.9768390980511, + 391.22232425262735, + 405.7943067033975, + 420.6927864503623, + 435.9177634935211, + 451.4692378328741, + 467.3472094684216, + 483.55167840016315, + 500.08264462809905, + 516.9401081522294, + 534.1240689725537, + 551.6345270890727, + 569.4714825017854, + 587.6349352106927, + 606.1248852157944, + 624.94133251709, + 644.0842771145803, + 663.5537190082645 + ], + [ + 319.75002550760126, + 307.3859810223446, + 295.34843383328223, + 283.6373839404143, + 272.25283134374047, + 261.1947760432609, + 250.46321803897558, + 240.05815733088465, + 229.9795939189879, + 220.22752780328537, + 210.80195898377713, + 201.70288746046322, + 192.93031323334355, + 184.4842363024181, + 176.36465666768694, + 168.57157432915005, + 161.1049892868075, + 153.96490154065913, + 147.151311090705, + 140.6642179369452, + 134.50362207937962, + 128.6695235180084, + 123.16192225283135, + 117.98081828384858, + 113.1262116110601, + 108.59810223446587, + 104.3964901540659, + 100.52137536986022, + 96.97275788184879, + 93.75063769003164, + 90.85501479440873, + 88.28588919498011, + 86.04326089174575, + 84.12712988470564, + 82.53749617385982, + 81.27435975920824, + 80.33772064075094, + 79.72757881848791, + 79.44393429241913, + 79.48678706254465, + 79.8561371288644, + 80.55198449137842, + 81.57432915008673, + 82.92317110498928, + 84.59851035608612, + 86.60034690337719, + 88.92868074686255, + 91.58351188654218, + 94.56484032241607, + 97.87266605448426, + 101.50698908274663, + 105.46780940720335, + 109.7551270278543, + 114.36894194469953, + 119.30925415773898, + 124.57606366697273, + 130.16937047240077, + 136.08917457402308, + 142.33547597183957, + 148.9082746658504, + 155.8075706560555, + 163.03336394245486, + 170.58565452504843, + 178.46444240383633, + 186.66972757881845, + 195.2015100499949, + 204.05978981736558, + 213.24456688093048, + 222.7558412406897, + 232.59361289664318, + 242.75788184879096, + 253.24864809713287, + 264.0659116416692, + 275.20967248239975, + 286.6799306193246, + 298.47668605244354, + 310.5999387817569, + 323.04968880726454, + 335.8259361289664, + 348.9286807468625, + 362.357922660953, + 376.1136618712375, + 390.1958983777165, + 404.6046321803898, + 419.3398632792572, + 434.40159167431904, + 449.7898173655749, + 465.50454035302505, + 481.5457606366698, + 497.91347821650845, + 514.6076930925414, + 531.6284052647688, + 548.9756147331904, + 566.6493214978063, + 584.6495255586163, + 602.9762269156206, + 621.6294255688194, + 640.6091215182124, + 659.9153147637998, + 679.5480053055811 + ], + [ + 319.90919293949594, + 307.70839710233645, + 295.8340985613712, + 284.2862973166004, + 273.0649933680237, + 262.17018671564125, + 251.60187735945306, + 241.36006529945928, + 231.44475053565967, + 221.85593306805427, + 212.59361289664318, + 203.6577900214264, + 195.04846444240383, + 186.76563615957556, + 178.80930517294155, + 171.17947148250178, + 163.87613508825632, + 156.89929599020508, + 150.24895418834814, + 143.92510968268545, + 137.927762473217, + 132.25691255994286, + 126.91255994286297, + 121.89470462197738, + 117.203346597286, + 112.83848586878891, + 108.80012243648608, + 105.08825630037752, + 101.70288746046322, + 98.6440159167432, + 95.91164166921743, + 93.50576471788595, + 91.42638506274871, + 89.67350270380575, + 88.24711764105706, + 87.14722987450261, + 86.37383940414244, + 85.92694622997655, + 85.80655035200492, + 86.01265177022754, + 86.54525048464443, + 87.4043464952556, + 88.58993980206102, + 90.10203040506073, + 91.94061830425468, + 94.10570349964289, + 96.59728599122539, + 99.41536577900214, + 102.55994286297319, + 106.03101724313849, + 109.828588919498, + 113.95265789205185, + 118.40322416079994, + 123.1802877257423, + 128.2838485868789, + 133.71390674420977, + 139.47046219773492, + 145.55351494745437, + 151.963064993368, + 158.69911233547597, + 165.7616569737782, + 173.15069890827468, + 180.8662381389654, + 188.90827466585043, + 197.2768084889297, + 205.97183960820328, + 214.99336802367108, + 224.3413937353331, + 234.01591674318945, + 244.0169370472401, + 254.344454647485, + 264.99846954392405, + 275.97898173655744, + 287.28599122538515, + 298.91949801040715, + 310.8795020916233, + 323.1660034690338, + 335.77900214263855, + 348.71849811243754, + 361.9844913784307, + 375.5769819406184, + 389.4959697990001, + 403.741454953576, + 418.31343740434653, + 433.211917151311, + 448.4368941944701, + 463.98836853382306, + 479.86634016937035, + 496.0708091011122, + 512.601775329048, + 529.4592388531781, + 546.6431996735027, + 564.1536577900213, + 581.9906132027345, + 600.1540659116416, + 618.644015916743, + 637.460463218039, + 656.603407815529, + 676.0728497092134, + 695.868788899092 + ], + [ + 320.394857667585, + 308.3573104785226, + 296.6462605856545, + 285.26170798898073, + 274.20365268850117, + 263.47209468421585, + 253.06703397612483, + 242.98847056422818, + 233.23640444852566, + 223.81083562901745, + 214.71176410570348, + 205.9391898785838, + 197.4931129476584, + 189.37353331292724, + 181.58045097439037, + 174.11386593204776, + 166.97377818589942, + 160.1601877359453, + 153.67309458218546, + 147.51249872461995, + 141.67840016324863, + 136.1707988980716, + 130.98969492908884, + 126.13508825630035, + 121.60697887970612, + 117.40536679930618, + 113.53025201510047, + 109.98163452708906, + 106.75951433527189, + 103.863891439649, + 101.29476584022035, + 99.05213753698601, + 97.13600652994589, + 95.54637281910007, + 94.28323640444849, + 93.3465972859912, + 92.73645546372816, + 92.45281093765938, + 92.49566370778489, + 92.86501377410465, + 93.56086113661867, + 94.58320579532696, + 95.93204775022953, + 97.60738700132636, + 99.60922354861746, + 101.9375573921028, + 104.59238853178242, + 107.57371696765631, + 110.88154269972448, + 114.51586572798692, + 118.47668605244357, + 122.76400367309452, + 127.37781858993976, + 132.31813080297925, + 137.58494031221298, + 143.178247117641, + 149.09805121926328, + 155.34435261707986, + 161.9171513110906, + 168.81644730129574, + 176.04224058769506, + 183.59453117028872, + 191.4733190490765, + 199.6786042240587, + 208.21038669523514, + 217.06866646260582, + 226.25344352617074, + 235.7647178859299, + 245.6024895418834, + 255.76675849403117, + 266.2575247423732, + 277.0747882869094, + 288.2185491276399, + 299.68880726456473, + 311.48556269768386, + 323.60881542699707, + 336.0585654525047, + 348.8348127742067, + 361.93755739210275, + 375.36679930619306, + 389.1225385164779, + 403.2047750229567, + 417.6135088256298, + 432.34873992449747, + 447.410468319559, + 462.79869401081515, + 478.51341699826537, + 494.55463728190983, + 510.9223548617488, + 527.6165697377817, + 544.6372819100089, + 561.9844913784307, + 579.6581981430464, + 597.6584022038567, + 615.9851035608609, + 634.6383022140595, + 653.6179981634526, + 672.9241914090396, + 692.5568819508213, + 712.5160697887969 + ], + [ + 321.2070196918682, + 309.33272115090296, + 297.784919906132, + 286.5636159575554, + 275.66880930517294, + 265.1004999489848, + 254.85868788899086, + 244.94337312519136, + 235.35455565758596, + 226.09223548617487, + 217.15641261095803, + 208.54708703193552, + 200.26425874910723, + 192.3079277624732, + 184.67809407203345, + 177.37475767778795, + 170.39791857973677, + 163.7475767778798, + 157.4237322722171, + 151.4263850627487, + 145.75553514947453, + 140.41118253239466, + 135.39332721150902, + 130.70196918681768, + 126.33710845832056, + 122.29874502601776, + 118.58687888990917, + 115.20151004999488, + 112.14263850627486, + 109.4102642587491, + 107.0043873074176, + 104.92500765228037, + 103.17212529333739, + 101.7457402305887, + 100.64585246403426, + 99.87246199367411, + 99.4255688195082, + 99.30517294153654, + 99.51127435975918, + 100.04387307417609, + 100.90296908478724, + 102.08856239159266, + 103.60065299459237, + 105.43924089378633, + 107.60432608917455, + 110.09590858075704, + 112.9139883685338, + 116.05856545250481, + 119.52963983267011, + 123.32721150902967, + 127.45128048158348, + 131.90184675033157, + 136.67891031527392, + 141.78247117641055, + 147.2125293337414, + 152.96908478726655, + 159.052137536986, + 165.46168758289969, + 172.1977349250076, + 179.2602795633098, + 186.6493214978063, + 194.3648607284971, + 202.40689725538203, + 210.7754310784613, + 219.47046219773486, + 228.4919906132027, + 237.84001632486482, + 247.51453933272109, + 257.5155596367717, + 267.84307723701664, + 278.4970921334558, + 289.4776043260891, + 300.7846138149168, + 312.41812059993873, + 324.378124681155, + 336.6646260585653, + 349.27762473217007, + 362.2171207019691, + 375.48311396796237, + 389.07560453014986, + 402.9945923885318, + 417.2400775431078, + 431.812059993878, + 446.71053974084276, + 461.93551678400155, + 477.4869911233548, + 493.3649627589021, + 509.5694316906436, + 526.1003979185798, + 542.9578614427098, + 560.1418222630342, + 577.6522803795531, + 595.489235792266, + 613.6526885011733, + 632.1426385062748, + 650.9590858075704, + 670.1020304050606, + 689.5714722987449, + 709.3674114886237, + 729.4898479746963 + ], + [ + 322.34567901234567, + 310.6346291194776, + 299.2500765228038, + 288.1920212223243, + 277.46046321803897, + 267.05540250994795, + 256.9768390980512, + 247.22477298234875, + 237.7992041628405, + 228.70013263952657, + 219.92755841240685, + 211.48148148148147, + 203.36190184675033, + 195.56881950821344, + 188.10223446587082, + 180.96214671972248, + 174.1485562697684, + 167.66146311600855, + 161.500867258443, + 155.66676869707172, + 150.1591674318947, + 144.97806346291193, + 140.12345679012344, + 135.59534741352923, + 131.39373533312929, + 127.51862054892358, + 123.97000306091215, + 120.747882869095, + 117.85225997347209, + 115.28313437404347, + 113.04050607080909, + 111.124375063769, + 109.53474135292318, + 108.2716049382716, + 107.3349658198143, + 106.72482399755127, + 106.4411794714825, + 106.48403224160799, + 106.85338230792776, + 107.54922967044178, + 108.57157432915008, + 109.92041628405264, + 111.59575553514946, + 113.59759208244056, + 115.92592592592592, + 118.58075706560552, + 121.56208550147942, + 124.8699112335476, + 128.50423426181, + 132.46505458626672, + 136.75237220691764, + 141.36618712376287, + 146.30649933680235, + 151.57330884603616, + 157.1666156514641, + 163.0864197530864, + 169.33272115090296, + 175.90551984491378, + 182.80481583511883, + 190.0306091215182, + 197.5828997041118, + 205.4616875828997, + 213.66697275788178, + 222.19875522905824, + 231.0570349964289, + 240.24181205999386, + 249.75308641975312, + 259.59085807570654, + 269.75512702785426, + 280.2458932761963, + 291.0631568207326, + 302.2069176614631, + 313.6771757983879, + 325.473931231507, + 337.59718396082036, + 350.0469339863279, + 362.82318130802975, + 375.92592592592587, + 389.3551678400163, + 403.1109070503009, + 417.19314355678, + 431.6018773594531, + 446.3371084583205, + 461.3988368533823, + 476.7870625446382, + 492.50178553208866, + 508.54300581573307, + 524.9107233955718, + 541.6049382716051, + 558.6256504438322, + 575.9728599122537, + 593.6465666768697, + 611.6467707376797, + 629.9734720946843, + 648.6266707478828, + 667.6063666972757, + 686.912559942863, + 706.5452504846444, + 726.5044383226203, + 746.7901234567901 + ], + [ + 323.81083562901745, + 312.2630343842465, + 301.04173043566976, + 290.1469237832875, + 279.5786144270993, + 269.3368023671054, + 259.42148760330576, + 249.83267013570048, + 240.57034996428936, + 231.63452708907252, + 223.02520151005, + 214.74237322722172, + 206.7860422405877, + 199.15620855014794, + 191.85287215590245, + 184.87603305785126, + 178.22569125599432, + 171.90184675033163, + 165.90449954086316, + 160.23364962758902, + 154.88929701050915, + 149.87144168962354, + 145.18008366493214, + 140.81522293643508, + 136.77685950413223, + 133.0649933680237, + 129.6796245281094, + 126.62075298438936, + 123.88837873686359, + 121.48250178553211, + 119.40312213039486, + 117.65023977145191, + 116.22385470870321, + 115.12396694214877, + 114.35057647178861, + 113.90368329762269, + 113.78328741965109, + 113.98938883787369, + 114.52198755229058, + 115.38108356290176, + 116.56667686970718, + 118.07876747270687, + 119.91735537190083, + 122.08244056728907, + 124.57402305887156, + 127.39210284664829, + 130.53667993061933, + 134.0077543107846, + 137.8053259871442, + 141.92939495969802, + 146.3799612284461, + 151.15702479338842, + 156.26058565452507, + 161.69064381185595, + 167.44719926538107, + 173.53025201510053, + 179.93980206101418, + 186.67584940312216, + 193.7383940414243, + 201.1274359759208, + 208.8429752066116, + 216.8850117334966, + 225.2535455565758, + 233.94857667584938, + 242.9701050913172, + 252.31813080297934, + 261.99265381083563, + 271.99367411488623, + 282.3211917151311, + 292.9752066115703, + 303.9557188042037, + 315.2627282930313, + 326.8962350780533, + 338.8562391592695, + 351.14274053668, + 363.75573921028456, + 376.6952351800836, + 389.9612284460769, + 403.55371900826447, + 417.47270686664615, + 431.7181920212224, + 446.2901744719926, + 461.1886542189572, + 476.4136312621162, + 491.96510560146913, + 507.84307723701676, + 524.0475461687582, + 540.5785123966941, + 557.4359759208245, + 574.6199367411489, + 592.1303948576675, + 609.9673502703806, + 628.1308029792878, + 646.6207529843895, + 665.4372002856852, + 684.5801448831751, + 704.0495867768595, + 723.845525966738, + 743.9679624528111, + 764.4168962350781 + ], + [ + 325.6024895418835, + 314.2179369452096, + 303.15988164473004, + 292.42832364044483, + 282.0232629323538, + 271.9446995204571, + 262.1926334047546, + 252.76706458524643, + 243.66799306193246, + 234.89541883481274, + 226.44934190388733, + 218.3297622691562, + 210.5366799306193, + 203.0700948882767, + 195.93000714212832, + 189.11641669217423, + 182.62932353841444, + 176.46872768084887, + 170.63462911947758, + 165.12702785430054, + 159.94592388531777, + 155.0913172125293, + 150.5632078359351, + 146.36159575553512, + 142.48648097132943, + 138.93786348331798, + 135.71574329150084, + 132.82012039587795, + 130.2509947964493, + 128.00836649321494, + 126.09223548617483, + 124.50260177532903, + 123.23946536067744, + 122.30282624222015, + 121.6926844199571, + 121.40903989388833, + 121.45189266401385, + 121.82124273033358, + 122.51709009284762, + 123.53943475155593, + 124.88827670645848, + 126.5636159575553, + 128.5654525048464, + 130.89378634833176, + 133.5486174880114, + 136.52994592388524, + 139.83777165595342, + 143.47209468421585, + 147.43291500867255, + 151.7202326293235, + 156.33404754616868, + 161.27435975920818, + 166.54116926844193, + 172.13447607387, + 178.0542801754922, + 184.3005815733088, + 190.8733802673196, + 197.77267625752472, + 204.998469543924, + 212.55076012651762, + 220.42954800530552, + 228.63483318028764, + 237.16661565146404, + 246.02489541883472, + 255.20967248239967, + 264.7209468421589, + 274.5587184981124, + 284.72298745026006, + 295.2137536986021, + 306.03101724313836, + 317.17477808386894, + 328.64503622079366, + 340.44179165391273, + 352.5650443832261, + 365.0147944087337, + 377.7910417304355, + 390.8937863483317, + 404.32302826242216, + 418.0787674727068, + 432.16100397918564, + 446.569737781859, + 461.30496888072634, + 476.36669727578794, + 491.7549229670441, + 507.46964595449424, + 523.5108662381389, + 539.8785838179776, + 556.5727986940105, + 573.593510866238, + 590.9407203346595, + 608.6144270992754, + 626.6146311600857, + 644.9413325170899, + 663.5945311702887, + 682.5742271196815, + 701.8804203652686, + 721.5131109070502, + 741.4722987450259, + 761.7579838791961, + 782.3701663095601 + ], + [ + 327.7206407509438, + 316.49933680236705, + 305.60453014998467, + 295.0362207937966, + 284.7944087338027, + 274.87909397000305, + 265.29027650239766, + 256.0279563309867, + 247.09213345576984, + 238.4828078767473, + 230.19997959391898, + 222.243648607285, + 214.61381491684523, + 207.31047852259974, + 200.3336394245485, + 193.68329762269158, + 187.35945311702892, + 181.36210590756048, + 175.6912559942863, + 170.34690337720644, + 165.3290480563208, + 160.63769003162946, + 156.27282930313237, + 152.23446587082952, + 148.52259973472098, + 145.1372308948067, + 142.07835935108665, + 139.3459851035609, + 136.94010815222939, + 134.86072849709217, + 133.1078461381492, + 131.68146107540053, + 130.58157330884606, + 129.80818283848592, + 129.36128966432, + 129.24089378634835, + 129.446995204571, + 129.9795939189879, + 130.83868992959907, + 132.0242832364045, + 133.53637383940418, + 135.37496173859816, + 137.54004693398636, + 140.03162942556887, + 142.84970921334565, + 145.99428629731662, + 149.46536067748195, + 153.2629323538415, + 157.3870013263953, + 161.83756759514344, + 166.61463116008574, + 171.71819202122236, + 177.14825017855324, + 182.90480563207842, + 188.98785838179782, + 195.3974084277115, + 202.13345576981948, + 209.19600040812168, + 216.58504234261812, + 224.30058157330888, + 232.34261810019393, + 240.71115192327323, + 249.40618304254667, + 258.4277114580145, + 267.7757371696766, + 277.4502601775329, + 287.45128048158364, + 297.7787980818284, + 308.4328129782676, + 319.413325170901, + 330.7203346597287, + 342.35384144475057, + 354.31384552596677, + 366.6003469033773, + 379.213345576982, + 392.1528415467809, + 405.41883481277426, + 419.01132537496187, + 432.93031323334367, + 447.1757983879196, + 461.74778083869006, + 476.64626058565455, + 491.87123762881333, + 507.4227119681666, + 523.3006836037139, + 539.5051525354557, + 556.0361187633915, + 572.8935822875217, + 590.0775431078463, + 607.5880012243648, + 625.4249566370777, + 643.5884093459853, + 662.0783593510866, + 680.8948066523826, + 700.0377512498725, + 719.5071931435567, + 739.3031323334355, + 759.4255688195083, + 779.8745026017756, + 800.6499336802367 + ], + [ + 330.1652892561984, + 319.1072339557188, + 308.3756759514335, + 297.97061524334254, + 287.89205183144577, + 278.13998571574325, + 268.71441689623504, + 259.6153453729211, + 250.84277114580144, + 242.39669421487602, + 234.27711458014485, + 226.48403224160802, + 219.0174471992654, + 211.87735945311704, + 205.06376900316292, + 198.5766758494031, + 192.4160799918376, + 186.5819814304663, + 181.07438016528926, + 175.8932761963065, + 171.038669523518, + 166.51056014692375, + 162.3089480665238, + 158.43383328231812, + 154.8852157943067, + 151.66309560248953, + 148.7674727068666, + 146.198347107438, + 143.95571880420366, + 142.03958779716353, + 140.44995408631772, + 139.18681767166618, + 138.25017855320883, + 137.6400367309458, + 137.35639220487704, + 137.39924497500255, + 137.76859504132233, + 138.46444240383633, + 139.4867870625446, + 140.8356290174472, + 142.51096826854402, + 144.5128048158351, + 146.84113865932045, + 149.4959697990001, + 152.47729823487398, + 155.7851239669421, + 159.41944699520457, + 163.38026731966124, + 167.6675849403122, + 172.28139985715742, + 177.22171207019687, + 182.48852157943065, + 188.08182838485868, + 194.00163248648096, + 200.24793388429748, + 206.82073257830828, + 213.7200285685134, + 220.94582185491277, + 228.4981124375063, + 236.37690031629418, + 244.58218549127636, + 253.11396796245282, + 261.9722477298234, + 271.15702479338836, + 280.6682991531476, + 290.50607080910106, + 300.6703397612489, + 311.1611060095908, + 321.9783695541271, + 333.1221303948576, + 344.5923885317825, + 356.3891439649015, + 368.51239669421483, + 380.9621467197224, + 393.7383940414243, + 406.84113865932034, + 420.2703805734108, + 434.0261197836955, + 448.10835629017447, + 462.5170900928476, + 477.25232119171517, + 492.31404958677683, + 507.7022752780327, + 523.4169982654831, + 539.4582185491275, + 555.8259361289665, + 572.5201510049994, + 589.5408631772267, + 606.8880726456484, + 624.5617794102642, + 642.5619834710742, + 660.8886848280787, + 679.5418834812772, + 698.5215794306705, + 717.8277726762575, + 737.4604632180389, + 757.4196510560147, + 777.7053361901847, + 798.3175186205491, + 819.2561983471074 + ], + [ + 332.9364350576471, + 322.04162840526476, + 311.47331904907657, + 301.2315069890828, + 291.3161922252831, + 281.72737475767775, + 272.46505458626666, + 263.5292317110499, + 254.91990613202728, + 246.63707784919904, + 238.68074686256497, + 231.05091317212523, + 223.7475767778798, + 216.77073767982853, + 210.1203958779716, + 203.7965513723089, + 197.7992041628405, + 192.1283542495663, + 186.78400163248642, + 181.7661463116008, + 177.07478828690944, + 172.70992755841235, + 168.67156412610953, + 164.95969799000096, + 161.57432915008667, + 158.51545760636665, + 155.78308335884088, + 153.37720640750936, + 151.29782675237215, + 149.54494439342918, + 148.11855933068048, + 147.01867156412607, + 146.24528109376587, + 145.79838791959997, + 145.67799204162836, + 145.88409345985096, + 146.41669217426787, + 147.275788184879, + 148.46138149168445, + 149.97347209468415, + 151.8120599938781, + 153.9771451892663, + 156.4687276808488, + 159.28680746862557, + 162.4313845525966, + 165.90245893276187, + 169.70003060912143, + 173.82409958167526, + 178.27466585042333, + 183.0517294153657, + 188.15529027650228, + 193.58534843383316, + 199.34190388735834, + 205.42495663707777, + 211.83450668299142, + 218.57055402509937, + 225.63309866340157, + 233.0221405978981, + 240.73767982858874, + 248.77971635547382, + 257.1482501785531, + 265.8432812978267, + 274.86480971329445, + 284.21283542495655, + 293.88735843281285, + 303.8883787368635, + 314.2158963371084, + 324.86991123354744, + 335.8504234261809, + 347.1574329150085, + 358.7909397000305, + 370.7509437812467, + 383.03744515865714, + 395.65044383226194, + 408.5899398020609, + 421.85593306805407, + 435.4484236302416, + 449.3674114886235, + 463.6128966431996, + 478.18487909396976, + 493.0833588409345, + 508.3083358840933, + 523.8598102234463, + 539.7377818589939, + 555.9422507907354, + 572.4732170186716, + 589.3306805428016, + 606.514641363126, + 624.025099479645, + 641.8620548923577, + 660.0255076012647, + 678.5154576063666, + 697.3319049076622, + 716.4748495051525, + 735.9442913988366, + 755.7402305887151, + 775.8626670747882, + 796.3116008570553, + 817.0870319355168, + 838.1889603101723 + ], + [ + 336.0340781552903, + 325.30252015100496, + 314.89745944291394, + 304.8188960310173, + 295.0668299153148, + 285.64126109580656, + 276.5421895724926, + 267.769615345373, + 259.3235384144475, + 251.20395877971634, + 243.41087644117948, + 235.9442913988369, + 228.80420365268853, + 221.9906132027344, + 215.5035200489746, + 209.34292419140905, + 203.5088256300378, + 198.00122436486075, + 192.82012039587798, + 187.9655137230895, + 183.43740434649527, + 179.23579226609533, + 175.3606774818896, + 171.8120599938782, + 168.58993980206102, + 165.69431690643813, + 163.12519130700952, + 160.88256300377515, + 158.96643199673505, + 157.3767982858892, + 156.11366187123764, + 155.17702275278037, + 154.5668809305173, + 154.28323640444853, + 154.32608917457404, + 154.6954392408938, + 155.39128660340785, + 156.41363126211613, + 157.7624732170187, + 159.4378124681155, + 161.43964901540664, + 163.76798285889197, + 166.4228139985716, + 169.4041424344455, + 172.71196816651363, + 176.34629119477606, + 180.30711151923276, + 184.5944291398837, + 189.20824405672894, + 194.14855626976845, + 199.41536577900214, + 205.0086725844302, + 210.92847668605248, + 217.17477808386903, + 223.7475767778798, + 230.6468727680849, + 237.87266605448428, + 245.4249566370779, + 253.3037445158657, + 261.5090296908479, + 270.0408121620243, + 278.89909192939496, + 288.08386899295994, + 297.5951433527191, + 307.4329150086726, + 317.5971839608204, + 328.08795020916244, + 338.9052137536986, + 350.0489745944291, + 361.51923273135395, + 373.3159881644731, + 385.4392408937863, + 397.88899091929403, + 410.66523824099585, + 423.767982858892, + 437.19722477298234, + 450.952963983267, + 465.03520048974593, + 479.4439342924192, + 494.1791653912865, + 509.2408937863484, + 524.6291194776044, + 540.3438424650545, + 556.3850627486992, + 572.7527803285379, + 589.4469952045712, + 606.4677073767983, + 623.8149168452197, + 641.4886236098358, + 659.4888276706458, + 677.8155290276501, + 696.4687276808489, + 715.4484236302417, + 734.7546168758291, + 754.3873074176104, + 774.346495255586, + 794.6321803897562, + 815.2443628201204, + 836.1830425466791, + 857.4482195694318 + ], + [ + 339.4582185491276, + 328.88990919293946, + 318.64809713294557, + 308.732782369146, + 299.14396490154064, + 289.88164473012955, + 280.9458218549127, + 272.3364962758902, + 264.05366799306194, + 256.0973370064279, + 248.4675033159881, + 241.16416692174263, + 234.18732782369148, + 227.5369860218345, + 221.2131415161718, + 215.21579430670337, + 209.54494439342923, + 204.2005917763493, + 199.18273645546373, + 194.49137843077233, + 190.12651770227524, + 186.08815426997242, + 182.37628813386385, + 178.9909192939496, + 175.93204775022951, + 173.19967350270377, + 170.79379655137225, + 168.71441689623504, + 166.96153453729212, + 165.53514947454337, + 164.43526170798893, + 163.6618712376288, + 163.21497806346287, + 163.09458218549125, + 163.30068360371388, + 163.83328231813076, + 164.69237832874194, + 165.87797163554734, + 167.39006223854705, + 169.228650137741, + 171.39373533312923, + 173.8853178247117, + 176.70339761248846, + 179.84797469645952, + 183.3190490766248, + 187.11662075298432, + 191.24068972553812, + 195.69125599428622, + 200.46831955922863, + 205.57188042036526, + 211.00193857769608, + 216.75849403122123, + 222.8415467809407, + 229.2510968268544, + 235.9871441689623, + 243.0496888072645, + 250.438730741761, + 258.15426997245174, + 266.19630649933674, + 274.564840322416, + 283.25987144168954, + 292.2813998571574, + 301.62942556881944, + 311.30394857667574, + 321.30496888072634, + 331.6324864809713, + 342.2865013774105, + 353.2670135700438, + 364.5740230588715, + 376.2075298438934, + 388.16753392510964, + 400.45403530252, + 413.0670339761248, + 426.00652994592383, + 439.272523211917, + 452.8650137741045, + 466.7840016324864, + 481.02948678706247, + 495.60146923783276, + 510.4999489847973, + 525.7249260279564, + 541.2764003673094, + 557.1543720028567, + 573.3588409345986, + 589.8898071625343, + 606.7472706866647, + 623.931231506989, + 641.4416896235076, + 659.2786450362207, + 677.4420977451279, + 695.9320477502292, + 714.7484950515253, + 733.8914396490152, + 753.3608815426998, + 773.1568207325781, + 793.2792572186509, + 813.7281910009182, + 834.5036220793794, + 855.6055504540353, + 877.0339761248852 + ], + [ + 343.2088562391593, + 332.80379553106826, + 322.7252321191715, + 312.9731660034691, + 303.5475971839608, + 294.44852566064685, + 285.6759514335272, + 277.22987450260183, + 269.11029486787066, + 261.31721252933374, + 253.85062748699116, + 246.71053974084282, + 239.89694929088873, + 233.40985613712888, + 227.24926027956332, + 221.41516171819208, + 215.90756045301507, + 210.7264564840323, + 205.87184981124378, + 201.3437404346496, + 197.14212835424962, + 193.26701357004393, + 189.71839608203248, + 186.49627589021534, + 183.60065299459245, + 181.0315273951638, + 178.78889909192944, + 176.87276808488932, + 175.2831343740435, + 174.01999795939196, + 173.08335884093466, + 172.47321701867162, + 172.18957249260282, + 172.23242526272836, + 172.60177532904814, + 173.29762269156217, + 174.31996735027045, + 175.668809305173, + 177.34414855626983, + 179.34598510356093, + 181.67431894704632, + 184.32915008672592, + 187.3104785225998, + 190.61830425466795, + 194.2526272829304, + 198.21344760738705, + 202.50076522803803, + 207.11458014488326, + 212.05489235792274, + 217.32170186715652, + 222.9150086725845, + 228.83481277420677, + 235.08111417202332, + 241.65391286603415, + 248.55320885623922, + 255.77900214263857, + 263.33129272523223, + 271.2100806040201, + 279.41536577900223, + 287.9471482501786, + 296.80542801754933, + 305.9902050811143, + 315.5014794408734, + 325.3392510968269, + 335.5035200489746, + 345.9942862973167, + 356.8115498418531, + 367.9553106825835, + 379.4255688195083, + 391.22232425262735, + 403.3455769819408, + 415.79532700744824, + 428.57157432915017, + 441.6743189470463, + 455.1035608611367, + 468.8593000714212, + 482.9415365779003, + 497.35027038057353, + 512.085501479441, + 527.1472298745025, + 542.5354555657588, + 558.250178553209, + 574.2913988368534, + 590.6591164166924, + 607.3533312927253, + 624.3740434649528, + 641.7212529333743, + 659.39495969799, + 677.3951637588003, + 695.7218651158046, + 714.3750637690031, + 733.3547597183962, + 752.6609529639833, + 772.2936435057649, + 792.2528313437405, + 812.5385164779103, + 833.1506989082748, + 854.0893786348332, + 875.3545556575862, + 896.9462299765331 + ], + [ + 347.2859912253852, + 337.0441791653913, + 327.12886440159167, + 317.5400469339864, + 308.27772676257524, + 299.3419038873584, + 290.73257830833586, + 282.4497500255076, + 274.4934190388736, + 266.86358534843384, + 259.56024895418835, + 252.5834098561371, + 245.9330680542802, + 239.60922354861748, + 233.61187633914906, + 227.9410264258749, + 222.596673808795, + 217.5788184879094, + 212.88746046321805, + 208.52259973472093, + 204.4842363024181, + 200.77237016630954, + 197.38700132639525, + 194.32812978267526, + 191.59575553514944, + 189.18987858381797, + 187.11049892868073, + 185.3576165697378, + 183.93123150698912, + 182.83134374043465, + 182.05795327007448, + 181.6110600959086, + 181.49066421793694, + 181.6967656361596, + 182.22936435057645, + 183.0884603611876, + 184.27405366799303, + 185.78614427099276, + 187.62473217018672, + 189.78981736557495, + 192.28139985715742, + 195.09947964493415, + 198.2440567289052, + 201.71513110907048, + 205.51270278543006, + 209.63677175798384, + 214.08733802673197, + 218.86440159167432, + 223.96796245281095, + 229.39802061014183, + 235.15457606366695, + 241.23762881338638, + 247.64717885930008, + 254.38322620140804, + 261.4457708397102, + 268.8348127742067, + 276.55035200489743, + 284.5923885317825, + 292.96092235486174, + 301.6559534741353, + 310.67748188960314, + 320.02550760126525, + 329.7000306091215, + 339.7010509131721, + 350.02856851341693, + 360.68258340985614, + 371.6630956024896, + 382.9701050913172, + 394.6036118763391, + 406.5636159575554, + 418.85011733496583, + 431.4631160085705, + 444.4026119783696, + 457.66860524436277, + 471.2610958065503, + 485.180083664932, + 499.42556881950816, + 513.9975512702786, + 528.8960310172431, + 544.1210080604019, + 559.6724823997552, + 575.5504540353024, + 591.754922967044, + 608.2858891949802, + 625.1433527191102, + 642.327313539435, + 659.8377716559535, + 677.6747270686664, + 695.8381797775737, + 714.3281297826752, + 733.144577083971, + 752.287521681461, + 771.7569635751454, + 791.5529027650241, + 811.6753392510968, + 832.1242730333637, + 852.8997041118254, + 874.0016324864808, + 895.430058157331, + 917.184981124375 + ], + [ + 351.68962350780527, + 341.61106009590856, + 331.85899398020604, + 322.4334251606979, + 313.3343536373839, + 304.56177941026425, + 296.1157024793388, + 287.99612284460767, + 280.20304050607075, + 272.73645546372813, + 265.59636771757977, + 258.7827772676257, + 252.2956841138659, + 246.13508825630032, + 240.30098969492906, + 234.79338842975204, + 229.61228446076927, + 224.75767778798075, + 220.22956841138654, + 216.02795633098657, + 212.1528415467809, + 208.60422405876946, + 205.3821038669523, + 202.4864809713294, + 199.91735537190078, + 197.6747270686664, + 195.7585960616263, + 194.16896235078045, + 192.9058259361289, + 191.9691868176716, + 191.35904499540857, + 191.0754004693398, + 191.11825323946528, + 191.48760330578506, + 192.1834506682991, + 193.20579532700737, + 194.55463728190995, + 196.22997653300675, + 198.23181308029785, + 200.5601469237832, + 203.21497806346284, + 206.1963064993367, + 209.50413223140487, + 213.1384552596673, + 217.099275584124, + 221.38659320477493, + 226.00040812162015, + 230.94072033465963, + 236.20752984389338, + 241.80083664932144, + 247.7206407509437, + 253.96694214876024, + 260.53974084277104, + 267.43903683297617, + 274.66483011937544, + 282.21712070196907, + 290.095908580757, + 298.3011937557391, + 306.8329762269155, + 315.69125599428617, + 324.8760330578511, + 334.38730741761043, + 344.2250790735638, + 354.3893480257115, + 364.88011427405354, + 375.6973778185898, + 386.84113865932045, + 398.3113967962451, + 410.1081522293642, + 422.23140495867756, + 434.6811549841852, + 447.457402305887, + 460.56014692378324, + 473.98938883787355, + 487.7451280481582, + 501.8273645546371, + 516.2360983573103, + 530.9713294561778, + 546.0330578512395, + 561.4212835424954, + 577.1360065299459, + 593.1772268135903, + 609.544944393429, + 626.2391592694621, + 643.2598714416894, + 660.6070809101111, + 678.280787674727, + 696.280991735537, + 714.6076930925416, + 733.2608917457401, + 752.240587695133, + 771.5467809407202, + 791.1794714825016, + 811.1386593204776, + 831.4243444546473, + 852.0365268850114, + 872.9752066115702, + 894.2403836343228, + 915.8320579532701, + 937.7502295684112 + ], + [ + 356.41975308641975, + 346.5044383226201, + 336.91562085501477, + 327.6533006836038, + 318.71747780838695, + 310.10815222936435, + 301.82532394653606, + 293.86899295990213, + 286.23915926946233, + 278.93582287521684, + 271.9589837771656, + 265.30864197530866, + 258.98479746964597, + 252.98745026017755, + 247.31660034690336, + 241.97224772982355, + 236.9543924089379, + 232.26303438424654, + 227.89817365574942, + 223.8598102234466, + 220.14794408733803, + 216.7625752474238, + 213.70370370370372, + 210.97132945617798, + 208.56545250484646, + 206.48607284970922, + 204.7331904907663, + 203.30680542801758, + 202.20691766146317, + 201.43352719110297, + 200.98663401693705, + 200.86623813896549, + 201.07233955718806, + 201.604938271605, + 202.46403428221612, + 203.64962758902158, + 205.16171819202128, + 207.00030609121524, + 209.16539128660344, + 211.65697377818591, + 214.4750535659627, + 217.6196306499337, + 221.09070503009903, + 224.88827670645856, + 229.0123456790124, + 233.46291194776046, + 238.2399755127028, + 243.34353637383944, + 248.77359453117035, + 254.5301499846955, + 260.61320273441487, + 267.0227527803286, + 273.7588001224366, + 280.8213447607388, + 288.2103866952352, + 295.925925925926, + 303.96796245281104, + 312.33649627589034, + 321.0315273951637, + 330.0530558106316, + 339.4010815222937, + 349.07560453015003, + 359.07662483420063, + 369.40414243444553, + 380.0581573308846, + 391.0386695235181, + 402.3456790123458, + 413.9791857973677, + 425.9391898785838, + 438.2256912559943, + 450.83868992959907, + 463.778185899398, + 477.04417916539137, + 490.6366697275789, + 504.5556575859607, + 518.8011427405366, + 533.373125191307, + 548.2716049382717, + 563.4965819814305, + 579.0480563207835, + 594.9260279563312, + 611.1304968880727, + 627.6614631160086, + 644.5189266401388, + 661.7028874604631, + 679.2133455769821, + 697.0503009896948, + 715.2137536986022, + 733.7037037037039, + 752.5201510049995, + 771.6630956024894, + 791.132537496174, + 810.9284766860525, + 831.0509131721254, + 851.4998469543925, + 872.2752780328536, + 893.3772064075097, + 914.8056320783593, + 936.5605550454038, + 958.641975308642 + ], + [ + 361.4763799612284, + 351.7243138455259, + 342.2987450260177, + 333.19967350270383, + 324.42709927558406, + 315.98102234465864, + 307.86144270992753, + 300.0683603713907, + 292.60177532904805, + 285.4616875828997, + 278.64809713294557, + 272.16100397918575, + 266.00040812162024, + 260.1663095602489, + 254.65870829507193, + 249.47760432608916, + 244.62299765330067, + 240.09488827670646, + 235.8932761963065, + 232.01816141210077, + 228.46954392408935, + 225.2474237322722, + 222.35180083664926, + 219.7826752372207, + 217.54004693398628, + 215.6239159269462, + 214.03428221610037, + 212.77114580144877, + 211.83450668299153, + 211.22436486072846, + 210.94072033465972, + 210.9835731047852, + 211.35292317110498, + 212.048770533619, + 213.07111519232728, + 214.41995714722987, + 216.09529639832667, + 218.09713294561777, + 220.42546678910313, + 223.08029792878276, + 226.06162636465666, + 229.36945209672476, + 233.00377512498721, + 236.9645954494439, + 241.25191307009487, + 245.86572798694004, + 250.80604019997955, + 256.0728497092133, + 261.66615651464133, + 267.5859606162636, + 273.83226201408013, + 280.40506070809096, + 287.30435669829603, + 294.53014998469536, + 302.0824405672889, + 309.9612284460769, + 318.16651362105904, + 326.69829609223547, + 335.5565758596061, + 344.741352923171, + 354.2526272829303, + 364.09039893888377, + 374.25466789103143, + 384.74543413937346, + 395.56269768390973, + 406.7064585246403, + 418.1767166615652, + 429.97347209468415, + 442.0967248239975, + 454.5464748495051, + 467.322722171207, + 480.42546678910304, + 493.85470870319347, + 507.61044791347814, + 521.6926844199571, + 536.1014182226302, + 550.8366493214977, + 565.8983777165595, + 581.2866034078155, + 597.0013263952656, + 613.0425466789103, + 629.4102642587491, + 646.104479134782, + 663.1251913070095, + 680.4724007754309, + 698.146107540047, + 716.146311600857, + 734.4730129578612, + 753.1262116110601, + 772.1059075604528, + 791.4121008060399, + 811.0447913478216, + 831.0039791857973, + 851.2896643199675, + 871.9018467503315, + 892.84052647689, + 914.1057034996429, + 935.6973778185899, + 957.6155494337313, + 979.8602183450668 + ], + [ + 366.85950413223134, + 357.270686664626, + 348.0083664932149, + 339.0725436179981, + 330.4632180389756, + 322.18038975614724, + 314.2240587695132, + 306.59422507907357, + 299.2908886848281, + 292.3140495867768, + 285.66370778491984, + 279.33986327925714, + 273.34251606978876, + 267.67166615651456, + 262.32731353943467, + 257.3094582185491, + 252.6181001938577, + 248.2532394653606, + 244.21487603305778, + 240.50300989694918, + 237.11764105703492, + 234.0587695133149, + 231.32639526578913, + 228.92051831445764, + 226.84113865932036, + 225.0882563003774, + 223.66187123762873, + 222.56198347107426, + 221.78859300071412, + 221.3416998265482, + 221.22130394857658, + 221.4274053667992, + 221.96000408121608, + 222.81910009182727, + 224.00469339863267, + 225.51678400163235, + 227.35537190082636, + 229.52045709621456, + 232.01203958779703, + 234.8301193755738, + 237.97469645954482, + 241.4457708397101, + 245.24334251606965, + 249.36741148862347, + 253.81797775737158, + 258.5950413223139, + 263.69860218345053, + 269.1286603407814, + 274.8852157943066, + 280.96826854402605, + 287.37781858993964, + 294.11386593204764, + 301.17641057034984, + 308.56545250484635, + 316.28099173553693, + 324.32302826242204, + 332.69156208550135, + 341.38659320477495, + 350.4081216202427, + 359.75614733190474, + 369.43067033976115, + 379.43169064381175, + 389.75920824405654, + 400.4132231404957, + 411.3937353331291, + 422.7007448219568, + 434.3342516069788, + 446.29425568819494, + 458.5807570656054, + 471.1937557392101, + 484.13325170900913, + 497.3992449750023, + 510.9917355371899, + 524.9107233955717, + 539.1562085501479, + 553.7281910009181, + 568.6266707478827, + 583.8516477910416, + 599.4031221303948, + 615.281093765942, + 631.4855626976838, + 648.0165289256197, + 664.8739924497496, + 682.0579532700743, + 699.5684113865929, + 717.4053667993061, + 735.5688195082133, + 754.0587695133147, + 772.8752168146106, + 792.0181614121004, + 811.4876033057847, + 831.2835424956635, + 851.4059789817363, + 871.8549127640036, + 892.6303438424649, + 913.7322722171203, + 935.1606978879704, + 956.9156208550145, + 978.9970411182532, + 1001.4049586776858 + ], + [ + 372.5691255994287, + 363.14355677992046, + 354.04448525660644, + 345.27191102948683, + 336.82583409856136, + 328.7062544638302, + 320.9131721252933, + 313.4465870829507, + 306.30649933680235, + 299.4929088868482, + 293.00581573308847, + 286.8452198755229, + 281.01112131415164, + 275.5035200489746, + 270.32241607999185, + 265.4678094072034, + 260.9397000306091, + 256.73808795020915, + 252.86297316600346, + 249.31435567799204, + 246.09223548617487, + 243.19661259055198, + 240.62748699112336, + 238.38485868788902, + 236.4687276808489, + 234.87909397000308, + 233.61595755535154, + 232.6793184368942, + 232.06917661463117, + 231.7855320885624, + 231.82838485868788, + 232.1977349250077, + 232.8935822875217, + 233.91592694623, + 235.26476890113256, + 236.94010815222939, + 238.9419446995205, + 241.27027854300584, + 243.92510968268547, + 246.90643811855932, + 250.2142638506275, + 253.84858687888988, + 257.8094072033466, + 262.0967248239976, + 266.7105397408428, + 271.65085195388224, + 276.917661463116, + 282.51096826854405, + 288.4307723701663, + 294.67707376798296, + 301.2498724619937, + 308.1491684521988, + 315.37496173859813, + 322.92725232119176, + 330.8060401999795, + 339.0113253749617, + 347.5431078461382, + 356.4013876135088, + 365.5861646770737, + 375.09743903683295, + 384.9352106927865, + 395.09947964493426, + 405.5902458932762, + 416.40750943781245, + 427.551270278543, + 439.02152841546786, + 450.81828384858693, + 462.9415365779002, + 475.3912866034078, + 488.1675339251097, + 501.2702785430059, + 514.6995204570961, + 528.4552596673809, + 542.5374961738598, + 556.9462299765331, + 571.6814610754004, + 586.7431894704622, + 602.1314151617182, + 617.8461381491685, + 633.8873584328129, + 650.2550760126519, + 666.9492908886848, + 683.9700030609121, + 701.3172125293338, + 718.9909192939496, + 736.9911233547598, + 755.317824711764, + 773.9710233649625, + 792.9507193143558, + 812.2569125599427, + 831.8896031017241, + 851.8487909397, + 872.1344760738699, + 892.7466585042343, + 913.6853382307929, + 934.9505152535454, + 956.5421895724928, + 978.460361187634, + 1000.7050300989697, + 1023.2761963064994 + ], + [ + 378.60524436282003, + 369.342924191409, + 360.4071013161922, + 351.7977757371697, + 343.5149474543414, + 335.55861646770734, + 327.92878277726754, + 320.6254463830221, + 313.64860728497086, + 306.99826548311387, + 300.6744209774512, + 294.67707376798273, + 289.0062238547087, + 283.66187123762876, + 278.6440159167431, + 273.9526578920518, + 269.5877971635547, + 265.5494337312519, + 261.8375675951433, + 258.452198755229, + 255.393327211509, + 252.66095296398322, + 250.2550760126517, + 248.17569635751448, + 246.4228139985715, + 244.99642893582282, + 243.89654116926837, + 243.1231506989082, + 242.6762575247423, + 242.5558616467707, + 242.7619630649933, + 243.2945617794102, + 244.15365779002133, + 245.33925109682679, + 246.8513416998265, + 248.68992959902045, + 250.8550147944087, + 253.34659728599115, + 256.1646770737679, + 259.3092541577389, + 262.7803285379042, + 266.57790021426376, + 270.70196918681756, + 275.1525354555657, + 279.929599020508, + 285.0331598816446, + 290.4632180389756, + 296.2197734925007, + 302.3028262422201, + 308.71237628813384, + 315.44842363024173, + 322.51096826854393, + 329.9000102030405, + 337.6155494337312, + 345.65758596061613, + 354.02611978369544, + 362.72115090296904, + 371.74267931843684, + 381.09070503009883, + 390.7652280379552, + 400.7662483420058, + 411.0937659422508, + 421.74778083868983, + 432.72829303132323, + 444.0353025201509, + 455.6688093051729, + 467.6288133863891, + 479.9153147637995, + 492.5283134374042, + 505.46780940720316, + 518.7338026731966, + 532.326293235384, + 546.2452810937658, + 560.4907662483419, + 575.0627486991121, + 589.9612284460767, + 605.1862054892357, + 620.7376798285889, + 636.6156514641362, + 652.8201203958778, + 669.3510866238139, + 686.2085501479439, + 703.3925109682683, + 720.9029690847872, + 738.7399244975, + 756.9033772064075, + 775.393327211509, + 794.2097745128046, + 813.3527191102949, + 832.8221610039791, + 852.6181001938575, + 872.7405366799305, + 893.1894704621975, + 913.9649015406591, + 935.0668299153145, + 956.4952555861644, + 978.2501785532088, + 1000.3315988164471, + 1022.73951637588, + 1045.4739312315069 + ], + [ + 384.96786042240586, + 375.86878889909195, + 367.09621467197223, + 358.65013774104693, + 350.53055810631577, + 342.73747576777885, + 335.2708907254362, + 328.13080297928786, + 321.3172125293338, + 314.83011937557393, + 308.6695235180084, + 302.8354249566371, + 297.32782369146014, + 292.14671972247737, + 287.2921130496889, + 282.7640036730947, + 278.56239159269467, + 274.68727680848895, + 271.1386593204776, + 267.91653912866036, + 265.0209162330375, + 262.4517906336089, + 260.2091623303745, + 258.29303132333445, + 256.7033976124886, + 255.440261197837, + 254.50362207937974, + 253.89348025711666, + 253.60983573104792, + 253.6526885011734, + 254.02203856749315, + 254.71788593000724, + 255.7402305887155, + 257.0890725436181, + 258.7644117947149, + 260.766248342006, + 263.09458218549133, + 265.74941332517096, + 268.73074176104484, + 272.038567493113, + 275.6728905213754, + 279.6337108458321, + 283.9210284664831, + 288.5348433833283, + 293.4751555963678, + 298.74196510560154, + 304.3352719110296, + 310.25507601265184, + 316.50137741046836, + 323.0741761044792, + 329.97347209468427, + 337.19926538108365, + 344.7515559636772, + 352.6303438424651, + 360.8356290174473, + 369.3674114886237, + 378.22569125599443, + 387.41046831955936, + 396.92174267931847, + 406.75951433527194, + 416.92378328741967, + 427.4145495357618, + 438.231813080298, + 449.37557392102855, + 460.8458320579533, + 472.64258749107245, + 484.7658402203858, + 497.21559024589334, + 509.9918375675952, + 523.0945821854913, + 536.5238240995818, + 550.2795633098664, + 564.3617998163454, + 578.7705336190185, + 593.505764717886, + 608.5674931129475, + 623.9557188042036, + 639.6704417916541, + 655.7116620752986, + 672.0793796551372, + 688.7735945311705, + 705.7943067033978, + 723.1415161718193, + 740.8152229364352, + 758.8154269972453, + 777.1421283542497, + 795.7953270074483, + 814.7750229568412, + 834.0812162024284, + 853.7139067442099, + 873.6730945821854, + 893.9587797163556, + 914.5709621467197, + 935.5096418732784, + 956.774818896031, + 978.3664932149779, + 1000.2846648301195, + 1022.5293337414549, + 1045.100499948985, + 1067.998163452709 + ], + [ + 391.6569737781859, + 382.7211509029691, + 374.11182532394645, + 365.82899704111827, + 357.8726660544842, + 350.2428323640445, + 342.93949596979894, + 335.9626568717478, + 329.3123150698908, + 322.9884705642281, + 316.9911233547597, + 311.3202734414855, + 305.97592082440565, + 300.95806550352, + 296.26670747882866, + 291.90184675033163, + 287.8634833180288, + 284.15161718192024, + 280.7662483420059, + 277.70737679828585, + 274.9750025507601, + 272.5691255994286, + 270.48974594429137, + 268.73686358534843, + 267.3104785225997, + 266.2105907560453, + 265.43720028568515, + 264.9903071115192, + 264.8699112335476, + 265.0760126517702, + 265.6086113661871, + 266.4677073767983, + 267.6533006836037, + 269.1653912866034, + 271.00397918579733, + 273.16906438118554, + 275.6606468727681, + 278.4787266605448, + 281.62330374451585, + 285.09437812468116, + 288.89194980104077, + 293.0160187735945, + 297.46658504234256, + 302.2436486072849, + 307.34720946842157, + 312.7772676257525, + 318.5338230792776, + 324.616875828997, + 331.0264258749107, + 337.7624732170186, + 344.8250178553209, + 352.2140597898174, + 359.9295990205081, + 367.9716355473931, + 376.34016937047227, + 385.03520048974593, + 394.0567289052138, + 403.40475461687583, + 413.07927762473213, + 423.08029792878267, + 433.40781552902763, + 444.06183042546684, + 455.0423426181001, + 466.34935210692777, + 477.98285889194966, + 489.94286297316603, + 502.22936435057653, + 514.8423630241812, + 527.7818589939802, + 541.0478522599734, + 554.6403428221611, + 568.5593306805428, + 582.8048158351188, + 597.3767982858891, + 612.2752780328537, + 627.5002550760124, + 643.0517294153657, + 658.9297010509131, + 675.1341699826548, + 691.6651362105906, + 708.522599734721, + 725.7065605550454, + 743.217018671564, + 761.0539740842771, + 779.2174267931842, + 797.707376798286, + 816.5238240995817, + 835.6667686970716, + 855.1362105907561, + 874.9321497806345, + 895.0545862667072, + 915.5035200489747, + 936.2789511274358, + 957.3808795020916, + 978.8093051729414, + 1000.5642281399855, + 1022.6456484032242, + 1045.0535659626566, + 1067.787980818284, + 1090.848892970105 + ], + [ + 398.67258443016016, + 389.90001020304044, + 381.453933272115, + 373.3343536373839, + 365.541271298847, + 358.0746862565043, + 350.934598510356, + 344.121008060402, + 337.63391490664213, + 331.47331904907657, + 325.6392204877053, + 320.13161922252823, + 314.9505152535455, + 310.09590858075694, + 305.5677992041627, + 301.36618712376276, + 297.4910723395571, + 293.9424548515457, + 290.7203346597285, + 287.82471176410564, + 285.255586164677, + 283.01295786144266, + 281.09682685440254, + 279.5071931435567, + 278.2440567289051, + 277.3074176104478, + 276.69727578818475, + 276.41363126211604, + 276.4564840322416, + 276.8258340985613, + 277.52168146107533, + 278.5440261197836, + 279.89286807468613, + 281.568207325783, + 283.57004387307404, + 285.8983777165594, + 288.55320885623905, + 291.534537292113, + 294.84236302418105, + 298.47668605244354, + 302.4375063769003, + 306.7248239975512, + 311.33863891439637, + 316.2789511274358, + 321.5457606366696, + 327.1390674420976, + 333.0588715437199, + 339.3051729415365, + 345.8779716355473, + 352.77726762575236, + 360.0030609121517, + 367.55535149474537, + 375.4341393735332, + 383.6394245485153, + 392.1712070196916, + 401.0294867870624, + 410.2142638506274, + 419.7255382103866, + 429.56330986634, + 439.72757881848776, + 450.2183450668298, + 461.03560861136606, + 472.1793694520966, + 483.64962758902135, + 495.4463830221404, + 507.56963575145375, + 520.0193857769615, + 532.7956330986633, + 545.8983777165594, + 559.3276196306498, + 573.0833588409346, + 587.1655953474134, + 601.5743291500866, + 616.309560248954, + 631.3712886440157, + 646.7595143352717, + 662.4742373227219, + 678.5154576063666, + 694.8831751862053, + 711.5773900622382, + 728.5981022344657, + 745.9453117028872, + 763.619018467503, + 781.6192225283133, + 799.9459238853176, + 818.5991225385164, + 837.5788184879092, + 856.8850117334963, + 876.5177022752779, + 896.4768901132536, + 916.7625752474233, + 937.3747576777878, + 958.3134374043462, + 979.5786144270992, + 1001.1702887460461, + 1023.0884603611872, + 1045.3331292725231, + 1067.9042954800527, + 1090.8019589837772, + 1114.0261197836953 + ], + [ + 406.0146923783288, + 397.40536679930625, + 389.1225385164779, + 381.1662075298439, + 373.5363738394041, + 366.2330374451587, + 359.25619834710744, + 352.6058565452505, + 346.2820120395878, + 340.28466483011937, + 334.6138149168453, + 329.26946229976534, + 324.25160697887975, + 319.5602489541884, + 315.19538822569126, + 311.1570247933885, + 307.4451586572799, + 304.0597898173656, + 301.00091827364554, + 298.26854402611986, + 295.86266707478836, + 293.7832874196511, + 292.0304050607081, + 290.6040199979594, + 289.504132231405, + 288.73074176104484, + 288.2838485868789, + 288.16345270890724, + 288.3695541271299, + 288.90215284154687, + 289.76124885215796, + 290.9468421589634, + 292.4589327619631, + 294.2975206611571, + 296.4626058565453, + 298.9541883481278, + 301.77226813590454, + 304.9168452198755, + 308.38791960004085, + 312.1854912764004, + 316.3095602489543, + 320.76012651770236, + 325.53719008264466, + 330.6407509437812, + 336.07080910111216, + 341.82736455463726, + 347.91041730435677, + 354.3199673502704, + 361.0560146923783, + 368.1185593306806, + 375.5076012651771, + 383.2231404958679, + 391.2651770227528, + 399.63371084583207, + 408.32874196510556, + 417.3502703805734, + 426.6982960922355, + 436.3728191000919, + 446.3738394041425, + 456.7013570043873, + 467.3553719008265, + 478.3358840934599, + 489.6428935822875, + 501.27640036730946, + 513.2364044485257, + 525.5229058259362, + 538.1359044995411, + 551.0754004693399, + 564.3413937353332, + 577.9338842975206, + 591.8528721559026, + 606.0983573104785, + 620.6703397612489, + 635.5688195082134, + 650.7937965513723, + 666.3452708907254, + 682.2232425262728, + 698.4277114580145, + 714.9586776859504, + 731.8161412100804, + 749.0001020304052, + 766.5105601469237, + 784.3475155596366, + 802.510968268544, + 821.0009182736455, + 839.8173655749415, + 858.9603101724315, + 878.4297520661157, + 898.2256912559945, + 918.3481277420672, + 938.797061524334, + 959.5724926027958, + 980.6744209774512, + 1002.1028466483014, + 1023.8577696153454, + 1045.9391898785836, + 1068.3471074380168, + 1091.0815222936435, + 1114.1424344454651, + 1137.5298438934803 + ], + [ + 413.6832976226915, + 405.2372206917661, + 397.117641057035, + 389.3245587184981, + 381.8579736761555, + 374.71788593000707, + 367.904295480053, + 361.4172023262932, + 355.2566064687276, + 349.42250790735636, + 343.9149066421793, + 338.7338026731966, + 333.8791960004081, + 329.3510866238139, + 325.14947454341393, + 321.2743597592082, + 317.7257422711968, + 314.5036220793796, + 311.6079991837567, + 309.03887358432803, + 306.7962452810937, + 304.88011427405365, + 303.29048056320784, + 302.02734414855627, + 301.0907050300989, + 300.48056320783587, + 300.1969186817671, + 300.2397714518926, + 300.60912151821236, + 301.3049688807264, + 302.32731353943467, + 303.6761554943373, + 305.35149474543414, + 307.3533312927252, + 309.6816651362106, + 312.3364962758902, + 315.31782471176405, + 318.62565044383217, + 322.25997347209454, + 326.22079379655133, + 330.50811141720226, + 335.12192633404754, + 340.06223854708696, + 345.3290480563207, + 350.9223548617488, + 356.842158963371, + 363.08846036118763, + 369.66125905519834, + 376.5605550454034, + 383.7863483318028, + 391.33863891439637, + 399.21742679318436, + 407.4227119681665, + 415.9544944393429, + 424.81277420671347, + 433.9975512702785, + 443.50882563003773, + 453.34659728599115, + 463.5108662381389, + 474.0016324864808, + 484.8188960310172, + 495.96265687174775, + 507.4329150086725, + 519.2296704417915, + 531.3529231711049, + 543.8026731966124, + 556.5789205183145, + 569.6816651362105, + 583.110907050301, + 596.8666462605855, + 610.9488827670646, + 625.3576165697376, + 640.0928476686051, + 655.1545760636669, + 670.542801754923, + 686.257524742373, + 702.2987450260176, + 718.6664626058565, + 735.3606774818895, + 752.3813896541168, + 769.7285991225385, + 787.4023058871543, + 805.4025099479643, + 823.7292113049688, + 842.3824099581673, + 861.3621059075605, + 880.6682991531476, + 900.300989694929, + 920.2601775329048, + 940.5458626670747, + 961.1580450974387, + 982.0967248239976, + 1003.3619018467501, + 1024.9535761656973, + 1046.8717477808384, + 1069.116416692174, + 1091.6875828997042, + 1114.585246403428, + 1137.8094072033468, + 1161.3600652994592 + ], + [ + 421.6784001632487, + 413.39557188042033, + 405.43924089378635, + 397.80940720334667, + 390.5060708091012, + 383.52923171104993, + 376.878889909193, + 370.55504540353036, + 364.5576981940619, + 358.8868482807877, + 353.5424956637078, + 348.5246403428222, + 343.83328231813084, + 339.4684215896338, + 335.43005815733096, + 331.7181920212224, + 328.33282318130813, + 325.2739516375881, + 322.5415773900623, + 320.1357004387308, + 318.0563207835936, + 316.3034384246506, + 314.877053361902, + 313.7771655953475, + 313.0037751249873, + 312.55688195082143, + 312.4364860728498, + 312.64258749107245, + 313.1751862054893, + 314.0342822161005, + 315.2198755229059, + 316.7319661259056, + 318.57055402509957, + 320.7356392204878, + 323.2272217120703, + 326.0453014998471, + 329.18987858381814, + 332.66095296398333, + 336.45852464034283, + 340.58259361289674, + 345.03315988164485, + 349.81022344658714, + 354.91378430772386, + 360.34384246505465, + 366.10039791857986, + 372.1834506682992, + 378.59300071421296, + 385.32904805632086, + 392.3915926946231, + 399.78063462911956, + 407.4961738598103, + 415.53821038669537, + 423.9067442097746, + 432.60177532904817, + 441.6233037445159, + 450.971329456178, + 460.6458524640344, + 470.6468727680851, + 480.9743903683298, + 491.6284052647689, + 502.6089174574024, + 513.9159269462301, + 525.549433731252, + 537.5094378124681, + 549.7959391898786, + 562.4089378634834, + 575.3484338332825, + 588.6144270992756, + 602.2069176614632, + 616.1259055198451, + 630.3713906744211, + 644.9433731251914, + 659.8418528721561, + 675.0668299153149, + 690.618304254668, + 706.4962758902153, + 722.7007448219571, + 739.2317110498931, + 756.0891745740232, + 773.2731353943476, + 790.7835935108665, + 808.6205489235793, + 826.7840016324865, + 845.2739516375881, + 864.0903989388838, + 883.233343536374, + 902.7027854300583, + 922.4987246199369, + 942.6211611060099, + 963.0700948882768, + 983.845525966738, + 1004.947454341394, + 1026.3758800122437, + 1048.130802979288, + 1070.2122232425263, + 1092.620140801959, + 1115.3545556575862, + 1138.4154678094073, + 1161.8028772574232, + 1185.5167840016327 + ], + [ + 430, + 421.88042036526883, + 414.0873380267319, + 406.62075298438936, + 399.480665238241, + 392.66707478828687, + 386.1799816345271, + 380.01938577696154, + 374.1852872155903, + 368.67768595041326, + 363.49658198143044, + 358.641975308642, + 354.11386593204776, + 349.9122538516478, + 346.03713906744207, + 342.48852157943065, + 339.26640138761354, + 336.3707784919907, + 333.801652892562, + 331.5590245893276, + 329.6428935822875, + 328.0532598714417, + 326.7901234567901, + 325.85348433833286, + 325.24334251606973, + 324.959697990001, + 325.00255076012655, + 325.3719008264463, + 326.06774818896037, + 327.0900928476686, + 328.4389348025712, + 330.114274053668, + 332.1161106009591, + 334.44444444444446, + 337.09927558412403, + 340.08060401999796, + 343.3884297520662, + 347.0227527803285, + 350.98357310478514, + 355.2708907254362, + 359.88470564228146, + 364.82501785532094, + 370.0918273645546, + 375.6851341699826, + 381.6049382716049, + 387.8512396694215, + 394.4240383634324, + 401.3233343536374, + 408.54912764003666, + 416.10141822263034, + 423.9802061014182, + 432.1854912764004, + 440.71727374757677, + 449.5755535149474, + 458.76033057851237, + 468.27160493827165, + 478.1093765942252, + 488.27364554637285, + 498.76441179471476, + 509.58167533925103, + 520.7254361799817, + 532.1956943169065, + 543.9924497500255, + 556.1157024793388, + 568.5654525048463, + 581.3416998265483, + 594.4444444444445, + 607.8736863585348, + 621.6294255688194, + 635.7116620752984, + 650.1203958779718, + 664.8556269768391, + 679.9173553719008, + 695.3055810631569, + 711.0203040506071, + 727.0615243342515, + 743.4292419140903, + 760.1234567901234, + 777.1441689623508, + 794.4913784307722, + 812.1650851953882, + 830.1652892561983, + 848.4919906132026, + 867.1451892664014, + 886.1248852157942, + 905.4310784613816, + 925.0637690031629, + 945.0229568411385, + 965.3086419753087, + 985.9208244056729, + 1006.8595041322313, + 1028.1246811549843, + 1049.7163554739311, + 1071.6345270890727, + 1093.879196000408, + 1116.4503622079378, + 1139.348025711662, + 1162.5721865115804, + 1186.1228446076932, + 1210 + ] + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + }, + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + }, + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "autotypenumbers": "strict", + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Surface(x=mx, y=my, z=mz)])\n", + "py.iplot(fig, show_link=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "The constraint may seem like too strong a limit but there are many cases that\n", + "generate matrices A that respect these constraints. For example numerical simulation problems\n", + "like that of the plane that we saw generates such a matrix, which moreover will be very sparse with about ten\n", + "of non-zero value per row even for a 1 billion by 1 billion matrix.\n", + "\n", + "It is for this type of matrix that an iterative method like the gradient offers an incredible performance gain\n", + "since we have the solution in almost $O(n^2)$ instead of $O(n^3)$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/en/ma53 Notations du produit scalaire.ipynb b/PVCM/cama/en/ma53 Notations du produit scalaire.ipynb new file mode 100644 index 0000000..64c897d --- /dev/null +++ b/PVCM/cama/en/ma53 Notations du produit scalaire.ipynb @@ -0,0 +1,99 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5, + "cells": [ + { + "cell_type": "markdown", + "id": "68749ef1", + "metadata": { + "lang": "en" + }, + "source": [ + "# Writings of the scalar product\n", + "\n", + "Here are 3 different ways to write the dot product. Some are clearer than others but all 3 are found in the literature.\n", + "\n", + "### ${\\bf v} \\,.\\, {\\bf w}$\n", + "\n", + "In the worksheet that follows and in the lesson thereafter, there are many dot products that use the point. It is important to note the order in which operators are solved in a formula like\n", + "\n", + "$$A \\, {\\bf v} \\, . \\, {\\bf w}$$\n", + "\n", + "* If we do $A ({\\bf v} \\, . \\, {\\bf w})$ then the result is a matrix.\n", + "* If we do $(A {\\bf v} )\\, . \\, {\\bf w}$ then the result is a real.\n", + "\n", + "In the majority of cases and in particular in this course, the 2nd reading is the correct one.\n", + "\n", + "#### Hazard\n", + "\n", + "This writing is dangerous.\n", + "Imagine multiplying our equation by $A^{-1}$. So we want to write\n", + "\n", + "$$\n", + "A^{-1} \\, A \\, {\\bf v} \\, . \\, {\\bf w} = {\\bf v} \\, . \\, {\\bf w}\n", + "$$\n", + "\n", + "but it is false (in the second case) because we forget what the point of the scalar product relates to.\n", + "\n", + "### ${\\bf v}^T \\, {\\bf w}$\n", + "\n", + "\n", + "The matrix notation of the previous example is written\n", + "\n", + "$${\\bf v}^T A \\, {\\bf w}$$\n", + "\n", + "In this case, you can do the calculations in any order you like. If we start with the first 2 we will have a horizontal vector, if we start with the last 2 we will have a vertical vector. This notation is less risky when making\n", + "more complex calculations.\n", + "\n", + "\n", + "With matrix notation this risk does not exist since multiplying by $A^{-1}$ gives\n", + "\n", + "$$\n", + "A^{-1} \\, {\\bf v}^T A \\, {\\bf w}\n", + "$$\n", + "\n", + "and we can clearly see that the A's are not simplified.\n", + "\n", + "### $<{\\bf v}, {\\bf w}>$\n", + "\n", + "\n", + "Another way to write the matrix product to avoid confusion is to use the signs\n", + "< and > which gives **** for the dot product between **a** and **b**. With this notation the error\n", + "reading of the scalar product with the point disappears:\n", + "\n", + "$$\n", + "A^{-1} \\, < A \\, {\\bf v} \\,, \\, {\\bf w}> \n", + "$$\n", + "\n", + "Sometimes parentheses are used instead of lower and upper but I find that less readable." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "db3e803c", + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" "b/PVCM/cama/en/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" new file mode 100644 index 0000000..f953767 --- /dev/null +++ "b/PVCM/cama/en/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" @@ -0,0 +1,182 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## The gradient method to solve A x = b\n", + "\n", + "The goal of this lab is to let you move forward on your own. Look at previous course and program the gradient method\n", + "to solve the $A {\\bf x} = {\\bf b}$ matrix system with A symmetric and diagonally dominant\n", + "($a_{ii} > \\sum_{k \\ne i} |a_{ik}|$).\n", + "\n", + "* Start in 2D with a 2x2 matrix, check that the result is good and plot the convergence curve\n", + "* Switch to nxn (we will show that it works with a 9x9 matrix)\n", + "\n", + "It may be interesting to normalize the matrix A to prevent the calculations from exploding." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "def solve_with_gradiant(A, b):\n", + " mu = 0.01\n" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[49, 13],\n", + " [13, 13]])" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "A = np.random.randint(10, size=(2,2))\n", + "A = A + A.T\n", + "A += np.diag(A.sum(axis=1))\n", + "A" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([62, 26])" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b = A.sum(axis=1)\n", + "b" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "solve_with_gradiant(A,b)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Introduce inertia\n", + "\n", + "Introduce inertia into the gradient method. What do we notice?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Optimal value of µ\n", + "\n", + "Note that two successive slope directions are orthogonal if the next point is the minimum in\n", + "given direction ($\\nabla J ({\\bf x}^k$)).\n", + "\n", + "$$\\nabla J ({\\bf x}^{k+1})^T \\; \\nabla J ({\\bf x}^k) = 0$$\n", + "\n", + "#### Demonstration\n", + "\n", + "\n", + "\n", + "
\n", + "We want to adjust µ to arrive at the minimum of J when we advance in the direction $- \\nabla J({\\bf x}^{k})$.\n", + "This means that the partial derivative of $J({\\bf x}^{k+1})$ with respect to µ must be\n", + "equal to 0 or by making µ appear in the equation:\n", + "\n", + "$$\n", + "\\frac{\\partial J ({\\bf x}^k - µ \\; \\nabla J ({\\bf x}^k))}{\\partial µ} = 0\n", + "$$\n", + "\n", + "By expanding we have\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{\\partial J ({\\bf x}^{k+1})}{\\partial {\\bf x}^{k+1}} \\; \n", + "\\frac{\\partial {\\bf x}^{k+1}}{\\partial µ} & = 0 \\\\\n", + "J'({\\bf x}^{k+1}) \\, . \\, (- \\nabla J ({\\bf x}^k)) & = 0 \\\\\n", + "(A\\, {\\bf x}^{k+1} - b) \\, . \\, \\nabla J ({\\bf x}^k) & = 0 \\quad \\textrm{since A is symetric}\\\\\n", + "\\nabla J ({\\bf x}^{k+1}) \\, . \\, \\nabla J ({\\bf x}^k) & = 0 \\quad \\textrm{QED}\n", + "\\end{align}\n", + "$$\n", + "\n", + "\n", + "\n", + "\n", + "
\n", + "\n", + "Using this property, evaluate the optimal value of µ to reach the minimum in the direction of\n", + "$\\nabla J ({\\bf x}^k)$.\n", + "\n", + "Write the gradient method with the calculation of the optimal µ at each iteration to solve $A {\\bf x} = {\\bf b}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma60 M\303\251thode du gradient conjugu\303\251.ipynb" "b/PVCM/cama/en/ma60 M\303\251thode du gradient conjugu\303\251.ipynb" new file mode 100644 index 0000000..7b0068b --- /dev/null +++ "b/PVCM/cama/en/ma60 M\303\251thode du gradient conjugu\303\251.ipynb" @@ -0,0 +1,405 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "This lesson has 3 virtues:\n", + "\n", + "* manipulate bases of subspaces\n", + "* mix partial derivatives and vectors\n", + "* find an algorithm more efficient than the gradient method to solve $A \\, {\\bf x} = {\\bf b}$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Conjugate gradient method\n", + "\n", + "We have seen that it is possible to compute the optimal µ of the gradiant method to\n", + "go directly to the minimum of the $J$ functional in along the line\n", + "${\\bf x}^k \\; + µ \\, \\nabla J({\\bf x}^k)$ with µ varying from $- \\infty$\n", + "at $+ \\infty$ (see ma33).\n", + "\n", + "We have also seen that if we have the optimal µ, then the next steepest slope,\n", + "$\\nabla J ({\\bf x}^{k+1})$, will be orthogonal to the slope which defines the line on which we seek µ. So we have\n", + "\n", + "$$\\nabla J ({\\bf x}^{k+1})^T \\, . \\, \\nabla J ({\\bf x}^k) = 0$$\n", + "\n", + "This is good because it means that the next minimum, ${\\bf x}^{k+2}$, will be the minimum of the space generated by $\\nabla J ({\\bf x}^{k+1})$ and $\\nabla J ({\\bf x}^k)$\n", + "(which is better than just being the minimum along a line).\n", + "\n", + "Unfortunately nothing tells me that ${\\bf x}^{k+3}$ will not be calculated along our\n", + "first direction, $\\nabla J({\\bf x}^k)$. We have seen in the case\n", + "of the gradient without searching for the optimal µ that we can oscillate between 2 values. That\n", + "is not possible with the optimal µ but we can go around in circles on a few values.\n", + "\n", + "Even if we don't go around in circles and we converge, is it likely that we are looking for\n", + "again a minimum in a part of the $ℝ^n$ space that we have already explored.\n", + "\n", + "An optimal search for the minimum of a convex function in a $ℝ^n$ space does not\n", + "should not take more than $n$ iteration if we are still able to calculate\n", + "the optimal µ in the chosen direction. To be convinced of this, it suffices to choose\n", + "as directions the vectors of the basis of our space $ℝ^n$. Once we\n", + "has found the minimum in all directions of the base, we have the global minimum.\n", + "There is no longer any possible direction of search which would not be the linear combination of the vectors\n", + "already used." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "#### 2D case\n", + "\n", + "
\n", + " \n", + "If we look for the point ${\\bf x} = (x_1, x_2)$ which minimizes $J({\\bf x})$ (convex)\n", + "and that we know how to calculate the optimal µ of our gradient method,\n", + "then we find the global minimum in 2 iterations at most.\n", + "\n", + "But id we\n", + "take a too large µ which makes us pass above the minimum\n", + "global, then at the next iteration the largest slope will be exactly\n", + "the opposite of the one we just used and we will oscillate.\n", + "\n", + "On the drawing we can see that we find the global minimum in 2 iterations\n", + "but we say to ourselves that it is a stroke of luck and besides is it really\n", + "in 2 iterations since it is written ${\\bf x}^k$? That's the limit\n", + "of a drawing that wants to explain what is happening in $ℝ^n$ to humans\n", + "accustomed to $ℝ^3$ (see this video on the 4th dimension outside\n", + "classes).\n", + "\n", + "\n", + "\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## Generate a base of $ℝ^n$\n", + "\n", + "If we want to find our global minimum in $n$ maximum iteration, we must\n", + "our directions is not redundant and therefore only the first $n$ directions\n", + "generate $ℝ^n$ or form a basis of $ℝ^n$.\n", + "\n", + "The new direction ${\\bf d}^k$ must therefore be orthogonal to all directions\n", + "preceding ones or that it makes it possible to find a base which generates a\n", + "space of dimension $k+1$ (we start with ${\\bf d}^0$).\n", + "\n", + "Is it possible ?\n", + "\n", + "### The $A {\\bf x} = {\\bf b}$ case\n", + "\n", + "In this case the functional to be minimized is\n", + "\n", + "$$\n", + "J({\\bf x}) = \\frac{1}{2} \\, {\\bf x}^T \\, A \\, {\\bf x} - {\\bf b}\\, . {\\bf x}\n", + "$$\n", + "\n", + "and its gradient is $\\nabla J({\\bf x}) = A \\; {\\bf x} - {\\bf b}$ if A is\n", + "symmetrical.\n", + "\n", + "\n", + "We know that if we calculate ${\\bf x}^k$ as before we only have orthogonality\n", + "from two successive directions. It happens when\n", + "µ is chosen to minimize $J$ along the direction line\n", + " $\\nabla J({\\bf x}^k)$.\n", + " \n", + "What happens if ${\\bf x}^{k+1}$ **minimizes $J$ in space\n", + "${\\bf G_k}$ generated by\n", + "all previous directions**?\n", + "\n", + "$$\n", + "J({\\bf x}^{k+1}) = \\min_{\\bf v \\in G_k} J({\\bf x}^k + {\\bf v})\n", + "$$\n", + "with ${\\bf G_k} = span\\{{\\bf d}^0, {\\bf d}^1,\\dots, {\\bf d}^k\\} \n", + " = \\left\\{ {\\bf v} = \\sum_{i=0}^{k} \\alpha_i \\, {\\bf d}^i \\quad \\forall \\alpha_i \\in ℝ \\right\\}$.\n", + "\n", + "Then all the partial derivatives with respect to the vectors of ${\\bf G_k}$\n", + "are zero (just like $\\partial J / \\partial x$ and $\\partial J / \\partial y$\n", + "are zero at the minimum of J in the drawing above). Vector\n", + "it is written like this:\n", + "\n", + "$$\n", + "\\nabla J({\\bf x}^{k+1}) \\, . \\, {\\bf w} = 0 \\quad \\forall {\\bf w} \\in {\\bf G_k}\n", + "$$\n", + "\n", + "which is easily verified if ${\\bf w}$ is one of the base vectors:\n", + "\n", + "$$\n", + "\\nabla J({\\bf x}^{k+1}) \\, . \\, {\\bf e}_i = \n", + "\\begin{bmatrix}\n", + "\\partial J / \\partial x_{1} \\\\\n", + "\\partial J / \\partial x_{2} \\\\\n", + "\\vdots \\\\\n", + "\\partial J / \\partial x_{i} \\\\\n", + "\\vdots \\\\\n", + "\\partial J / \\partial x_{n} \\\\\n", + "\\end{bmatrix}\n", + "\\, . \\,\n", + "\\begin{bmatrix}\n", + "0 \\\\\n", + "0 \\\\\n", + "\\vdots \\\\\n", + "1 \\\\\n", + "\\vdots \\\\\n", + "0 \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\frac{\\partial J}{\\partial x_i}({\\bf x}^{k+1}) \n", + "$$\n", + "\n", + "Note that saying the partial derivative of $J$ in a direction ${\\bf w}$\n", + "of ${\\bf G_k}$ is null,\n", + "is equivalent to saying that $\\nabla J({\\bf x}^{k+1})$ is orthogonal to ${\\bf w}$\n", + "(or null if $\\nabla J({\\bf x}^{k+1})$ the same dimension as ${\\bf G_k}$).\n", + "\n", + "#### Let's generate directions ${\\bf d}^i$\n", + "\n", + "So our iterative formula becomes:\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = {\\bf x}^k - µ^k\\, {\\bf d}^k\n", + "$$\n", + "\n", + "To calculate the ${\\bf d}^k$ we use the formula which tells us that the\n", + "partial derivatives of $J$ with respect to a vector ${\\bf w \\in G_k}$ are\n", + "null. And as the ${\\bf d}^i$ directions generate the ${\\bf G_k}$ space\n", + "it is enough that the partial derivatives of $J$ with respect to all ${\\bf d}^i$\n", + "are zero:\n", + "\n", + "$$\n", + "\\nabla J({\\bf x}^{k+1}) \\, . \\, {\\bf d}^i = 0 \\quad \\forall i \\le k \\qquad (1)\n", + "$$\n", + "\n", + "We perform the calculations\n", + "\n", + "$$\n", + "\\begin{align}\n", + "(A\\, {\\bf x}^{k+1} - b) \\, . \\, {\\bf d}^i &= 0 \\quad \\forall i \\le k \\\\\n", + "(A\\, ({\\bf x}^{k} - µ^k \\, {\\bf d}^k) - b) \\, . \\, {\\bf d}^i &= 0 \\quad \\forall i \\le k \\\\\n", + "(A\\, {\\bf x}^{k} - b) \\, . \\, {\\bf d}^i - µ^k \\, A \\, {\\bf d}^k \\, . \\, {\\bf d}^i &= 0 \\quad \\forall i \\le k \\\\\n", + "\\nabla J({\\bf x}^{k}) \\, . \\, {\\bf d}^i - µ^k \\, A \\, {\\bf d}^k \\, . \\, {\\bf d}^i &= 0 \\quad \\forall i \\le k \\\\\n", + "\\end{align}\n", + "$$\n", + "\n", + "If $i < k$ then the first term is zero which gives\n", + "\n", + "$$\n", + "A \\, {\\bf d}^k \\, . \\, {\\bf d}^i = 0 \\quad \\forall i < k \\qquad (2)\n", + "$$\n", + "\n", + "As A is symmetric, we also have $A \\, {\\bf d}^i \\, . \\, {\\bf d}^k = 0 \\quad \\forall i < k\\quad$ ($\\sum_{m=1}^N \\sum_{n=1}^N a_{m,n}\\, d^i_n\\, d^k_m = \\sum_{n=1}^N \\sum_{m=1}^N a_{n,m}\\, d^k_m\\, d^i_n$).\n", + "\n", + "So we have conditions to build the new direction ${\\bf d}^k$.\n", + "\n", + "We assume that the new direction is the gradient + a correction which is a linear combination of the previous directions:\n", + "$$\n", + "{\\bf d}^k = \\nabla J({\\bf x}^k) + \\sum_{j=0}^{k-1} β_j {\\bf d}^j\n", + "$$\n", + "then equation (2) becomes\n", + "$$\n", + "A \\, \\left( \\nabla J({\\bf x}^k) + \\sum_{j=0}^{k-1} β_j {\\bf d}^j \\right) . {\\bf d}^i = 0 \\quad \\forall i < k\n", + "$$\n", + "The sum will reveal $A\\, {\\bf d}^j {\\bf d}^i$ which are all null according to (2) and its symmetric version except $A\\, {\\bf d}^i {\\bf d}^i$. So\n", + "\n", + "$$\n", + "β_i = - \\frac{A\\, \\nabla J({\\bf x}^k) \\, . \\, {\\bf d}^i}{A\\, {\\bf d}^i \\, . \\, {\\bf d}^i} \n", + "$$\n", + "\n", + "and so\n", + "$$\n", + "{\\bf d}^k = \\nabla J({\\bf x}^k) \n", + " - \\sum_{i=0}^{k-1} \\frac{A\\, \\nabla J({\\bf x}^k) \\, . \\, {\\bf d}^i}\n", + " {A\\, {\\bf d}^i \\, . \\, {\\bf d}^i} \\; {\\bf d}^i\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Calculation of $μ^k$\n", + "\n", + "We have seen that $\\nabla J({\\bf x}^{k+1}) \\, . \\, {\\bf d}^i = 0$ gives\n", + "\n", + "$$\n", + "\\nabla J({\\bf x}^{k}) \\, . \\, {\\bf d}^i - µ^k \\, A \\, {\\bf d}^k \\, . \\, {\\bf d}^i = 0 \\quad \\forall i \\le k\n", + "$$\n", + "\n", + "so also for $i = k$ which allows to calculate $μ^k$:\n", + "\n", + "$$\n", + "µ^k = \\frac{\\nabla J({\\bf x}^{k}) \\, . \\, {\\bf d}^k}\n", + " {A \\, {\\bf d}^k \\, . \\, {\\bf d}^k}\n", + " = \\frac{(A \\, {\\bf x}^{k} - b) \\, . \\, {\\bf d}^k}\n", + " {A \\, {\\bf d}^k \\, . \\, {\\bf d}^k} \\\\\n", + "\\, \n", + "$$\n", + "\n", + "We therefore have the method to calculate ${\\bf d}^k$ and $µ^k$ which makes it possible to find\n", + "${\\bf x}^{k+1}$ from ${\\bf x}^k$.\n", + "\n", + "### Property\n", + "\n", + "$$\n", + "\\nabla J({\\bf x}^{k+1}) \\perp \\nabla J({\\bf x}^i) \\quad \\forall i \\le k\n", + "$$\n", + "\n", + "**Exercise** Prove this property by induction starting from (0), knowing that the first direction is\n", + "${\\bf d}^0 = \\nabla J({\\bf x}^0)$.\n", + "\n", + "This property shows that the set of gradients of $J$ at points\n", + "${\\bf x}^i$ form a basis of space $\\bf G_k$. So we are sure\n", + "that our algorithm converges in $n$ iterations at most." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## 2nd attempt\n", + "\n", + "The method found is good because it shows that we can optimize the gradient descent but the calculation\n", + "of ${\\bf d}^k$ is way too heavy. So we're going to start all over again to find another more efficient way.\n", + "\n", + "### Let's work in the base of $\\nabla J({\\bf x}^i)$\n", + "\n", + "We start from equation (0) which allows us to\n", + "show that the $\\nabla J({\\bf x}^i), i \\le k$ form a basis of the subspace $\\bf G_k$. Also any vector is expressed in this basis and therefore\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = {\\bf x}^k + μ^k \\, {\\bf d}^k \\quad \\textrm{avec} \\quad {\\bf d}^k = - \\nabla J({\\bf x}^k) + \\sum_{i=0}^{k-1} γ^i \\, \\nabla J({\\bf x}^i)\n", + "$$\n", + "\n", + "Note that these ${\\bf d}^i, i \\le k$ also form a basis of $\\bf G_k$.\n", + "\n", + "Equation (2) tells us that $A \\, {\\bf d}^k \\, . \\, {\\bf d}^i = 0 \\quad \\forall i < k$, therefore\n", + "\n", + "$$\n", + "\\begin{align}\n", + "< A \\, {\\bf d}^k, {\\bf x}^{j+1} - {\\bf x}^j > &= 0 \\quad \\forall j < k \\\\ \n", + "< {\\bf d}^k, A \\, ({\\bf x}^{j+1} - {\\bf x}^j) > &= 0 \\quad \\textrm{since A is symetrical} \\\\\n", + "< {\\bf d}^k, A \\, {\\bf x}^{j+1} - {\\bf b} - A {\\bf x}^j + {\\bf b} > &= 0 \\\\\n", + "< {\\bf d}^k, \\nabla J({\\bf x}^{j+1}) - \\nabla J({\\bf x}^j) > &= 0 \\\\\n", + "< - \\nabla J({\\bf x}^k) + \\sum_{i=0}^{k-1} γ^i \\, \\nabla J({\\bf x}^i) , \\nabla J({\\bf x}^{j+1}) - \\nabla J({\\bf x}^j) > &= 0 \\quad (3) \\\\\n", + "\\end{align}\n", + "$$\n", + "\n", + "If j = k-1 then\n", + "$$\n", + "\\begin{align}\n", + "< - \\nabla J({\\bf x}^k), \\nabla J({\\bf x}^k) > + \\, γ^{k-1} < \\nabla J({\\bf x}^{k-1}), -\\nabla J({\\bf x}^{k-1}) > &= 0 \\\\\n", + "γ^{k-1} = -\\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >}\n", + "\\end{align}\n", + "$$\n", + "\n", + "If j = k-2 then\n", + "$$\n", + "\\begin{align}\n", + "γ^{k-1} \\, < \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) > + \\, γ^{k-2} < \\nabla J({\\bf x}^{k-2}), -\\nabla J({\\bf x}^{k-2}) > &= 0 \\\\\n", + "γ^{k-2} = γ^{k-1} \\frac{< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >} \n", + " {< \\nabla J({\\bf x}^{k-2}), \\nabla J({\\bf x}^{k-2}) >}\n", + " = \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{k-2}), \\nabla J({\\bf x}^{k-2}) >}\n", + "\\end{align}\n", + "$$\n", + "and continuing the calculations, we have $\\forall j < k-1$\n", + "$$\n", + " γ^j = \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{j}), \\nabla J({\\bf x}^{j}) >}\n", + "$$\n", + "\n", + "The general formula of ${\\bf d}^k$ is therefore\n", + "$$\n", + "\\begin{align}\n", + "{\\bf d}^k &= -\\nabla J({\\bf x}^k) \n", + " - \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >} \\, \\nabla J({\\bf x}^{k-1})\n", + " + \\sum_{i=0}^{k-2} \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{i}), \\nabla J({\\bf x}^{i}) >} \\, \\nabla J({\\bf x}^i) \\\\\n", + " &= -\\nabla J({\\bf x}^k) + β \\left( -\\nabla J({\\bf x}^{k-1}) \n", + " + \\sum_{i=0}^{k-2} \\frac{< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >} \n", + " {< \\nabla J({\\bf x}^{i}), \\nabla J({\\bf x}^{i}) >} \\, \\nabla J({\\bf x}^i) \\right) \\\\\n", + " &= -\\nabla J({\\bf x}^k) + β \\, {\\bf d}^{k-1} \\quad \\textrm{with} \\quad β = \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >} \n", + "\\end{align}\n", + "$$\n", + "\n", + "We have therefore succeeded in expressing the new direction only as a function of the current gradient and the previous direction." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### New calculation of μ\n", + "\n", + "The previous calculation of μ remains valid since this calculation does not depend on the way of expressing ${\\bf d}^k$.\n", + "\n", + "$$\n", + "µ^k = -\\frac{\\nabla J({\\bf x}^{k}) \\, . \\, {\\bf d}^k}\n", + " {A \\, {\\bf d}^k \\, . \\, {\\bf d}^k}\n", + "\\, \n", + "$$\n", + "\n", + "With our choice of ${\\bf d}^k$ this gives\n", + "\n", + "$$\n", + "µ^k = -\\frac{<\\nabla J({\\bf x}^{k}), - \\nabla J({\\bf x}^{k}) + β \\, {\\bf d}^{k-1}>}\n", + " {}\n", + " = \\frac{<\\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k})>}\n", + " {}\n", + "$$\n", + "since ${\\bf d}^{k-1} \\perp \\nabla J({\\bf x}^{k})$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma61 Syst\303\250me matriciel non lin\303\251aire.ipynb" "b/PVCM/cama/en/ma61 Syst\303\250me matriciel non lin\303\251aire.ipynb" new file mode 100644 index 0000000..93e0001 --- /dev/null +++ "b/PVCM/cama/en/ma61 Syst\303\250me matriciel non lin\303\251aire.ipynb" @@ -0,0 +1,502 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Système matriciel non linéaire\n", + "\n", + "Si la matrice A dépend de ${\\bf x}$, ce qu'on écrit $A({\\bf x})$, alors le système\n", + "matriciel \n", + "\n", + "$$\n", + "A({\\bf x}) \\, {\\bf x} = {\\bf b}\n", + "$$\n", + "\n", + "n'est pas linéaire.\n", + "\n", + "#### Exemple\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "1 & x_1 \\\\\n", + "2x_1 & -x_2 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "b_{1} \\\\\n", + "b_{2} \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "donne le système suivant qui n'est clairement pas linéaire puisqu'on a des\n", + "carrés :\n", + "\n", + "$$\n", + "\\begin{align}\n", + "x_1 + x_1 \\, x_2 &= b_1 \\\\\n", + "2 \\, x_1^2 - x_2^2 &= b_2 \n", + "\\end{align}\n", + "$$\n", + "\n", + "Comment résoudre un tel système ? A-t-il une solution ?\n", + "\n", + "On voit bien qu'il y a toujours autant d'équations que d'inconnues donc il y a\n", + "de l'espoir. Par contre on sait que les équations du 2e degré ont plusieurs solutions donc il devrait en être de même dans certains cas." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### La méthode du point fixe\n", + "\n", + "La méthode du point fixe consiste à appliquer l'algorithme itératif suivant :\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = {\\bf g}({\\bf x}^k)\n", + "$$\n", + "\n", + "dans le but de résoudre l'équation ${\\bf g}({\\bf x}) = {\\bf x}$.\n", + "\n", + "Si vous ne connaissez pas cette méthode voici un exemple d'utilisation en 1D avec\n", + "la courbe $g$ dessinée pour bien comprendre." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "image/jpeg": "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\n", + "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import YouTubeVideo\n", + "YouTubeVideo('ufPZOgrdHK4')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On voit (si on a regardé la vidéo), on sait (sinon) que suivant le point de départ, la méthode converge ou diverge.\n", + "\n", + "\n", + "Regardons comment on peut résoudre notre système non linéaire avec la méthode du point fixe." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### La méthode du point fixe pour résoudre $A({\\bf x}) \\, {\\bf x} = {\\bf b}$\n", + "\n", + "La première chose est de définir la fonction $\\bf g$ telle que la solution de \n", + "${\\bf g}({\\bf x}) = {\\bf x}$ soit aussi la solution du système matriciel non linéaire.\n", + "Cela implique que ${\\bf g}$ est :\n", + "\n", + "$$\n", + "{\\bf g}({\\bf x}) = A^{-1}({\\bf x}) \\, {\\bf b}\n", + "$$\n", + "\n", + "Bien sûr on sait qu'inverser A est trop cher aussi on préfère écrire notre\n", + "algorithme itératif ${\\bf x^{k+1}} = {\\bf g}({\\bf x^k})$ sous forme de problème matriciel linéaire à résoudre :\n", + "\n", + "$$\n", + "A({\\bf x}^k) \\, {\\bf x}^{k+1} = {\\bf b}\n", + "$$\n", + "\n", + "Si on connait ${\\bf x}^k$ alors on peut évaluer $A({\\bf x}^k)$ et donc il\n", + "s'agit d'une matrice de réels. On voit qu'alors le système est bien linéaire\n", + "et qu'il permet de trouver ${\\bf x}^{k+1}$.\n", + "\n", + "Cet algorithme itératif peut donc marcher mais on sent bien que cela va\n", + "dépendre du type de la matrice A (on a l'habitude) et de la valeur initiale\n", + "${\\bf x}^0$ comme souligné dans la vidéo. De plus on voit qu'il va être\n", + "très cher puisqu'on a un système matriciel à résoudre à chaque itération !" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Test\n", + "\n", + "Regardons comment marche cet algorithme pour résoudre\n", + "\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "x_0 - 2 x_1 & x_1 \\\\\n", + "x_0 & 2 x_0 + x_1 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_0 \\\\\n", + "x_1 \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "1 \\\\\n", + "9 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Il y a deux solutions qui sont [1, 2] et [2, 1]." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x^1 = [1.5 2.5] erreur² = 0.48999999999999977\n", + "x^2 = [0.73913043 1.43478261] erreur² = 0.18534274820344412\n", + "x^3 = [1.37617066 2.74037461] erreur² = 0.6387945198307682\n", + "x^4 = [0.72846505 1.45602065] erreur² = 0.18097695808599654\n", + "x^5 = [1.37323934 2.74623359] erreur² = 0.6430523663786714\n", + "x^6 = [0.72824232 1.45646606] erreur² = 0.1808855461166179\n", + "x^7 = [1.37317932 2.74635363] erreur² = 0.6431399506048754\n", + "x^8 = [0.72823777 1.45647516] erreur² = 0.1808836795920618\n", + "x^9 = [1.37317809 2.74635608] erreur² = 0.6431417383272344\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "def A(x):\n", + " return np.array([[x[0] - 2*x[1], x[1]] ,\n", + " [x[0] , x[1] + 2*x[0]]]) / 10 \n", + "\n", + "b = np.array([1, 9]) / 10 # avec normalisation grossière\n", + "\n", + "x = np.array([1, 1])\n", + "for i in range(1, 10):\n", + " x = lin.solve(A(x), b)\n", + " print(f'x^{i} = ', x, end=' ')\n", + " print(f'erreur² = ', np.square(A(x) @ x - b).sum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "La solution oscille sans converger. On peut tester d'autre ${\\bf x}^0$ \n", + "mais on obtient souvent le même résultat.\n", + "\n", + "La méthode du point fixe de base a un petit rayon de convergence à savoir il\n", + "faut que la valeur initial soit proche de la solution pour converger.\n", + "\n", + "### Appliquons l'inertie\n", + "\n", + "Ou la méthode de surrelaxation qui consite à avancer moins vite vers le prochain\n", + "point." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x^1 = [1.99601592 1.00199403] erreur² = 2.845730924209918e-06\n", + "x^2 = [1.98435526 1.00784963] erreur² = 4.338186795289511e-05\n", + "x^3 = [1.94167764 1.02955991] erreur² = 0.00057735040271093\n", + "x^4 = [1.81575881 1.09680461] erreur² = 0.005006527863139465\n", + "x^5 = [1.58849624 1.23874527] erreur² = 0.017837680043912996\n", + "x^6 = [1.3654867 1.43296028] erreur² = 0.023567622207356913\n", + "x^7 = [1.21494033 1.62266463] erreur² = 0.015938576382362332\n", + "x^8 = [1.12471347 1.76667765] erreur² = 0.007550226984782101\n", + "x^9 = [1.07194609 1.86111664] erreur² = 0.0030000984268709436\n" + ] + } + ], + "source": [ + "µ = 0.5 # j'avance de moitié vers le prochain x\n", + "\n", + "x = np.array([1.998, 1])\n", + "for i in range(1, 10):\n", + " x_old = x\n", + " x = lin.solve(A(x), b)\n", + " x = µ * x + (1-µ) * x_old\n", + " print(f'x^{i} = ', x, end=' ')\n", + " print(f'erreur² = ', np.square(A(x) @ x - b).sum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Et là la convergence est rapide. L'inertie augmente significativement le rayon\n", + "de convergence de la méthode du point fixe (plus µ est petit et plus le rayon\n", + "de convergence est grand mais moins on avance vite).\n", + "\n", + "Bien sûr l'algorithme converge vers l'une des solutions et y reste. Il ne peut\n", + "pas trouver toutes les solutions. Si on veut trouver au autre solution il y\n", + "faut choisir un autre point initial et avoir de la chance d'être dans le \n", + "rayon de convergence de cette autre solution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## La méthode de Newton-Raphson\n", + "\n", + "Il s'agit d'appliquer la méthode de Newton pour une fonction vectorielle.\n", + "\n", + "Voici une vidéo qui rappelle ce qu'est la méthode de Newton pour une fonction\n", + "en 1D. Vous pouvez vous arrêter à la 4e minute." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/jpeg": "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\n", + "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import YouTubeVideo\n", + "YouTubeVideo('h0XUxE47l00')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dans notre cas on veut toujours résoudre notre système matriciel non linéaire.\n", + "\n", + "On va donc définir la méthode itérative par analogie avec la méthode 1D. En 1D on a :\n", + "\n", + "$$\n", + "x^{k+1} = x^k - \\frac{f(x^k)}{f'(x^k)} \\quad \\textrm{ou bien} \\\\\n", + "f'(x^k) \\; (x^{k+1} - x^k) = - f(x^k)\n", + "$$\n", + " \n", + "Cela donne en $n$ dimensions :\n", + "\n", + "$$\n", + "J_{\\bf f}({\\bf x}^k) \\; ({\\bf x}^{k+1} - {\\bf x}^k) = - {\\bf f}({\\bf x}^k)\n", + "$$\n", + "\n", + "avec $J_{\\bf f}$ la matrice Jacobienne de ${\\bf f}$ :\n", + "\n", + "$$\n", + "J_{\\bf f}\\left({\\bf x}\\right)=\n", + "\\begin{pmatrix} \n", + "\\dfrac{\\partial f_1}{\\partial x_1} & \\cdots & \\dfrac{\\partial f_1}{\\partial x_n} \\\\\n", + "\\vdots & \\ddots & \\vdots \\\\\n", + "\\dfrac{\\partial f_n}{\\partial x_1} & \\cdots & \\dfrac{\\partial f_n}{\\partial x_n}\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "et pour notre système non linéaire\n", + "\n", + "$$\n", + "{\\bf f}({\\bf x}) = A({\\bf x})\\, {\\bf x} - {\\bf b}\n", + "$$\n", + "\n", + "On notera que ${\\bf f}$ est une fonction vectorielle à savoir qu'elle retourne\n", + "un vecteur." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Test\n", + "\n", + "On reprend le même système matriciel :\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "x_0 - 2 x_1 & x_1 \\\\\n", + "x_0 & 2 x_0 + x_1 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_0 \\\\\n", + "x_1 \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "1 \\\\\n", + "9 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "La matrice Jacobienne de la fonction ${\\bf f}$ définie ci-dessus est : \n", + "\n", + "$$\n", + "J_{\\bf f}({\\bf x}) = \n", + "\\begin{bmatrix}\n", + "2 x_0 - 2 x_1 & 2 x_1 - 2 x_0\\\\\n", + "2 x_0 + 2 x_1 & 2 x_0 + 2 x_1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x^0 = [0.80714286 1.40214286] erreur² = 0.1738391124362817\n", + "x^1 = [0.82661178 1.47589539] erreur² = 0.14013193945500102\n", + "x^2 = [0.84449678 1.53832416] erreur² = 0.11305725653981773\n", + "x^3 = [0.86066582 1.59186587] erreur² = 0.09127299702681221\n", + "x^4 = [0.87518409 1.63820488] erreur² = 0.07372379277598218\n", + "x^5 = [0.88818095 1.67857971] erreur² = 0.0595731611254003\n", + "x^6 = [0.89980142 1.71393945] erreur² = 0.04815469077192336\n", + "x^7 = [0.91018754 1.74503332] erreur² = 0.038935573039892035\n", + "x^8 = [0.91947123 1.77246602] erreur² = 0.03148872349291875\n", + "x^9 = [0.92777209 1.79673415] erreur² = 0.025471148220392294\n", + "x^10 = [0.9351973 1.81825117] erreur² = 0.020606983474307096\n", + "x^11 = [0.94184231 1.83736516] erreur² = 0.01667410290306686\n", + "x^12 = [0.94779187 1.85437189] erreur² = 0.013493486464829903\n", + "x^13 = [0.9531212 1.86952455] erreur² = 0.010920748632859209\n", + "x^14 = [0.95789703 1.88304134] erreur² = 0.00883936731257032\n", + "x^15 = [0.96217855 1.89511126] erreur² = 0.007155259635295223\n", + "x^16 = [0.96601835 1.90589887] erreur² = 0.005792428863449946\n", + "x^17 = [0.96946319 1.91554793] erreur² = 0.0046894658536456735\n", + "x^18 = [0.97255463 1.92418452] erreur² = 0.003796734034536249\n", + "x^19 = [0.97532973 1.93191956] erreur² = 0.0030741021940233564\n", + "x^20 = [0.97782148 1.93885083] erreur² = 0.0024891170269789866\n", + "x^21 = [0.98005934 1.94506477] erreur² = 0.002015529173331623\n", + "x^22 = [0.9820696 1.95063793] erreur² = 0.0016321037099287408\n", + "x^23 = [0.98387574 1.95563824] erreur² = 0.0013216597493956443\n", + "x^24 = [0.98549877 1.96012605] erreur² = 0.0010702947077985679\n", + "x^25 = [0.98695747 1.96415505] erreur² = 0.0008667575172292292\n", + "x^26 = [0.98826867 1.96777309] erreur² = 0.0007019420351895113\n", + "x^27 = [0.98944742 1.97102285] erreur² = 0.0005684774962019743\n", + "x^28 = [0.99050723 1.9739424 ] erreur² = 0.0004603973426083823\n", + "x^29 = [0.99146019 1.9765658 ] erreur² = 0.0003728713824135844\n" + ] + } + ], + "source": [ + "def f(x):\n", + " return A(x) @ x - b\n", + "\n", + "def J_f(x):\n", + " return 2 * np.array([[x[0] - x[1], x[1] - x[0]],\n", + " [x[0] + x[1], x[0] + x[1]]])\n", + "\n", + "x = np.array([1, 1.1])\n", + "for i in range(30):\n", + " delta = lin.solve(J_f(x), -f(x))\n", + " x = x + delta\n", + " print(f'x^{i} = ', x, end=' ')\n", + " print(f'erreur² = ', np.square(A(x) @ x - b).sum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On converge alors que la méthode du point fixe oscille \n", + "sans convreger pour cette valeur initiale.\n", + "\n", + "On converge néanmoins moins vite qu'avec la méthode du point fixe sur-relaxée.\n", + "\n", + "**Remarques** sur la méthode de Newton-Raphson\n", + "\n", + "* Le coût de construction de la matrice Jacobienne peut être très lourd\n", + "* Une technique pour aller plus vite consiste à dire que d'une itération à une\n", + " autre on n'a pas beaucoup bougé et donc la matrice Jacobienne n'a pas du trop \n", + " changer. Aussi on recalcule cette matrice que toutes les 3 ou plus itérations\n", + "* Il s'agit d'une matrice pleine qu'il rend plus compliqué la résolution du système\n", + " lors de l'iteration (une méthode de gradiant ne marchera pas en général)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/en/ma62 Gradient conjugu\303\251 -- Exercice.ipynb" "b/PVCM/cama/en/ma62 Gradient conjugu\303\251 -- Exercice.ipynb" new file mode 100644 index 0000000..0bca368 --- /dev/null +++ "b/PVCM/cama/en/ma62 Gradient conjugu\303\251 -- Exercice.ipynb" @@ -0,0 +1,409 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Programmer le gradient conjugué\n", + "\n", + "A partir de ce [cours sur le gradient conjugué](http://perso.unifr.ch/ales.janka/numeroptim/07_conjgrad.pdf) programmez en Python + Numpy le gradient conjugué en exploitant les astuces mathématiques indiquées pour optimiser\n", + "votre code.\n", + "\n", + "* Effectuez des tests pour valider votre code. \n", + "* Comparez la vitesse de convergence à celle du gradient avec μ optimal. Tracez des courbes de convergence (cf la feuille qui en parle)\n", + "* Comparez les temps de calcul.\n", + "\n", + "\n", + "Note : Veuillez écrire des fonctions les plus propres possibles, en particulier qui n'utilisent pas des variables globales comme c'est le cas dans ma correction du gradient (ma33)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def make_system(N):\n", + " A = 1.0 * np.random.randint(-10, 10, size=(N,N))\n", + " A[np.diag_indices(N)] = 0.1 + np.abs(A).sum(axis=0) # diag dominante\n", + " A = A + A.T # symétrique\n", + " A = A / np.abs(A).sum(axis=0).mean()\n", + " b = 1.0 * np.random.randint(-10,10,size=(N))\n", + " return A, b\n", + "\n", + "A, b = make_system(2)\n", + "print(A, \"\\n\\n\", b)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def gradient_conjugué(A, x0, b, error=1E-9, convergence=False):\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# vérfions que ca marche\n", + "\n", + "# combien faut-il d'itérations\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_error(N, method=gradient_conjugué):\n", + " A, b = make_system(N)\n", + " x = method(A, np.zeros(N), b)\n", + " err = A @ x - b\n", + " return np.sqrt(err @ err)\n", + "\n", + "compute_error(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparons avec le gradient simple" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def gradient(A, x0, b, e = 1E-9, convergence=False, max_iterations=1000):\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# vérifions que ca marche\n", + "\n", + "compute_error(10, method=gradient)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Perfs" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# comparons les performances\n", + "\n", + "seed = 123\n", + "np.random.seed(seed)\n", + "\n", + "%timeit compute_error(1000, method=gradient)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "seed = 123\n", + "np.random.seed(seed)\n", + "\n", + "%timeit compute_error(1000, method=gradient_conjugué)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Nombre d'iteration dans les 2 cas\n", + "\n", + "On teste avec N=1000 puis N=10000." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "N = 1000\n", + "A,b = make_system(N)\n", + "x0 = np.zeros(N)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Pour le gradient simple" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "err = gradient(A, x0, b, convergence=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#plot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Pour le gradient conjugué" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "err = gradient_conjugué(A, x0, b, convergence=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#plot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Un cas réel\n", + "\n", + "Logiquement vous devriez être décu aussi on va tester avec un problème réel qui correspond à cet exemple\n", + "de l'[équation de Poisson](https://doc.freefem.org/tutorials/poisson.html). Le système matriciel de ce problème est téléchargeable \n", + "[ici](https://www.lrde.epita.fr/~ricou/cama/data/Ab.npz). Une fois le fichier sauvé, pour récupérer\n", + "A et b faites :\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "npz = np.load('/tmp/Ab.npz',allow_pickle=True)\n", + "A = npz['A']\n", + "b = npz['b']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Faites une étude rapide de A, indiquez quel pourcentage des valeurs de A est différent de 0. Afficher l'image de la matrice avec `plt.imshow(A)` (faire une grande image pour voir quelque chose).\n", + "* Refaites la comparaison entre les deux méthodes avec ce système matriciel.\n", + "* Regardez la documentation de `lin.solve` (en particulier les options) et comparer `lin.solve` à vos deux algorithmes." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparaison gradient simple et conjugué" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%time err = gradient_conjugué(A, np.zeros(len(A)), b, convergence=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#plot" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# le gradient simple\n", + "\n", + "%time err = gradient(A, np.zeros(len(A)), b, convergence=True, max_iterations=10000)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On voit la supériorité du gradient conjugué tant en nombre d'itérations (175 contre 7800) qu'en temps de calcul (environ 40 fois plus rapide)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparaison avec `lin.solve` de Scipy\n", + "\n", + "Le solveur de Scipy a des option que celui de Numpy n'a pas." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# regarder la doc pour avoir les options optimales\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# calculer le résidu\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On note aussi `lin.solve` est plus rapide et sa solution est nettement meilleure... `lin.solve` utilise une méthode directe ici. Cela est dû au fait que Scipy utilise la bibliothèque Lapack (qui est imbatable)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Le gradient conjugué de Scipy (avec Lapack)\n", + "\n", + "Le gradient conjugué à tout son sens pour les matrices creuses aussi il est dans la partie \"sparse\" de Scipy.\n", + "On a vu que notre matrice à plus de 99 % de valeur nulles ce qui en fait bien une matrice creuse. Aussi je\n", + "la charge dans le format COO (téléchargez __[Acoo.npz](https://www.lrde.epita.fr/~ricou/cama/data/Acoo.npz)__) qui ne stocke que les valeurs non nulles et" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import scipy.sparse as sparse\n", + "from scipy.sparse.linalg import cg\n", + "\n", + "Ac = sparse.load_npz('/tmp/Acoo.npz')\n", + "%time x = cg(Ac, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On gagne un ordre de grandeur." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/_Table des mati\303\250res.ipynb" "b/PVCM/cama/fr/_Table des mati\303\250res.ipynb" new file mode 100644 index 0000000..e9f57a1 --- /dev/null +++ "b/PVCM/cama/fr/_Table des mati\303\250res.ipynb" @@ -0,0 +1,236 @@ + +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + +"## Table des matières.ipynb\n", +"* [ma1 Jupyter](ma1%20Jupyter.ipynb)\n", +" - Utilisation de Jupyter\n", +" - Manipulation des cellules\n", +" - Configuration\n", +" - IPython\n", +" - Complétion et aide\n", +" - Shell sous IPython\n", +" - Commandes magiques\n", +"* [ma1 np01 Numpy Introduction](ma1%20np01%20Numpy%20Introduction.ipynb)\n", +" - NumPy - An N-dimensional Array manipulations library\n", +" - Création d'un tableau\n", +" - dtype : le choix du type des éléments\n", +" - Méthodes prédéfinies\n", +" - Avec des valeurs aléatoires\n", +" - En redéfinissant sa forme\n", +" - Mélanger les valeurs\n", +" - Avec une fonction de son choix\n", +" - Opérations de base\n", +" - Parcourir un tableau\n", +" - Travailler en vectoriel\n", +"* [ma1 np02 Filtres](ma1%20np02%20Filtres.ipynb)\n", +" - Filtrer via les indices\n", +" - Les filtres logiques\n", +" - Un filtre = une condition logique\n", +" - `where` pour gérer les valeurs hors filtre\n", +" - Mettre à jour un tableau avec un filtre\n", +"* [ma1 np03 Manipulations](ma1%20np03%20Manipulations.ipynb)\n", +" - Les axes\n", +" - Réorganisation d'un tableau\n", +" - Réordonner les axes\n", +" - Changer l'ordre des éléments d'un tableau\n", +" - Agrégation\n", +" - Concaténation\n", +" - Empilage\n", +" - Découpage\n", +" - From Python to Numpy\n", +" - Pandas aussi\n", +"* [ma1 np05 Notation Einstein](ma1%20np05%20Notation%20Einstein.ipynb)\n", +" - Présentation de la notation d'Einstein\n", +" - Mise en pratique\n", +"* [ma1 np06 Linalg pour le calcul matriciel](ma1%20np06%20Linalg%20pour%20le%20calcul%20matriciel.ipynb)\n", +" - Linalg (linear algebra)\n", +" - Opérations de base\n", +" - Extractions\n", +" - Opérations sur la matrice\n", +"* [ma1 np90 petits exercices](ma1%20np90%20petits%20exercices.ipynb)\n", +" - Numpy - Exercices\n", +" - Matrice carrée\n", +" - Norme d'un vecteur\n", +" - Sous-matrice\n", +" - Vecteur aléatoire\n", +" - Trace\n", +" - Matrice de multiples de 3\n", +" - Nombre de 9\n", +" - Colonne qui a la plus petite moyenne\n", +" - ChessSum\n", +" - 2 minimums\n", +" - Lignes dans l'ordre\n", +" - Valeurs uniques\n", +" - Tenseur magique\n", +" - Plans d'un tenseur\n", +"* [ma20 Rappels sur les matrices](ma20%20Rappels%20sur%20les%20matrices.ipynb)\n", +" - Vecteur\n", +" - Matrices et applications linéaires\n", +" - Déterminant d'une matrice\n", +" - Normes\n", +" - Norme d'un vecteur\n", +" - Norme d'une matrice\n", +" - Propriétés\n", +"* [ma21 Transformations isometriques](ma21%20Transformations%20isometriques.ipynb)\n", +" - Transformations isométriques\n", +" - Matrice de rotation centrée en (0,0)\n", +" - Propriétés\n", +" - Symétrie axiale\n", +" - Translation\n", +" - Exercice 1.1\n", +"* [ma22 Changement de repere](ma22%20Changement%20de%20repere.ipynb)\n", +" - Matrice de passage\n", +" - Vecteurs dans le nouveau repère\n", +" - Matrice de passage vue comme une transformation\n", +" - Points dans le nouveau repère\n", +" - Notre souris dans le nouveau repère\n", +" - Exercice -- Et l'inverse ?\n", +" - Une application linéaire transposée dans le nouveau repère\n", +"* [ma24 Vectors propres](ma24%20Vectors%20propres.ipynb)\n", +" - $A^n \\textbf{x}$\n", +" - Vecteurs propres et valeurs propres\n", +" - Le cas des matrices de rotation\n", +" - Symétrie axiale horizontale\n", +" - Diagonalisation d'une matrice\n", +"* [ma25 Drones -- Exercice](ma25%20Drones%20--%20Exercice.ipynb)\n", +" - Spectacle de drones\n", +" - Figure 1\n", +" - Figure 2\n", +" - Figure 3\n", +"* [ma26 Vecteurs propres -- Exercices](ma26%20Vecteurs%20propres%20--%20Exercices.ipynb)\n", +" - Cas d'utilisation des valeurs et vecteurs propres\n", +" - Fibonnacci\n", +" - Google page rank\n", +" - Approche itérative\n", +" - Un autre approche\n", +"* [ma30 ACP](ma30%20ACP.ipynb)\n", +" - Analyse en composantes principales (ACP)\n", +" - Nuage de points\n", +" - Matrice de covariance\n", +"* [ma31 Système d'équations](ma31%20Système%20d'équations.ipynb)\n", +" - Systèmes matriciels\n", +" - Résolution d'un système matriciel\n", +" - Méthode du pivot de Gauss\n", +" - Complexité du pivot de Gauss\n", +" - Décomposition LU (Lower, Upper)\n", +" - Gauss Jordan\n", +" - Comparaison de la vitesse de méthodes\n", +" - Erreurs d'arrondi\n", +" - Solution au problème d'arrondi dans le cas du pivot de Gauss\n", +"* [ma32 Conditionnement d'une matrice](ma32%20Conditionnement%20d'une%20matrice.ipynb)\n", +" - Conditionnement d'une matrice\n", +" - Pourquoi ?\n", +" - Perturbons la matrice\n", +" - Propriétés\n", +" - Préconditionnement\n", +"* [ma34 ACP -- Exercice](ma34%20ACP%20--%20Exercice.ipynb)\n", +" - Exercice : Nuage de points en 3D\n", +" - Données de l'expérience\n", +" - Calculs pour trouver les caractéristiques de notre nuage\n", +"* [ma35 Système matriciel -- Exercices](ma35%20Système%20matriciel%20--%20Exercices.ipynb)\n", +" - Méthode du pivot de Gauss partiel\n", +" - Factorisation de Choleski\n", +" - Amméliorer Jacobi\n", +"* [ma40 Méthodes itératives](ma40%20Méthodes%20itératives.ipynb)\n", +" - La simulation numérique\n", +" - Méthodes itératives\n", +" - Méthode de Jacobi\n", +" - Pourquoi le 2e cas marche ?\n", +" - Temps calcul\n", +"* [ma41 Convergence de Jacobi avec inertie](ma41%20Convergence%20de%20Jacobi%20avec%20inertie.ipynb)\n", +" - Ajouter de l'inertie à Jacobi\n", +" - Programmons l'inertie pour Jacobi\n", +" - Étudions la convergence\n", +" - Testons d'autres matrices avec cet algorithme\n", +" - Exercice 20.1\n", +" - Normaliser\n", +"* [ma42 Surrelaxation pour Gauss-Seidel -- Exercice](ma42%20Surrelaxation%20pour%20Gauss-Seidel%20--%20Exercice.ipynb)\n", +" - Exercice ma21\n", +" - Gauss-Seidel\n", +" - Surrelaxation de Gauss-Seidel\n", +" - Programmons Gauss-Seidel surrelaxé\n", +" - Le bon cas\n", +" - Étude de $w$\n", +"* [ma50 Optimisation - Méthode du gradient](ma50%20Optimisation%20-%20Méthode%20du%20gradient.ipynb)\n", +" - Problème d'optimisation\n", +" - Problème d'optimisation avec contrainte\n", +" - La méthode du gradient\n", +" - Étude de la convergence du gradient\n", +"* [ma51 x.T A x sur un maillage en Numpy ](ma51%20x.T%20A%20x%20sur%20un%20maillage%20en%20Numpy%20.ipynb)\n", +" - Calculons ${\\bf x}^T \\, A \\, {\\bf x} $ avec Numpy\n", +" - Cas test avec A = 2 Id\n", +" - Un vrai cas\n", +" - Optimisons\n", +" - Passer par une fonction J\n", +" - Utiliser `np.tensordot`\n", +" - Conclusion\n", +"* [ma52 Méthode du gradiant pour système matriciel](ma52%20Méthode%20du%20gradiant%20pour%20système%20matriciel.ipynb)\n", +" - A x = b vu comme un problème d'optimisation\n", +" - Calcul de dérivée\n", +" - Définition\n", +" - Calculons la dérivée de J suivant une direction\n", +" - A symétrique\n", +" - Gradient et dérivée\n", +"* [ma53 Notations du produit scalaire](ma53%20Notations%20du%20produit%20scalaire.ipynb)\n", +" - Écritures du produit scalaire\n", +" - ${\\bf v} \\,.\\, {\\bf w}$\n", +" - ${\\bf v}^T \\, {\\bf w}$\n", +" - $<{\\bf v}, {\\bf w}>$\n", +"* [ma54 Gradient pour résoudre Ax = b -- Exercice](ma54%20Gradient%20pour%20résoudre%20Ax%20=%20b%20--%20Exercice.ipynb)\n", +" - La méthode du gradient pour résoudre A x = b\n", +" - Introduire de l'inertie\n", +" - Valeur optimale de µ\n", +"* [ma60 Méthode du gradient conjugué](ma60%20Méthode%20du%20gradient%20conjugué.ipynb)\n", +" - Méthode du gradient conjugué\n", +" - Générer une base de $ℝ^n$\n", +" - Le cas $A {\\bf x} = {\\bf b}$\n", +" - 2e tentative\n", +" - Travaillons dans la base des $\\nabla J({\\bf x}^i)$\n", +" - Nouveau calcul de μ\n", +"* [ma61 Système matriciel non linéaire](ma61%20Système%20matriciel%20non%20linéaire.ipynb)\n", +" - Système matriciel non linéaire\n", +" - La méthode du point fixe\n", +" - La méthode du point fixe pour résoudre $A({\\bf x}) \\, {\\bf x} = {\\bf b}$\n", +" - Test\n", +" - Appliquons l'inertie\n", +" - La méthode de Newton-Raphson\n", +"* [ma62 Gradient conjugué -- Exercice](ma62%20Gradient%20conjugué%20--%20Exercice.ipynb)\n", +" - Programmer le gradient conjugué\n", +" - Comparons avec le gradient simple\n", +" - Perfs\n", +" - Nombre d'iteration dans les 2 cas\n", +" - Un cas réel\n", +" - Comparaison gradient simple et conjugué\n", +" - Comparaison avec `lin.solve` de Scipy\n", +" - Le gradient conjugué de Scipy (avec Lapack)\n", + + "" + ]}], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.7" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} + diff --git a/PVCM/cama/fr/data/Ab.npz b/PVCM/cama/fr/data/Ab.npz new file mode 100644 index 0000000..073d461 Binary files /dev/null and b/PVCM/cama/fr/data/Ab.npz differ diff --git a/PVCM/cama/fr/data/Acoo.npz b/PVCM/cama/fr/data/Acoo.npz new file mode 100644 index 0000000..8b49671 Binary files /dev/null and b/PVCM/cama/fr/data/Acoo.npz differ diff --git a/PVCM/cama/fr/data/cours.mplstyle b/PVCM/cama/fr/data/cours.mplstyle new file mode 100644 index 0000000..2b7f135 --- /dev/null +++ b/PVCM/cama/fr/data/cours.mplstyle @@ -0,0 +1,13 @@ +# https://matplotlib.org/tutorials/introductory/customizing.html +# https://github.com/matplotlib/matplotlib/blob/master/matplotlibrc.template + +figure.figsize: 10,5 + +axes.titlesize : 16 +axes.labelsize : 16 +lines.linewidth : 2 +lines.markersize : 8 +xtick.labelsize : 12 +ytick.labelsize : 12 + +image.aspect: equal diff --git a/PVCM/cama/fr/data/mouse.npy b/PVCM/cama/fr/data/mouse.npy new file mode 100644 index 0000000..bd75652 Binary files /dev/null and b/PVCM/cama/fr/data/mouse.npy differ diff --git "a/PVCM/cama/fr/images/500px-Cercle_des_cor\303\251lations_d'une_ACP_norm\303\251e.svg.png" "b/PVCM/cama/fr/images/500px-Cercle_des_cor\303\251lations_d'une_ACP_norm\303\251e.svg.png" new file mode 100644 index 0000000..b9779d7 Binary files /dev/null and "b/PVCM/cama/fr/images/500px-Cercle_des_cor\303\251lations_d'une_ACP_norm\303\251e.svg.png" differ diff --git a/PVCM/cama/fr/images/cercle_trigo.svg b/PVCM/cama/fr/images/cercle_trigo.svg new file mode 100644 index 0000000..48bbfb6 --- /dev/null +++ b/PVCM/cama/fr/images/cercle_trigo.svg @@ -0,0 +1,355 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + θ + θ + cos + 0 + + + + (0, -1) + (1, 0) + (0, 1) + (-1, 0) + + θ + sin + + + + + diff --git a/PVCM/cama/fr/images/drone_boat.png b/PVCM/cama/fr/images/drone_boat.png new file mode 100644 index 0000000..ed95de0 Binary files /dev/null and b/PVCM/cama/fr/images/drone_boat.png differ diff --git a/PVCM/cama/fr/images/gradient.png b/PVCM/cama/fr/images/gradient.png new file mode 100644 index 0000000..b3ac56e Binary files /dev/null and b/PVCM/cama/fr/images/gradient.png differ diff --git a/PVCM/cama/fr/images/nasa-x57-pression.jpg b/PVCM/cama/fr/images/nasa-x57-pression.jpg new file mode 100644 index 0000000..451899c Binary files /dev/null and b/PVCM/cama/fr/images/nasa-x57-pression.jpg differ diff --git a/PVCM/cama/fr/ma1 Jupyter.ipynb b/PVCM/cama/fr/ma1 Jupyter.ipynb new file mode 100644 index 0000000..41d16d1 --- /dev/null +++ b/PVCM/cama/fr/ma1 Jupyter.ipynb @@ -0,0 +1,346 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Utilisation de Jupyter\n", + "\n", + "#### Cellules\n", + "\n", + "Une feuille Jupyter est composée de cellules que vous pouvez deviner si vous cliquez sur le texte. Il existe différents\n", + "types de cellules que l'on choisit avec le menu déroulant au milieu des icônes en haut de la page :\n", + "\n", + "* du code Python (par défaut)\n", + "* du texte enrichi ([Markdown](https://en.wikipedia.org/wiki/Markdown))\n", + "* du texte brut (utile pour désactiver une cellule de code)\n", + "\n", + "Vous pouvez ajouter\n", + "une cellule avec le symbole + en haut de la page, supprimer une cellule avec les ciseaux, déplacer une cellule avec les flèches et l'éditer en double-cliquant dessus. On verra qu'on exécute les cellules pour obtenir le résultat du code écrit. Tout cela se retrouve dans le menu\n", + "`Cell`.\n", + "\n", + "#### Noyau (kernel)\n", + "\n", + "Jupyter tient son nom de 3 langages à savoir Julia, Python et R. Aujourd'hui la liste des langages que l'on peut\n", + "utiliser dans une feuille Jupyter est bien plus longue mais dans tous les cas il faut un noyau qui fasse l'interface\n", + "entre Jupyter et le langage. Dans le cas de Python le noyau est iPython. On le choisit à la création de la feuille\n", + "et on peut interagir dessus à l'aide du menu `Kernel`. \n", + "\n", + "Les autres menus sont plus classiques et ne demandent pas d'explication (oubliez `Widget`).\n", + "\n", + "#### Note\n", + "\n", + "Si vous ne connaissez pas Python ni Jupyter, il est conseillé de revenir ici après avoir lu le premier chapitre.\n", + "\n", + "## Manipulation des cellules\n", + "\n", + "#### Etat et exécution\n", + "\n", + "* Une cellule peut avoir 3 états :\n", + " * pas sélectionnée (pas de cadre autour de la cellule)\n", + " * sélectionnée (cadre bleu ou barre bleue à gauche)\n", + " * sélectionnée et en mode édition (changement de la couleur du fond et parfois cadre vert)\n", + "* Cliquer selectionne une cellule (voire la passe directement en mode édition pour les cellules de calcul)\n", + "* Double cliquer selectionne et passe en mode édition (sur une zone de texte, la syntaxe Markdown apparait)\n", + "* Enter comme cliquer permet de descendre dans les états quand Esc permet d'en remonter. \n", + "* Pour que Python recalcule le résultat d'une cellule\n", + " * Shift+Enter fait le calcul et passe à la cellule suivante\n", + " * Crtl+Enter fait le calcul et reste sur la cellule\n", + " * Alt+Enter fait le calcul et ajoute une cellule vide ensuite.\n", + "\n", + "#### Affichage \n", + " \n", + " * `[out]` Pour ne pas afficher de résultat, finir la dernière ligne de la cellule avec `;`.\n", + " * `[In]` Pour ne pas afficher une cellule, utiliser 'Hide input' de nbextessions (cf config dans le menu Edit).\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(2)\n", + "1+1; # remove the ; to see the difference" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Configuration\n", + "\n", + "Jupyter dispose de nombreuses commandes pour manipuler sa feuille de note et bien sûr il est possible de\n", + "définir des raccourcis clavier.\n", + "\n", + "Pour afficher la liste des commandes (la *palette de commandes*) cliquer sur le petit clavier dans la barre d'icones.\n", + "Avec Chrome, on peut afficher cette palette de commandes avec Ctrl+Shift+P.\n", + "\n", + "Pour afficher et définir ses raccourcis clavier vous pouvez passer le menu d'aide ou taper `shortcut` dans\n", + "la palette de commandes.\n", + "\n", + "Par exemple, pour mon usage j'ai redéfini le changement de type de cellule avec\n", + "\n", + "* Crtl+1 pour le mode Code\n", + "* Crtl+2 pour le mode Markdown\n", + "* Crtl+3 pour le mode Raw (données non interprétées)\n", + "\n", + "Cela fonctionne lorsque la cellule est sélectionnée mais pas en mode édition (donc cadre bleu ou barre bleue)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Exercice \n", + "\n", + "Choisir ses raccourcis pour passer d'un mode à un autre puis passer la cellule ci-dessous en mode Code et l'exécuter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "print('$qsD!Me+nsodd= 1l lre3W$'[-2:2:-2])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Les raccourcis de manipulation des cellules sont bons à connaitre ou à redéfinir lorsqu'on commence à utiliser Jupyter sérieusement." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## IPython\n", + "\n", + "Lorsqu'on utilise Python dans Jupyter, on s'appuie sur [IPython](https://ipython.org/) qui enrichit Python.\n", + "\n", + "Cela donne les fonctionnalités suivantes :\n", + "\n", + "* Complétion en appuyant sur Tab\n", + "* Aide avec `?` et `??` pour encore plus d'aide pour les objets (voire le code)\n", + "* [Accès au shell](https://ipython.readthedocs.io/en/stable/interactive/shell.html) avec `!`\n", + "* Les commandes magiques" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Complétion et aide\n", + "\n", + "`a`Tab va donner une liste dont `abs`\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Pour les exemples d'aide il faut lancer les cellules pour voir le résultat." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "abs?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Pour fermer la fenêtre d'aide cliquer sur la croix en haut à droite de la fenêtre ou utiliser Esc.?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mot = \"Coucou\"\n", + "mot.split?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Shell sous IPython" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "!pwd" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "vlib = '/var/lib/'\n", + "res = !ls $vlib\n", + "res = res.grep('lib')\n", + "for f in res:\n", + " print(f)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(type(res))\n", + "res??" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Commandes magiques\n", + "\n", + "Les commandes magiques améliorent l'usage de Python. Elles commencent par \n", + "\n", + " * `%` et s'appliquent à la ligne\n", + " * `%%` et s'appliquent à la cellule (lorsque cela a un sens)\n", + "\n", + "La première commande magique à lancer est `%quickref` pour avoir la liste des possibilités d'iPython." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%quickref" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Voici une selection de quelques commandes magiques :\n", + " \n", + "* `%time` pour avoir le temps que prends la ligne (`%%time` pour le temps d'exécution de la cellule).\n", + "* `%timeit` est comme `%time` mais il relance plusieur fois la ligne pour avoir une estimation plus juste \n", + "* `%prun` pour lancer la ligne à travers le profiler de Python et voir où ca prend du temps\n", + "\n", + "* `%matplotlib inline` pour que les graphiques s'affichent dans la page Jupyter\n", + "* `%load` pour charger un ficher Pyhton dans la cellule (met %load en commentaire un fois exécuté)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "!echo 'print(\"coucou\")' > /tmp/prog.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%load /tmp/prog.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import scipy.linalg as lin\n", + "\n", + "%prun lin.solve(np.random.random([3000,3000]), np.random.random(3000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "{{ PreviousNext('Introduction.ipynb','../lesson1 Python basics/00 - Premiers calculs.ipynb') }}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma1 np01 Numpy Introduction.ipynb b/PVCM/cama/fr/ma1 np01 Numpy Introduction.ipynb new file mode 100644 index 0000000..bd593c2 --- /dev/null +++ b/PVCM/cama/fr/ma1 np01 Numpy Introduction.ipynb @@ -0,0 +1,933 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## NumPy - An N-dimensional Array manipulations library\n", + "\n", + "[NumPy](https://docs.scipy.org/doc/numpy/user/index.html) est une première boîte à outils pour le développement de programmes scientifiques. Cette\n", + "bibliothèque offre en particulier des tableaux multidimensionnels simples à manipuler et **performants** (ce qui n'est pas le cas des listes de Python).\n", + "\n", + "Il est à noter que l'on retrouve la syntaxe de Numpy pour la manipulation des tableaux dans d'autres langages comme R ou Julia et que les bibliothèques d'IA comme PyTorch, TensorFlow ou JAX utilisent aussi cette syntaxe." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np # np is the convention" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "À la différence des listes, __les tableaux ont toutes leurs valeurs du même type__.\n", + "\n", + "## Création d'un tableau" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 2 3]\n", + " [4 5 7]]\n", + "shape: (2, 3)\n", + "type: \n" + ] + } + ], + "source": [ + "a = np.array([[1,2,3], [4,5,7]]) # 2D array built from a list\n", + "print(a)\n", + "print(\"shape: \",a.shape)\n", + "print(\"type: \",type(a[0,0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### dtype : le choix du type des éléments\n", + "\n", + "Lorsqu'on fait du calcul scientifique il est important de choisir le type des tableaux afin d'optimiser la mémoire, les erreurs, la vitesse.\n", + "\n", + "NumPy propose les types suivants :\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
Data typeDescription
boolBoolean (True or False) stored as a byte
intPlatform integer (normally either int32 or int64)
int8Byte (-128 to 127)
int16Integer (-32768 to 32767)
int32Integer (-2147483648 to 2147483647)
int64Integer (-9223372036854775808 to 9223372036854775807)
uint8Unsigned integer (0 to 255)
uint16Unsigned integer (0 to 65535)
uint32Unsigned integer (0 to 4294967295)
uint64Unsigned integer (0 to 18446744073709551615)
floatShorthand for float64.
float16Half precision float: sign bit, 5 bits exponent,\n", + "10 bits mantissa
float32Single precision float: sign bit, 8 bits exponent,\n", + "23 bits mantissa
float64Double precision float: sign bit, 11 bits exponent,\n", + "52 bits mantissa
complexShorthand for complex128.
complex64Complex number, represented by two 32-bit floats (real\n", + "and imaginary components)
complex128Complex number, represented by two 64-bit floats (real\n", + "and imaginary components)
" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [0 1 2 3] uint8\n", + "x = [254 1 2 3] uint8\n", + "y = [254. 1. 2. 3.] float32\n" + ] + } + ], + "source": [ + "x = np.arange(4, dtype= np.uint8) # arange is the numpy version of range to produce an array\n", + "print(\"x =\", x, x.dtype)\n", + "\n", + "x[0] = -2 # 0 - 2 = max -1 for unsigned int\n", + "print(\"x =\", x, x.dtype)\n", + "\n", + "y = x.astype('float32') # conversion\n", + "print(\"y =\", y, y.dtype)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On peut connaitre la taille mémoire (en octets) qu'occupe un élément du tableau et l'occupation de tout le tableau :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "4\n" + ] + }, + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(x[0].itemsize)\n", + "print(y[0].itemsize)\n", + "y.nbytes" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Méthodes prédéfinies\n", + "\n", + "On a déjà vu la méthode `arange` pour créer un tableau, il en existe aussi pour\n", + "créer un tableau vide ou de la dimension de son choix avec que des 0 ou que des 1 ou ce qu'on veut.\n", + "En fait il existe tellement de méthodes qu'on en présente qu'une petite partie ici, pour les autres voir la\n", + "[liste des méthodes de création prédéfinies](https://docs.scipy.org/doc/numpy/reference/routines.array-creation.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Empty float:\n", + " [[2.42350504e-316 0.00000000e+000]\n", + " [4.94065646e-324 nan]]\n", + "Float zeros:\n", + " [[0. 0.]\n", + " [0. 0.]]\n", + "Complex ones:\n", + " [[1.+0.j 1.+0.j 1.+0.j]\n", + " [1.+0.j 1.+0.j 1.+0.j]]\n", + "Full of 3.2:\n", + " [[3.2 3.2]\n", + " [3.2 3.2]]\n", + "La matrice suivante est affichée partiellement car trop grande : \n", + "[[1. 0. 0. ... 0. 0. 0.]\n", + " [0. 1. 0. ... 0. 0. 0.]\n", + " [0. 0. 1. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 1. 0. 0.]\n", + " [0. 0. 0. ... 0. 1. 0.]\n", + " [0. 0. 0. ... 0. 0. 1.]]\n" + ] + } + ], + "source": [ + "a = np.empty((2,2), dtype=float) # empty do not set any value, it is faster\n", + "print(\"Empty float:\\n\", a)\n", + "\n", + "print(\"Float zeros:\\n\", np.zeros((2,2), dtype=float)) # matrix filled with 0\n", + "\n", + "print(\"Complex ones:\\n\", np.ones((2,3), dtype=complex)) # matrix filled with 1\n", + "\n", + "print(\"Full of 3.2:\\n\", np.full((2,2), 3.2))\n", + "\n", + "print(\"La matrice suivante est affichée partiellement car trop grande : \")\n", + "print(np.identity(1000)) # identity matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Avec des valeurs aléatoires\n", + "\n", + "La sous-bibliothèque [`np.random`](https://docs.scipy.org/doc/numpy/reference/routines.random.html) offre des méthodes pour générer des tableaux de valeurs aléatoires." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Random integers < 10:\n", + " [[7 5 7 2]\n", + " [6 7 0 8]\n", + " [6 3 8 3]]\n", + "Random reals between 0 and 1 :\n", + " [[0.45228105 0.39674551 0.02142443 0.14342572]\n", + " [0.95223097 0.85798264 0.85777533 0.28784271]\n", + " [0.5142878 0.36823048 0.87704756 0.44096786]]\n" + ] + } + ], + "source": [ + "print(\"Random integers < 10:\\n\", np.random.randint(10, size=(3,4))) # can also choose a min\n", + "\n", + "print(\"Random reals between 0 and 1 :\\n\", np.random.random(size=(3,4)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On peut choisir la loi de distribution (loi uniforme par défaut)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1.44216124, 2.5586318 , 4.28770816],\n", + " [2.16814785, 1.82332334, 4.53031302]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "loc = 3\n", + "scale = 1.5\n", + "np.random.normal(loc, scale, size=(2,3)) # Gauss distribution" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### En redéfinissant sa forme\n", + "\n", + "Un cas classique pour faire des tests est de créer un petit tableau multidimensionnelle avec des valeurs différentes.\n", + "Pour cela le plus simple est de mettre 0,1,2,...,N dans les cases de notre tableau de forme (3,4) par exemple. \n", + "Cela se fait avec `arange` qu'on a déjà vu pour générer les valeurs et `reshape` pour avoir la forme voulue :" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "arr = np.arange(3*4).reshape((3,4))\n", + "arr" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "arr[1, 0]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Attention, la numérotation des cases d'un tableau est effectuée avec des boucles imbriquées aussi c'est toujours la dernière dimension qui varie le plus vite. En 3D cela veut dire que passer d'un élément au suivant fait varier le dernier indice (suivant z). Cela ne correspond pas à la manière humaine de remplir un cube (on a tendance à faire des empilements de tableaux 2D). À l'usage cela ne pose pas de problème, c'est\n", + "seulement bizarre lorsqu'on affiche des tests pour voir.\n", + "\n", + "```\n", + " humain Numpy\n", + " ┌─┬─┐ ┌─┬─┐ \n", + "┌─┬─┐│5│ ┌─┬─┐│3│\n", + "│0│1│┼─┤ │0│2│┼─┤\n", + "├─┼─┤│7│ ├─┼─┤│7│\n", + "│2│3│┴─┘ │4│6│┴─┘\n", + "└─┴─┘ └─┴─┘ \n", + "``` " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[0, 1],\n", + " [2, 3]],\n", + "\n", + " [[4, 5],\n", + " [6, 7]]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.arange(8).reshape(2,2,2) # a[0,1,0] is 2 and a[0,1,1] is 3\n", + "A" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "L'inverse de reshape est `flatten()` qui transforme un tableau à plusieurs dimensions en un tableau à 1 dimension. On peut aussi utiliser `flat` pour avoir une vue 1D sur le tableau sans le transformer." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5\n", + "(2, 2, 2)\n" + ] + } + ], + "source": [ + "print(A.flat[5])\n", + "print(A.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Mélanger les valeurs\n", + "\n", + "Si on veut travailler avec les valeurs d'un tableau prises dans un ordre aléatoire alors on peut mélanger\n", + "le tableau avec `np.random.permutation()`. Attention la permutation s'effectue sur les éléments du premier niveau du tableau, `A[:]`, à savoir des tableaux\n", + "si le tableau est à plusieurs dimensions (un tableau de tableaux)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11],\n", + " [ 0, 1, 2, 3]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = np.arange(12).reshape(3,4)\n", + "np.random.permutation(data) # permutes lines only" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Si on veut mélanger toutes les valeurs il faut applatir le tableau et lui redonner sa forme :" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[10, 3, 11, 8],\n", + " [ 4, 1, 2, 7],\n", + " [ 0, 9, 6, 5]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = np.random.permutation(data.flatten()).reshape(data.shape) # it works because flatten returns a copy\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Avec une fonction de son choix\n", + "\n", + "On peut aussi créer un tableau avec une fonction qui donne la valeur du tableau pour chaque indice (i,j) :" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, -1, -2, -3],\n", + " [ 2, 1, 0, -1],\n", + " [ 4, 3, 2, 1]])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def f(i,j):\n", + " return 2*i - j\n", + "\n", + "np.fromfunction(f, shape=(3,4), dtype=int)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Opérations de base\n", + "\n", + "Numpy permet d'appliquer les [opérations mathématiques](https://numpy.org/doc/stable/reference/routines.math.html) usuelles à tous les éléments des tableaux :" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A + 1:\n", + " [[2 3]\n", + " [4 5]] \n", + "\n", + "2 A + Id:\n", + " [[3. 4.]\n", + " [6. 9.]] \n", + "\n", + "A * A (element-wise product):\n", + " [[ 1 4]\n", + " [ 9 16]] \n", + "\n", + "A @ A (matrix or dot product):\n", + " [[ 7 10]\n", + " [15 22]]\n" + ] + } + ], + "source": [ + "A = np.array([[1,2], [3,4]])\n", + "\n", + "print(\"A + 1:\\n\", A + 1, '\\n')\n", + "print(\"2 A + Id:\\n\", 2 * A + np.identity(2), '\\n')\n", + "print(u\"A * A (element-wise product):\\n\", A * A, '\\n') # or np.square(A)\n", + "print(u\"A @ A (matrix or dot product):\\n\", A @ A) # or A.dot(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On peut transposer un tableau avec `.T`. Cela ne fait rien avec un tableau en 1D, pour faire la différence entre vecteur horizontal et un vecteur vertical, il faut l'écrire en 2D :" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 3 5]] \n", + "\n", + " [[1]\n", + " [3]\n", + " [5]] \n", + "\n", + "Guess what v + v.T means:\n", + " [[ 2 4 6]\n", + " [ 4 6 8]\n", + " [ 6 8 10]]\n" + ] + } + ], + "source": [ + "v = np.array([[1,3,5]])\n", + "print(v, '\\n\\n', v.T, '\\n')\n", + "print(\"Guess what v + v.T means:\\n\", v + v.T)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On dispose aussi des fonctions trigonométriques, hyperboliques, exposant, logarithme..." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.841, 0.909],\n", + " [ 0.141, -0.757]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.set_printoptions(precision=3) # set printing precision for reals\n", + "np.sin(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Enfin Numpy offre un ensemble de méthodes pour faire des calculs sur les élements du tableau : \n", + "\n", + "* `sum()` pour additionner tous les élements \n", + "* `mean()` pour avoir la moyenne des éléments et `average()` pour avoir la moyenne pondérée, \n", + "* `prod()` pour multiplier tous les élements, \n", + "* `min()` et `max()` pour avoir la valeur minimale et la valeur maximale,\n", + "* `argmin()` et `argmax()` pour avoir les indices des valeurs minimales et maximales du tableau\n", + "* `cumsum()` et `cumprod()` pour les additions et multiplication cumulatives, \n", + "* `diff()` pour avoir l'écart avec l'élément suivant (utile pour calculer une dérivée).\n", + "\n", + "Chaque méthode `A.sum()` existe aussi en fonction `np.sum(A)`." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.argmax()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 1, 1])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.diff(A.flatten())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Parcourir un tableau\n", + "\n", + "La façon naturelle pour parcourir tous les éléments d'un tableau à plusieurs dimensions est de faire une boucle pour chaque dimension :" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0 1\n", + " 2 3\n", + " 4 5\n" + ] + } + ], + "source": [ + "a = np.arange(6).reshape(3,2)\n", + "for ligne in a:\n", + " for element in ligne:\n", + " print(\" \", element, end=\"\") # end=\"\" avoid the return after each print\n", + " print()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On a vu dans la manipulation de la forme d'un tableau qu'on peut l'applatir, mais plutôt que d'utiliser `flatten()` qui fabrique un tableau en 1 dimension, on préfère utiliser `flat` qui donne [itérateur](https://fr.wikipedia.org/wiki/It%C3%A9rateur) pour parcourir tous les éléments du tableau." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n" + ] + } + ], + "source": [ + "for v in a.flat:\n", + " print(v)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Il est aussi possible de faire une boucle sur les indices mais c'est nettement moins performant." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n" + ] + } + ], + "source": [ + "for i in range(len(a)):\n", + " for j in range(len(a[i])):\n", + " print(a[i,j])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Travailler en vectoriel\n", + "\n", + "Faire des boucles correspond souvent à la facon de penser de ceux qui programment depuis longtemps mais ce n'est pas efficace en Python. Il est préférable \n", + "de travailler directement sur le tableau. Ainsi plutôt que de faire la boucle\n", + "\n", + "```\n", + "for i in range(len(x)):\n", + " z[i] = x[i] + y[i]\n", + "```\n", + "\n", + "on fera\n", + "\n", + "```\n", + "z = x + y\n", + "```\n", + " \n", + "Non seulement c'est plus lisible mais c'est aussi plus rapide." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.5 ms ± 494 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", + "35.3 ms ± 139 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", + "36.9 µs ± 156 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "def double_loop(a):\n", + " for i in range(a.shape[0]):\n", + " for j in range(a.shape[1]):\n", + " a[i,j] = np.sqrt(a[i,j]) # change in-place\n", + "\n", + "def iterate(a):\n", + " for x in a.flat:\n", + " x = np.sqrt(x) # modification not saved in a, x is a local var\n", + "\n", + "b = np.random.random(size=(200,200))\n", + "a = b.copy() # we need a copy to be sure to use the same data each time\n", + "%timeit double_loop(a)\n", + "\n", + "a = b.copy() \n", + "%timeit iterate(a)\n", + "\n", + "a = b.copy()\n", + "%timeit np.sqrt(a) # vectorial operation, 1000 times faster" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma1 np02 Filtres.ipynb b/PVCM/cama/fr/ma1 np02 Filtres.ipynb new file mode 100644 index 0000000..1de9ccc --- /dev/null +++ b/PVCM/cama/fr/ma1 np02 Filtres.ipynb @@ -0,0 +1,411 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 1, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Regardons comment extraire des morceaux d'un tableau ou modifier seulement certaines de ses parties. Pour cela nous\n", + "disposons de deux outils :\n", + " \n", + "* l'extraction suivant les indices\n", + "* l'extraction suivant un filtre logique sur les valeurs" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Filtrer via les indices\n", + "\n", + "On peut extraire des valeurs d'un tableau en fonction de ses indices comme on l'a fait pour les listes. Pour chaque dimension du tableau on peut indiquer\n", + "\n", + "* la valeur de l'indice voulu (un entier)\n", + "* une liste d'indices `debut:fin:saut`. Ainsi `1:6:2` veut dire les valeurs impaires entre l'indice 1 et l'indice 6 exclus. Les valeurs `debut`, `fin` et `saut` sont optionnelles :\n", + " * `:5` donne les 5 première valeurs (indices 0,1,2,3 et 4)\n", + " * `3:` donne de la 4-ième à la dernière valeurs\n", + " * `::3` donne une valeur sur 3 du début à la fin du tableau.\n", + "* une liste d'indices explicite comme `[1,3,-2]` (les valeurs négatives commencent par la fin, `-2` est l'avant dernier indice)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3]\n", + " [ 4 5 6 7]\n", + " [ 8 9 10 11]] \n", + "\n", + "[4 5 6 7] \n", + "\n", + "[[0 1]\n", + " [4 5]] \n", + "\n", + "[ 3 11] \n", + "\n", + "[[ 0 3]\n", + " [ 4 7]\n", + " [ 8 11]]\n" + ] + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "print(a, '\\n')\n", + "print(a[1, :], '\\n') # 2nd line\n", + "print(a[0:2, 0:2], '\\n') # top left sub-matrix\n", + "print(a[::2, -1], '\\n') # even lines, last column\n", + "print(a[:, [0,-1]]) # first and last column" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Il est ainsi possible d'indiquer qu'une opération ne s'applique qu'à un extrait du tableau en indiquant \n", + "quelles sont les cases du tableau qui seront modifiées :" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 101, 2, 103],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 109, 10, 111]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[::2, 1::2] += 100\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Cela permet aussi d'écrire simplement des calculs comme extraire une image en niveau de gris d'une image en couleur :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "image = np.random.randint(256, size=(800, 600, 3)) # RGB 800x600 image\n", + "gray_image = 0.2126 * image[:,:,0] + 0.7152 * image[:,:,1] + 0.0722 * image[:,:,2]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On peut aussi utiliser `...` pour remplacer plusieurs indices ainsi `image[...,0] == image[:,:,0]`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Les filtres logiques\n", + "\n", + "### Un filtre = une condition logique\n", + "\n", + "Numpy permet d'extraire simplement les valeurs qui répondent à une condition logique.\n", + "\n", + "Pour cela on utilise un filtre, à savoir un tableau booléen que l'on pose sur un tableau de même dimension en imaginant que les cases True sont des fenêtres et False des murs. Le résultat est l'ensemble des valeurs qu'on voit à travers les fenêtres ordonnées par leur indice.\n", + "\n", + "Le résultat est toujours un tableau en 1 dimension sauf si on utilise `where`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The filter a > 5 is\n", + " [[False False False False]\n", + " [False False True True]\n", + " [ True True True True]]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([ 6, 7, 8, 9, 10, 11])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "fil = a > 5 # a > 5 means all VALUES greater than 5\n", + "print(\"The filter a > 5 is\\n\", fil)\n", + "a[fil] # apply the filter and show the result (1D array)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Il est bien plus simple et lisible d'écrire la condition logique là où on met normalement les indices, à savoir entre les crochets :" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 6, 7, 8, 9, 10, 11])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a[a>5]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Lorsque le but est le filtre\n", + "\n", + "Le filtre peut servir à autre chose qu'a séléctionner les valeurs de notre tableau. Il peut être le résultat sur lequel on veut travailler, par exemple pour une population `fil = (age == weight)`. C'est un tableau de booléen qui donne des cas vrai et d'autre faux c.a.d. des 0 et des 1.\n", + "\n", + "Ainsi, avec un filtre `fil`, on peut savoir\n", + "\n", + "| | | |\n", + "|:-|:-|:-|\n", + "| combien de cas sont vrai : |`fil.sum()` | |\n", + "| s'il y a au moins un cas vrai : |`fil.sum() > 0` | Numpy offre aussi `np.any(fil)` |\n", + "| si tous les cas sont vrai : |`fil.prod() == 1` | Numpy offre aussi `np.all(fil)` |\n", + "| si au moins un cas est faux : |`fil.prod() == 0` ||\n", + "| si tous les cas sont faux : | `fil.sum() == 0` ||" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### `where` pour gérer les valeurs hors filtre\n", + "\n", + "Pour conserver la forme du tableau il est nécessaire de lui indiquer ce qu'il doit faire des valeurs qui ne remplissent pas la condition. Pour cela on utilise la fonction [`where`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html) :" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 0, 0, 0],\n", + " [ 0, 0, 6, 7],\n", + " [ 8, 9, 10, 11]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.where(a > 5, a, 0) # if a > 5 then a else 0" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On peut faire tous les filtres imaginables qui donnent un tableau de booléan." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, -1, -1, 6],\n", + " [-1, -1, 12, -1],\n", + " [-1, 18, -1, -1]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.where(a%3 == 0, 2*a, -1) # if a modulo 3 is 0 then 2 times a else -1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Mettre à jour un tableau avec un filtre\n", + "\n", + "Une autre facon de conserver la forme du tableau consiste à ne modifier que les valeurs qui correspondent au filtre." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0, 1, 2, 3],\n", + " [ 4, 5, 200, 200],\n", + " [200, 200, 200, 200]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "a[a > 5] = 200\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Voici comment ajouter 100 à toutes les valeurs du tableau qui sont des carrés parfait ainsi qu'à la valeur 5 :" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[100, 101, 2, 3],\n", + " [104, 105, 6, 7],\n", + " [ 8, 109, 10, 11]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(12).reshape(3,4)\n", + "a[(np.round(np.sqrt(a)) - np.sqrt(a) == 0) | (a==5)] += 100 # | is OR (AND is &)\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "variables": { + " PreviousNext(\"np01 Numpy Introduction.ipynb\", \"np03 Manipulations.ipynb\")": "                                                                                                                                                                                                                                                                                                                                                                                                               
np01 Numpy Introduction  ← △ →  np03 Manipulations

 " + } + }, + "source": [ + "{{ PreviousNext(\"np01 Numpy Introduction.ipynb\", \"np03 Manipulations.ipynb\")}}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma1 np03 Manipulations.ipynb b/PVCM/cama/fr/ma1 np03 Manipulations.ipynb new file mode 100644 index 0000000..b676e65 --- /dev/null +++ b/PVCM/cama/fr/ma1 np03 Manipulations.ipynb @@ -0,0 +1,823 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Les [manipulations d'un tableau](https://docs.scipy.org/doc/numpy-1.15.1/reference/routines.array-manipulation.html) comprennent :\n", + "\n", + "* la réorganisation du tableau (réindexation) \n", + "* l'aggrégation de 2 tableaux ou plus\n", + "* le découpage d'un tableau en 2 ou plus\n", + "\n", + "Avant de regarder ces points, regardons comment Numpy présente les\n", + "dimensions d'un tableau multidimensionnel avec la notion d'axes." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2, 4, 3)" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "# An array of marks of 3 exams for 4 students in two subjects \n", + "# (therefore 6 marks per students or 12 per subjects)\n", + "\n", + "# stud.1 stud.2 stud.3 stud.4\n", + "marks = np.array([[[7,13,11], [7,7,13], [5,9,11], [7,17,15]], # subject 1\n", + " [[8,12,14], [8,12,12], [8,12,10], [12,16,12]]]) # subject 2\n", + "marks.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Les axes\n", + "\n", + "Un tableau a des axes qui correspondent aux axes d'un repère dans l'espace. L'ordre des axes\n", + "est celui de l'inclusion des crochets. En 2D un tableau de tableau est un tableau de lignes avec\n", + "chaque ligne qui est un tableau 1D de valeurs. L'ordre est donc lignes puis colonnes (contrairement à l'axes $(x,y)$ dans\n", + "l'espace). En 3D l'ordre est ligne, colonne, profondeur si on désire avoir une image, sinon c'est 0, 1 et 2.\n", + "\n", + "De très nombreuses opérations sur les tableaux se font suivant un des axes du tableau aussi il est important de \n", + "comprendre ce que sont les axes.\n", + "\n", + "Regardons l'exemple des notes ci-dessus. Les axes sont\n", + "\n", + "0. les matières\n", + "1. les étudiants \n", + "2. les examens" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Faire la moyenne des valeurs suivant l'axe 1 revient à prendre les données suivant l'axe 1 et effectuer les calculs dessus, donc ici en sortir une moyenne." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 6.5, 11.5, 12.5],\n", + " [ 9. , 13. , 12. ]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "marks.mean(axis=1) # give means for each exam in each subject" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Un autre facon de voir les axes est de les considérer comme des __axes de projection__. Si je projette un objet 3D\n", + "suivant l'axe des $y$, le résultat est un objet 2D en $(x,z)$. On a ainsi une réduction de dimension.\n", + "\n", + "Si je somme sur l'axe 0 un tableau de dimension (2,4,3) comme l'est notre tableau de notes, cela veut dire que je perds la dimension 0 et donc la dimension du résultat est (4,3).\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(4, 3)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "marks.mean(axis=0).shape # mean along axis 0 (subjects) therefore this axis disapears" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Quelques fonctions qui supportent les axes\n", + "\n", + "Toutes les fonctions qui s'appliquent à un ensemble de valeur pour produire un résultat\n", + "doivent pouvoir utiliser de concept d'axe (je ne les ai pas toutes\n", + "vérifiées mais n'hésitez pas à m'indiquer un contre-exemple). On a les fonctions mathématiques suivantes :\n", + "\n", + "* arithmétiques : `sum`, `prod`, `cumsum`, `cumprod` \n", + "* statistiques : `min`, `max`, `argmin`, `argmax`, `mean` (moyenne), `average` (moyenne pondérée), `std` (écart type), `var`, `median`, `percentile`, `quantile`\n", + "* autres : `gradiant`, `diff`, `fft`\n", + "\n", + "De plus il est possible de trier les valeurs d'un tableau suivant l'axe de son choix avec `sort`.\n", + "Par contre on ne peut les mélanger, avec [`shuffle`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.random.shuffle.html#numpy.random.shuffle), que suivant l'axe 0.\n", + "\n", + "#### Appliquer une fonction suivant un axe\n", + "\n", + "La fonction [`apply_along_axis`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.apply_along_axis.html)\n", + "permet d'appliquer une fonction 1D de son choix à un tableau suivant un axe. C'est l'axe qui va disparaître dans le résultat :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-> [ 7 13 11] 6\n", + "-> [ 7 7 13] 6\n", + "-> [ 5 9 11] 6\n", + "-> [ 7 17 15] 10\n", + "-> [ 8 12 14] 6\n", + "-> [ 8 12 12] 4\n", + "-> [ 8 12 10] 4\n", + "-> [12 16 12] 4\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[ 6, 6, 6, 10],\n", + " [ 6, 4, 4, 4]])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def diff_min_max(a):\n", + " print('->', a, a.max() - a.min())\n", + " return a.max() - a.min()\n", + "\n", + "np.apply_along_axis(diff_min_max, axis=-1, arr=marks) # -1 is the last axis, marks in our case" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Question : c'est l'écart entre les notes de quoi ?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Appliquer une fonction suivant plusieurs axes\n", + "\n", + "Certaines opérations peuvent prendre une liste d'axes et non un seul axe.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a.max \n", + " [17 16] \n", + "\n", + "a.max keepdim \n", + " [[[17]]\n", + "\n", + " [[16]]] \n", + "\n" + ] + } + ], + "source": [ + "print('a.max \\n', marks.max(axis=(1,2)), '\\n') \n", + "print('a.max keepdim \\n', marks.max(axis=(1,2), keepdims=True), '\\n') " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Question : à quoi correspondent les 2 valeurs sorties ?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Il est également peut utiliser la fonction [`apply_over_axes`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.apply_over_axes.html#numpy.apply_over_axes) pour lui indiquer quelle\n", + "fonction doit être appliquée suivant les axes donnés.\n", + "\n", + "Attention la fonction donnée en argument recevra l'ensemble du tableau et l'axe sur lequel elle doit\n", + "travailler, les axes étant donnés les uns après les autres et le tableau étant modifié à chaque étape." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Apply over axis 1\n", + "[[[ 7 13 11]\n", + " [ 7 7 13]\n", + " [ 5 9 11]\n", + " [ 7 17 15]]\n", + "\n", + " [[ 8 12 14]\n", + " [ 8 12 12]\n", + " [ 8 12 10]\n", + " [12 16 12]]] \n", + "\n", + "Apply over axis 2\n", + "[[[ 7 17 15]]\n", + "\n", + " [[12 16 14]]] \n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[[17]],\n", + "\n", + " [[16]]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def mymax(array, axis):\n", + " print('Apply over axis', axis)\n", + " print(array, '\\n')\n", + " return array.max(axis)\n", + "\n", + "np.apply_over_axes(mymax, marks, axes=(1,2))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Réorganisation d'un tableau\n", + "\n", + "On a déjà vu `reshape` pour changer la forme d'un tableau, `flatten` pour l'applatir en 1 dimension, regardons\n", + "d'autres fonctions de manipulation des tableaux.\n", + "\n", + "### Réordonner les axes\n", + "\n", + "#### `moveaxis` déplace un axe\n", + "\n", + "Dans notre exemple de notes, les 3 axes sont les matières, les étudiants et les examens.\n", + "La fonction `moveaxis` permet de déplacer un axe. Si ainsi je désire que les examens deviennent le premier axe\n", + "afin d'en faire ressortir les notes, je déplace l'axe 2 à la position 0 et les autres axes glissent pour faire de la place, l'axe 0 devient l'axe 1 et l'axe 1 devient l'axe 2 :" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "marks.shape = (2, 4, 3) \n", + "\n", + "b.shape = (3, 2, 4)\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[[ 7, 7, 5, 7],\n", + " [ 8, 8, 8, 12]],\n", + "\n", + " [[13, 7, 9, 17],\n", + " [12, 12, 12, 16]],\n", + "\n", + " [[11, 13, 11, 15],\n", + " [14, 12, 10, 12]]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print('marks.shape = ',marks.shape, '\\n')\n", + "b = np.moveaxis(marks, 2, 0) \n", + "print('b.shape = ', b.shape)\n", + "b" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Il est plus simple de voir ainsi que le premier examen a été difficile." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### `swapaxes` échange 2 axes\n", + "\n", + "Plutôt que d'insérer un axe à une nouvelle position et faire glisser les autres, on peut vouloir en échanger deux.\n", + "Voici comme avoir les notes pour chaque matière et chaque examen : " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[ 7, 7, 5, 7],\n", + " [13, 7, 9, 17],\n", + " [11, 13, 11, 15]],\n", + "\n", + " [[ 8, 8, 8, 12],\n", + " [12, 12, 12, 16],\n", + " [14, 12, 10, 12]]])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "marks.swapaxes(1,2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### `transpose` pour tout faire\n", + "\n", + "Enfin `transpose` permet de réordonner tous les axes comme on veut, ainsi : `transpose((2,0,1))` met\n", + "\n", + "* l'axe 2 en place 0, \n", + "* l'axe 0 en place 1 \n", + "* l'axe 1 en place 2.\n", + "\n", + "#### Un apply over axis plus simple et plus rapide\n", + "\n", + "Malheureusement la fonction `apply_over_axis` n'est pas optimisée, aussi dans certaints il peut\n", + "être préférable de faire une boucle sur son tableau, ce qui veut dire mettre les axes qui vont rester au début et ceux sur lesquels on fait notre réduction à la fin :" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Means per students [10.833333333333334, 9.833333333333334, 9.166666666666666, 13.166666666666666]\n", + "24 µs ± 2.01 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n", + "29.6 µs ± 1.23 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "print(\"Means per students\", [m.mean() for m in marks.transpose((1,0,2))])\n", + "\n", + "%timeit [m.mean() for m in marks.transpose((1,0,2))]\n", + "%timeit np.apply_over_axes(np.mean, marks, axes=(0,2))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Changer l'ordre des éléments d'un tableau\n", + "\n", + "On peut inverser les valeurs d'un tableau suivant un axe avec [`flip`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.flip.html#numpy.flip)\n", + "ce qui peut aussi être fait en l'indiquant au niveau des indices. Ainsi `np.flip(a, n)` est équivalent à \n", + "`a[:,:,..,::-1,:,..,:]` avec `::-1` en $n$-ième position.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[12, 13, 14, 15],\n", + " [16, 17, 18, 19],\n", + " [20, 21, 22, 23]],\n", + "\n", + " [[ 0, 1, 2, 3],\n", + " [ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11]]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.arange(24).reshape([2,3,4])\n", + "np.flip(a,0)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On peut faire glisser les valeurs suivant un axe avec `roll` en spécifiant de combien on les fait glisser :" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[ 4, 5, 6, 7],\n", + " [ 8, 9, 10, 11],\n", + " [ 0, 1, 2, 3]],\n", + "\n", + " [[16, 17, 18, 19],\n", + " [20, 21, 22, 23],\n", + " [12, 13, 14, 15]]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.roll(a, 2, axis=1) # roll elements by 2 along axis 1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "La transposée s'applique aussi quelque soit la dimension. Par défaut elle inverse l'ordre des axes mais on peut \n", + "spécifier l'ordre voulu en sortie." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[ 0, 12],\n", + " [ 4, 16],\n", + " [ 8, 20]],\n", + "\n", + " [[ 1, 13],\n", + " [ 5, 17],\n", + " [ 9, 21]],\n", + "\n", + " [[ 2, 14],\n", + " [ 6, 18],\n", + " [10, 22]],\n", + "\n", + " [[ 3, 15],\n", + " [ 7, 19],\n", + " [11, 23]]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a.T" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[ 0, 4, 8],\n", + " [ 1, 5, 9],\n", + " [ 2, 6, 10],\n", + " [ 3, 7, 11]],\n", + "\n", + " [[12, 16, 20],\n", + " [13, 17, 21],\n", + " [14, 18, 22],\n", + " [15, 19, 23]]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.transpose(a, (0,2,1))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Agrégation\n", + "\n", + "### Concaténation\n", + "\n", + "La fonction de base est [`concatenate`](https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.concatenate.html) en indiquant l'axe choisi pour la concaténation. C'est à mon avis la méthode\n", + "la plus sûre et elle marche quelque soit la dimension.\n", + "\n", + "Cela étant on peut utiliser pour des tableaux 2D ou 3D :\n", + "\n", + "* `vstack` ou `row_stack` pour la concaténation vertical \n", + "* `hstack` ou `column_stack` pour la concaténation horizontal\n", + "* `dstack` pour la concaténation en profondeur (_deep_).\n", + "\n", + "Toutes ces fonctions prennent une liste de tableaux à concaténer comme argument. Bien sûr les tailles des tableaux doivent être compatibles." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. 0.]\n", + " [0. 0. 0.]\n", + " [1. 1. 1.]\n", + " [1. 1. 1.]] \n", + "\n", + "[[0. 0. 0. 1. 1. 1.]\n", + " [0. 0. 0. 1. 1. 1.]]\n" + ] + } + ], + "source": [ + "a = np.zeros((2,3))\n", + "b = np.ones((2,3))\n", + "\n", + "print(np.concatenate((a,b), axis=0), '\\n') # same than vstack\n", + "print(np.hstack((a,b))) # same than concatenate with axis=1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Empilage\n", + "\n", + "A la différence de la concaténation, l'empilage ajoute une dimension.\n", + "Empiler est utile pour stocker un paquet de tableaux 2D, des images par exemple, dans un tableau 3D. \n", + "On utilise la fonction [`stack`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.stack.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[0., 0., 0.],\n", + " [0., 0., 0.]],\n", + "\n", + " [[1., 1., 1.],\n", + " [1., 1., 1.]]])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = np.stack((a,b)) # c[0] is a\n", + "c" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Notez que `stack` a une option `axis` pour indiquer la direction dans laquelle on désire stocker les tableaux donnés." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Découpage\n", + "\n", + "La fonction inverse de la concaténation est le découpage avec [`split`](https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.split.html#numpy.split) qui demande comme arguments :\n", + "\n", + "* le tableau à découper\n", + "* en combien de morceaux ou à quels indices\n", + "* la direction (l'axe)\n", + "\n", + "Pour retrouver nos deux tableaux qui ont généré le résultat de la cellule précédante on coupe en 2 suivant l'axe 0. On peut aussi couper suivant un autre axe." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "split part 1\n", + " [[[0. 0. 0.]]\n", + "\n", + " [[1. 1. 1.]]] \n", + "\n", + "split part 2\n", + " [[[0. 0. 0.]]\n", + "\n", + " [[1. 1. 1.]]]\n" + ] + } + ], + "source": [ + "e,f = np.split(c, 2, 1) # splits in 2 along axis 1\n", + "print(\"split part 1\\n\", e, '\\n')\n", + "print(\"split part 2\\n\", f)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Il existe aussi `hsplit`, `vsplit` et `dsplit` pour découper suivant les axes 0, 1 et 2.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## From Python to Numpy\n", + "\n", + "Si vous désirez creuser et regarder de nombreux exemples, vous pouvez lire le livre de N. Rougier [From Python to Numpy](https://www.labri.fr/perso/nrougier/from-python-to-numpy/)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "\n", + "## Pandas aussi\n", + "\n", + "On retrouvera ces manipulations avec Pandas qui est le super tableur de Python. Il travaille aussi sur des \n", + "structures en forme de tableau mais sans la contrainte que toutes les valeurs soient du même type.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "variables": { + " PreviousNext(\"np02 Filtres.ipynb\", \"np04 Xarray.ipynb\")": "                                                                                                                                                                                                                                                                                                                                                                                                               
np02 Filtres  ← △ →  np04 Xarray

 " + } + }, + "source": [ + "{{ PreviousNext(\"np02 Filtres.ipynb\", \"np04 Xarray.ipynb\")}}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma1 np05 Notation Einstein.ipynb b/PVCM/cama/fr/ma1 np05 Notation Einstein.ipynb new file mode 100644 index 0000000..1fc6ed7 --- /dev/null +++ b/PVCM/cama/fr/ma1 np05 Notation Einstein.ipynb @@ -0,0 +1,323 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Présentation de la notation d'Einstein\n", + "\n", + "Cette notation permet d'exprimer de facon concise un nombre extraordinaire d'opérations. Cette section n'est pas\n", + "nécessaire pour la suite mais c'est un exercice intellectuel intéressant.\n", + "\n", + "L'idée est base est de sommer les termes d'une équation lorsqu'on y trouve 2 fois un même indice qui n'est pas défini par ailleurs. Ainsi :\n", + "\n", + "$$ A_{i,i} \\quad \\textrm{veut dire} \\quad \\sum_{i=1}^N A_{i,i} \\; \\textrm{(la trace de la matrice)}$$\n", + "\n", + "Si on regarde la multiplication matricielle $A\\, B$ on a pour tout indice (i,j) du résultat :\n", + "\n", + "$$ C_{i,j} = A_{i,k} \\, B_{k,j} \\quad \\textrm{c.a.d} \\quad C_{i,j} = \\sum_{k=1}^N A_{i,k} \\, B_{k,j} $$ \n", + "\n", + "Le nom complet de la notation d'Einstein étant la convention de sommation d'Einstein, la fonction de Numpy est [`einsum`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.einsum.html). Voici ce que cela donne pour nos 2 premiers exemples :" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Trace 'ii' : 12 \n", + "\n", + "Multiplication matricielle A A 'ij,jk->ik' :\n", + "[[ 15 18 21]\n", + " [ 42 54 66]\n", + " [ 69 90 111]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "A = np.arange(9).reshape(3,3)\n", + "\n", + "print(\"Trace 'ii' : \", np.einsum('ii', A), '\\n') # 0 + 4 + 8 = 12\n", + "\n", + "print(\"Multiplication matricielle A A 'ij,jk->ik' :\")\n", + "print(np.einsum('ij,jk->ik', A, A)) # notez que j'ai nommé différement les indices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 15, 18, 21],\n", + " [ 42, 54, 66],\n", + " [ 69, 90, 111]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.dot(A) # on vérifie" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On note que les arguments de `einsum` sont :\n", + "\n", + "* la règle de sommation dans une chaine de caractères avec une virgule pour séparer chaque composant\n", + "* les composants sur lesquels s'applique la règle\n", + "\n", + "On peut aller un peu plus loin avec Numpy. Voici l'ensemble des règles qu'utilise `einsum` :\n", + "\n", + "#### Règles de base et complémentaires\n", + "\n", + "1. un indice répété implique une sommation sur cet indice sauf si cet indice est cité dans le résultat
(cf exemple diagonale de A ci-dessous pour l'exception)\n", + "2. les indices qui se répètent d'un composant à un autre impliquent que les éléments référencés seront multipliés entre eux
(cf exemple du produit matriciel)\n", + "3. un lettre omise dans le résultat (après `->`) implique que l'on sommme les éléments sur cet indice
(cf exemple de la somme des éléments d'un vecteur ci-dessous)\n", + "4. si on ne met pas la flèche, einsum la met pour vous avec à droite tous les indices qui ne sont pas doublés rangés par ordre alphabétique
(cf exemple de la transposée ci-dessous)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Voici une liste d'opérations prises sur le [blog du Dr Goulu](https://www.drgoulu.com/2016/01/17/einsum) :\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
Signature de einsuméquivalent NumPyDescription
('i->', v)sum(v)somme des valeurs du vecteur v
('i,i->i', u, v)u \\* vmultiplication des vecteurs u et v élément par élément
('i,i', u, v)inner(u, v)produit scalaire de u et v
('i,j', u, v)outer(u, v)produit dyadique de u et v
('ij', A)Arenvoie la matrice A
('ji', A)A.Ttransposée de A
('ii->i', A)diag(A)diagonale de A
('ii', A)trace(A)somme de la diagonale de A
('ij->', A)sum(A)somme des valeurs de A
('ij->j', A)sum(A, axis=0)somme des colonnes de A
('ij->i', A)sum(A, axis=1)somme des lignes de A
('ij,ij->ij', A, B)A \\* Bmultiplication des matrices A et B élément par élément
('ij,ji->ij', A, B)A \\* B.Tmultiplication des matrices A et B transposée élément par élément
('ij,jk', A, B)dot(A, B)produit scalaire de A et B
('ij,jk->ij', A, B)inner(A, B)produit intérieur de A et B
('ij,jk->ijk', A, B)A[:, None] \\* Bchaque ligne de A multipliée par B
('ij,kl->ijkl', A, B)A[:, :, None, None] \\* Bchaque valeur de A multipliée par B
\n", + "\n", + "Le `None` dans les deux dernières lignes est une facon de redimensionner un tableau. Ainsi `np.arange(6)` est un tableau de dimension 1, `np.arange(6)[:]` est le même tableau de dimension 1, alors que `np.arange(6)[:,None]` est un tableau de dimension 2 à savoir `6 x 1` quand `np.arange(6)[None,:,None]` a 3 dimensions : `1 x 6 x 1`." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Mise en pratique\n", + "\n", + "On va comparer les performances d'`einsum` et des fonctions Numpy correspondante. Pour cela calculez\n", + "\n", + "* le cube de chaque élement d'un vecteur\n", + "* d'une matrice carrée, $A^3$,\n", + "\n", + "avec `einsum` et sans. Comparez la vitesse d'exécution dans tous les cas avec 10000 éléments." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# a vous de jouer\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solution :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "11.5 µs ± 112 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n", + "15.2 µs ± 131 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n" + ] + } + ], + "source": [ + "u = np.random.random(10000)\n", + "\n", + "%timeit u*u*u\n", + "%timeit np.einsum('i,i,i->i', u,u,u)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "138 µs ± 9.48 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n", + "134 ms ± 1.12 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "A = u.reshape(100,100)\n", + "\n", + "%timeit A.dot(A).dot(A)\n", + "%timeit np.einsum('ij,jk,kl->il', A, A, A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On constate qu'`einsum` est plus lent (\\*). Mais en regardant sur le web on constate que cela n'a pas toujours été le cas et que c'est lié à la version de la bibliothèque Numpy. Conclusion si on veut de la performance, il faut tester son code avant pour choisir la méthode la plus rapide.\n", + "\n", + "(\\*) un peu plus lent pour le calcul vectoriel mais 1000 fois plus lent sur mon portable pour `A.dot(A)` (tous mes processeurs tournent à 100% alors que le calcul par `einsum` n'est fait que sur 1 seul processeur). La version `A.dot(A)` est nettement plus rapide grace à la bibliothèque MKL qu'utilise Numpy sur ma machine." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma1 np06 Linalg pour le calcul matriciel.ipynb b/PVCM/cama/fr/ma1 np06 Linalg pour le calcul matriciel.ipynb new file mode 100644 index 0000000..642bf0d --- /dev/null +++ b/PVCM/cama/fr/ma1 np06 Linalg pour le calcul matriciel.ipynb @@ -0,0 +1,426 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 1, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Linalg (linear algebra)\n", + "\n", + "Numpy intègre le calcul matriciel (ou l'algèbre linéaire) dans sa sous-bibliothèque [numpy.linalg](https://docs.scipy.org/doc/numpy/reference/routines.linalg.html). Pour être efficace il est\n", + "important que Numpy soit relié aux bibliothèques [Lapack](https://www.netlib.org/lapack/) et [BLAS](https://www.netlib.org/blas/) (la version d'Intel est [MKL](https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl.html)). Ces bibliothèques sont imbatables, Numpy relié à ces bibliothèques sera largement plus rapide qu'un programme dans n'importe quel autre langage qui ne les utilise pas (vous relevez le défi ?).\n", + "\n", + "La bibliothèque [Scipy](https://scipy.org/) a aussi une sous-bibliothèque [linalg](https://docs.scipy.org/doc/scipy/reference/linalg.html) qui est très proches. Si vous ne trouvez pas\n", + "ce que vous cherchez dans la version de Numpy, il peut être intéressant de regarder si Scipy l'a." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "blas_mkl_info:\n", + " NOT AVAILABLE\n", + "blis_info:\n", + " NOT AVAILABLE\n", + "openblas_info:\n", + " libraries = ['openblas', 'openblas']\n", + " library_dirs = ['/usr/local/lib']\n", + " language = c\n", + " define_macros = [('HAVE_CBLAS', None)]\n", + " runtime_library_dirs = ['/usr/local/lib']\n", + "blas_opt_info:\n", + " libraries = ['openblas', 'openblas']\n", + " library_dirs = ['/usr/local/lib']\n", + " language = c\n", + " define_macros = [('HAVE_CBLAS', None)]\n", + " runtime_library_dirs = ['/usr/local/lib']\n", + "lapack_mkl_info:\n", + " NOT AVAILABLE\n", + "openblas_lapack_info:\n", + " libraries = ['openblas', 'openblas']\n", + " library_dirs = ['/usr/local/lib']\n", + " language = c\n", + " define_macros = [('HAVE_CBLAS', None)]\n", + " runtime_library_dirs = ['/usr/local/lib']\n", + "lapack_opt_info:\n", + " libraries = ['openblas', 'openblas']\n", + " library_dirs = ['/usr/local/lib']\n", + " language = c\n", + " define_macros = [('HAVE_CBLAS', None)]\n", + " runtime_library_dirs = ['/usr/local/lib']\n", + "Supported SIMD extensions in this NumPy install:\n", + " baseline = SSE,SSE2,SSE3\n", + " found = SSSE3,SSE41,POPCNT,SSE42,AVX,F16C,FMA3,AVX2\n", + " not found = AVX512F,AVX512CD,AVX512_KNL,AVX512_KNM,AVX512_SKX,AVX512_CLX,AVX512_CNL,AVX512_ICL\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3)\n", + "np.show_config()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "lang": "fr" + }, + "source": [ + "## Opérations de base\n", + "\n", + "On a vu que les opérateurs +, -, \\* et / sont appliqués terme à terme ce qui est juste pour + et - dans le cadre du calcul matriciel mais pas pour \\* et /.\n", + "\n", + "* Le __produit scalaire__ utilise la méthode `dot` ou l'opérateur `@`\n", + "* La division que l'on peut imaginer comme \n", + " * la __résolution__ d'un système matriciel utilise la fonction `solve`\n", + " * le calcul de l'__inverse__ de la matrice utilise la fonction `inv`" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "multiplication terme à terme : \n", + " [[ 1 4]\n", + " [ 9 16]]\n", + "produit matriciel : \n", + " [[ 7 10]\n", + " [15 22]]\n" + ] + } + ], + "source": [ + "A = np.array([[1,2],[3,4]])\n", + "print(\"multiplication terme à terme : \\n\",A * A) # tous les opérateurs sont appliqués terme à terme\n", + "print(\"produit matriciel : \\n\", A.dot(A)) # A @ A can be used too" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Résolution de système matriciel :" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [3. 7.]\n", + "verification : [17. 37.]\n" + ] + } + ], + "source": [ + "b = np.array([17,37])\n", + "x = lin.solve(A, b) # bien mieux que de calculer la matrice inverse (plus rapide et plus stable)\n", + "print(\"x = \", x)\n", + "print(\"verification : \", A @ x)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Si on le désire vraiment, on peut calculer la matrice inverse (mais c'est plus long) :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A⁻¹ :\n", + " [[-2. 1. ]\n", + " [ 1.5 -0.5]]\n", + "x = [3. 7.]\n" + ] + } + ], + "source": [ + "print(\"A⁻¹ :\\n\", lin.inv(A)) # la matrice inverse\n", + "print(\"x = \", lin.inv(A).dot(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Enfin __la transposée__ est simplement `T` :" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 3],\n", + " [2, 4]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.T" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Extractions\n", + "\n", + "On peut récupérer\n", + "\n", + "* la diagonale d'une matrice avec la fonction `diag` (attention le résultat est un vecteur si l'argument est une matrice et une matrice si l'argument est un vecteur)\n", + "* la matrice triangulaire inférieur avec la fonction `tril` (l pour lower) et supérieure avec `triu` (u pour upper). Il est possible de décaler la diagonale du triangle, voir la doc\n", + "\n", + "On peut aussi construire une matrice triangulaire avec des 1 et 0 avec `tri`et donc aussi une matrice triangulaire quelconque :" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4., 0., 0.],\n", + " [8., 9., 0.],\n", + " [5., 5., 4.]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.tri(3,3) * np.random.randint(1, 10, size=(3,3))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Et voici comme extraire une matrice tridiagonale :" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[3, 7, 0, 0, 0],\n", + " [6, 1, 8, 0, 0],\n", + " [0, 3, 5, 9, 0],\n", + " [0, 0, 4, 4, 7],\n", + " [0, 0, 0, 6, 3]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.random.randint(1, 10, size=(5,5))\n", + "np.tril(np.triu(A, k=-1), k=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Opérations sur la matrice\n", + "\n", + "La bibliothèque offre des fonctions de\n", + "\n", + "* décomposition (LU, Choleski, QR, SVD...)\n", + "* valeurs et vecteurs propres\n", + "* norme, déterminant, conditionnement et rang" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-0.349 0.585 0.132 0.359 0.624]\n", + " [-0.697 -0.557 0.221 -0.298 0.257]\n", + " [-0.465 -0.061 -0.052 0.668 -0.576]\n", + " [-0.349 0.585 0.132 -0.564 -0.447]\n", + " [-0.232 0.036 -0.956 -0.134 0.115]] \n", + "\n", + " [[ -8.602 -7.44 -10.927 -13.252 -10.23 ]\n", + " [ 0. 7.527 -0.039 3.907 7.559]\n", + " [ 0. 0. 1.61 -3.513 -0.301]\n", + " [ 0. 0. 0. 4.333 0.656]\n", + " [ 0. 0. 0. 0. 1.302]]\n", + "\n", + "Vérification :\n", + " [[3. 7. 4. 8. 9.]\n", + " [6. 1. 8. 5. 3.]\n", + " [4. 3. 5. 9. 4.]\n", + " [3. 7. 4. 4. 7.]\n", + " [2. 2. 1. 6. 3.]]\n" + ] + } + ], + "source": [ + "Q,R = lin.qr(A) # Q est orthogonale, R est triangulaire supérieur\n", + "print(Q, '\\n\\n', R)\n", + "print(\"\\nVérification :\\n\", Q.dot(R))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Valeurs propres et vecteurs propres" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([23.099+0.j , -3.442+1.822j, -3.442-1.822j, -1.408+0.j ,\n", + " 1.192+0.j ]),\n", + " array([[-0.547+0.j , -0.191+0.047j, -0.191-0.047j, -0.51 +0.j ,\n", + " 0.487+0.j ],\n", + " [-0.457+0.j , -0.035-0.466j, -0.035+0.466j, -0.462+0.j ,\n", + " -0.423+0.j ],\n", + " [-0.476+0.j , 0.441+0.128j, 0.441-0.128j, 0.41 +0.j ,\n", + " -0.519+0.j ],\n", + " [-0.447+0.j , -0.536+0.j , -0.536-0.j , -0.167+0.j ,\n", + " -0.101+0.j ],\n", + " [-0.257+0.j , 0.435+0.233j, 0.435-0.233j, 0.575+0.j ,\n", + " 0.552+0.j ]]))" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lin.eig(A) # donne les valeurs propres et les vecteurs propres de A" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Déterminant, norme etc. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Déterminant : -587.9999999999999\n", + "Norme 2 : 26.343879744638983 \n", + "Norme 1 : 32.0\n", + "Conditionnement : 35.929347867977604\n" + ] + } + ], + "source": [ + "print(\"Déterminant :\", lin.det(A))\n", + "print(\"Norme 2 :\", lin.norm(A), \"\\nNorme 1 :\", lin.norm(A, 1) )\n", + "print(\"Conditionnement :\", lin.cond(A,2)) # I choose norm 2 to compute the condition number" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma1 np90 petits exercices.ipynb b/PVCM/cama/fr/ma1 np90 petits exercices.ipynb new file mode 100644 index 0000000..8b08f12 --- /dev/null +++ b/PVCM/cama/fr/ma1 np90 petits exercices.ipynb @@ -0,0 +1,529 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "048aaf2b", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Numpy - Exercices\n", + "\n", + "Voici une série de tests pour vérifier ses connaissances en Numpy. Le but est que cette bibliothèque et la programmation vectorielle qu'elle implique deviennent naturelles. Il faut oublier la programmation classique avec des boucles (il ne faut pas utiliser de boucle `for` ou autre dans cette feuille en dehors de construction de [liste en compréhension](../../lesson1%20Python%20basics/03%20-%20Tests%20et%20boucles.ipynb) ).\n", + "\n", + "Les fonctions ne doivent jamais modifier les arguements.\n", + "\n", + "Les exercices indique le nombre de ligne de la réponse. Cela comprend l'en-tête de la fonction lorsqu'il y en a une.\n", + "\n", + "Pensez à tester vos résultats." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8c0a79d0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3]\n", + " [ 4 5 6 7]\n", + " [ 8 9 10 11]] \n", + "\n", + "[[ 3 -8 -8 -4 7]\n", + " [ 9 0 -9 -10 7]\n", + " [ 5 -1 -10 4 -10]\n", + " [ 5 9 4 -6 -10]\n", + " [ 6 -6 7 -7 -8]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "rand = np.random.RandomState(123)\n", + "\n", + "A = np.arange(12).reshape(3,4)\n", + "B = rand.randint(-10, 10, size=(5,5))\n", + "print(A, '\\n')\n", + "print(B)" + ] + }, + { + "cell_type": "markdown", + "id": "51317493", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Matrice carrée\n", + "\n", + "Créer la matrice carrée 5x5 qui contient les 25 premiers entiers, de 1 à 25.\n", + "\n", + "1 ligne" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "14ccdaf5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1, 2, 3, 4, 5],\n", + " [ 6, 7, 8, 9, 10],\n", + " [11, 12, 13, 14, 15],\n", + " [16, 17, 18, 19, 20],\n", + " [21, 22, 23, 24, 25]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.arange(1, 26).reshape(5,5)" + ] + }, + { + "cell_type": "markdown", + "id": "3b797402", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Norme d'un vecteur\n", + "\n", + "Retourner la norme euclidienne d'un vecteur sans utiliser la fonction `norm`.\n", + "\n", + "2 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "079b9d00", + "metadata": {}, + "outputs": [], + "source": [ + "def norm(v):\n", + " return np.sqrt(v.dot(v))" + ] + }, + { + "cell_type": "markdown", + "id": "05888df0", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Sous-matrice\n", + "\n", + "Extraire la sous-matrice de taille (n-2)x(m-2) qui retire les bords de la matrice A de taille nxm.\n", + "\n", + "2 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1c313908", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 6, 7, 8],\n", + " [11, 12, 13],\n", + " [16, 17, 18]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def submat(A):\n", + " return A[1:-1,1:-1]" + ] + }, + { + "cell_type": "markdown", + "id": "d8569c30", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Vecteur aléatoire\n", + "\n", + "Créer une fonction qui prend une taille n et retourne un vecteur d'entiers aléatoire de taille n compris entre -a et +a et centré le plus possible en 0.\n", + "\n", + "3 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "e93d8900", + "metadata": {}, + "outputs": [], + "source": [ + "def rand_vec(n, a):\n", + " return np.random.normal(scale=a/2,size=n)" + ] + }, + { + "cell_type": "markdown", + "id": "fedb8b70", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Trace\n", + "\n", + "Retourner la trace d'une matrice sans utiliser la fonction `trace` (à vous de chercher les éléments qui vous manque).\n", + "\n", + "2 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "8df7f55b", + "metadata": {}, + "outputs": [], + "source": [ + "def trace(A):\n", + " return np.sum(np.diag(A))" + ] + }, + { + "cell_type": "markdown", + "id": "4e1c14f2", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Matrice de multiples de 3\n", + "\n", + "Arrondir la matrice donnée au multiple de 3 le plus proche (pour chaque valeur).\n", + "\n", + "2 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "55860b91", + "metadata": {}, + "outputs": [], + "source": [ + "def round3(A):\n", + " return np.vectorize(lambda n : 3 * round(n / 3))(A)\n", + " #return [3 * round(number / 3) for number in row for row in A]" + ] + }, + { + "cell_type": "markdown", + "id": "68b9db16", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Nombre de 9\n", + "\n", + "Compter le nombre de 9 dans une matrice d'entier A donnée en paramètre.\n", + "\n", + "2 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9296a705", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def nb9(A):\n", + " return len(A[A == 9])" + ] + }, + { + "cell_type": "markdown", + "id": "b2927718", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Colonne qui a la plus petite moyenne\n", + "\n", + "Retourner l'indice de la colonne d'une matrice ayant la plus petite moyenne.\n", + "\n", + "2 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c3c9d6a1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "np.int64(0)" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def min_col_mean(A):\n", + " return np.argmin(A.mean(axis=0))" + ] + }, + { + "cell_type": "markdown", + "id": "1e2591d1", + "metadata": { + "lang": "fr" + }, + "source": [ + "### ChessSum\n", + "\n", + "On regarde la matrice comme un échequier avec des cases blanches et des cases noires qui alternent. La case en [0,0] est noire. \n", + "Calculer la somme des valeurs sur les cases blanches.\n", + "\n", + "2 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "3921063c", + "metadata": {}, + "outputs": [], + "source": [ + "def chess_sum(A):\n", + " return np.sum(A[0::2,1::2]) + np.sum(A[1::2,0::2])" + ] + }, + { + "cell_type": "markdown", + "id": "5e0ffb99", + "metadata": { + "lang": "fr" + }, + "source": [ + "### 2 minimums\n", + "\n", + "Retourner les 2 plus petites valeurs d'une matrice avec une méthode de complexité linéaire. Attention, si la matrice a sa valeur minimal en double, la réponse est deux fois cette valeur minimale.\n", + "\n", + "6 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b680cc53", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[np.int64(1), np.int64(2)]" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def mins(A):\n", + " t = np.min(A)\n", + " if len(A[A == t]) == 1:\n", + " return [t,np.min(A[A > t])]\n", + " return [t,t]" + ] + }, + { + "cell_type": "markdown", + "id": "0265738a", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Lignes dans l'ordre\n", + "\n", + "Ranger les lignes d'une matrice dans l'ordre croissant de leur moyenne.\n", + "\n", + "2 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "5784c5be", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 2, 3],\n", + " [4, 5, 6],\n", + " [7, 8, 9]])" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def sort_lines(A):\n", + " return A[A.sum(axis=1).argsort()]\n", + "sort_lines(np.array([[4, 5, 6],\n", + " [1, 2, 3], \n", + " [7, 8, 9]]))" + ] + }, + { + "cell_type": "markdown", + "id": "0c80e353", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Valeurs uniques\n", + "\n", + "Donner la liste des valeurs uniques (qui n'apparaissent qu'une fois) dans un tableau numpy (la fonction `unique` sera utile).\n", + "\n", + "3 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "id": "c95ce1bb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([], dtype=int64)" + ] + }, + "execution_count": 97, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def val_unique(A):\n", + " res = np.unique(A, equal_nan=False, return_index=True, return_counts=True)\n", + " return A.flatten()[res[1][res[2] == 1]]\n", + "val_unique(np.array([[1,1,1],[3,3,3]]))" + ] + }, + { + "cell_type": "markdown", + "id": "006b473a", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Tenseur magique\n", + "\n", + "Constuire un tenseur 3D de taille nxnxn en utilisant n fois les n² premiers entiers et de sorte que la sommme des éléments de chaque plan (coupe) est toujours la même.\n", + "\n", + "3 lignes" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c1ca40c0", + "metadata": {}, + "outputs": [], + "source": [ + "def mk_magic_tensor(n):\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "405f3308", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Plans d'un tenseur\n", + "\n", + "Extraire tous les plans d'un tenseur 3d. On retourne une liste de tableaux.\n", + "\n", + "5 lignes (2 lignes avec la fonction `take`)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "e4d39b2a", + "metadata": {}, + "outputs": [], + "source": [ + "def extract_planes(T):\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "761e6ee4", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/PVCM/cama/fr/ma20 Rappels sur les matrices.ipynb b/PVCM/cama/fr/ma20 Rappels sur les matrices.ipynb new file mode 100644 index 0000000..d686249 --- /dev/null +++ b/PVCM/cama/fr/ma20 Rappels sur les matrices.ipynb @@ -0,0 +1,531 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "**Note** : Le code Python doit être ignoré jusqu'au premier TP." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def arrow2D(a,b, color='k', text=\"\", **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " a,b = np.array(a), np.array(b)\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))\n", + " direction = (b - a) / np.sqrt(np.square(b - a).sum())\n", + " plt.text(*(b + 0.1 * direction), r\"$\\bf\" + text + r\"$\", horizontalalignment='center', size=14)\n", + " \n", + "def vector(v, color='k', text='', **kargs):\n", + " arrow2D([0,0], v, color, text)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Vecteur\n", + "\n", + "Un vecteur est\n", + "\n", + "* une flèche qui indique une direction et dont la longueur mesure une intensité (vision de physicien)\n", + "* un tableau avec 2 valeurs en 2D ou 3 en 3D (vision d'informaticien)\n", + "* un concept qui vérifie certaines propriétés (vision de mathématicien)\n", + "\n", + "Dans le cadre de ce cours on se concentre sur les 2 premières visions et on ajoute\n", + "\n", + "* un vecteur à son origine en (0,0)\n", + "\n", + "D'un point de vue typographique les vecteurs sont notés avec une flèche $\\vec v$ ou en gras $\\bf v$. On utilisera cette dernière notation dans ce cours. Une fonction vectorielle (qui retourne un vecteur) est aussi notée comme un vecteur $\\bf f(\\,)$." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAABHgAAAI/CAYAAAAMf26tAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAABYlAAAWJQFJUiTwAABN2ElEQVR4nO3dfZiWdZ03/jcIgzyG7o2AwI0kLoIo+RS2mdYaSWvHYnC0qYshFrv+7o52q9UyTTfXTN01zbQ1zTJIK20rRZIF3FrRUG4WZK1E7DZkBQtRGx0eBNT5/UEzMTAzzFzzcD29Xsfh0cx5ntc5nwvOrrmuN5/P9+xRX19fHwAAAADKVs9iFwAAAABAxwh4AAAAAMqcgAcAAACgzAl4AAAAAMqcgAcAAACgzAl4AAAAAMqcgAcAAACgzAl4AAAAAMqcgAcAAACgzAl4AAAAAMqcgAcAAACgzAl4AAAAAMqcgAcAAACgzAl4AAAAAMqcgAcAAACgzAl4AKBCrFy5MitXrix2GQAAFIGApwBr1qzJmjVril0GZcQ1QyFcN0BX8zpDe7lmaC/XDIVw3RRGwAMAAEC3+MEPfpBx48Y1+e9f//VfWzz+v/7rv/Y5/tOf/nQ3VgzlQ8ADAABAt3j/+9+fvn37Ntn2wAMPtHh8c/s++MEPdnpdUAkEPAAAAHSLAQMG5L3vfW+Tbb/+9a+zdu3afY594403smjRoibbhg0blne+851dWiOUKwEPAAAA3WbGjBn7bGuuU2f58uV58cUXm2ybNm1aevb0MRaa4/8ZAAAAdJuTTjophx56aJNtP/nJT/Y5rrltxrOgZQIeAAAAuk2PHj0ybdq0Jtuee+65PPHEE43f79q1K0uWLGlyzLHHHpsxY8Z0S41QjgQ8AAAAdKvp06fvs23BggWNXz/yyCN55ZVXmuxvbrQL+CMBDwAAAN3qf//v/50TTjihybaFCxfmzTffTLLvmjx9+/bN+9///m6rD8qRgAcAAIBut/d6Oi+88EJWrFiRHTt25D/+4z+a7JsyZUoGDBjQneVB2RHwAAAA0O2mTp2avn37Ntn2k5/8JP/5n/+ZrVu3Ntne3EgX0JSABwAAgG43YMCAvO9972uybdGiRbnvvvuabBsxYkROOumk7iwNypKABwAAgKLYuzOntrZ2n/GsadOmpUePHt1ZFpQlAQ8AAABFMXny5IwYMaLF/T169DCeBW0k4AEAAKAoevTokTPPPLPF/SeccEJGjRrVfQVBGRPwAAAAUDQf/OAHWxzB0r0DbSfgAQAAoGhGjRqVE088cZ/t/fr1y+mnn16EiqA89Sp2AQBQrp555pl885vfzGOPPZYXXnghNTU1GTNmTKZOnZqPfOQj6dOnT5vPtX79+tx666159NFHs3nz5vTv3z/HHntszjvvPHcOAaDifec73yl2CVD2dPAAQAEWLVqUM888Mz/84Q8zcODATJs2LX/2Z3+W3/zmN7nuuutyzjnnZOvWrW0618qVKxvPNWLEiMyYMSPHHntsHnnkkcyaNSt33nlnFz8bAADKnQ4eAGinTZs25eKLL87OnTvz2c9+Nueff37jvueffz5/9Vd/lV/+8pe5/fbb8/d///etnmv79u256KKLsm3btlx77bVNFppctWpVZs2alWuuuSaTJ0/OEUcc0VVPCQCAMqeDBwDa6d577822bdsyadKkJuFOkhx66KH56Ec/miRZvHjxfs+1cOHCbNy4MSeffPI+dxE57rjjctZZZ2XXrl2ZO3dup9UPAEDlEfAAQDudfPLJ+eIXv5hPfepTze5/61vfmiT53e9+t99zNYRAU6dObXZ/w+KSS5YsKaRUAACqhBEtAGino446KkcddVSL+1944YUkyUEHHbTfcz355JNJkgkTJrT4s5KktrY2GzZsyMiRI9tbLgAAVUAHDwB0ovr6+vzbv/1bkpa7chrs3LkzmzZtSpIMHz682WP69u2bwYMHJ9l9py0AKBe1tcmaNX3yxBMHpr6+2NVA5Su4g2fNmjWdWUdZ2b59e5Lq/jOgfVwzFMJ1U55++MMfZvXq1Rk4cGBOPfXUVv/+Xn311cavn3vuucawZ2+9e/dOkqxduzYHH3zwfmtwzdBWXmdoL9cMDerrk1df7ZmNG3vn+edrsnFj78b/nn9+9/9u2XJAkt1jy1u2rM+f/dm24hZN2aj215rx48cX9DgjWgDQSe69997ceeed6dWrVz7zmc9kwIABrR6/Y8eOxq979Wr5V3JDwLPn8QDQ1bZs6Zn/+Z/9BTj7V1PzZsaM2dnF1QIFBzyFJkqVoCFFrOY/A9rHNUMhXDflo76+Ptdee22+/e1vp6amJl/+8pfzvve9b7+PGzZsWOPXY8eOTZ8+fVo9/vDDD2/1eli5cmUS1wxt53WG9nLNVI/HH09OOSV57bWOn2v27Jfz539+RMdPRNXwWlMYHTwA0AE7duzIRRddlEWLFmXQoEG56aabctJJJ7Xpsf3792/8euvWrS0GPFu2bEmSDBw4sOMFA0Ab9O2b7NrV8fMMGbIrH/vYi0n+V8dPBrTKIssAUKCdO3fmb//2b7No0aKMHDky3//+99sc7iRJTU1NRowYkSTZuHFjs8fU1dU1rtUzZsyYjhcNAG1w5JHJZz/b8fN86lOb07+/FZahOwh4AKAAb775Zi666KI8+uijGT9+fL7//e/n8MMPb/d5Jk6cmCR54oknmt2/evXqJMmQIUOajHQBQFe7/PLkD7+mCnLCCclf/uUrnVcQ0CoBDwAU4Oabb86///u/5/DDD88dd9yRIUOGFHSehlupL1y4sNn9CxYsSJKcccYZhRUKAAXq0ye5447kgLatpbyPr3wl6ekTJ3Qb/3cDgHZ65plncuutt6Z37965+eabc9BBB+33MUuWLMnUqVMzZ86cJtunTJmSMWPGZMWKFbn77rub7HvooYcyf/789OvXL7Nnz+7U5wAAbXHCCYWNan34w8k739n59QAts8gyALTTbbfdltdffz2jRo3K9773vVaP/fjHP57Bgwenrq4u69at22d/7969c/3112f27Nm5/PLLc//992fs2LHZsGFDli1blp49e+bqq682ngVA0Zx9dnLttckbb7Tt+D59dh8PdC8BDwC00/PPP58kee655zJv3rxWj501a1YGDx7c6jETJkzIfffdl1tuuSUPP/xwVq9enUGDBmXKlCm54IIL3CIUgKJ4443kq19NLrmk7eFOklx4YTJ6dNfVBTRPwAMA7fSd73yn3Y+ZPn16pk+f3uL+YcOG5YorruhIWQDQaZ5+Ojn//OTnP2/f44YPTy6+uGtqAlpnDR4AAACS7O7UueGGZNKk5sOdfv1af/zVVycDBnRNbUDrBDwAAADk6aeTU09NPv3p5LXXmu4bPDiZOzd56KGW76p1/PHJued2eZlACwQ8AAAAVWx/XTtnnJH86lfJRz7S+l213BYdisv//QAAAKpUW7p27r8/OfTQP26//PJk4sSmx374w8nJJ3d5uUArBDwAAABVpj1dOz16NN3Xp09yxx1/HNVyW3QoDQIeAACAKlJI187eTjghufTS3V9/7nNuiw6lwG3SAQAAqsAbbyRf/WpyySX7BjvJ7q6d225rPdjZ0xe+sHs0a/z4Ti0TKJCABwAAoMI9/XRy/vnNj2MNHpzceOPuO2DtPY7Vmh49kgkTOq1EoIOMaAEAAFSojqy1A5QXHTwAAAAVqCu6doDSpYMHAACggujageqkgwcAAKBC6NqB6qWDBwAAoMzp2gF08AAAAJQxXTtAooMHAACgLOnaAfakgwcAAKDM6NoB9qaDBwAAoEzo2gFaooMHAACgDOjaAVqjgwcAAKCE6doB2kIHDwAAQInStQO0lQ4eAACAEqNrB2gvHTwAAAAlRNcOUAgdPAAAACVA1w7QETp4AAAAikzXDtBROngAAACKRNcO0Fl08AAAABSBrh2gM+ngAQAA6Ea6doCuoIMHAACgm+jaAbqKDh4AAIAupmsH6Go6eAAAALqQrh2gO+jgAQAA6AK6doDupIMHAACgk+naAbqbDh4AAIBOomsHKBYdPAAAAJ1A1w5QTDp4AAAAOkDXDlAKdPAAAAAUSNcOUCp08AAAALSTrh2g1OjgAQAAaAddO0Ap0sEDAADQBrp2gFKmgwcAAGA/dO0ApU4HDwAAQAt07QDlQgcPAABAM3TtAOVEBw8AAMAedO0A5UgHDwAAwB/o2gHKlQ4eAACg6unaAcqdDh4AAKCq6doBKoEOHgAAoCrp2gEqiQ4eAACg6ujaASqNDh4AAKBq6NoBKpUOHgAAoCro2gEqmQ4eAACgounaAaqBDh4AAKBi6doBqoUOHgDogPr6+sybNy/HHHNMxo0bl+XLl7fr8cuXL8+4ceP2+9/3vve9LnoGAJVJ1w5QbXTwAECBXnzxxXzuc5/L0qVLO3yuoUOH5vTTT29x/7hx4zr8MwCqha4doBoJeACgAMuWLcuFF16Yl156KTNnzszixYvzwgsvFHy+0aNH59JLL+3ECgGqzxtvJF/9anLJJclrr+27/4wzkttuSw49tPtrA+hqAh4AKMCPfvSj7Nq1KzfffHOmTJmSn/3sZ8UuCaCq6doBqp2ABwAKMGnSpHzyk5/MyJEji10KQFXTtQOwm4AHAApw7rnnFrsEgKqnawfgjwQ8AFAi6urq8tOf/jS/+c1v8uabb2bUqFE59dRTM3To0GKXBlBSdO0A7KvggGfNmjWdWUdZ2b59e5Lq/jOgfVwzFMJ1U1527tyZJFm/fn0GDRrU5setX78+SfLUU0/lXe96V+Pfe4NevXplxowZOfvss9t8TtcMbeV1hvYqhWvm2Wdr8vnPD8+qVf322Tdw4Bu55JJN+cu/fCWvvJK88koRCqSJUrhmKD/Vft2MHz++oMfp4AGAErBt27ZMmzYtp512WoYMGZLa2to88MADmT9/fu6+++706dMn06dPL3aZAEXzxhvJnXcenK98ZUh27Oi5z/5TT63LFVf8Locc8noRqgMovh719fX1xS6i3DSkiIWmalQf1wyFcN2Ulz//8z/Pxo0bM2/evEyePLnNj9uyZUvWrVuXwYMHZ9SoUfvs//rXv54bbrgh/fv3z89//vP07du3xXOtXLkySXL88ce3/wlQlbzO0F7FumastVO+vM5QCNdNYfaNvgGAbjNgwIAcffTRzYY7SXL++efnwAMPzNatW/P44493c3UAxfXGG8kNNySTJjUf7pxxRvKrXyUf+YhwB0DAAwAlrKamJkOGDEmSvPTSS0WuBqD7PP10cuqpyac/ve9CyoMHJ3PnJvffbyFlgAYCHgAosvr6+rQ0MV1fX5/a2tokyVve8pZurAqgOHTtABRGwAMARXTeeeflmGOOycKFC5vdv3Tp0tTV1aVXr16ZNGlSN1cH0L107QAUTsADAN1gyZIlmTp1aubMmdNk+wknnJCdO3fmmmuuybPPPttk36ZNm3LVVVclSWbMmKGDB6hYunYAOs5t0gGgnWpra/O1r31tn21Jctddd+XBBx9s3D5z5syMHj06dXV1Wbdu3T7nmjNnTh577LGsWLEiH/jAB/Lud787hxxySDZv3pyHH34427dvz9vf/vZcfPHFXfqcAIrFHbIAOoeABwDaacuWLZk3b16z+xYtWtTk+/e+970ZPXp0i+fq06dPvv3tb+eee+7JggULsnz58mzdujUDBw7MpEmTMm3atEybNi0HHHBApz4HgGJ7443kq19NLrlk33GsZHfXzm23GccCaCsBDwC008iRI7N27dp2PWb69OmZPn16s/t69eqVc845J+ecc05nlAdQ8nTtAHQ+a/AAAADdwlo7AF1HBw8AANDldO0AdC0dPAAAQJfRtQPQPXTwAAAAXULXDkD30cEDAAB0Kl07AN1PBw8AANBpdO0AFIcOHgAAoMN07QAUlw4eAACgQ3TtABSfDh4AAKAgunYASocOHgAAoN107QCUFh08AABAm+naAShNOngAAIA2efbZmnz+88OzatW++3TtABSXgAcAAGjVG28kX/1q8rnPjcmOHfsOAZxxRnLbbcmhhxahOACSCHgAAIBWNF1rp2m4o2sHoHRYgwcAANiHtXYAyosOHgAAoInW7pA1cOAbufnmA3TtAJQYHTwAAECS/XftnHpqXe6//ze6dgBKkA4eAACg1a6dhrV2Tjhhg2AHoETp4AEAgCpmrR2AyqCDBwAAqlRbunastQNQHnTwAABAldG1A1B5dPAAAEAV0bUDUJl08AAAQBXQtQNQ2XTwAABAhdO1A1D5dPAAAECF0rUDUD108AAAQAXStQNQXXTwAABABdG1A1CddPAAAECF0LUDUL108AAAQJnTtQOADh4AAChjunYASHTwAABAWdK1A8CedPAAAECZ0bUDwN508AAAQJnQtQNAS3TwAABAGdC1A0BrdPAAAEAJ07UDQFvo4AEAgBKlaweAttLBAwAAJUbXDgDtpYMHAABKiK4dAAqhgwcAAEqArh0AOkIHD/zBqaeemt/97neN348aNSoPPvhgk2NWrVqVs88+u8m2pUuXZujQoY3f79q1KyeeeGK2b9/euG38+PG5+uqru6hyAKDc6doBoKN08MAfvP3tb2/y/XPPPZfNmzc32bZy5cp9Hrf3tieffLJJuJMkEydO7KQqAYBKomsHgM4i4IE/2DvgSfYNb5oLeFatWrXfY44++ugOVgcAVJqnn05OPTX59KeT115rum/w4GTu3OT++5NDDy1KeQCUGQEP/MFJJ520z7Y9w5v6+vo8/vjj+xzzX//1X61+X1NTk3HjxnVSlQBAudO1A0BXEPDAH4waNSqH7vVPZHt24zzzzDOpra3d53Fr167Nli1bGr/fu6Nn0qRJ6dOnT+cWCwCUJV07AHQVAQ/sYe8xraeeeqpxPZ09g5sjjjgigwYNSpK8+eabjfueeeaZ/P73v2/1nABA9dG1A0BXE/DAHvYOY15//fWsXr06SdNunhNOOCFve9vbGr9v2Nfc+juTJ0/u/EIBgLKhaweA7iDggT00F8Y0dOfsGd4cf/zxOf744xu/b9jX3Po7ewZBAED10LUDQHfqVewCoJSMHDkyI0aMyMaNGxu3rVq1Ki+88EKee+65xm3HH398hg0b1vj9L37xi+zcuXOfDp63ve1t1t8BgCr09NPJ+ec3H+wMHpzceGNy7rmCHQA6jw4e2MveXTyrV69u0pkzfPjwHHrooTnmmGPSu3fvJMlrr72Wn/70p9mwYUOr5wIAKpuuHQCKRcADe9l7HZ4tW7bku9/9buP3DaNZffr0ycSJExu333bbbfucS8ADANXDWjsAFJOAB/bSXCizYsWKxq+PO+64Zr/+1a9+1eQxBx54YCZNmtQFFQIApUTXDgClQMADezn00EMzcuTIFvfvubjynl/v7W1ve1tqamo6tTYAoLTo2gGgVAh4oBktjVYNGjQof/qnf9r4/XHHHZceLfxT3N6jXgBA5dC1A0CpEfBAM1oKZ972trelZ88//t/moIMOylvf+tZmj7X+DlSH+vr6zJs3L8ccc0zGjRuX5cuXF3Se9evX55JLLsl73vOeTJw4MZMnT84FF1yQxx57rJMrBjpK1w4ApUjAA8046aSTmt3e3EhWc9v69u2bY445ptPrAkrLiy++mL/5m7/JVVddlR07dhR8npUrV+bMM8/MD3/4w4wYMSIzZszIsccem0ceeSSzZs3KnXfe2YlVA4XStQNAKetV7AKgFA0bNixr165t07FXXnllrrzyyi6uCCg1y5Yty4UXXpiXXnopM2fOzOLFi/PCCy+0+zzbt2/PRRddlG3btuXaa6/NmWee2bhv1apVmTVrVq655ppMnjw5RxxxRCc+A6A9nn46Of/85oOdwYOTG29Mzj1XsANA8ejgAYAC/OhHP8quXbty880357LLLkvv3r0LOs/ChQuzcePGnHzyyU3CnWT3Ol9nnXVWdu3alblz53ZC1UB76doBoFwIeACgAJMmTcqPf/zjTJkypUPnWbx4cZJk6tSpze4//fTTkyRLlizp0M8B2s9aOwCUEwEPABTg3HPPzciRIzt8nieffDJJMmHChGb3H3XUUUmS2trabNiwocM/D9g/XTsAlCNr8EA3qd1Rm9/W/bbD5xnUZ1D61/TvhIqAYtu5c2c2bdqUJBk+fHizx/Tt2zeDBw9ObW1t1q9f3ymhEtAya+0AUK4KDnjWrFnTmXWUle3btyep7j8D2ueup+7KVU9c1SnnqulZk3tPvzeHDTysU85H6fJaU1527tyZZPftzgcNGtSmx7z66quNXz/33HONYc/eGtb3Wbt2bQ4++OD9ntc1Q1t5nfmjN95I7rzz4HzlK0OyY8e+Te6nnlqXK674XQ455PU89VQRCiwRrhnayzVDIar9uhk/fnxBj9PBA91gYO+BnXauN+rfSE3Pmk47H1A8e95avVevln8lNwQ8HbkVO9CyZ5+tyec/PzyrVvXbZ9/AgW/kkks25S//8hVdOwCUtIIDnkITpUrQkCJW858B7VNfX59HNj+SBf+zoMPnOnfSuTnthNM6oSpKndea8lJTszt4HT16dJv/zoYNG9b49dixY9OnT59Wjz/88MNbPffKlSuTuGZou2p/nXnjjeSrX00uuWTfRZST3Wvt3HbbATn00EOTWEk5cc3Qfq4ZCuG6KYxFlqEb9OjRI/94/D9m3J+M69B5DuhxQC5916WdVBVQbP37/3E9ra1bt7Z43JYtW5IkAwd2XjcgVDt3yAKg0gh4oJv0790/93zonhzY68CCz3HupHMz9uCxnVgVUEw1NTUZMWJEkmTjxo3NHlNXV9e4Vs+YMWO6rTaoVO6QBUClEvBANzpm6DG56f03FfRY3TtQmSZOnJgkeeKJJ5rdv3r16iTJkCFDmox0Ae2naweASibggW720WM/mr8++q/b/bjT3npaDj/o8C6oCCimqVOnJkkWLlzY7P4FC3av3XXGGWd0W01QaXTtAFANBDzQzXr06JGvf+Dr7V6PZ/EzizP59sl54NcPpL6+vouqA7rKkiVLMnXq1MyZM6fJ9ilTpmTMmDFZsWJF7r777ib7HnroocyfPz/9+vXL7Nmzu7NcqBi6dgCoFm6TDkUwoGZA7vnQPZl8++S89nozt+1owYrnV+SM756REw89MV949xfy/rHvTw//1Ajdrra2Nl/72tf22ZYkd911Vx588MHG7TNnzszo0aNTV1eXdevW7XOu3r175/rrr8/s2bNz+eWX5/7778/YsWOzYcOGLFu2LD179szVV19tPAvaqW13yBLsAFA5BDxQJA3r8cy5f87+D96LoAeKa8uWLZk3b16z+xYtWtTk+/e+970ZPXp0q+ebMGFC7rvvvtxyyy15+OGHs3r16gwaNChTpkzJBRdc4Bah0E5PP52cf37z41iDByc33pice65xLAAqi4AHiuijx340//nsf+auX9zV4jEf+NMPpFfPXrn3qXv32SfogeIYOXJk1q5d267HTJ8+PdOnT29x/7Bhw3LFFVd0tDSoarp2AKhm1uCBItrfejwH9DggXzn9K/nxh3+cVX+zKmceeWazxzUEPdboAaBaWWsHgGon4IEia1iP58BeB+6z7yOTPpLDD95956xjhx8r6AGAvbhDFgDsJuCBEtCwHs+eDuhxQC5916X7HCvoAYDddO0AwB8JeKBEfPTYj+avj/7rxu/37N5pjqAHgGqlawcA9iXggRLRsB7PhCET0r93/2a7d5oj6AGgmujaAYDmCXighAyoGZDlH1ue//d3/6/V7p3mCHoAqGS6dgCgdQIeKDEDagZk2IBhBT9e0ANApdG1AwD7J+CBCiXoAaDc6doBgLYT8ECFE/QAUI507QBA+wh4oEoIegAoB7p2AKAwAh6oMoIeAEqVrh0AKJyAB6qUoAeAUqFrBwA6TsADVU7QA0Ax6doBgM4h4AGSCHoA6F66dgCgcwl4gCYEPQB0NV07AND5BDxAswQ9AHQ2XTsA0HUEPECrBD0AdAZdOwDQtQQ8QJsIegAohK4dAOgeAh6gXQQ9ALSVrh0A6D4CHqAggh4AWqJrBwC6n4AH6BBBDwB70rUDAMUh4AE6haAHoLrp2gGA4hLwAJ1K0ANQfXTtAEDxCXiALiHoAah8unYAoHQIeIAuJegBqEy6dgCgtAh4gG4h6AGoDLp2AKA0CXiAbiXoAShfunYAoHQJeICiEPQAlA9dOwBQ+gQ8QFEJegBKm64dACgPAh6gJAh6AEqLrh0AKC8CHqCkCHoAik/XDgCUHwEPUJIEPQDdT9cOAJQvAQ9Q0gQ9AN1D1w4AlDcBD1AWBD0AXUPXDgBUBgEPUFYEPQCd59lnazJr1mhdOwBQAQQ8QFkS9AAUrqFr54MfHJNVq/rts1/XDgCUHwEPUNYEPQDts+daOzt2NH0rqGsHAMqXgAeoCIIegNZZawcAKpuAB6gogh6AfbV2h6yBA9/QtQMAFUDAA1QkQQ/A/rt2Tj21Lvff/xtdOwBQAQQ8QEUT9ADVqrWunYa1dv71XzfkkENeL0p9AEDnEvAAVUHQA1QLa+0AQHUS8ABVRdADVLK2dO1YawcAKpOAB6hKgh6gkujaAQAEPEBVE/QA5U7XDgCQCHgAkgh6gPKjawcA2JOAB2APgh6gHOjaAQD2JuABaIagByhFunYAgJYIeABaIegBSoWuHQCgNQIegDYQ9ADFomsHAGgLAQ9AOwh6gO6kawcAaCsBD0ABBD1AV9K1AwC0l4AHoAMEPUBn07UDABSiV7ELAKgEDUHP4799PP+09J9y71P37nNMQ9Bz4qEn5gvv/kLeP/b96eGf3sva+vXrc+utt+bRRx/N5s2b079//xx77LE577zzctJJJ7XpHMuXL89HPvKR/R73hS98IWeffXZHS6aEvfFG8tWvJpdcsm+wk+zu2rntNsEOANA8AQ9AJxL0VI+VK1fmYx/7WLZt25YTTzwxp5xySjZt2pRHHnkkP/vZz3LZZZdl5syZbT7f0KFDc/rpp7e4f9y4cZ1RNiXq6aeT889vfhxr8ODkxhuTc881jgUAtEzAA9AFBD2Vbfv27bnooouybdu2XHvttTnzzDMb961atSqzZs3KNddck8mTJ+eII45o0zlHjx6dSy+9tIsqplTp2gEAOos1eAC6kDV6KtPChQuzcePGnHzyyU3CnSQ57rjjctZZZ2XXrl2ZO3ducQqkLFhrBwDoTAIegG4g6KksixcvTpJMnTq12f0No1ZLlizptpooH+6QBQB0BQEPQDdqT9Bz1n+clYd++5CgpwQ9+eSTSZIJEyY0u/+oo45KktTW1mbDhg3dVhelT9cOANBVBDwARdCWoOcXL/8i/9/D/5+OnhKzc+fObNq0KUkyfPjwZo/p27dvBg8enGT3nbbaqq6uLvfdd19uuOGGfPnLX84999zT+LMob7p2AICu1qO+wE8Ma9as6exaysb27duT7H4DD23hmmF/nvz9k7nlyVvyHxv/o8Vjjj746Pyfo/5PThl2isWYi+jVV19tvK35Pffck5qammaPmzNnTjZv3pzPfvazecc73tHi+X7xi1/ksssuy6BBg7Jr167G14sGvXr1yowZM9p0i/Rt27YlSfr169fWp0M3ePbZmnz+88OzatW+fy8DB76RSy7ZlL/8y1eKEuz4/UR7uWZoL9cMhaj262b8+PEFPc5dtABKwISDJuSmd97UatDT0NEj6CmuHTt2NH7dq1fLv0Z79+69z/Gt2bZtW6ZNm5bTTjstQ4YMSW1tbR544IHMnz8/d999d/r06ZPp06d3rHi61RtvJHfeeXC+8pUh2bFj36bpU0+tyxVX/C6HHPJ6EaoDACpNwR081ayhe6nQVI3q45qhvR7/7eO56CcXtdrR4/bqxfH73/8+J510UpLkiSeeSJ8+fZo97j3veU+ef/753HTTTXnf+97X4vm2bNmSdevWZfDgwRk1atQ++7/+9a/nhhtuSP/+/fPzn/+81X/JWrlyZZLk+OOPb89Togs8/XRy/vnNj2MNHpzceGNy7rnFH8fy+4n2cs3QXq4ZCuG6KYw1eABK0LHDj81N77wp/zbl39x1q8T079+/8eutW7e2eNyWLVuSJAMHDmz1fAMGDMjRRx/dbLiTJOeff34OPPDAbN26NY8//ngBFdOdrLUDABSLgAeghE04aILbq5eYmpqajBgxIkmycePGZo+pq6vLq6++miQZM2ZMh3/ekCFDkiQvvfRSh85F13KHLACgmAQ8AGWgPbdXF/R0vYkTJybZPaLVnNWrVydJhgwZkmHDhu33fPX19S3+fdXX16e2tjZJ8pa3vKX9xdLldO0AAKVAwANQRgQ9pWHq1KlJkoULFza7f8GCBUmSM844Y7/nOu+883LMMce0eK6lS5emrq4uvXr1yqRJkwqsmK6iawcAKBUCHoAyJOgprilTpmTMmDFZsWJF7r777ib7HnroocyfPz/9+vXL7NmzG7cvWbIkU6dOzZw5c5ocf8IJJ2Tnzp255ppr8uyzzzbZt2nTplx11VVJkhkzZujgKSG6dgCAUuM26QBlrCHoefy3j+eflv5T7n3q3n2OaQh63HWr8/Tu3TvXX399Zs+encsvvzz3339/xo4dmw0bNmTZsmXp2bNnrr766ibjWXV1dVm3bt0+55ozZ04ee+yxrFixIh/4wAfy7ne/O4ccckg2b96chx9+ONu3b8/b3/72XHzxxd35FGlFudwhCwCoLgIegAog6Ol+EyZMyH333ZdbbrklDz/8cFavXp1BgwZlypQpueCCC9p8W88+ffrk29/+du65554sWLAgy5cvz9atWzNw4MBMmjQp06ZNy7Rp03LAAQd08TNif954I/nqV5NLLtl3HCvZ3bVz223GsQCA4uhRr2e/3dasWZMkbX7zDq4ZCtGR66a1oKeBoKfyrFy5Mkly/PHHF7mSylOpXTt+P9FerhnayzVDIVw3hbEGD0AFskYPdA5r7QAA5ULAA1DBBD1QOHfIAgDKiYAHoAoIeqDtdO0AAOVIwANQRQQ90DpdOwBAuRLwAFQhQQ80pWsHACh3Ah6AKiboAV07AEBlEPAAIOihKunaAQAqiYAHgEaCHqqFrh0AoNIIeADYh6CHSqVrBwCoVAIeAFok6KGS6NoBACqZgAeA/RL0UM507QAA1UDAA0CbCXooN7p2AIBqIeABoN0EPZQ6XTsAQLUR8ABQMEEPpUjXDgBQjQQ8AHSYoIdSoGsHAKhmAh4AOo2gh2LRtQMAVDsBDwCdTtBDd9G1AwCwm4AHgC4j6KEr6doBAPgjAQ8AXU7QQ2fStQMAsC8BDwDdRtBDR+naAQBonoAHgG4n6KG9dO0AALROwANA0Qh6aAtdOwAA+yfgAaDoBD00R9cOAEDbCXgAKBmCHhro2gEAaB8BDwAlR9BTvXTtAAAURsADQMkS9FQXXTsAAIUT8ABQ8gQ9lU3XDgBAxwl4ACgbgp7Ko2sHAKBzCHgAKDuCnvKnawcAoHMJeAAoW4Ke8qRrBwCg8wl4ACh7gp7yoGsHAKDrCHgAqBiCntKlawcAoGsJeACoOIKe0qFrBwCgewh4AKhYgp7i0rUDANB9BDwAVDxBT/fStQMA0P0EPABUDUFP19O1AwBQHAIeAKqOoKfz6doBACguAQ8AVUvQ0zl07QAAFJ+AB4CqJ+gpjK4dAIDSIeABgD8Q9LSdrh0AgNIi4AGAvQh6WqZrBwCgNAl4AKAFgp6mdO0AAJQuAQ8A7Ee1Bz26dgAASp+ABwDaqBqDHl07AADlQcADAO1UDUGPrh0AgPIi4AGAAlVq0KNrBwCg/Ah4AKCDKiXo0bUDAFC+BDwA0EnKOejRtQMAUN4EPADQycop6NG1AwBQGQQ8ANBFSj3o0bUDAFA5BDwA0MVKLejRtQMAUHkEPADQTUoh6NG1AwBQmQQ8AFCg9evX55JLLsl73vOeTJw4MZMnT84FF1yQxx57rNXHtSfoOeorR3VK0KNrBwCgsgl4AKAAK1euzJlnnpkf/vCHGTFiRGbMmJFjjz02jzzySGbNmpU777xzv+doCHrufNedecvzb2n2mDWvrulwR4+uHQCAyifgAYB22r59ey666KJs27Yt1157be68885cccUV+frXv5558+alpqYm11xzTX7961+36Vzf/OI3M/Q/h+bLR3y5U0e3dO0AAFQPAQ8AtNPChQuzcePGnHzyyTnzzDOb7DvuuONy1llnZdeuXZk7d267zvXpcz7daWv06NoBAKguAh4AaKfFixcnSaZOndrs/tNPPz1JsmTJkoLOtecaPe8e+u5mH9dS0KNrBwCgOvUqdgEAUG6efPLJJMmECROa3X/UUUclSWpra7Nhw4aMHDmyoHMdO/zYPDDrgRz5niPz0sSXsnXU1n2OaQh6Tjz0xEzpfV4WfOXcPPHf+/6cwYOTG29Mzj1XsAMAUIl08ABAO+zcuTObNm1KkgwfPrzZY/r27ZvBgwcn2X2nrY6ea1j9sIx4eES+9fZvtTi61efRFXn4oY/niePOSGq2NNmnawcAoPL1qC/gdhwrV67siloAgDZ46pWncvvTt+c/N/1nkmTyc8nPv5UcUJ/ceXTy8f9ZnVdfmZSBA1/PP/zDcznjjJcFOwAAZeT4449v92OMaAFAmTnyLUfmuhOvy1OvPJV5v7w1N970cA74wz/XzPxF8mx+kEUnj86ll/5PhgzZVdxiAQDoFgV18FS7NWvWJEnGjx9f5EooF64ZCuG6KU2///3vc9JJJyVJnnjiifTp06fZ497znvfk+eefz0033ZT3ve99XXeuz3wm+Zd/abJp8WcezJRrTtO1w355naG9XDO0l2uGQrhuCmMNHgBoh/79+zd+vXXrvoseN9iyZfc6OAMHDuy6cz32WPLlLzfZtPmDH8z7rhXuAABUGwEPALRDTU1NRowYkSTZuHFjs8fU1dXl1VdfTZKMGTOma861fXty3nnJm282bto5dGg2/P3ft/m5AABQOQQ8ANBOEydOTLJ7rKo5q1evTpIMGTIkw4YN65pz/eM/JmvXNjn22csuy5sDBuyvfAAAKpCABwDaaerUqUmShQsXNrt/wYIFSZIzzjija87VzGhW5sxJ3R/W8wEAoPoIeACgnaZMmZIxY8ZkxYoVufvuu5vse+ihhzJ//vz069cvs2fPbty+ZMmSTJ06NXPmzOnYuZoZzcqoUcl113XqcwQAoLy4TToAtFPv3r1z/fXXZ/bs2bn88stz//33Z+zYsdmwYUOWLVuWnj175uqrr24yUlVXV5d169Z1/FzNjGbl9tuTQYO68ikDAFDiBDydYOnSpfn+97+f//7v/05tbW369euXsWPH5gMf+EA+/OEPp1cvf8w09cwzz+Sb3/xmHnvssbzwwgupqanJmDFjMnXq1HzkIx9p8VbJVLf6+vp85zvfyXXXXZcdO3Zk3rx5mTx5crHLqloTJkzIfffdl1tuuSUPP/xwVq9enUGDBmXKlCm54IIL2nVbzzafq4XRrPXjxuXWSy7JjBkzkiSTJ0/Osccem/POO6/xNuywt/r6+ixYsCDz5s3Lzp07vabQqob3LkuXLs3vf//79OnTx3sX9mvp0qX5xje+kaeffjpbtmzxOYl2WbFiRc4888wk8TuqjXrU19fXF7uIcrNmzZokyfjx4/OlL30pc+fOTc+ePfOOd7wjI0eOzG9/+9s8+uij2bVrV0466aR84xvfSE1NTZGrppj2vGYWLVqUCy+8MDt37syRRx6ZiRMn5pVXXsnPf/7zbNu2LRMnTsy8efOa3D6Z6rTndfPiiy/mc5/7XJYuXdq43y+6KrN9e3LssU27d0aNyuPf+U7O/+Qns23btnz3u99NknzjG9/II488kl27duWyyy7LzJkzi1Q0pcprCu2x53uXww47LGPHjk2PHj28d6FVe35OOvroo3PkkUf6nESbrVixIn/3d3+Xl19+OYnfUW0lMu2ABx98MHPnzk3//v0zd+7cHH300Y37nnrqqZx99tl57LHH8t3vfjfnnXde8QqlZGzatCkXX3xxdu7cmc9+9rM5//zzG/c9//zz+au/+qv88pe/zO23356/d6tj/mDZsmW58MIL89JLL2XmzJlZvHhxXnjhhWKXRXdrZjRrx9e+ln+44ops27Yt1157beP2r3/961m1alVmzZqVa665JpMnT84RRxzR3RVTovZ8TfmLv/iLPPbYY41voGFve793ecc73pFk9z8+eO9CS/b8nHTFFVdk7Nixjd2oPifRFt/85jfz8ssv56CDDsrvf//7YpdTNiyy3AE/+MEPkiTnn39+k3AnSY488sj81V/9VZLkP/7jP7q9NkrTvffem23btmXSpElNwp0kOfTQQ/PRj340SbJ48eJilEeJ+tGPfpRdu3bl5ptvzmWXXZbevXsXuyS6WwujWT/ZtSsbN27MySef3NjC3OC4447LWWedlV27dmXu3LndVyslb8/XlL/5m7/JAQccUOySKGHeu1CIPT8njR07tsk+n5PYn4ceeig/+9nPctJJJ/kHqnbSwdMBn/jEJ/KhD30oEydObHb/6NGjkyRbt27tzrIoYSeffHIOPvjgjBw5stn9b33rW5Mkv/vd77qzLErcpEmT8slPfrLF64YK18pdsxZ/5jNJ/nir9b2dfvrpmTdvXpYsWZIvfvGL3VAs5WDP15SGUVBoifcuFGLPz0nNdV/4nERL6urqctlll6V///6ZM2dObr311mKXVFYEPB0wceLEFsOdJHnuueeSJIcffnh3lUSJO+qoo3LUUUe1uL9h7Oaggw7qrpIoA+eee26xS6CYWrlr1pNPPplk9yLNzWl4vamtrc2GDRuEhCTxmkL7eO9CIfb8nNRcwONzEi350pe+lE2bNuUTn/hE/uRP/qTY5ZQdI1pd5Gc/+1nuvPPO1NTUZM6cOcUuhzJQX1+ff/u3f0vS8r/GA1WmhdGsvO992blzZzZt2pQkGT58eLMP79u3bwYPHpwkWb9+fVdWClQh710ohM9JtGTp0qX50Y9+lJNPPjmnnXZascspSzp4OsmmTZty++23Z+vWrVmzZk2efPLJHHXUUbniiivyp3/6p8UujzLwjW98I6tXr87gwYP9sgNaHc1Kki1btjRubu3ONf369Uttba02eKDTee9CW7z00kv58Y9/nD59+vicRIu2bNmSyy+/PAMGDMgXv/jF1NbWFruksiTg+YNPfepTbZ5DHzBgQK688som215++eXMmzev8fuRI0fmne98Z/7X//pfnVonpaOj18yevvWtb+X6669P7969c+ONN+Ytb3lLZ5VJCWnPNTN06NBcfPHFXVwRJa2V0awk2bFjR+Pm1hbebrj97Pbt2zu/RqBqee9CW73yyitZsGBB4/c+J9Gca665Jr/97W/zT//0Txk+fLiAp0ACnj/YuHFj1q1b16ZjhwwZss+28ePHZ+3atdm+fXueffbZzJ8/P9/61rdy55135hvf+EZOOOGEzi6ZIuvoNZPsbm2+9tprc8cdd6SmpiZf/vKXc9JJJ3VmmZSQ9lwzO3fu7OJqKGmtjGY1OPDAAxu/3rVrV/r06dPsqRqupb59+3Z+nUDVqa+vzx133JH58+d770KbvPWtb829996bww47zOckmvXzn/88P/jBD/KOd7wjH/7wh4tdTlkT8PzBPffc0+ZjW/sX+L59+2b8+PEZP358RowYkSuvvDKf+cxn8uCDD6ZnT0seVZKOXjM7duzIRRddlEWLFmXQoEG56aabvEGqcO25ZpLWX2uoYPsZzWqw51jW1q1bWwx4Gka5Bg4c2OmlAtVlx44d+Zd/+ZcsW7bMexfazeckmrNly5Z8/vOfT//+/d3xsxMIeLrQ9OnTc+WVV2bjxo359a9/nXHjxhW7JErEzp0787d/+7d59NFHM3LkyNx2223uIgDstp/RrAY1NTUZMWJENm7cmI0bN+bggw/e51R1dXV59dVXkyRjxozpspKByrfne5ehQ4fmjjvu8N6FgvmcRIPvf//7ef755zNq1Kj88z//c+P2hvcvv/71r5MkN910U+66665Mnjw5f/3Xf12UWsuBgKdA27dvz5e+9KW8+OKLufTSS5u9hVuPHj3So0eP1NfX57XXXitClZSiN998MxdddFEeffTRjB8/Pt/4xjdaHOECqkwbRrP2NHHixGzcuDFPPPFEjj766H32r169OsnuMdFhw4Z1drVAldjzvcuYMWNy+eWXC3do0datW3PjjTc2fk5qjs9JNGhYI/C5557Lc8891+JxK1asSLL75hG0TMBToAMPPDD3339/Xn755bzjHe/Ihz70oX2O+dWvfpX6+vr06NEjo0aNKkKVlKKbb745//7v/57DDz88d9xxRw466KBilwSUgjaOZu1p6tSpWbRoURYuXNjsv2Y1LGp5xhlndHa1QBXZ873LP/7jP2bQXh2FsKd+/fo1+Zw0ceLEfY7xOYkGn/jEJ/KJT3xin+0NSxV86Utfyv/9v/838+bNy+TJk7u7vLJj2LFAPXr0aFwA6stf/nLW7tVOv3nz5lx11VVJklNOOaXZ1nmqzzPPPJNbb701vXv3zs033yzcAf6ojaNZe5oyZUrGjBmTFStW5O67726y76GHHsr8+fPTr1+/zJ49uysqBqrA3u9dhDvsz96fk5599tkm+31Ogq6jg6cD/s//+T/55S9/mYcffjjTp0/P5MmTM3LkyGzevDnLly/P1q1bM2LEiFxxxRXFLpUScdttt+X111/PqFGj8r3vfa/VYz/+8Y9n8ODB3VMYJauurq7xTVCDhttG3nXXXXnwwQcbt8+cOTOjR4/uzvLoLO0czWrQu3fvXH/99Zk9e3Yuv/zyfPe7302SfOxjH8uyZcvSs2fPXH311cazaFRbW5uvfe1rjd+//PLLjQtxe02hOXu/d3n55ZeTpNkP5d670GDPz0n/8A//kIkTJ+bII4/0OQm6mICnA2pqanLbbbdl/vz5uffee/Pkk09m+fLl6dOnTw477LD8+Z//eWbNmuXOJTR6/vnnk+yeMZ03b16rx86aNcubJLJt27YWr5VFixY1+f69732vD2PlqIDRrD1NmDAh9913X2655ZbGbU8++WSmTJmSCy64IOPHj+/kgilnW7Zs8ZpCu3jvQiH2/Jx01113Zd26dfnVr37lcxJ0sR719fX1xS6i3DTMA3rTTFu5ZiiE66ZKfOYzyb/8S9Ntixbtt3unOStXrkySHH/88Z1RGVXA6wzt5ZqhvVwzFMJ1Uxhr8ABAsRQ4mgUAAHsT8ABAMXRwNAsAAPYk4AGAYijgrlkAANASAQ8AdDejWQAAdDIBDwB0J6NZAAB0AQEPAHQno1kAAHQBAQ8AdBejWQAAdBEBDwB0B6NZAAB0IQEPAHQHo1kAAHQhAQ8AdDWjWQAAdDEBDwB0JaNZAAB0AwEPAHQlo1kAAHQDAQ8AdBWjWQAAdBMBDwB0BaNZAAB0IwEPAHQFo1kAAHQjAQ8AdDajWQAAdDMBDwB0JqNZAAAUgYAHADqT0SwAAIpAwAMAncVoFgAARSLgAYDOYDQLAIAiEvAAQGcwmgUAQBEJeACgo4xmAQBQZAIeAOgIo1kAAJQAAQ8AdITRLAAASoCABwAKZTQLAIASIeABgEIYzQIAoIQIeACgEEazAAAoIQIeAGgvo1kAAJQYAQ8AtIfRLAAASpCABwDaw2gWAAAlSMADAG1lNAsAgBIl4AGAtjCaBQBACRPwAEBbGM0CAKCECXgAYH+MZgEAUOIEPADQGqNZAACUAQEPALTGaBYAAGVAwAMALTGaBQBAmehV7AIAoCTtZzRr/fr1ufXWW/Poo49m8+bN6d+/f4499ticd955Oemkk9r8Y5YvX56PfOQj+z3uC1/4Qs4+++z2PgsAAKqEgAcAmtPKaNbKlSvzsY99LNu2bcuJJ56YU045JZs2bcojjzySn/3sZ7nssssyc+bMdv24oUOH5vTTT29x/7hx4wp5FgAAVAkBDwDsrZXRrO3bt+eiiy7Ktm3bcu211+bMM89sPGTVqlWZNWtWrrnmmkyePDlHHHFEm3/k6NGjc+mll3bSEwAAoNpYgwcA9rSf0ayFCxdm48aNOfnkk5uEO0ly3HHH5ayzzsquXbsyd+7c7qsZAICqJ+ABgD3t565ZixcvTpJMnTq12Yc3jFktWbKk62oEAIC9CHgAoEEb7pr15JNPJkkmTJjQ7CmOOuqoJEltbW02bNjQNXUCAMBerMEDAMl+R7OSZOfOndm0aVOSZPjw4c2epm/fvhk8eHBqa2uzfv36jBw5ss0l1NXV5ac//Wl+85vf5M0338yoUaNy6qmnZujQoQU9JQAAqkfBAc+aNWs6s46ysn379iTV/WdA+7hmKITrpnsdct11+ZO9RrP+5/LLs3XjxmTjxiTJq6++2rjvueeeawx79ta7d+8kydq1a3PwwQe3+nPXr1+fJHnqqafyrne9q/HvvUGvXr0yY8aMdt0i3TVDW3mdob1cM7SXa4ZCVPt1M378+IIep4MHgKp13XXXZd26dRn/yiv56qpVTfYtGD4813/3u8l3v5skOfjgg/N3f/d3jft79Wr5V2hDwLNjx44217Jt27ZMmzYtp512WoYMGZLa2to88MADmT9/fu6+++706dMn06dPb8/TAwCgihQc8BSaKFWChhSxmv8MaB/XDIVw3XS9urq6vPjcc/mH9etzwB7bn+/VK5f367e7e2cPRx99dOPXY8eOTZ8+fVo9/+GHH77fv79Ro0Zl/PjxGTx4cEaNGtVk3ymnnJLDDjssN9xwQ374wx/m05/+dPr27dviuVauXJnENUPbeZ2hvVwztJdrhkK4bgpjkWUAqtY999yTJz74wbx1164m2w/9yU+y6v/9v6xdu7bxv5/+9Kfp379/4zFbt25t8bxbtmxJkgwcOHC/NQwYMCBHH330PuFOg/PPPz8HHnhgtm7dmscff7wtTwsAgCok4AGgerXhrll7qqmpyYgRI5IkG/fq7mlQV1fXuFbPmDFjOlxiTU1NhgwZkiR56aWXOnw+AAAqk4AHgOrUhrtmNWfixIlJkieeeKLZ/atXr06SDBkyJMOGDWtTKfX19amvr29xX21tbZLkLW95S5vOBwBA9RHwAFCd/vEfk73umpXbb08GDWr1YVOnTk2SLFy4sNn9CxYsSJKcccYZbSrjvPPOyzHHHNPi+ZYuXZq6urr06tUrkyZNatM5AQCoPgIeAKpPO0ez9jRlypSMGTMmK1asyN13391k30MPPZT58+enX79+mT17dpN9S5YsydSpUzNnzpwm20844YTs3Lkz11xzTZ599tkm+zZt2pSrrroqSTJjxgwdPAAAtMht0gGoLgWOZjXo3bt3rr/++syePTuXX3557r///owdOzYbNmzIsmXL0rNnz1x99dX7jGfV1dVl3bp1+5xvzpw5eeyxx7JixYp84AMfyLvf/e4ccsgh2bx5cx5++OFs3749b3/723PxxRd35FkDAFDhBDwAVJcCR7P2NGHChNx333255ZZb8vDDD2f16tUZNGhQpkyZkgsuuKBdt/Ts06dPvv3tb+eee+7JggULsnz58mzdujUDBw7MpEmTMm3atEybNi0HHHDA/k8GAEDVEvAAUD06MJq1t2HDhuWKK65o8/HTp0/P9OnTm93Xq1evnHPOOTnnnHPaXQcAACTW4AGgWnRwNAsAAEqZgAeA6tAJo1kAAFCqBDwAVL5OHM0CAIBSJOABoLIZzQIAoAoIeACobEazAACoAgIeACqX0SwAAKqEgAeAymQ0CwCAKiLgAaAyGc0CAKCKCHgAqDxGswAAqDICHgAqi9EsAACqkIAHgMpiNAsAgCok4AGgchjNAgCgSgl4AKgMRrMAAKhiAh4AKoPRLAAAqpiAB4DyZzQLAIAqJ+ABoLwZzQIAAAEPAGXOaBYAAAh4AChjRrMAACCJgAeAcmU0CwAAGgl4AChPRrMAAKCRgAeA8mM0CwAAmhDwAFBejGYBAMA+BDwAlBejWQAAsA8BDwDlw2gWAAA0S8ADQHkwmgUAAC0S8ABQHoxmAQBAiwQ8AJQ+o1kAANAqAQ8Apc1oFgAA7JeAB4DSZjQLAAD2S8ADQOkymgUAAG0i4AGgNBnNAgCANhPwAFCajGYBAECbCXgAKD1GswAAoF0EPACUFqNZAADQbgIeAEqL0SwAAGg3AQ8ApcNoFgAAFETAA0BpMJoFAAAFE/AAUBqMZgEAQMEEPAAUn9EsAADoEAEPAMVlNAsAADpMwANAcRnNAgCADhPwAFA8RrMAAKBTCHgAKA6jWQAA0GkEPAAUh9EsAADoNAIeALqf0SwAAOhUAh4AupfRLAAA6HQCHgC6l9EsAADodAIeALqP0SwAAOgSAh4AuofRLAAA6DICHgC6h9EsAADoMgIeALqe0SwAAOhSAh4AupbRLAAA6HICHgC6VgWPZtXX12fevHk55phjMm7cuCxfvrzgc61fvz6XXHJJ3vOe92TixImZPHlyLrjggjz22GOdWDEAAJWqV7ELAKCCVfBo1osvvpjPfe5zWbp0aYfPtXLlynzsYx/Ltm3bcuKJJ+aUU07Jpk2b8sgjj+RnP/tZLrvsssycObMTqgYAoFIJeADoGhU8mrVs2bJceOGFeemllzJz5swsXrw4L7zwQkHn2r59ey666KJs27Yt1157bc4888zGfatWrcqsWbNyzTXXZPLkyTniiCM66RkAAFBpjGgB0DUqeDTrRz/6UXbt2pWbb745l112WXr37l3wuRYuXJiNGzfm5JNPbhLuJMlxxx2Xs846K7t27crcuXM7WDUAAJVMwANA56vg0awkmTRpUn784x9nypQpHT7X4sWLkyRTp05tdv/pp5+eJFmyZEmHfxYAAJVLwANA56rg0awG5557bkaOHNkp53ryySeTJBMmTGh2/1FHHZUkqa2tzYYNGzrlZwIAUHkEPAB0rgoezepsO3fuzKZNm5Ikw4cPb/aYvn37ZvDgwUl232kLAACaU/Aiy2vWrOnMOsrK9u3bk1T3nwHt45qhEOV43Rz43/+dw7785fTYY9vvP/Sh/G7UqKSMnkd77dy5M8nuAGZQO4KsV199tfHr5557rjHs2VvDGj9r167NwQcfvN/zltM1Q3GV4+sMxeWaob1cMxSi2q+b8ePHF/Q4d9ECoFP0eO21HHrJJemxx2jWrmHD8sJFFxWxqtZdd911WbduXZuOPfjgg3PllVd26s/fsWNH49e9erX8K7kh4NnzeAAA2FPBAU+hiVIlaEgRq/nPgPZxzVCIsrtuPvOZZK+wpPfcuRl34olFKmj/6urqsnHjxjYf39LfRU1NTZJk9OjR7fr7GjZsWOPXY8eOTZ8+fVo9/vDDD2/1/CtXrmy1Tthb2b3OUHSuGdrLNUMhXDeF0cEDQMeV6V2z7rnnnqL+/P79+zd+vXXr1hYDni1btiRJBg4c2C11AQBQfiyyDEDHVMFds7pKTU1NRowYkSQtdhLV1dU1rtUzZsyYbqsNAIDyIuABoGPcNatDJk6cmCR54oknmt2/evXqJMmQIUOajHQBAMCeBDwAFK5MR7NKydSpU5MkCxcubHb/ggULkiRnnHFGt9UEAED5EfAAUBijWe2yZMmSTJ06NXPmzGmyfcqUKRkzZkxWrFiRu+++u8m+hx56KPPnz0+/fv0ye/bs7iwXAIAyY5FlAApTpaNZtbW1+drXvrbPtiS566678uCDDzZunzlzZkaPHp1k91o6zd2SvXfv3rn++usze/bsXH755bn//vszduzYbNiwIcuWLUvPnj1z9dVXG88CAKBVAh4A2q+KR7O2bNmSefPmNbtv0aJFTb5/73vf2xjwtGbChAm57777csstt+Thhx/O6tWrM2jQoEyZMiUXXHCBW4QCALBfAh4A2qfKR7NGjhyZtXt3LrXB9OnTM3369Bb3Dxs2LFdccUVHSgMAoIpZgweA9qnS0SwAAChlAh4A2q6KR7MAAKCUCXgAaJsqH80CAIBSJuABoG2MZgEAQMkS8ACwf0azAACgpAl4AGid0SwAACh5Ah4AWmc0CwAASp6AB4CWGc0CAICyIOABoHlGswAAoGwIeABontEsAAAoGwIeAPZlNAsAAMqKgAeApoxmAQBA2RHwANCU0SwAACg7Ah4A/shoFgAAlCUBDwC7Gc0CAICyJeABYDejWQAAULYEPAAYzQIAgDIn4AGodkazAACg7Al4AKqd0SwAACh7Ah6AamY0CwAAKoKAB6BaGc0CAICKIeABqFZGswAAoGIIeACqkdEsAACoKAIegGpjNAsAACqOgAeg2hjNAgCAiiPgAagmRrMAAKAiCXgAqoXRLAAAqFgCHoBqYTQLAAAqloAHoBoYzQIAgIom4AGodEazAACg4gl4ACqd0SwAAKh4Ah6ASmY0CwAAqoKAB6BSGc0CAICqIeABqFRGswAAoGoIeAAqkdEsAACoKgIegEpjNAsAAKqOgAeg0hjNAgCAqiPgAagkRrMAAKAqCXgAKoXRLAAAqFoCHoBKYTQLAACqloAHoBIYzQIAgKom4AEod0azAACg6gl4AEpYj507k7/4i+TjH09eeaX5g4xmAQBA1RPwAJSwA3/5y2ThwuRf/zWZODH5939veoDRLAAAIAIegJLWe+PGP36zYUPy/vcnH/3o7m4eo1kAAMAf9Cp2AQC0rEnA0+Bb30oWL05OPNFoFgAAkETAA1DSej//fPM7NmzY/d+ejGYBAEDVMqIFUMKa7eBpztChRrMAAKCKCXgASlhNWwOeTZuST32q5TttAQAAFU3AA1Cq3nyz5RGt5nzrW83faQsAAKh4Ah6AEtVr8+b0eP319j1o7zttAQAAVUHAA1Ci2rz+TnO+9a3khBOS117rvIIAAICSJeABKFEdCniS5PXXk/r6zikGAAAoaQIegBJVcMBTU5N89rPJf/930rdv5xZFE/X19Zk3b16OOeaYjBs3LsuXL2/3OZYvX55x48bt97/vfe97XfAMAACoFL2KXQAAzWvXAssNpk9P/vmfk8MP7/yCaOLFF1/M5z73uSxdurRTzjd06NCcfvrpLe4fN25cp/wcAAAqk4AHoES1q4PnbW9Lbrghefe7u6oc9rBs2bJceOGFeemllzJz5swsXrw4L7zwQofOOXr06Fx66aWdVCEAANXGiBZAiappS8BzyCHJ7bcn//Vfwp1u9KMf/Si7du3KzTffnMsuuyy9e/cudkkAAFQ5HTwApejNN9Prt79teX9NTfKpTyWXXJIMGtR9dZEkmTRpUj75yU9m5MiRxS4FAACSCHgAStPvfpeeu3Y1v2/GjN3r7Lz1rd1bE43OPffcYpcAAABNCHgAStGzz+67zTo7Fa+uri4//elP85vf/CZvvvlmRo0alVNPPTVDhw4tdmkAAJS4ggOeNWvWdGYdZWX79u1JqvvPgPZxzdBegx59NCP+8PXrBx+cFz71qbxy5pnJAQckrqOSs3PnziTJ+vXrM6idI3Pr169Pkjz11FN517ve1fh60aBXr16ZMWNGzj777Daf02sNbeX3E+3lmqG9XDMUotqvm/Hjxxf0OB08ACVo+4QJ2XrUUak74YS88vGP580BA4pdUkW67rrrsm7dujYde/DBB+fKK6/sslq2bduWadOm5bTTTsuQIUNSW1ubBx54IPPnz8/dd9+dPn36ZPr06V328wEAKG8FBzyFJkqVoCFFrOY/A9rHNUO7jR+fNYcd9ocvXTddpa6uLhvbcTv6lv4uampqkuy+1Xl7/75GjRqV8ePHZ/DgwRk1alSTfaecckoOO+yw3HDDDfnhD3+YT3/60+nbt2+L51q5cmWrdcLe/H6ivVwztJdrhkK4bgqjgweAqnXPPfcUu4QMGDAgRx99dIv7zz///Nxyyy3ZunVrHn/88fzZn/1ZN1YHAEC56FnsAgCAltXU1GTIkCFJkpdeeqnI1QAAUKoEPABQZPX19amvr29xX21tbZLkLW95SzdWBQBAORHwAEARnXfeeTnmmGOycOHCZvcvXbo0dXV16dWrVyZNmtTN1QEAUC4EPADQDZYsWZKpU6dmzpw5TbafcMIJ2blzZ6655po8++yzTfZt2rQpV111VZJkxowZOngAAGiRRZYBoB1qa2vzta99bZ9tSXLXXXflwQcfbNw+c+bMjB49OsnuO3Y1d0v2OXPm5LHHHsuKFSvygQ98IO9+97tzyCGHZPPmzXn44Yezffv2vP3tb8/FF1/cdU8KAICyJ+ABgHbYsmVL5s2b1+y+RYsWNfn+ve99b2PA05I+ffrk29/+du65554sWLAgy5cvz9atWzNw4MBMmjQp06ZNy7Rp03LAAQd02nMAAKDyCHgAoB1GjhyZtWvXtvtx06dPz/Tp05vd16tXr5xzzjk555xzOloeAABVyho8AAAAAGVOwAMAAABQ5gQ8AAAAAGVOwAMAAABQ5gQ8AAAAAGVOwAMAAABQ5gQ8AAAAAGVOwAMAAABQ5gQ8AAAAAGVOwAMAAABQ5gQ8AAAAAGVOwAMAAABQ5gQ8AAAAAGVOwAMAAABQ5gQ8AAAAAGWuR319fX2xiwAAOm7lypVJkuOPP77IlQAA0N0EPAAAAABlzogWAAAAQJkT8AAAAACUOQEPAAAAQJkT8AAAAACUOQEPAAAAQJkT8AAAAACUOQEPAAAAQJkT8AAAAACUOQEPAAAAQJkT8AAAAACUOQEPAAAAQJkT8AAAAACUuf8fqiZesRm5sBwAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 287, + "width": 572 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "vector([3,2], 'b', \"v\")\n", + "vector([-2,1], 'g', \"w\")\n", + "vector([-1,-1.5], 'r')\n", + "plt.gca().spines[:].set_position('zero')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Les opérations de base sur les vecteurs sont\n", + "\n", + "* l'addition \n", + "$$ \\begin{bmatrix}\n", + " v_1 \\\\\n", + " v_2\n", + " \\end{bmatrix} \n", + " +\n", + " \\begin{bmatrix}\n", + " w_1 \\\\\n", + " w_2\n", + " \\end{bmatrix} \n", + " = \n", + " \\begin{bmatrix}\n", + " v_1 + w_1 \\\\\n", + " v_2 + w_2\n", + " \\end{bmatrix} \n", + "$$ \n", + "* la multiplication par un scalaire :\n", + "$$\n", + " α \\,\n", + " \\begin{bmatrix}\n", + " w_1 \\\\\n", + " w_2\n", + " \\end{bmatrix} \n", + " =\n", + " \\begin{bmatrix}\n", + " α \\, w_1 \\\\\n", + " α \\, w_2\n", + " \\end{bmatrix} \n", + "$$\n", + "\n", + "Bien sûr les vecteurs existent en 3D et en n'importe quelle dimension." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Matrices et applications linéaires\n", + "\n", + "Les matrices sont\n", + "\n", + "* une représentation d'une application linéaire (vision de mathématicien)\n", + "* un tableau en 2D (vision d'informaticien qui n'a pas tout compris)\n", + "* un outil bien pratique pour faire plein de choses\n", + "\n", + "Une application ou transformation ${\\bf f}$ est dite linéaire si elle vérifie :\n", + "\n", + "* ${\\bf f(v)} + {\\bf f(w)} = {\\bf f(v + w)}$ \n", + "* ${\\bf f}(α \\, {\\bf v}) = α \\, {\\bf f(v)}$ avec α un scalaire. \n", + "\n", + "Cela offre 2 propriétés :\n", + "\n", + "* l'origine (0,0) reste en (0,0)\n", + "* toute ligne reste une ligne après sa transformation par une application linéaire.\n", + "\n", + "Pour définir une application linéaire il suffit d'indiquer comment est transformée la base :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAABHgAAAJVCAYAAAClEEKRAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAABYlAAAWJQFJUiTwAABeo0lEQVR4nO3dfVjUdaL//xcIqCCIFCsorJGagveWYebqWhF8sz25WrvuSgqF6ak92+bmSetru3ZzeZNWu1rqdlyTtbzJmzSL1C2PYt5kELlHOH7L1AR+gqnEzRCgzu8Pm8mRGZgZBubu+biurpjPzfvzno6z43nyuQkwGo1GAQAAAAAAwGsFunsCAAAAAAAAaBkCDwAAAAAAgJcj8AAAAAAAAHg5Ag8AAAAAAICXI/AAAAAAAAB4OQIPAAAAAACAlyPwAAAAAAAAeDkCDwAAAAAAgJcj8AAAAAAAAHg5Ag8AAAAAAICXI/AAAAAAAAB4OQIPAAAAAACAlyPwAAAAAAAAeDkCDwAAAAAAgJcj8AAAAAAAAHg5Ag8AAAB8wqxZs9SnTx+Lfw4dOuTuaQEA0CYIPAAAAAAAAF6OwAMAAAAAAODlgtw9AQAAAMAVbr/9doWHh1ssi4mJcdNsAABoWwFGo9Ho7kkAAAAAAADAeVyiBQAAAAAA4OUIPAAAAPAJPEULAODPCDwAAAAAAABejsADAAAAAADg5Qg8AAAAAAAAXo7AAwAAAAAA4OUIPAAAAAAAAF6OwAMAAAAAAODlCDwAAAAAAABejsADt6uvr9ebb76pSZMmKTk5WUlJSerTp4/5n82bNzfa5+LFixo7dqzFdgcOHLDYZtasWRbr+/Tpo0OHDjUa69VXX7XYZs6cOa32XgEAAAAAaA0EHrhVdXW1Jk6cqHnz5umzzz5TRUWFLl261Ox+b7/9tr766ivz60GDBum2225zag6TJ09Wx44dza83btyooqIip8YCAAAAAMAdCDxwqzfeeENHjx51aB+DwaDly5dbLHvkkUecnkNUVJQeeOAB8+vLly/r1VdfdXo8AAAAAADaWpC7JwD/tnPnzkbL+vbtqyFDhig4OFiS1KtXL4v169at07lz58yv4+PjdeeddzYa5/bbb1d4eLjFspiYGKvzmDJlirKzs82v//u//1tHjx5Vv3797H8zAAAAAAC4CYEHblVcXGzxOjQ0VBs2bFD79u2tbn/p0iWtWbPGYtnYsWMVEBDQaNtf/OIX+sUvfmHXPOLi4jRkyBB9/vnn5mVvvvmmXnrpJbv2BwAAAADAnbhEC25VX19v8bpLly42444k7du3TyUlJRbLxo4d65K5XDvOjh07VFlZ6ZKxAQAAAABoTQQetLklS5aYn1h1rZKSkkZPvrraBx98YPH6hhtu0E033WT1OPY+Rcvk7rvvtnhdV1enf/7zn/a+LQAAAAAA3IbAA69y8OBBi9eDBw922dhdu3ZVbGxsk8cDAACe6/Lly42WtWvXzg0zAQCg7RF44DVOnz6tM2fOWCwbOHCgS49x7XiHDx9WUVERj00HfBCfbcD3VFRUNFrWqVOntp8IAJfjextoHjdZRpsbNGiQJk+eLEkWT66SpLCwME2YMMHqflffANkkKSnJpXNLSkrSjh07zK9LS0t1/vx5RUVFufQ4AADAtS5cuNDo7wqBgYGKi4tz04wAAGhbBB60uVGjRmnUqFGSGgeeyMhIPfPMM1b3Ky8vb7TM1eHF2ngEHgAAPNfSpUv1zTffaP/+/Y0ejtC/f3/O4AEA+A0CD7zGuXPnGi2LjIx06TGsjWftdG8AAOAZNm/e3OgJmyaZmZltPBsAANyHe/DAa1RVVTVaFhYW5tJjWPstX01NjUuPAQAAWt+kSZN0zz33uHsaAAC0Gc7ggdcIDw9vtKy6utqlZ/G0RUQCAACuFxgYqIiICPXo0UN33HGHpk+f7u4pAQDQpgg88BpdunRptOy7775zaeD57rvvGi3r3Lmzy8YHAACu9fHHH1u8zsvLc9NMAABwLy7Rgtf4yU9+0mjZ+fPnXXoMa/f54QbLAAAAAABPR+CB1xg8eHCjZUVFRS49xrXjxcbG6rrrrnPpMQAAAAAAcDUCD7zGDTfcoOjoaItl//rXv1x6jC+++MLi9bBhw1w6PgAAAAAArYHAA6+SnJxs8fraINMSZWVlOnPmjMWy4cOHu2x8AAAAAABaC4EHXuXax50eP35cx48fd8nYO3futHgdEhKilJQUl4wNAAAAAEBrIvDAq4wePVoxMTEWy95//32XjH3tOHfffbciIiJcMjYAAAAAAK2JwAOvEhQUpPT0dItlrgg8xcXF+vzzzy2WZWRktHhcAAAAAADaQpC7JwD/duzYMYf3+e1vf6uVK1fqwoULkqSTJ09q9+7dGjNmjMV28+fP1/z58+0ac/Xq1RavR48erQEDBjg8NwAAAAAA3IEzeOB1wsLC9O///u8Wy5YvX+70eOfPn9c777xjfh0YGKg//OEPTo8HAAAAAEBbI/DAK02aNEk9e/Y0vy4oKNCBAwecGis7O1u1tbXm1/fff7+SkpJaPEcAAAAAANoKl2jBKwUFBemDDz5wyVh/+MMfOGMHAIAfGI1G/eMf/9CiRYtUV1en7OxsJScnOzzOqVOntGLFCh04cEBnz55VWFiYhgwZooyMDA0fPtzqPnV1dVqzZo3ef/99nThxQkajUQkJCbr33nuVnp6u9u3bt/TtAQDgswg8AAAAkCR9++23mj17tvbu3duicfLy8pSVlSWDwaBhw4Zp1KhRKisr0759+7R7927NmTOn0UMTDAaDHn74YeXn5ys2NlZpaWmSpNzcXC1cuFAff/yxVq5cqQ4dOrRobgAA+CoCDwAAALR//349+eSTOnfunNLT07Vz506Vl5c7PE5tba1mzpwpg8GgBQsWaNy4ceZ1+fn5mjJliubPn6/k5GT17t3bvG7p0qXKz8/X6NGjtWTJEvPZOtXV1crKytJnn32m119/XTNmzGjxewUAwBdxDx4AAABo8+bNamho0NKlSzVnzhwFBwc7NU5OTo5KSko0cuRIi7gjSUOHDtXEiRPV0NBg8QRLg8GgtWvXKigoSHPnzrW4FKtTp07605/+JElas2aNvv/+e6fmBQCAryPwAAAAQIMGDdKWLVuUkpLSonF27twpSeZLrK6VmpoqSdq1a5d52b59+2QwGDRw4EDFxsY22icxMVHx8fGqqanRJ5980qL5AQDgqwg8AAAA0IMPPqi4uLgWj1NYWChJNp9I2a9fP0lSRUWFiouLJUlHjx61WNfUfqbxAQCAJe7BAzSnoUGBdXVSZWXLxmnXTgoLc82cAADwQPX19SorK5Mkq2fiSFLHjh0VGRmpiooKnTp1SnFxcebQExMTY3Ns03gnT5507aQBAPARTgeeoqIiV84D8Ejtzp1T73vvVdB337lkvDOzZ+vCgw+6ZCwALVNbWyuJ7zPAlvr6eklXHnceERFh1z6VV/0y5PTp0+bYcy3T/X2OHTumqKgonTlzRpJUVVVl8zNpMBgkSWVlZU1u88ADD6hLly5avXq12rVrZ9e8AXg+vrfhTxITE53aj0u0gCYYg4IUcPGiy8YL+OEvywAA+KK6ujrzz0FBtn+PaAo8pu1N/25qH9O6q49xrXXr1unEiRPKz8833wsIAAB/4fQZPM4WJcDbFL/wguKeeKLlA0VGquucOerauXPLxwLQYqbfAPJ9BlgXEhIiSerRo4fdn5OrL7Hq1auXxdOwrOnZs6cSExN1/fXXS5Kuv/56m8eKjIyUJF133XVWt6mpqbF4MtfKlSv1+OOPcxYP4CP43gaaxxk8QDOqUlN1/re/bflAM2ZIxB0AgA8Lu+peczU1NTa3q66uliSFh4db7OfIPtdatmyZzp49a35dWFiojRs32jlzAAC8H4EHsEP5f/6nNHSo8wNERkq//73L5gMAgCcKCQlR9+7dJUklJSVWt6mqqjLfqychIcHi36WlpTbHNo1n2vZqNTU1WrhwYaPlzz33nC5duuTAOwAAwHsReAA7GENCpA0bJDtvMtkIZ+8AAPxE//79JUlHjhyxur6goECSFB0dbb6kq7l9JOmLL76QJA0cOLDRumvP3jHhLB4AgD8h8AD26tlTWrnS8f2Cg6VHHnH9fAAA8EBpaWmSpJycHKvrt2/fLkkaO3asedmIESMUERGho0eP6ptvvmm0z8GDB3X27FlFRUVp+PDhFutsnb1jwlk8AAB/QeABHHH//dLvfufYPg0NVy7vWrpU+v771pkXAABtbNeuXUpLS9PUqVMtlqekpCghIUGHDx/W+vXrLdbt2bNH27ZtU2hoqDIzM83LQ0JClJGRocuXL2vOnDn6/qrvy4qKCr344ouSpGnTpjV60pats3dMOIsHAOAvAoxGo9HdkwA8WaM79tfVSbffLuXlOT5Yt27S7NlSVpbUoYMLZwnAUTyNA/hRRUWFXnvtNYtlmzZtUk1NjVJTU9W1a1fz8vT0dPXo0UObN2/W7NmzlZCQoA8//NBi38LCQmVmZqqiokLDhg1Tr169VFxcrP379ysgIECLFy82n+ljUl9fr0cffVS5ubmKjY3ViBEjdOnSJe3du1fnz59XamqqXnnlFYunYtXU1CghIaHJwCNd+Zz/61//4olagBfjextontOPSQf8Vvv20vr1V87K+eEmkXYrLZX+4z+kefMIPQAAj1FdXa3s7Gyr63bs2GHx+q677lKPHj2aHC8pKUlbt27VsmXLlJubq4KCAkVERCglJUXTp0+3+v+ghYSEaPny5Vq3bp22bNlivsTrpptu0owZMzRhwgQFBlqefN7c2TsmRUVF2rhxo3796183uy0AAN6KM3iAZtj8bcHGjdIDD9jeMTJSysiQVqyQamutb8MZPYDb8JtAwLvZe/aOSVJSko4cOcJZPICX4nsbaB734AGc1dz9eGbMkF55Rfr66ys/d+zYeBvTGT09e3KPHgAAHGDv2Tsm3IsHAODrCDxASyxadOVSrWtFRkq///2Vn2NipMWLCT0AALhIc0/OsoUnagEAfBmBB2iJ9u2lDRukiAjL5TNmSJ07Wy4j9AAA4BKOnr1jwlk8AABfRuABWqpnT2nlyh9fX332jjWEHgAAnObs2TsmnMUDAPBVBB7AFe6//8eo89RTjc/esYbQAwCAw5w9e8eEs3gAAL6Kp2gBzbD7jv1Go/Svf0kDBkgBAY4f6MwZ6aWXpGXLeOoW0AZ4GgfgfYxGo2JjY1VWVtaicW6++WZ99tlnLpoVgLbA9zbQPM7gAVwlIEAaONC5uCNxRg8AAM0wGo0aOHCgwsPDG/3TqVOnRttb2y48PFz9+/d3w+wBAGhdnMEDNMNtvy3gjB6gVfGbQMC3VFZWqvNVl0iHh4ersrLSjTMC4Ep8bwPN4wwewFNxRg8AAAAAwE4EHsDTEXoAAAAAAM0g8ADegtADAAAAALCBwAN4G0IPAAAAAOAaBB7AWxF6AAAAAAA/IPAA3o7QAwAAAAB+j8AD+ApCDwAAAAD4LQIP4GsIPQAAAADgdwg8gK8i9AAAAACA3yDwAL6O0AMAAAAAPo/AA/gLQg8AAAAA+CwCD+BvCD0AAAAA4HMIPIC/IvQAAAAAgM8g8AD+jtADAAAAAF6PwAPgCkIPAAAAAHgtAg8AS4QeAAAAAPA6BB4A1hF6AAAAAMBrEHgANI3QAwAAAAAej8ADwD6EHgAAAADwWAQeAI4h9AAAAACAxyHwAHAOoQcAAAAAPAaBB0DLEHoAAAAAwO0IPABcg9ADAAAAAG5D4AHgWoQeAAAAAGhzBB4ArYPQAwAAAABthsADoHURegAAAACg1RF4ALQNQg8AAAAAtBoCD4C2RegBAAAAAJcj8ABwD0IPAAAAALgMgQeAexF6AAAAAKDFCDwAPAOhBwAAAACcRuAB4FkIPQAAAADgMAIPAM9E6AEAAAAAuxF4AHg2Qg8AAAAANIvAA8A7EHoAAAAAwKYAo9FodPckAE9WVFQkSUpMTHTzTGDhzBnppZekZcuk2lrr23TrJs2eLWVlSR06tO384PH4bAONnTp1SitWrNCBAwd09uxZhYWFaciQIcrIyNDw4cPtGuPBBx/Up59+ate2H330keLi4iRJd9xxh0pKSprcftCgQdqwYYPVdZWVlercubP5dXh4uCorK+2aBwDPx/c20Lwgd08AAJxiOqNn5kzbocd0Rs+8eYQeAGhGXl6esrKyZDAYNGzYMI0aNUplZWXat2+fdu/erTlz5ig9Pb3ZcVJTU9W3b1+b6xsaGrRu3ToFBwerU6dOjdaPHz/e6nJJ6t69u/1vCAAAP0PgAeDdCD0A0GK1tbWaOXOmDAaDFixYoHHjxpnX5efna8qUKZo/f76Sk5PVu3fvJsdqLgItX75cRqNRDz30kCIjIxutf+yxx8xn9QAAAPtxDx4AvoF79ACA03JyclRSUqKRI0daxB1JGjp0qCZOnKiGhgatXr26RccpLi7W8uXL1a1bN02fPr1FYwEAAEsEHgC+hdADAA7buXOnJCktLc3q+tTUVEnSrl27WnScF154QbW1tZo1a5Y6WvvfZwAA4DQCDwDfROgBALsVFhZKkpKSkqyu79evnySpoqJCxcXFTh0jNzdXu3fv1q233moORgAAwHUIPAB8G6EHAJpUX1+vsrIySVJsbKzVbTp27Gi+X86pU6ccPobRaNTLL78sSZoxY0az2x46dEjLli3TwoUL9be//U0FBQUOHxMAAH/DTZYB+AduxgwAVlVXV5t/DgsLs7ldaGioKioqVFNT4/AxPv74YxUWFmrEiBEaMmRIk9tmZGRYPUto2LBhWrx4sbp27erw8QEA8AdOB56ioiJXzgPwWLU/RAD+zPuQrCy1u+8+Xff3v6vL+vUKvPaMnR9CT8Pzz+vc1KmquP9+Gdu3d89c0Wr4bANXnD171vzzV199pcDApk/wPn78uMOfm6VLl0qS7rzzTpv71tfXS5IiIyM1bdo09e7dW0ajUfn5+Vq1apUOHz6syZMna9GiRQoKavxX2KtDlSRdvnyZzzfgQ/jehj9JTEx0aj/O4AHgly5FR6v8qad07qGHbIae4PJyxbz4oq574w1CDwCf1f6q/127ePGiQkJCrG7X0NDQaHt7fPPNNyosLNT111+voUOH2tzumWee0aVLl5SQkGARmW6//XbdeOONevzxx3Xy5Enl5uZqzJgxDs0BAAB/4HTgcbYoAd7G9FsC/sz7qMREadQoaf58m5dumUJPzKpVXLrlQ/hsA1eYzpyRpPj4eEVFRVndrq6uTtKVz4wjn5vt27dLku677z6bN3E2jdvUunvvvVebN2/W119/rUcffbTRNpWVlRavAwMD+XwDPoTvbaB53GQZACRuxgzAb4WEhKh79+6SpJKSEqvbVFVVmQNKQkKCQ+ObHq3+85//3PlJSoqLi5MknT9/vkXjAADgqwg8AHA1Qg8AP9S/f39J0pEjR6yuNz3FKjo6WjExMXaPe/r0aZ06dUodOnTQ4MGDm93+8uXLNtdduHBBktS5c2e7jw8AgD8h8ACANYQeAH4kLS1NkpSTk2N1vekyq7Fjxzo0rikM9ezZ0+a9fSRp/fr1Sk5O1rRp06yur6ur00cffSRJTd7HBwAAf0bgAYCmEHoA+IGUlBQlJCTo8OHDWr9+vcW6PXv2aNu2bQoNDVVmZqZ5+a5du5SWlqapU6faHPfLL7+UJN1www1NHn/EiBGqrq7W3r179fbbb1usu3TpkhYsWKDS0lJFRUVp3Lhxjr05AAD8BE/RAgB7mELPzJk2b8ZsDj3z5nEzZgBeJTg4WC+//LIyMzP17LPP6r333lOvXr1UXFys/fv3KzAwUPPmzbO4PKuqqkonTpxoctwzZ85Iks0bN5vEx8fr6aef1vPPP6+5c+dq48aNGjBggBoaGvTpp5/q9OnT6ty5s5YsWaLw8PCWv2EAAHwQZ/AAgCM4oweAj0pKStLWrVs1ceJElZaWauPGjSosLFRKSoo2btxovozLEVVVVZKk0NDQZredNGmS1q5dq3vuuUfnzp3Tpk2blJOTo44dOyorK0vvvfeebrnlFofnAACAvwgwGo1Gd08C8GQ8khFNOnPG9hk9Jt26cUaPB+KzDfiWyspKixswh4eHN3p0OgDvxfc20DzO4AGAluCMHgAAAAAegMADAK5A6AEAAADgRgQeAHAlQg8AAAAANyDwAEBrIPQAAAAAaEMEHgBoTYQeAAAAAG2AwAMAbYHQAwAAAKAVEXgAoC0RegAAAAC0AgIPALgDoQcAAACACxF4AMCdCD0AAAAAXIDAAwCegNADAAAAoAUIPADgSQg9AAAAAJxA4AEAT0ToAQAAAOAAAg8AeDJCDwAAAAA7EHgAwBsQegAAAAA0gcADAN6E0AMAAADACgIPAHgjQg8AAACAqxB4AMCbEXoAAAAAiMADAL6B0AMAAAD4NQIPAPgSQg8AAADglwg8AOCLCD0AAACAXyHwAIAvI/QAAAAAfoHAAwD+gNADAAAA+DQCDwD4E0IPAAAA4JMIPADgjwg9AAAAgE8h8ACAPyP0AAAAAD6BwAMAIPQAAAAAXo7AAwD4EaEHAAAA8EoEHgBAY4QeAAAAwKsQeAAAthF6AAAAAK9A4AEANI/QAwAAAHg0Ag8AwH6EHgAAAMAjEXgAAI4j9AAAAAAehcADAHAeoQcAAADwCAQeAEDLEXoAAAAAtyLwAABch9ADAAAAuAWBBwDgeoQeAAAAoE0ReAAArYfQAwAAALQJAg8AoPURegAAAIBWReABALQdQg8AAADQKgg8AIC2R+gBAAAAXIrAAwBwH0IPAAAA4BIEHgCA+xF6AAAAgBYh8AAAPAehBwAAAHAKgQcA4HkIPQAAAIBDCDwAAM9F6AHa1KlTp/T0009rzJgx6t+/v5KTkzV9+nQdPHjQ7jEOHTqkPn36NPvP2rVrG+1bV1enlStXavz48RoyZIgGDx6sX/7yl1q5cqXq6upc+VYBAPA5Qe6eAAAAzTKFnpkzpZdekpYtk2prLbcxhZ5586TZs6WsLKlDB/fMF/BCeXl5ysrKksFg0LBhwzRq1CiVlZVp37592r17t+bMmaP09HS7x+vatatSU1Ntru/Tp4/Fa4PBoIcfflj5+fmKjY1VWlqaJCk3N1cLFy7Uxx9/rJUrV6oDn2sAAKwi8AAAvAehB2gVtbW1mjlzpgwGgxYsWKBx48aZ1+Xn52vKlCmaP3++kpOT1bt3b7vG7NGjh5555hm757B06VLl5+dr9OjRWrJkidq3by9Jqq6uVlZWlj777DO9/vrrmjFjhkPvDQAAf8ElWgAA78OlW4BL5eTkqKSkRCNHjrSIO5I0dOhQTZw4UQ0NDVq9enWrHN9gMGjt2rUKCgrS3LlzzXFHkjp16qQ//elPkqQ1a9boez7LAABYReABAHgvQg/gEjt37pQk82VR1zJdarVr165WOf6+fftkMBg0cOBAxcbGNlqfmJio+Ph41dTU6JNPPmmVOQAA4O0IPAAA7+dE6Anghq2AWWFhoSQpKSnJ6vp+/fpJkioqKlRcXOzy4x89etTiOE3NwTRXAABgicADAPAdDoSenqmp6vLWW5zRA79XX1+vsrIySbJ69owkdezYUZGRkZKuPGnLXlVVVdq6dateeeUVLV68WBs2bDAf62qmaBQTE2NzLNPcTp48affxAQDwJ07fZLmoqMiV8wA8Vu0PN3DlzzzgZbKy1O6++3Td3/+uLuvXK/CakBNcXq6YF19Uwxtv6NzUqaq4/34Zr7rvB+AvKisrzT+fPn3aaoCRpODgYEnSsWPHFBUVZXM8UwD63//9X/3sZz8zf4+aBAUFacKECfrNb35jXnbmzBlJV4KQre9bg8EgSSorK7O6TXV1tcXry5cv890N+BD+Tg5/kpiY6NR+nMEDAPBZl6KjVf7UU/pqxw6dmzJFl608TcsUekxn9HDpFvxN3VV/5oOCbP/uzxR46uz8jBgMBt1zzz16/fXX9c477+iNN97QL3/5SxmNRq1fv16bN29uNIemjm9aZ+/xAQDwN06fweNsUQK8jem3BPyZB7xYYqI0apQ0f77Nx6ubQk/MqlU8Xh1+5erLonr16mXxBCtrevbs2eR3Ynx8vBITExUZGan4+HiLdaNGjdINN9ygV155RZs2bdKMGTPUsWNHXX/99ZKk66+/3ubYpkvErrvuOqvbXH0mkiQFBgby3Q34EP5ODjSPM3gAAP7jqnv02Dqjh6duwd+EhYWZf66pqbG5nekSqPDw8CbH69SpkwYMGNAo7pg89NBD6tChg2pqavT5559bzMEVxwcAwF8ReAAA/icmxnzpFo9Xh78LCQlR9+7dJUklJSVWt6mqqjKfIZOQkNDi40VHR0uSzp07ZzFmaWmpzf1Mc2vp8QEA8FUEHgCA37oUHe3w49UJPfBF/fv3lyQdOXLE6vqCggJJUnR0dJNPujIxGo0yGo0211VUVEiSOnfubNfxJemLL76QJA0cOLDZ4wMA4I8IPAAAXPt4dS7dgp9JS0uTJOXk5Fhdv337dknS2LFjmx0rIyNDAwcOtDnW3r17VVVVpaCgIA0aNEiSNGLECEVEROjo0aP65ptvGu1z8OBBnT17VlFRURo+fLhd7wkAAH9D4AEAwMQUek6c4Iwe+JWUlBQlJCTo8OHDWr9+vcW6PXv2aNu2bQoNDVVmZqZ5+a5du5SWlqapU6dabH/LLbeovr5e8+fP18mTJy3WlZWV6cUXX5QkTZgwwXwGT0hIiDIyMnT58mXNmTNH31/1uaqoqDDvM23atCaftAUAgD8LMNo6fxaAJO7YD/gquz7bZ87YfOqWWbduPHULPqGwsFCZmZmqqKjQsGHD1KtXLxUXF2v//v0KCAjQ4sWLzWf6SNLmzZs1e/ZsJSQk6MMPPzQvr6ur08MPP6zDhw8rODhYP//5z/WTn/xEZ8+eVW5urmpra3XrrbdqxYoVCg0NNe9XX1+vRx99VLm5uYqNjdWIESN06dIl7d27V+fPn1dqaqpeeeUVtWvXzur8KysrzcFIunIz5mufrAXAe/F3cqB5BB6gGXyZAL7Joc82oQd+4syZM1q2bJlyc3NVXl6uiIgIDRs2TNOnT2/0WbEVeCTp4sWL2rBhg7Zv364vv/xSNTU1Cg8PV9++fXXffffpvvvusxpqLl68qHXr1mnLli36+uuvJUk33XST7r//fk2YMEGBgbZPPifwAL6Nv5MDzSPwAM3gywTwTU59tgk9gMci8AC+jb+TA83jHjwAANjr2psxc48eAAAAeAgCDwAAjiL0AAAAwMMQeAAAcBahBwAAAB6CwAMAQEsRegAAAOBmBB4AAFyF0AMAAAA3IfAAAOBqhB4AAAC0MQIPAACthdADAACANkLgAQCgtRF6AAAA0MoIPAAAtBVCDwAAAFoJgQcAgLZG6AEAAICLEXgAAHAXQg8AAABchMADAIC7EXoAAADQQgQeAAA8BaEHAAAATiLwAADgaQg9AAAAcBCBBwAAT0XoAQAAgJ0IPAAAeDpCDwAAAJpB4AEAwFsQegAAAGADgQcAAG9D6AEAAMA1CDwAAHgrQg8AAAB+QOABAMDbEXoAAAD8HoEHAABfQegBAADwWwQeAAB8DaEHAADA7xB4AADwVYQeAAAAv0HgAQDA1xF6AAAAfB6BBwAAf0HoAQAA8FkEHgAA/A2hBwAAwOcQeAAA8FeEHgAAAJ9B4AEAwN8RegAAALwegQcAAFxB6AEAAPBaBB4AAGCJ0AMAAOB1CDwAAMA6Qg8AAIDXIPAAAICmEXoAAAA8HoEHAADYh9ADAADgsQg8AADAMYQeAAAAj0PgAQAAziH0AAAAeAwCDwAAaBlCDwAAgNsReAAAgGsQegAAANyGwAMAAFyL0AMAANDmCDwAAKB1EHoAAADaDIEHAAC0LkIPAABAqyPwAACAtkHoAQAAaDUEHgAA0LYIPQAAAC5H4AEAAO5B6AEAAHAZAg8AAHAvQg8AAECLBRiNRqO7JwF4sqKiIklSYmKim2cCwJX4bHuwM2ekl16Sli2Tamutb9OtmzR7tpSVJXXo0Lbz82GnTp3SihUrdODAAZ09e1ZhYWEaMmSIMjIyNHz4cIfGOn78uFauXKmDBw+qvLxcISEhSkhIUFpamiZPnqz27dtbbH/HHXeopKSkyTEHDRqkDRs2WF1XWVmpzp07m1+Hh4ersrLSoTkD8Fx8bwPNI/AAzeDLBPBNfLa9AKGnTeXl5SkrK0sGg0HDhg1Tz549VVZWpn379qmhoUFz5sxRenq6XWPt2LFDTz75pOrr69W3b1/1799f3333nT755BMZDAb1799f2dnZCgsLM+9jCjzjx49Xp06drI7bvXt3ZWRkWF1H4AF8G9/bQPMIPEAz+DIBfBOfbS9C6Gl1tbW1Gjt2rEpKSrRgwQKNGzfOvC4/P19TpkyR0WjUli1b1Lt37ybHKisrU1pamgwGg5566ik99NBD5nWlpaX61a9+pbNnz+rRRx/V448/bl5nCjwfffSR4uLiHH4PBB7At/G9DTSPe/AAAADPxj16Wl1OTo5KSko0cuRIi7gjSUOHDtXEiRPV0NCg1atXNzvWu+++K4PBoEGDBlnEHUnq1q2bHn74YUnSzp07XTZ/AABA4AEAAN6C0NNqTLElLS3N6vrU1FRJ0q5du5oda+TIkXrhhRf0xBNPWF1/4403SpLOnDnjzFQBAIANBB4AAOBdCD0uV1hYKElKSkqyur5fv36SpIqKChUXFzc5Vr9+/fTAAw/otttus7q+vLxcktSlSxdnpwsAAKwg8AAAAO9E6HGJ+vp6lZWVSZJiY2OtbtOxY0dFRkZKuvKkLWcZjUZt3LhRku2zhYxGow4dOqRly5Zp4cKF+tvf/qaCggKnjwkAgL8IcnZH002uAF9X+8MNPfkzD/gWPts+JitL7e67T9f9/e/qsn69Aq8NOT+Enobnn9e5qVNVcf/9Ml7zmG5/dfWNiE+fPm2OPdcKDg6WJB07dkxRUVFOHWvTpk0qKChQeHi4Ro8ebfH5q6+vlyRNmjTJ6hz69eunP/7xjzaPXV1dbfH68uXLfL4BH8L3NvyJszcT5wweAADgEy5FR6v8qaf01Y4dOjdlii5beZpWcHm5Yl58UT1TU9XlrbcUUFfnhpl6lrqr/hsEBdn+3Z8p8NQ5+d/s3Xff1Zo1axQUFKT//M//tPko9OjoaD3//PNat26d1q5dq5kzZ+r666/X0aNH9dxzz+nixYtOHR8AAF/HY9KBZvBIRsA38dn2Azxe3S4XLlzQ8OHDJUlHjhxRextnNo0ZM0alpaVasmSJ7r77brvHNxqNWrBggVatWqWQkBAtXrzY6v7Hjh3TxYsXlZiYqMBAy99BfvPNN/rFL36h77//vtFj3E14TDrg2/jeBprHGTwAAMA3cY8eu4SFhZl/rqmpsbmd6RKo8PBwu8euq6vT448/rlWrVikiIkJvvPGGzTjUp08f9evXr1HckaSf/vSnuueeeyRJ+/bts/v4AAD4EwIPAADwbYSeJoWEhKh79+6SpJKSEqvbVFVVmc+GSUhIsGvc+vp6TZs2TTt27FBcXJzWrVtnPlPIGXFxcZKk8+fPOz0GAAC+jMADAAD8A6HHpv79+0u6comWNaanWEVHRysmJqbZ8S5fvqyZM2fqwIEDSkxM1Lp169SzZ0+79rPlwoULkmRxGRYAAPgRgQcAAPgXQk8jpkeW5+TkWF2/fft2SdLYsWPtGm/p0qX68MMP1bNnT61atUrR0dFNbr9+/XolJydr2rRpVtfX1dXpo48+kiQNHTrUrjkAAOBvCDwAAMA/EXrMUlJSlJCQoMOHD2v9+vUW6/bs2aNt27YpNDRUmZmZ5uW7du1SWlqapk6darH98ePHtWLFCgUHB2vp0qXq0qVLs8cfMWKEqqurtXfvXr399tsW6y5duqQFCxaotLRUUVFRVm+wDAAAeIoW0Czu2A/4Jj7baMTPn7pVWFiozMxMVVRUaNiwYerVq5eKi4u1f/9+BQQEaPHixeYzfSRp8+bNmj17thISEvThhx+alz/11FN69913FR8frzFjxjR5zMcee0yRkZGSpLfeekvPP/+8jEaj+vXrpwEDBqihoUGffvqpTp8+rc6dO+v111/XLbfcYnUsnqIF+Da+t4HmEXiAZvBlAvgmPtuwyY9Dz5kzZ7Rs2TLl5uaqvLxcERERGjZsmKZPn97os2Ir8Dz44IP69NNP7TreRx99ZL55siR9/vnnys7OVn5+vs6dO6fg4GDFxcVp1KhRmjx5srp27WpzLAIP4Nv43gaaR+ABmsGXCeCb+GyjWX4cerwRgQfwbXxvA83jHjwAAADWcI8eAADgRQg8AAAATSH0AAAAL0DgAQAAsAehBwAAeDACDwAAgCMIPQAAwAMReAAAAJxB6AEAAB6EwAMAANAShB4AAOABCDwAAACuQOgBAABuROABAABwJUIPAABwAwIPAABAayD0AACANkTgAQAAaE2EHgAA0AYIPAAAAG2B0AMAAFoRgQcAAKAtEXoAAEArIPAAAAC4A6EHAAC4EIEHAADAnQg9AADABQg8AAAAnoDQAwAAWoDAAwAA4EkIPQAAwAkEHgAAAE9E6AEAAA4g8AAAAHgyQg8AALADgQcAAMAbEHoAAEATCDwAAADehNADAACsIPAAAAB4I0IPAAC4CoEHAADAmxF6AACACDwAAAC+gdADAIBfI/AAAAD4EkIPAAB+icADAADgiwg9AAD4FQIPAACALyP0AADgFwg8AAAA/oDQAwCATyPwAAAA+BNCDwAAPonAAwAA4I8IPQAA+BQCDwAAgD8j9AAA4BMIPAAAACD0APBrs2bNUp8+fSz+OXTokLunBTiEwAMAAIAfEXoAAPBKBB4AAAA0RugBAMCrBLl7AgAAAPBgptAzc6b00kvSsmVSba3lNqbQM2+eNHu2lJUldejgnvkCgBNuv/12hYeHWyyLiYlx02wA5wQYjUajuycBeLKioiJJUmJioptnAsCV+GwDTjpzxnboMenWrc1DT2VlpTp37mx+HR4ersrKyjY5NoDWx/c20Dwu0QIAAID9uHQLAACPROABAACA4wg9AHwIT9GCLyDwAAAAwHmEHgAAPAKBBwAAAC1H6AEAwK0IPAAAAHAdQg8AAG5B4AEAAIDrEXoAAGhTBB4AAAC0HkIPAABtgsADAACA1kfoAQCgVRF4AAAA0HYIPYBf+vWvf60hQ4Zo7dq1unTpkrunA/gkAg8AAAAkSadOndLTTz+tMWPGqH///kpOTtb06dN18OBB14/lQOipiY1Vw6uvEnoAL/bee++poKBAv/3tb9W/f39CD9AKCDwAAABQXl6exo0bp02bNql79+6aMGGChgwZon379mnKlClas2ZN64z1Q+gx/M//6P0+fVQbENBovLCKCgU/8YSMN97IGT2AD/jf//1fQg/QCgg8AAAAfq62tlYzZ86UwWDQggULtGbNGs2dO1fLly9Xdna2QkJCNH/+fH355ZetNtbSjRs1w2jUnN/+Vhcff9zqGT0B/9//x6VbgA8h9ACuReABAADwczk5OSopKdHIkSM1btw4i3VDhw7VxIkT1dDQoNWrV7fKWAaDQWvXrlVQUJD++NJLCnr1Ve7RA/gRQg/gGgQeAAAAP7dz505JUlpamtX1qampkqRdu3a1ylj79u2TwWDQwIEDFRsbe2XhNffo+T7Qyl9brwo9wX/7m9o3OzsAnozQA7QMgQcAAMDPFRYWSpKSkpKsru/Xr58kqaKiQsXFxS4f6+jRoxbrLPwQel7IzNTfu3RRQ3Bw421KS9Vx5kwdl/SYROgBvByhB3BOkLsnAAAAAPepr69XWVmZJP149sw1OnbsqMjISFVUVOjUqVOKi4tz6Vim0BMTE2Nznp169dKC6Gh986tf6c9hYdKyZVJtrcU23SUtlfSUpJ9VVSk0NLSJdw6gLdVe83m1hyn0PPfcc3r44YdtnhkI4IoAo9FodHSnvLy81pgLAAAAYJegb79VzD/+oeiNGxVYV9do/b2S3m/7aQFoRUOHDtXf/va3Vhl7+fLl2rt3r8Wy//t//6/NsxGB1nbzzTc7vA+BBwAAAF4r6NtvdcNzzyli/35d/YD1eZKedtekALSKPn366K233nL3NIA24UzgceoSLWcOBHiroqIiSVJiYqKbZwLAlfhsA1dcuHBBw4cPlyQdOXJE7dtbv4PNmDFjVFpaqiVLlujuu+926VjTp0/X7t279ec//1m/+c1vrO7z17/+Va+99prGjBmj5cuX/7hizRrpwAGLbS9J+ripNw3Aq3Tr1k2ZmZm6//77NXjwYHdPB/BY3IMHAADAj4WFhZl/rqmpsRllqqurJUnh4eEuH8u0X01Njc2xrR5/zRpp8mTpqhPSjYGB+nLuXG2dMcPmWADa3nXXXafvv//eoX26deum2bNnKysrSydOnGilmQG+g8ADAADgx0JCQtS9e3eVlJSopKREUVFRjbapqqpSZWWlJCkhIcHlY5n+XVpaanPskpISy+NbiTtq105fv/iiau66ixssAx4mICCg+Y1+cHXY6dChQyvOCvAtPCYdAADAz/Xv31/SlcuqrCkoKJAkRUdHN/mkK2fHam4fSfriiy8kSQMHDrQZd7RunSruuqvJ+QHwXN26ddOSJUt0/Phx/e53vyPuAA4i8AAAAPg506OHc3JyrK7fvn27JGns2LGtMtaIESMUERGho0eP6ptvvmm0z8GDB3X27FlFRUXptuPHbcYd3X9/s/MD4HkIO4BrEHgAAAD8XEpKihISEnT48GGtX7/eYt2ePXu0bds2hYaGKjMz07x8165dSktL09SpU1s8VkhIiDIyMnT58mXNmTPH4j4dFRUVevHFFyVJCwYMULvMTOIO4CMIO4BrcQ8ewAHHjx/XypUrdfDgQZWXlyskJEQJCQlKS0vT5MmTbd5MEoDnMxqN+sc//qFFixaprq5O2dnZSk5Odve0gDYRHBysl19+WZmZmXr22Wf13nvvqVevXiouLtb+/fsVGBioefPmWVyeVVVVZfWmp86MJUlTp07V559/rtzcXKWlpWnEiBG6dOmS9u7dq/Pnz+uZHj30s//6L5tx59SpU1qxYoUmTJggSUpOTtaQIUOUkZFhfrIXAM/g6D12jEajtm/fruzsbNXX1/MdDdhA4AHstGPHDj355JOqr69X3759ddttt+m7777TJ598okWLFunDDz9Udna2xRNEAHiHb7/9VrNnz9bevXvdPRXAbZKSkrR161YtW7ZMubm5KigoUEREhFJSUjR9+nQlJia26lghISFavny51q1bpy1btpgv8brpppv06i236NbXXlOAjbiTl5enrKwsGQwGc+AZMmSI9u3bp927d2vOnDlKT09v2X8gAC0ycuRIHTt2TDNnznTo5sl8RwP2CzAar/6mBHCtoqIinTt3Tv/xH/8hg8Ggp556Sg899JB5fWlpqX71q1/p7NmzevTRR/X444+7cbYA7FVUVCRJunDhgp588kmdO3dO6enp2rlzp8rLy/ntIOApmrihsu6/X7W1tRo7dqxKSkq0YMECxcfHS5Juvvlm5efna8qUKTIajdqyZYt69+7tpjcBwGg0OvQkLUnav3+/+Tv6nnvu0cGDB3X+/Hm+owEbuAcPYIfdu3fLYDBo0KBBFnFHunKK6cMPPyxJ2rlzpzumB6AFNm/erIaGBi1dulRz5sxRcHCwu6cEwKSZuCNduZlzSUmJRo4cqXHjxlnsPnToUE2cOFENDQ1avXp1G04cwLUcjTuS5Xf0I488onbt2rXCzADfQeAB7DBkyBC98MILeuKJJ6yuv/HGGyVJZ86cactpAXCBQYMGacuWLUpJSXH3VABczY64I/34yxXT07uulZqaKunKTaEBeBe+owHHcA8ewA49e/Zs8t4D5eXlkqQuXbq01ZQAuMiDDz7o7ikAuJadcUeSCgsLJV257481/fr1k3TlaVzFxcWKi4trnTkDcDm+owHHcAYP0EJGo1EbN26UZPu3hwAAwE4OxJ36+nqVlZVJkmJjY60O17FjR0VGRkqSTp061SpTBgDAExB4gBZ64403VFBQoMjISE2dOtXd0wEAwHs5EHckqbq62vxzU0+xDA0NlSTV1NS4bq4AAHgYLtGC33niiSfMT89pTteuXTVr1iyb6//+97/r5ZdfVnBwsP7yl7+oc+fOrpomAAe58rMNwA0cjDuSVFdXZ/65qRukh4SESJJqa2tdM1cAADwQgQd+p6SkRCdOnLBr2/r6eqvLjUajFixYoFWrVikkJESLFy/W8OHDXTlNAA5yxWcbgJs4EXckqUOHDuafGxoa1L59e6vbmT7zHTt2dM18AQDwQAQe+J0NGzY4tP21ZwTU1dVp5syZ2rFjhyIiIrRkyRLiDuABWvrZBuAmTsYdyfKyrJqaGpuBx3QpV3h4eMvnCwCAh+IePIAD6uvrNW3aNO3YsUNxcXFat24dcQcAAGe1IO5IVy696t69u6QrZ/FZU1VVpcrKSklSQkJCy+cMAICHIvAAdrp8+bJmzpypAwcOKDExUevWrVPPnj3dPS0AALxTC+OOSf/+/SVJR44csbq+oKBAkhQdHa2YmBinpwsAgKcj8AB2Wrp0qT788EP17NlTq1atUnR0tLunBACAd3JR3JGktLQ0SVJOTo7V9du3b5ckjR071rm5AgDgJQg8gB1Onz6tFStWKDg4WEuXLlWXLl3cPSUAALyTC+OOJKWkpCghIUGHDx/W+vXrLdbt2bNH27ZtU2hoqDIzM1s6cwAAPFqA0Xj1tyuAaxUVFekvf/mLdu/erfj4eI0ZM6bJ7R977DFFRka2zeQAOK2oqEhVVVXatWuXxfJNmzappqZGqamp6tq1q3l5enq6evTo0dbTBHyLi+OOSWFhoTIzM1VRUaG3335bkrRs2TLt379fAQEBWrx4sflMHwDeoaKiQq+99pr59fnz5/XRRx+ptraW72jABp6iBdihvLxc0pUzebKzs5vcdsqUKQQewEsYDAabn+kdO3ZYvL7rrrv4yyPQEq0UdyQpKSlJW7du1bJly8zLCgsLlZKSounTpysxMbFF4wNoe9XV1XxHAw7iDB6gGaZHKfOXQ8C38NkG2lArxp1r5eXlSZJuvvlml44LwL343gaaxz14AAAA0HraMO4AAODPCDwAAABoHcQdAADaDIEHAAAArkfcAQCgTRF4AAAA4FrEHQAA2hyBBwAAAK5D3AEAwC0IPAAAAHAN4g4AAG5D4AEAAEDLEXcAAHArAg8AAABahrgDAIDbEXgAAADgPOIOAAAegcADAAAA5xB3AADwGAQeAAAAOI64AwCARyHwAAAAwDHEHQAAPA6BBwAAAPYj7gAA4JEIPAAAALAPcQcAAI9F4AEAAEDziDsAAHg0Ag8AAACaRtwBAMDjEXgAAABgG3EHAACvQOABAACAdcQdAAC8BoEHAAAAjRF3AADwKgQeAAAAWCLuAADgdQg8AAAA+BFxBwAAr0TgAQAAwBXEHQAAvBaBBwAAAMQdAAC8HIEHAADA3xF3AADwegQeAAAAf0bcAQDAJxB4AAAA/BVxBwAAn0HgAQAA8EfEHQAAfAqBBwAAwN8QdwAA8DlB7p4AAAAA2pCVuGNs105r/+3f9MZrr+nsn/+ssLAwDRkyRBkZGRo+fLjDhzh+/LhWrlypgwcPqry8XCEhIUpISFBaWpomT56s9u3bW2x/xx13qKSkpMkxBw0apA0bNjg8FwAA/AWBBwAAwF9YizuBgfrP+HhtO3pUw4YN06hRo1RWVqZ9+/Zp9+7dmjNnjtLT0+0+xI4dO/Tkk0+qvr5effv21W233abvvvtOn3zyiRYtWqQPP/xQ2dnZCgsLa7Tv+PHj1alTJ6vjdu/e3fH3CwCAHyHwAAAA+AMbZ+7M7dtX2xoatGDBAo0bN868Lj8/X1OmTNH8+fOVnJys3r17N3uIsrIyzZo1S/X19Xrqqaf00EMPmdeVlpbqV7/6lf7nf/5H//Vf/6XHH3+80f6PPfaY4uLiWvY+AQDwU9yDBwAAwNfZuOfOoSee0NqGBo0cOdIi7kjS0KFDNXHiRDU0NGj16tV2Hebdd9+VwWDQoEGDLOKOJHXr1k0PP/ywJGnnzp0tejsAAKAxAg8AAIAva+KGym9WVUmS0tLSrO6ampoqSdq1a5ddhxo5cqReeOEFPfHEE1bX33jjjZKkM2fO2Dt7AABgJy7RAgAA8FXNPC2r8K9/lSQlJSVZ3b1fv36SpIqKChUXFzd7+VS/fv3M+1hTXl4uSerSpYsj7wIAANiBwAMAAOCLmok79fX1KisrkyTFxsZaHaJjx46KjIxURUWFTp061aL74xiNRm3cuFGS7TOGjEajDh06pPz8fFVVVSkyMlK33nqrBg8e7PRxAQDwFwQeAAAAX9NM3JGk6upq8yprT7QyCQ0NVUVFhWpqalo0pTfeeEMFBQWKjIzU1KlTrW6TkZGh4uLiRsuHDRumxYsXq2vXri2aAwAAvszpwFNUVOTKeQAeq7a2VhJ/5gFfw2cbvmbRokU6ceKE7jpzRrOKiixutHhJ0vN9+2rv669Lr7+uqKgo/f73vzev/+qrrxQY2PStGY8fP+705+Xdd9/V6tWrFRQUpD/+8Y8qLS1VaWmpeX19fb0kKTIyUtOmTVPv3r1lNBqVn5+vVatW6fDhw5o8ebIWLVqkoCD7/vrKZxvwLXxvw58kJiY6tR9n8AAAAPiA8vJy3VxUpFlnzljEnYuSZsTGakdDg1RSIulKUGnfvv2P21y8qJCQEKvjNjQ0SJLF9vYyGo1atWqVtm3bpuDgYM2YMUMDBgxotN0zzzyjS5cuKSEhwSI03X777brxxhv1+OOP6+TJk8rNzdWYMWMcngcAAP7A6cDjbFECvI3ptwT8mQd8C59t+Jr3fv1r6f33LRe2a6egdev01x8uy7qa6awZSYqPj1dUVJTVcevq6iRd+aw48nmpq6vTzJkztWPHDkVERGjJkiUaPny41W2bGjcxMVH33nuvNm/erK+//lqPPvpok8fNy8trdkwA3ofvbaB5PCYdAADA29lxz51rhYSEqHv37pKkkh/O7LlWVVWVKisrJUkJCQl2T6e+vl7Tpk3Tjh07FBcXp3Xr1tmMO/Yw3dz5/PnzTo8BAICvI/AAAAB4Myfijkn//v0lSUeOHLG6vqCgQJIUHR2tmJgYu6Zz+fJlzZw5UwcOHFBiYqLWrVunnj172rWfLRcuXJAkde7c2a45AADgjwg8AAAA3qoFcUf68XHlOTk5Vtdv375dkjR27Fi7p7R06VJ9+OGH6tmzp1atWqXo6Ogmt1+/fr2Sk5M1bdo0q+vr6ur00UcfSZKGDh1q9zwAAPA3BB4AAABv1MK4I0kpKSlKSEjQ4cOHtX79eot1e/bs0bZt2xQaGqrMzEyLdbt27VJaWlqjx50fP35cK1asUHBwsJYuXaouXbo0O4cRI0aourpae/fu1dtvv22x7tKlS1qwYIFKS0sVFRWlcePG2fW+AADwRzxFCwAAwNu4IO5IUnBwsF5++WVlZmbq2Wef1XvvvadevXqpuLhY+/fvV2BgoObNm9fo8qyqqiqdOHGi0Xh/+9vfdPHiRcXHx2vt2rVNHvuxxx5TZGSk4uPj9fTTT+v555/X3LlztXHjRg0YMEANDQ369NNPdfr0aXXu3FlLlixReHi43e8NAAB/Q+ABAADwJi6KOyZJSUnaunWrli1bptzcXBUUFCgiIkIpKSmaPn26Q0+sKS0tlSSdPn1a2dnZTW47ZcoURUZGSpImTZqkpKQkZWdnKz8/X5s2bVJwcLDi4uKUlZWlyZMnq2vXrg6/NwAA/EmA0Xj13w4AXItHMgK+ic82vJKL444vMj0m/eabb3bzTAC4Et/bQPO4Bw8AAIA3IO4AAIAmEHgAAAA8HXEHAAA0g8ADAADgyYg7AADADgQeAAAAT0XcAQAAdiLwAAAAeCLiDgAAcACBBwAAwNMQdwAAgIMIPAAAAJ6EuAMAAJxA4AEAAPAUxB0AAOAkAg8AAIAnIO4AAIAWIPAAAAC4G3EHAAC0EIEHAADAnYg7AADABQg8AAAA7kLcAQAALkLgAQAAcAfiDgAAcCECDwAAQFsj7gAAABcj8AAAALQl4g4AAGgFBB4AAIC2QtwBAACthMADAADQFog7AACgFRF4AAAAWhtxBwAAtDICDwAAQGsi7gAAgDZA4AEAAGgtxB0AANBGCDwAAACtgbgDAADaEIEHAADA1Yg7AACgjRF4AAAAXIm4AwAA3IDAAwAA4CrEHQAA4CYEHgAAAFcg7gAAADci8AAAALQUcQcAALgZgQcAAKAliDsAAMADEHgAAACcRdwBAAAegsADAADgDOIOAADwIAQeAAAARxF3AACAhyHwAAAAOIK4AwAAPBCBBwAAwF7EHQAA4KEIPAAAAPYg7gAAAA9G4AEAAGgOcQcAAHg4Ag8AAEBTiDsAAMALEHgAAABsIe4AAAAvQeABAACwhrgDAAC8CIEHAADgWsQdAADgZQg8AAAAVyPuAAAAL0TgAQAAMCHuAAAAL0XgAQAAkIg7AADAqxF4AAAAiDsAAMDLEXgAAIB/I+4AAAAfQOABAAD+i7gDAAB8RJC7JwAAAOAWxB2zU6dOacWKFTpw4IDOnj2rsLAwDRkyRBkZGRo+fLjd4xw6dEiTJ09udrs///nP+s1vfmOxrK6uTmvWrNH777+vEydOyGg0KiEhQffee6/S09PVvn17h98XAAD+hMADAAD8D3HHLC8vT1lZWTIYDBo2bJhGjRqlsrIy7du3T7t379acOXOUnp7u0Jhdu3ZVamqqzfV9+vSxeG0wGPTwww8rPz9fsbGxSktLkyTl5uZq4cKF+vjjj7Vy5Up16NDB8TcIAICfIPAAAAD/Qtwxq62t1cyZM2UwGLRgwQKNGzfOvC4/P19TpkzR/PnzlZycrN69e9s9bo8ePfTMM8/Yvf3SpUuVn5+v0aNHa8mSJeazdaqrq5WVlaXPPvtMr7/+umbMmGH3mAAA+BvuwQMAAPwHccdCTk6OSkpKNHLkSIu4I0lDhw7VxIkT1dDQoNWrV7faHAwGg9auXaugoCDNnTvX4lKsTp066U9/+pMkac2aNfr+++9bbR4AAHg7Ag8AAPAPxJ1Gdu7cKUnmS6KuZbrMateuXa02h3379slgMGjgwIGKjY1ttD4xMVHx8fGqqanRJ5980mrzAADA2xF4AACA7yPuWFVYWChJSkpKsrq+X79+kqSKigoVFxe3yhyOHj1qcaym5mGaLwAAaIx78AAAAN9G3LGqvr5eZWVlkmT1zBlJ6tixoyIjI1VRUaFTp04pLi7O7vGrqqr08ccf6+uvv9bly5cVHx+v0aNHq2vXrhbbmcJRTEyMzbFM8zt58qTdxwcAwN8QeAAAgO8i7thUXV1t/jksLMzmdqGhoaqoqFBNTY3dY3/55ZcaPXp0o32Cg4P1yCOP6Pe//32jeTQ3B0kOzQEAAH/jdOApKipy5TwAj1VbWyuJP/OAr+Gz7fsitm1Tt9mzFXBV3DG2a6eSRYtU1a+f5GP/t1+0aJFOnDhh17ZRUVEWkeWrr75SYGDTV+4fP3682c/LqVOnJF05e+e+++7TnXfeqejoaFVUVOiDDz7Qtm3b9Nprr6mqqkrjx4+XJJ07d06S9O2339ocv6KiwrytvZ9ZPtuAb+F7G/4kMTHRqf04gwcAAPicJuPODzcO9jXl5eUqKSmxa9v6+nqLp1VdvHhRISEhVrdtaGiQJIvtbenVq5cWLVqk8PBwi0uxoqOjNWXKFIWGhuqtt97SO++8o7Fjx6p9+/bmcS9evGhzXNM6e+YAAIC/cjrwOFuUAG9j+i0Bf+YB38Jn24etWSPNnt3osqyAdesU58OXZb333nsObV9fX2/+OT4+XlFRUVa3q6urk3Tls2LP52Xo0KE2182aNUubNm1SbW2tDAaDBg8ebL73Tnh4uM3xO3ToIOnKvXiam0NeXp55vgB8B9/bQPN4ihYAAPAd3HPHbiEhIerevbsk2Tzzp6qqSpWVlZKkhIQElxwzOjpa0o+XZpnGLS0ttbmfaX6umAMAAL6KwAMAAHwDccdh/fv3lyQdOXLE6vqCggJJVy6xauopV1czGo0yXv1/g2vWme6n07lzZ7vmIElffPGFJGngwIF2zQEAAH9E4AEAAN6PuOOUtLQ0SVJOTo7V9du3b5ckjR071q7xMjIyNHDgQJvj7d27V1VVVQoKCtKgQYMkSSNGjFBERISOHj2qb775ptE+Bw8e1NmzZxUVFaXhw4fbNQ8AAPwRgQcAAHg34o7TUlJSlJCQoMOHD2v9+vUW6/bs2aNt27YpNDRUmZmZFut27dqltLQ0TZ061WL5Lbfcovr6es2fP18nT560WFdWVqYXX3xRkjRhwgTzGTwhISHKyMjQ5cuXNWfOHH3//ffmfSoqKsz7TJs2TUFBPB8EAABb+JYEAADei7jTIsHBwXr55ZeVmZmpZ599Vu+995569eql4uJi7d+/X4GBgZo3b16jy7OqqqqsPpJ96tSpOnjwoA4fPqx7771XP//5z/WTn/xEZ8+eVW5urmpra3Xrrbdq1qxZjfb7/PPPlZubq7S0NI0YMUKXLl3S3r17df78eaWmpurBBx9s1f8WAAB4OwIPAADwTsQdl0hKStLWrVu1bNky5ebmqqCgQBEREUpJSdH06dMdemJN+/bt9eabb2rDhg3avn27Dh06pJqaGoWHh2vQoEG67777dN9996ldu3YW+4WEhGj58uVat26dtmzZYr7E66abbtKMGTM0YcIEBQZy4jkAAE0JMNq6Cx4ASTySEfBVfLa9HHEHNpgek37zzTe7eSYAXInvbaB5/CoEAAB4F+IOAABAIwQeAADgPYg7AAAAVhF4AACAdyDuAAAA2ETgAQAAno+4AwAA0CQCDwAA8GzEHQAAgGYReAAAgOci7gAAANiFwAMAADwTcQcAAMBuBB4AAOB5iDsAAAAOIfAAAADPQtwBAABwGIEHAAB4DuIOAACAUwg8AADAMxB3AAAAnEbgAQAA7kfcAQAAaBECDwAAcC/iDgAAQIsReAAAgPsQdwAAAFyCwAMAANyDuAMAAOAyBB4AAND2iDsAAAAuReABAABti7gDAADgcgQeAADQdog7AAAArYLAAwAA2gZxBwAAoNUQeAAAQOsj7gAAALQqAg8AAGhdxB0AAIBWR+ABAACth7gDAADQJgg8AACgdRB3AAAA2gyBBwAAuB5xBwAAoE0ReAAAgGsRdwAAANocgQcAALgOcQcAAMAtCDwAAMA1iDsAAABuQ+ABAAAtR9wBAABwKwIPAABoGeIOAACA2xF4AACA84g7AAAAHoHAAwAAnEPcAQAA8BgEHgAA4DjiDgAAgEch8AAAAMcQdwAAADwOgQcAANiPuAMAAOCRCDwAAMA+xB0AAACPReABAADNI+4AAAB4NAIPAABoGnEHAADA4xF4AACAbcQdAAAAr0DgAQAA1hF3AAAAvAaBBwAANEbcAQAA8CoEHgAAYIm4AwAA4HUIPAAA4EfEHQAAAK9E4AEAAFcQdwAAALwWgQcAABB3AAAAvFyQuycAAADcjLjj906dOqUVK1bowIEDOnv2rMLCwjRkyBBlZGRo+PDhdo/z4IMP6tNPP7Vr248++khxcXGSpDvuuEMlJSVNbj9o0CBt2LDB7rkAAOBvCDwAAPgz4o7fy8vLU1ZWlgwGg4YNG6ZRo0aprKxM+/bt0+7duzVnzhylp6fbNVZqaqr69u1rc31DQ4PWrVun4OBgderUqdH68ePHW10uSd27d7fvDQEA4KcIPAAA+Cvijt+rra3VzJkzZTAYtGDBAo0bN868Lj8/X1OmTNH8+fOVnJys3r17NztecyFo+fLlMhqNeuihhxQZGdlo/WOPPWY+qwcAADiGe/AAAOCPiDuQlJOTo5KSEo0cOdIi7kjS0KFDNXHiRDU0NGj16tUtPlZxcbGWL1+ubt26afr06S0eDwAAWCLwAADgb4g7+MHOnTslSWlpaVbXp6amSpJ27drV4mO98MILqq2t1axZs9SxY8cWjwcAACwReAAA8CfEHVylsLBQkpSUlGR1fb9+/SRJFRUVKi4udvo4ubm52r17t2699VZzNAIAAK7FPXgAAPAXxB1cpb6+XmVlZZKk2NhYq9t07NhRkZGRqqio0KlTp5y6P47RaNTLL78sSZoxY0az2x46dEj5+fmqqqpSZGSkbr31Vg0ePNjh4wIA4G+cDjxFRUWunAfgsWprayXxZx7wNf722Y7Ytk3dZs9WwFVxx9iunUoWLVJVv36Sn/x3wI8qKyvNP58+fdoce64VHBwsSTp27JiioqIcPs6nn36qwsJCDRo0SB06dLD6mauvr5ckTZo0yeo8+vXrpz/+8Y8OHd9fPtuAv/C37234t8TERKf24wweAAB8XJNxh8tlfMaiRYt04sQJu7aNiorS73//e/ProCDbfyU0BZ66ujqn5vXuu+9Kkv7t3/6t2W2jo6P1u9/9Tr1795bRaFR+fr5WrVqlo0eP6rnnntOiRYuanCsAAP7M6W9IZ4sS4G1MvyXgzzzgW/zms71mjTR7dqPLsgLWrVMcl2X5lKqqKpWUlNi9/YABA8w/9+rVS+3bt29y+549ezr8efnyyy9VWFio2NhYTZo0SQEBAVa3W7lypS5evKjExEQFBv54i8ihQ4fq7rvv1i9+8QudPHlSx48fb/S0r2vl5eVJ8oPPNuBn/OZ7G2gBfgUCAICv4p47fmXDhg0ObW+6LEqSampqbAae6upqSVJ4eLjDczKdvXPPPffYjDuS1KdPH5vrfvrTn+qee+7R5s2btW/fvmYDDwAA/oqnaAEA4IuIO2hGSEiIunfvLkk2z/ypqqoy36snISHB4WOYHq/+85//3LlJ/sB0c+fz58+3aBwAAHwZgQcAAF9D3IGd+vfvL0k6cuSI1fUFBQWSrtwbJyYmxqGxT58+rVOnTqlDhw52PQXr8uXLNtdduHBBktS5c2eH5gAAgD8h8AAA4EuIO3BAWlqaJCknJ8fq+u3bt0uSxo4d6/DYpjjUs2dPhYSE2Nxu/fr1Sk5O1rRp06yur6ur00cffSTpyj15AACAdQQeAAB8BXEHDkpJSVFCQoIOHz6s9evXW6zbs2ePtm3bptDQUGVmZlqs27Vrl9LS0jR16lSbY3/55ZeSpBtuuKHJOYwYMULV1dXau3ev3n77bYt1ly5d0oIFC1RaWqqoqCjuvwMAQBO4yTIAAL6AuAMnBAcH6+WXX1ZmZqaeffZZvffee+rVq5eKi4u1f/9+BQYGat68eY0uz6qqqmr2kexnzpyRdOWR7E2Jj4/X008/reeff15z587Vxo0bNWDAADU0NOjTTz/V6dOn1blzZy1ZssSpGz0DAOAvCDwAAHg74g5aICkpSVu3btWyZcuUm5urgoICRUREKCUlRdOnT3f6kcRVVVWSpNDQ0Ga3nTRpkpKSkpSdna38/Hxt2rRJwcHBiouLU1ZWliZPnqyuXbs6NQ8AAPxFgNF49d8GAVyrqKhIkpz+Cy4Az+Qzn23iDmAhLy9PknTzzTe7eSYAXMlnvreBVsQ9eAAA8FbEHQAAAPyAwAMAgDci7gAAAOAqBB4AALwNcQcAAADXIPAAAOBNiDsAAACwgsADAIC3IO4AAADABgIPAADegLgDAACAJhB4AADwdMQdAAAANIPAAwCAJyPuAAAAwA4EHgAAPBVxBwAAAHYi8AAA4ImIOwAAAHAAgQcAAE9D3AEAAICDCDwAAHgS4g4AAACcQOABAMBTEHcAAADgJAIPAACegLgDAACAFiDwAADgbsQdAAAAtBCBBwAAdyLuAAAAwAUIPAAAuAtxBwAAAC5C4AEAwB2IOwAAAHAhAg8AAG2NuAMAAAAXI/AAANCWiDsAAABoBQQeAADaCnEHAAAArYTAAwBAWyDuAAAAoBUReAAAaG3EHQAAALQyAg8AAK2JuAMAAIA2QOABAKC1EHcAAADQRgg8AAC0BuIOAAAA2hCBBwAAVyPuAAAAoI0ReAAAcCXiDgAAANyAwAMAgKsQdwAAAOAmBB4AAFyBuAMAAAA3IvAAANBSxB0AAAC4GYEHAICWIO4AAADAAxB4AABwFnEHAAAAHoLAAwCAM4g7AAAA8CAEHgAATPLypFGjpA8/bHo74g4AAAA8DIEHAACThQul3Fzpvvuk7dutb0PcAQAAgAci8AAAIEkGw49Rp75emjChceQh7gAAAMBDEXgAAJCkDz64EnlMro08xB0AAAB4MAIPAACS9M47jZeZIs8TTxB3AAAA4NGC3D0BAADc7urLs65VXy+9+qrlMuIOAAAAPAxn8AAAcO3lWU0h7gAAAMADEXgAALB2eZYtM2YQdwAAAOBxCDwAAP/W1OVZ1vzlL45tDwAAALQBAg8AwL85cnmWZPsR6gAAAIAbEXgAAP7NkcuzTIg88EFGo1HZ2dkaOHCg+vTpo0OHDjk91qlTp/T0009rzJgx6t+/v5KTkzV9+nQdPHjQ5j51dXVauXKlxo8fryFDhmjw4MH65S9/qZUrV6qurs7puQAA4C8IPAAAvxVQW+t8pDFFng8/dO2kADf49ttv9cgjj+jFF19scUzJy8vTuHHjtGnTJnXv3l0TJkzQkCFDtG/fPk2ZMkVr1qxptI/BYFBGRoYWLlyo8+fPKy0tTf/n//wfnT17VgsXLtRDDz2k77//vkXzAgDA1/GYdACA3+q0d69jl2ddq75eWrhQSktz3aSANrZ//349+eSTOnfunNLT07Vz506Vl5c7NVZtba1mzpwpg8GgBQsWaNy4ceZ1+fn5mjJliubPn6/k5GT17t3bvG7p0qXKz8/X6NGjtWTJErVv316SVF1draysLH322Wd6/fXXNWPGjBa9VwAAfBln8AAA/FbEjh0t2DlCSk+XXn3VZfMB3GHz5s1qaGjQ0qVLNWfOHAUHBzs9Vk5OjkpKSjRy5EiLuCNJQ4cO1cSJE9XQ0KDVq1eblxsMBq1du1ZBQUGaO3euOe5IUqdOnfSnP/1JkrRmzRrO4gEAoAkEHgBAm6mvr9ebb76pSZMmKTk5WUlJSerTp4/5n82bNzfa5+LFixo7dqzFdgcOHLDYZtasWRbrbd0/5NVXXzWvHzdunBYeOeLYGzBFnW3bpPJy6R//kAYOdGwMwMMMGjRIW7ZsUUpKSovH2rlzpyQpzcZZbampqZKkXbt2mZft27dPBoNBAwcOVGxsbKN9EhMTFR8fr5qaGn3yySctniMAAL6KS7QAAG2iurpakydP1tGjRx3a7+2339ZXX31lfj1o0CDddtttTs1h8uTJevPNN1VbWytJ2hQWpknt2yuxqXuORERI//Zv0q9+Jd19t3TV2QWAL3jwwQddNlZhYaEkKSkpyer6fv36SZIqKipUXFysuLg48/8mmNbZ2u/06dMqLCzUnXfe6bL5AgDgSziDBwDQJt544w2H447BYNDy5cstlj3yyCNOzyEqKkoPPPCA+fXlgAC9et11jTc0namzdeuPZ+r84hfEHaAJ9fX1KisrkySrZ+JIUseOHRUZGSnpypO2JKm4uFiSFBMTY3Ns03gnT5500WwBAPA9Tp/BU1RU5Mp5AB7L9Jt+/swDLbPdytOqbrjhBvXt21dBQVe+jtq1a2fxWXv33Xd17tw58+uuXbuqW7dujT6PN9xwg+69916LZTU1NVY/t7fffruys7PNr/+7Uycdbd9efYODVT1mjCrT0lRz++0yhoRc2eDrrx1/s4AXq6+vl3QlwERERNi9X2Vlpfnn06dPm2PPtUz3+Dl27JiioqJ05swZSVJVVZXN71rDDzdDLysrs/v7mO9twLfwd3L4k8TERKf24xItAECbuPb/2evQoYMWLlyoEFNIucalS5f0/vvvWyz72c9+poCAgEbbjh49WqNHj7ZrHl27dlWf3r117MsvzcteT03Vfzz33I9RB/BCixYt0okTJ+zaNioqSs8//7xLj3/149VN0dYaU+AxbW/6d1P7mNa19BHuAAD4MqcDj7NFCfA2pt8S8GceaJmGhgaL19ddd50GDRpkc/s9e/bo7NmzFsumTJmim266qcVzeeDXv9YLL7xgfp174oTmJSQ4dLYC4GmqqqpUUlJi9/a2vtdM0bVHjx4OffddfYlVr169LJ6GZU3Pnj2VmJio66+/XpJ0/fXX2zye6bKu6667rtk55eXlSeJ7G/A1/J0caB5n8AAAWs2SJUu0dOlSq+tKSkrUp08fi2XHjh0z//zBBx9YrLvhhhtsxp1Zs2Zpy5YtFsuys7OVnJxsdfu7777bIvDU1dXpn//8p8aPH2/7zQAebsOGDW49flhYmPnnmpoam4GnurpakhQeHm6xX01Njc2xr90HAAA0xk2WAQAe6eDBgxavBw8e7LKxu3btaj5rwNbxADgmJCRE3bt3lySbZxJVVVWZ79WTkJBg8e/S0lKbY5vGM20LAAAaI/AAADzO6dOnzTdeNRk4cKBLj3Ht2UCHDx926fiAP+rfv78k6ciRI1bXFxQUSJKio6PNl3Q1t48kffHFF5Jc/78DAAD4Ei7RAgC0mkGDBmny5MmSZPHkKunKZRkTJkywut/nn3/eaFlSUpJL55aQkKD9+/ebX5eWlqqsrExdu3Z16XEAf5KWlqYdO3YoJydHkyZNarTe9DS9sWPHmpeNGDFCEREROnr0qL755hv99Kc/tdjn4MGDOnv2rKKiojR8+PDWfQMAAHgxAg8AoNWMGjVKo0aNktQ48ERGRuqZZ56xul95eXmjZVFRUS6dW+fOna0el8ADNG/Xrl1avHix4uPj9cYbb5iXp6SkKCEhQYcPH9b69ev161//2rxuz5492rZtm0JDQ5WZmWleHhISooyMDP31r3/VnDlztGLFCnXo0EGSVFFRoRdffFGSNG3atCaftAUAgL/jWxIA4HHOnTvXaJnpKTquYu1mrefPn3fpMQBPV1FRoddee63RMkl666239M9//tO8PD09XT169JB05V461h7JHhwcrJdfflmZmZl69tln9d5776lXr14qLi7W/v37FRgYqHnz5lk8cUuSpk6dqs8//1y5ublKS0vTiBEjdOnSJe3du1fnz59XamqqHnzwQRe/ewAAfAuBBwDgcaqqqhotu/oJPa4QGhraaJnp5q+Av6iurm50dp3Jjh07LF7fdddd5sDTlKSkJG3dulXLli1Tbm6uCgoKFBERoZSUFE2fPt3qI45DQkK0fPlyrVu3Tlu2bFFOTo6kK/fKmjFjhiZMmKDAQG4dCQBAUwg8AACPY+3smurqapeexWPtkcwREREuGx/wBnFxcTp27JjD+40fP17jx4+3uT4mJkZz5851aMygoCClp6crPT3d4fkAAACeogUA8EBdunRptOy7775z6TGqq6vtOi4AAADgDQg8AACP85Of/KTRMlffH8daMOIGywAAAPBWBB4AgMcZPHhwo2VFRUUuPcbXX39t8To2NpbAAwAAAK9F4AEAeJwbbrhB0dHRFsv+9a9/ufQY/+///T+L18OGDXPp+AAAAEBbIvAAADxScnKyxesvvvjCZWOXlZU1ehT78OHDXTY+AAAA0NYIPAAAj3TPPfdYvD5+/LiOHz/ukrF37txp8TokJEQpKSkuGRsAAABwBwIPAMAjjR49WjExMRbL3n//fZeMfe04d999N49IBwAAgFcj8AAAPFJQUJDS09MtltkKPJcvX260rF27dla3LS4u1ueff26xLCMjw7lJAgAAAB4iyN0TAAD4h2PHjjm8z29/+1utXLlSFy5ckCSdPHlSu3fv1pgxYyy2q6ioaLRvp06drI65evVqi9ejR4/WgAEDHJ4bAAAA4Ek4gwcA4LHCwsL07//+7xbLli9fbvH6woULjc7ICQwMVFxcXKPxzp8/r3feecdiuz/84Q+umzAAAADgJpzBAwDwaJMmTdL69evNN1guKCjQgQMHlJeXp2+++Ub79+9XZWWlxT79+/e3egZPdna2amtrza/vvPNOJSUlte4bAAAAANoAgQcA4NGCgoL0wQcfNFr+zDPPqKSkxOo+mZmZVpf/4Q9/MJ+xU1RU5LI5AgAAAO7GJVoAAJ8yadKkRo9YBwAAAHwdZ/AAALxaYGCgIiIiNGDAAE2cOFF33XWXu6cEAAAAtDkCDwDAK3388cfungIAAADgMQKMRqPR3ZMAAAAAXCEvL0+SdPPNN7t5JgAAtC0CDwAAAAAAgJfjJssAAAAAAABejsADAAAAAADg5Qg8AAAAAAAAXo7AAwAAAAAA4OUIPAAAAAAAAF6OwAMAAAAAAODlCDwAAAAAAABejsADAAAAAADg5Qg8AAAAAAAAXo7AAwAAAAAA4OUIPAAAAAAAAF6OwAMAAAAAAODlCDwAAAAAAABe7v8HPjcnGtIJrSsAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 298, + "width": 572 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# base d'origine\n", + "vector([1,0], text='i')\n", + "vector([0,1], text='j')\n", + "# base transformée\n", + "vector([-2,1], 'r', 'f(i)')\n", + "vector([-1,-1], 'r', 'f(j)')\n", + "plt.gca().spines[:].set_position('zero')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Pour tout vecteur ${\\bf v}$ on a \n", + "\n", + "$$ {\\bf f(v)} = {\\bf f}( v_1 \\, {\\bf i} + v_2 \\, {\\bf j}) = v_1 \\, {\\bf f(i)} + v_2 \\, {\\bf f(j)} $$\n", + "\n", + "puisque $\\bf f$ est linéraire. Cela montre bien qu'il suffit de connaitre la transformation de la base.\n", + "\n", + "En déroulant les calculs on a dans le cas du graphique ci-dessus \n", + "\n", + "$$ \n", + "v_1 \\, {\\bf f(i)} + v_2 \\, {\\bf f(j)} = \n", + "v_1 \\,\n", + "\\begin{bmatrix}\n", + " -2 \\\\\n", + " 1\n", + "\\end{bmatrix} \n", + "+\n", + "v_2 \\,\n", + "\\begin{bmatrix}\n", + " -1 \\\\\n", + " -1\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + " -2 \\, v_1 \\\\\n", + " 1 \\, v_1 \n", + "\\end{bmatrix} \n", + "+\n", + "\\begin{bmatrix}\n", + " -1 \\, v2\\\\\n", + " -1 \\, v2\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + " -2 \\, v_1 -1 \\, v2\\\\\n", + " 1 \\, v_1 -1 \\, v2\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + " -2 & -1 \\\\\n", + " 1 & -1\n", + "\\end{bmatrix} \n", + "\\,\n", + "\\begin{bmatrix}\n", + " v_1 \\\\\n", + " v_2\n", + "\\end{bmatrix} \n", + "$$\n", + "\n", + "On introduit ainsi la matrice et le produit matriciel. \n", + "\n", + "L'application linéaire $\\bf f$ de notre graphique peut donc être représentée par une opération matricielle : ${\\bf f}({\\bf v}) = A \\, {\\bf v}$ où la matrice A est\n", + "\n", + "$$\n", + "A =\n", + "\\begin{bmatrix}\n", + " -2 & -1 \\\\\n", + " 1 & -1\n", + "\\end{bmatrix} \n", + "$$\n", + "\n", + "On remarque que l'on trouve $\\bf f(i)$ dans la première colonne et $\\bf f(j)$ dans la seconde colonne.\n", + "\n", + "On pourra vérifier en exercice que l'application ${\\bf f} : {\\bf v} \\mapsto A \\, {\\bf v}$ est bien linéaire." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Déterminant d'une matrice\n", + "\n", + "Le déterminant indique l'agrandissement la surface d'un objet après transformation par $\\bf f$ ou, ce qui est pareil, après multiplication par A." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAABHgAAAJjCAYAAAB3M6YhAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAABYlAAAWJQFJUiTwAACJlUlEQVR4nOzdeVxVdeL/8TfIKouIK4IpueKaJm6ZZmUyZpNpU864l2ZTTZvZMn1tmTZtslm0zCl/pePkUqm5pmaOgnuSWkqmpoSQiAsKXGQRfn8gd7hwL1zgXu72ej4e8xi459zP+VyuGLw853O8iouLiwUAAAAAAACX5e3oCQAAAAAAAKB2CDwAAAAAAAAujsADAAAAAADg4gg8AAAAAAAALo7AAwAAAAAA4OIIPAAAAAAAAC6OwAMAAAAAAODiCDwAAAAAAAAujsADAAAAAADg4gg8AAAAAAAALo7AAwAAAAAA4OIIPAAAAAAAAC6OwAMAAAAAAODiCDwAAAAAAAAujsADAAAAAADg4gg8AAAAANzG888/rw4dOpj8b8+ePY6eFgDYHYEHAAAAAADAxRF4AAAAAAAAXJyPoycAAAAAALZy0003KSQkxOSx5s2bO2g2AFB3vIqLi4sdPQkAAAAAAADUHJdoAQAAAAAAuDgCDwAAAAC3wV20AHgqAg8AAAAAAICLI/AAAAAAAAC4OAIPAAAAAACAiyPwAAAAAAAAuDgCDwAAAAAAgIsj8AAAAAAAALg4Ag8AAAAAAICLI/AAsLn8/Hx98sknGjNmjPr06aNOnTqpQ4cOxv+tWLGiwnMKCwt15513muy3a9cuk32ef/55k+0dOnTQnj17Koz197//3WSfGTNm2O21AgAAAIAzIPAAsKns7GyNHj1ab731lr799ltlZmbq6tWrVT7v008/1fHjx42fd+/eXf369avRHMaPH6/AwEDj559//rmSkpJqNBYAAAAAuAICDwCb+vDDD3X48OFqPcdgMOiDDz4weeyhhx6q8RzCw8P1u9/9zvh5UVGR/v73v9d4PAAAAABwdj6OngAA97Jp06YKj3Xs2FE9evSQr6+vJKlt27Ym25cuXarz588bP2/ZsqVuu+22CuPcdNNNCgkJMXmsefPmZucxYcIELVq0yPj5f//7Xx0+fFidO3e2/sUAAAAAgIsg8ACwqdOnT5t8Xr9+fS1fvlz+/v5m97969aoWL15s8tidd94pLy+vCvvedddduuuuu6yaR1RUlHr06KHvvvvO+Ngnn3yiv/71r1Y9HwAAAABcCZdoAbCp/Px8k88bNmxoMe5IUkJCglJTU00eu/POO20yl/LjbNy4UZcvX7bJ2AAAAADgTAg8AGptzpw5xjtWlZeamlrhzldlrV+/3uTz1q1bq3379maPY+1dtErdcccdJp/n5eXp66+/tvZlAQAAAIDLIPAAcKjdu3ebfH7DDTfYbOxmzZopIiKi0uMBAAD3UlRUVOGxevXqOWAmAFC3CDwAHCYlJUVnzpwxeaxbt242PUb58fbt22fT8QEAgHPJzMys8FhwcHDdTwQA6hiLLAOote7du2v8+PGSZHLnKkkKCgrSqFGjzD6v7ALIpTp16mTTuXXq1EkbN240fp6Wlqb09HQ1a9bMpscBAACOd/HixQo/X3h7eysqKspBMwKAukPgAVBrAwcO1MCBAyVVDDxhYWF68cUXzT7v7NmzFR4LDw+36dzMjXf27FkCDwAAbmTu3Ln65ZdftHPnzgo3VOjSpQtn8ADwCAQeAA5z/vz5Co+FhYXZ9Bjmxrtw4YJNjwEAABxrxYoVFe7KWWrSpEl1PBsAcAzW4AHgMFlZWRUeCwoKsukxzP2LHbdKBwDAM4wZM0bDhg1z9DQAoE5wBg8AhwkJCanwWHZ2tk3P4jEXkUJDQ202PgAAcB7e3t4KDQ1V165dNXr0aN1+++2OnhIA1BkCDwCHadiwYYXHLl26ZNPAc+nSJauOCwAAXNc333xj8vn+/fsdNBMAcByPv0QrKSlJSUlJjp4GHID33vGaNm1a4TFbr49jbp2fy5cv8957KL7vPRPvu+fivQc8D9/3nov3nsADwIFuuOGGCo/Z+i/l8uNFRESoUaNGNj0GAAAAADgagQeAw7Ru3VpNmjQxeez777+36TEOHjxo8nlsbKxNxwcAAAAAZ0DgAeBQffr0Mfm8fJCpjfT0dJ05c8bksb59+9psfAAAAABwFgQeAA5V/talJ06c0IkTJ2wy9qZNm0w+9/Pz05AhQ2wyNgAAAAA4EwIPAIcaNGiQmjdvbvLYunXrbDJ2+XHuuOMObpEOAAAAwC0ReAA4lI+Pj8aOHWvymC0Cz+nTp/Xdd9+ZPDZx4sRajwsAAAAAzsjH0RMA4F6OHj1a7ef84Q9/0IIFC3Tx4kVJ0qlTp7R161YNHjzYZL+ZM2dq5syZVo25cOFCk88HDRqkrl27VntuAAAAAOAKOIMHgMMFBQXpj3/8o8ljH3zwQY3Hu3Dhgj777DPj597e3nryySdrPB4AAAAAODsCDwCnMGbMGLVp08b4+YEDB7Rr164ajbVo0SLl5uYaP7/33nvVqVOnWs8RAAAAAJwVl2gBcAo+Pj5av369TcZ68sknOWMHAIBaKC4u1r///W+98847ysvL06JFi9SnT59qj5OcnKz58+dr165dysjIUFBQkHr06KGJEyeqb9++Zp+Tl5enxYsXa926dTp58qSKi4sVHR2t4cOHa+zYsfL396/tywMAt0TgAQAAAGB07tw5vfDCC9q+fXutxtm/f78mT54sg8Gg2NhYDRw4UOnp6UpISNDWrVs1Y8aMCjdaMBgMevDBB5WYmKiIiAjFxcVJkuLj4/X222/rm2++0YIFCxQQEFCruQGAOyLwAAAAAJAk7dy5U88884zOnz+vsWPHatOmTTp79my1x8nNzdX06dNlMBg0a9YsjRgxwrgtMTFREyZM0MyZM9WnTx+1a9fOuG3u3LlKTEzUoEGDNGfOHOPZOtnZ2Zo8ebK+/fZbvf/++3r66adr/VoBwN2wBg8AAAAASdKKFStUUFCguXPnasaMGfL19a3ROBs2bFBqaqoGDBhgEnckqWfPnho9erQKCgpM7nppMBi0ZMkS+fj46NVXXzW5FCs4OFgvv/yyJGnx4sW6cuVKjeYFAO6MwAMAAABAktS9e3etXLlSQ4YMqdU4mzZtkiTjJVblDR06VJK0efNm42MJCQkyGAzq1q2bIiIiKjwnJiZGLVu2VE5Ojnbs2FGr+QGAOyLwAAAAAJAkjRs3TlFRUbUe58iRI5Jk8S6WnTt3liRlZmbq9OnTkqTDhw+bbKvseaXjAwD+h8ADAAAAwGby8/OVnp4uSWbPxJGkwMBAhYWFSSq505YkY+hp3ry5xbFLxzt16pSNZgsA7qPGiywnJSXZch4Ok5ubK8l9Xg+sx3vvoYqK1GDOHPmdOaNMn9qtM1/s46MLf/iD8sssDgnnxve9Z+J991y897WXn58vqSTChIaGWvWcy5cvGz9OSUkxxp7yStf3OXr0qMLDw3XmzBlJUlZWlsX3zGAwSJLS09MrfV83b96sK1euqH79+lbNGe6D73vP5U7vfUxMTI2ex120AHgU35QUtZg/32bjFfv4KP3FF202HgAAri4vL8/4sU8l/5hSGnhK9y/9/8qeU7qt7DHKO3nypF588UUVFRWpcePG6tixo/WTB+DSwsPDHT0Fh6px4KlpUXI2pXXPXV4PrMd776EaNFDxLbfI67//tclw4X/6k8L5M+Qy+L73TLzvnov3vvb8/PwkSa1atbL661j2Equ2bdua3A3LnDZt2igmJkaNGzeWJDVu3NjisUov62rUqJHFfd58800VFRVJkv7973/rjTfesGreAFxfYGCgR/+dzxo8ADzHr79KR47I68knpRYtaj/eb34j9elT+3EAAHAjQUFBxo9zcnIs7pednS1JCgkJMXledZ5T3tGjR/Xpp58aP9+7d69+/PFHK2cOAK6NwAPAM/z6q3Tt7hwKCpJmzJCunRpeYy+/XPt5AQDgZvz8/BQZGSlJSk1NNbtPVlaWca2e6Ohok/9PS0uzOHbpeKX7lvf6668bz94p9e9//7saswcA10XgAeD+ysadUm3bSn/8Y83H5OwdAAAs6tKliyTp0KFDZrcfOHBAktSkSRPjJV1VPUeSDh48KEnq1q1bhW3lz94pxVk8ADwFgQeAezMXd0oNHy4NGlSzcTl7BwAAi+Li4iRJGzZsMLt97dq1kqQ777zT+Fj//v0VGhqqw4cP65dffqnwnN27dysjI0Ph4eHq27dvhe3mzt4pxVk8ADwBgQeA+6os7kiSl5f01FPVX4/Hx0faskUqcxtYAAA80ebNmxUXF6cpU6aYPD5kyBBFR0dr3759WrZsmcm2bdu2afXq1apfv74mTZpkfNzPz08TJ05UUVGRZsyYoStXrhi3ZWZmGhdLnjp1aoU7bVk6e6cUZ/EA8ATcJh2Ae6oq7pQqXY/nT3+SCgutG7uwUHrxRWn2bGnaNOmxx6TQ0NrNFwAAB8vMzNR7771X4TFJ+s9//qOvv/7a+PjYsWPVqlUrZWVl6eTJkxXG8vX11bvvvqtJkybppZde0po1a9S2bVudPn1aO3fulLe3t9566y2TO25J0pQpU/Tdd98pPj5ecXFx6t+/v65evart27frwoULGjp0qMaNG1fheJWdvVOKO2oBcHcEHgDux9q4U6ptW+mRR6R//rN6x7lwgdADAHAb2dnZWrRokdltGzduNPn89ttvV6tWrSodr1OnTvryyy81b948xcfH68CBAwoNDdWQIUP08MMPm72VsZ+fnz744AMtXbpUK1euNF7i1b59ez399NMaNWqUvL1NL0Ko6uydUnv37tXRo0fVoUOHKvcFAFfkVVxcXOzoSThSUlKSJJn9DwzcG++9m6pu3ClVXCy98Ya0bVvl+wUGSrm55reFhxN6nBzf956J991z8d57hnHjxmnx4sVW7dunTx+9/vrrdp4RAEeJjIz06L/zWYMHgPuoadyRrFuPJzZW+vRTafz4kku7yis9oyc6WnrzTdboAQDAzqw9e6fUnj17dPToUTvOCAAch8ADwD3UJu6UKl2Px8fC1avjxknBwSX/v3gxoQcAAAezZu2d8rijFgB3ReAB4PpsEXdKla7HU15srFT2dE9CDwAADlXds3dKcRYPAHdF4AHg2mwZd0oNHy7dcovpY2bu2CGJ0AMAgIPU5OydUpzFA8AdEXgAuC57xB2pZD2eJ5/833o85c/eMYfQAwBAnanp2TulOIsHgDsi8ABwTfaKO6WCgqS//EW6446Su2JZi9ADAIDd1ebsnVKWbgkPAK6KwAPA9dg77pRq1UqaPr3yO2tZQugBAMBu4uPjaz3GDz/8oOLiYhvMBgCcg4VbxQCAk6qruGMrpaHnnnuklSulL76QcnJM9ykNPbNnS9OmlZwxFBrqmPkCAOAC1qxZo927d5vd9sgjj6iwsND4+WOPPSZfX98K+7Vp00ZeXl52myMA1DUCDwDX4WpxpyxCDwAANtO1a1d17drV7LbHH3/cJPDExcXJ39+/rqYGAA7DJVoAXIMrx52yuHQLAAAAgB0QeAA4P3eJO2URegAAAADYEIEHgHNzx7hTFqEHAAAAgA0QeAA4L3ePO2URegAAAADUAoEHgHPypLhTFqEHAAAAQA0QeAA4H0+NO2URegAAAABUA4EHgHMh7pgi9AAAAACwAoEHgPMg7lhG6AEAAABQCQIPAOdA3LEOoQcAAACAGQQeAI5H3Kk+Qg8AAACAMgg8AByLuFM7hB4AAAAAIvAAcCTiju0QegAAAACPRuAB4BjEHfsg9AAAAAAeicADoO4Rd+yP0AMAAAB4FAIPgLpF3KlbhB4AAADAIxB4ANQd4o7jEHoAAAAAt0bgAVA3iDvOgdADAAAAuCUCDwD7I+44H0IPAAAA4FYIPADsi7jj3Ag9AAAAgFsg8ACwH+KO6yD0AAAAAC6NwAPAPog7ronQAwAAALgkAg8A2yPuuD5CDwAAAOBSCDwAbIu4414IPQAAAIBLIPAAsB3ijvsi9AAAAABOjcADwDaIO56B0AMAAAA4JQIPgNoj7ngeQg8AAADgVAg8AGqHuOPZCD0AAACAUyDwAKg54g5KEXoAAAAAhyLwAKgZ4g7MIfQAAAAADkHgAVB9xB1UhdADAAAA1CkCD4DqIe6gOgg9AAAAQJ0g8ACwHnEHNUXoAQAAAOyKwAPAOsQd2AKhBwAAALALAg+AqhF3YGuEHgAAAMCmCDwAKkfcgT0RegAAAACbIPAAsIy4g7pC6AEAAABqhcADwDziDhyB0AMAAADUiI+jJwDACRF34Giloeeee6SVK6UvvpByckz3KQ09s2dL06ZJjz0mhYY6Zr4A4EaSk5M1f/587dq1SxkZGQoKClKPHj00ceJE9e3b16oxxo0bp71791q175YtWxQVFSVJuvXWW5Wamlrp/t27d9fy5cutGhsAPAmBB4Ap4g6cCaEHAOrU/v37NXnyZBkMBsXGxmrgwIFKT09XQkKCtm7dqhkzZmjs2LFVjjN06FB17NjR4vaCggItXbpUvr6+Cg4OrrB95MiRZh+XpMjISOtfEAB4EAIPgP8h7sBZEXoAwO5yc3M1ffp0GQwGzZo1SyNGjDBuS0xM1IQJEzRz5kz16dNH7dq1q3SsqiLQBx98oOLiYj3wwAMKCwursP3RRx81ntUDALAOa/AAKEHcgStgjR4AsJsNGzYoNTVVAwYMMIk7ktSzZ0+NHj1aBQUFWrhwYa2Oc/r0aX3wwQdq0aKFHn744VqNBQD4HwIPAOIOXA+hBwBsbtOmTZKkuLg4s9uHDh0qSdq8eXOtjvP6668rNzdXzz//vAIDA2s1FgDgfwg8gKcj7sCVVTP0NJo/X97Z2XU/TwBwAUeOHJEkderUyez2zp07S5IyMzN1+vTpGh0jPj5eW7duVe/evY3BCABgG6zBA3gy4g7chZVr9DT9xz8U/skn0rPPskYPAJSRn5+v9PR0SVJERITZfQIDAxUWFqbMzEwlJydXe42c4uJivfvuu5Kkp59+usp99+zZo8TERGVlZSksLEy9e/fWDTfcUK1jAoAnqXHgSUpKsuU8HCY3N1eS+7weWM/T3/tQg0EtLl6Ul6MnAtiSFaHH59Il6cUXVfj227owcaIujhmjIgt3aoF78PS/7z0Z7731Lpe5jDUlJcUYe8rz9fWVJB09elTh4eHVOsbevXt15MgRde/eXQEBAWbfl/z8fEnSmDFjzM6hc+fOmjZtWqXHLi4urta8ALiP3Nxct/g7PyYmpkbP4xItwAMRd+D2rLh0y+fSJTX9xz/UZsgQLt0C4PHy8vKMH/v4WP434NLAU3Z/a61atUqS9Nvf/rbKfZs0aaLXXntNS5cu1ZIlSzR9+nQ1btxYhw8f1l/+8hcVFhZW+/gA4O68ij08cZfWvZoWMrguj33vuSwLnig72/KlW6XCw7m9upvy2L/vwXtfDRcvXlTfvn0lSYcOHZK/v7/Z/QYPHqy0tDTNmTNHd9xxh9XjHzt2TMOHD1dERIS2bt0qLy/z/8x09OhRFRYWKiYmRt7epv8W/csvv+iuu+7SlStXKtzGvazAwEBduXLF+PnatWstvh4A7iUyMtKj/87nDB7AkxB34Km46xYAVCqozN+LOZZCuKTsa2c7hoSEVGv80rN3hg0bZjHuSFKHDh3UuXPnCnFHkq677joNGzZMkpSQkFCt4wOAJyDwAJ6CuAMQegDAAj8/P0VGRkqSUlNTze6TlZVlXKsnOjq6WuOX3lr9lltuqfkkJePCzhcuXKjVOADgjgg8gCcg7gCmCD0AUEGXLl0klVyiZc6BAwcklayP07x5c6vHTUlJUXJysgICAqy6C1ZRUZHFbRcvXpQkNWjQwOrjA4CnIPAA7o64A1hG6AEAo7i4OEnShg0bzG5fu3atJOnOO++s1rilYahNmzby8/OzuN+yZcvUp08fTZ061ez2vLw8bdmyRZLUs2fPas0BADwBgQdwZ8QdwDqEHgDQkCFDFB0drX379mnZsmUm27Zt26bVq1erfv36mjRpkvHxzZs3Ky4uTlOmTLE47rFjxyRJrVu3rvT4/fv3V3Z2trZv365PP/3UZNvVq1c1a9YspaWlKTw83OICywDgySzfAxGAayPuANVXGnruucfyXbdKQ8/s2dx1C4Bb8fX11bvvvqtJkybppZde0po1a9S2bVudPn1aO3fulLe3t9566y2Ty7OysrJ08uTJSsc9c+aMJCk8PLzS/Vq2bKk///nPeu211/Tqq6/q888/V9euXVVQUKC9e/cqJSVFDRo00Jw5c6q9yDMAeALO4AHcEXEHqB3O6AHgoTp16qQvv/xSo0ePVlpamj7//HMdOXJEQ4YM0eeff268jKs6srKyJEn169evct8xY8ZoyZIlGjZsmM6fP68vvvhCGzZsUGBgoCZPnqw1a9aoV69e1Z4DAHgCr+Li4mJHT8KRkpKSJEkxMTEOngnqmtu+98QdwPaysy2f0VMqPJwzepyU2/59jyrx3numwMBAXblyxfj52rVr5e/v78AZAagrkZGRHv13PmfwAO6EuAPYB2f0AAAAwMkReAB3QdwB7I/QAwAAACdF4AHcAXEHqFuEHgAAADgZAg/g6og7gOMQegAAAOAkCDyAKyPuAM6B0AMAAAAHI/AAroq4AzgfQg8AAAAchMADuCLiDuDcCD0AAACoYwQewNUQdwDXQegBAABAHSHwAK6EuAO4JkIPAAAA7IzAA7gK4g7g+gg9AAAAsBMCD+AKiDuAeyH0AAAAwMYIPICzI+4A7ovQAwAAABsh8ADOjLgDeAZCDwAAAGqJwAM4K+IO4HkIPQAAAKghAg/gjIg7gGcj9AAAAKCaCDyAsyHuAChF6AEAAICVCDyAMyHuADCH0AMAAIAqEHgAZ0HcAVAVQg8AAAAsIPAAzoC4A6A6CD0AAAAoh8ADOBpxB0BNEXoAAABwDYEHcCTiDgBbIPQAAAB4PAIP4CjEHQC2RugBAADwWAQewBGIOwDsidADAADgcQg8QF0j7gCoK4QeAAAAj0HgAeoScQeAIxB6AAAA3B6BB6grxB0AjkboAQAAcFsEHqAuEHcAOBNCDwAAgNsh8AD2RtwB4KwIPQAAAG6DwAPYE3EHgCsg9AAAALg8Ag9gL8QdAK6G0AMAAOCyCDyAPRB3ALgyQg8AAIDL8XH0BAC3Q9wB4C5KQ88990grV0pffCHl5JjuUxp6Zs+Wpk2THntMCg11zHwBAE6nsLBQGzdu1P79+3X+/HlJUsuWLfXMM884eGaA+yHwALZE3AHgjgg9AOAw+fn5OnDggI4cOaK0tDRdvHhRV65ckbe3t/z9/dWwYUNFRkaqc+fOuuGGG1SvXj1HT9nEkiVLtHv3bpPHLl265KDZID8/X6tWrdL27dtVXFysdu3a6cknn3T0tGAjBB7AVog7ANwdoQcA6lRiYqI+++wzXTZzGWxRUZEKCwuVk5Oj06dPa8+ePWrYsKEmTJigdu3aOWC2FeXm5mrv3r2SJG9vb40bN04xMTG6evWqg2fmmX755Rd98sknSk9Pd/RUYCcEHsAWiDsAPAmhBwDsbvfu3fr3v/8tSfLx8VHv3r3VrVs3RUREqH79+ioqKtLly5d16tQpxcfH65dfftHFixf13nvv6amnnlKrVq0c/AqkCxcuqKioSJLUrl079e7d28Ez8kxFRUXatGmT1q9fr6tXr8rf3195eXmOnhbsgEWWgdoi7gDwVCzGDAB2ceXKFS1fvlyS5Ovrq6eeekpjxoxR165d1bhxY9WvX1/BwcFq0aKF+vfvr+nTp2vAgAGSpIKCAi1ZssSR0zcyGAzGjxs0aODAmXiuvLw8/e1vf9OaNWt09epVxcTE6E9/+pOjpwU7IfAAtUHcAQBCDwDY2OHDh41nWMTGxqp169aV7u/t7a17771XwcHBkqQzZ84oNTXV3tOsUnFxsfFjLy8vB87EcxkMBv3888+qV6+e7rnnHj366KMK5Yxat8UlWkBNEXcAwBSXbgGATZTebUqSGjVqZNVzfH199dhjj8nX11dNmzaVt7fpv+WvW7dO69evlySNHTtW/fr1szjWjBkzdOHCBUnSe++9Z7Jt0aJF2rNnjyTpr3/9q7KysrR69Wr9+OOPKigo0JNPPqmEhATjPqX27NljfCw8PFyvvfaayfZz584pISFBx44dU0ZGhnJzc+Xj46PQ0FC1atVK/fr1U0xMTJVfh6ysLO3Zs0cHDx5URkaGDAaDAgMD1bJlS/Xq1UuxsbGVLkR95coV7d69Wz/88INOnz4tg8GggIAANWjQQB07dlT//v0VERFR5TycSdOmTTVp0iRdd911jp4K7IzAA9QEcQcALCP0AECt+Pj879e0lJQUq5/XsmVLe0zHouzsbP3zn/9UZmam8bHCwsJqj7Njxw4tX768wnPz8/N17tw5nTt3Tvv371fv3r01bty4CvGq1MGDB7Vo0SJduXKlwjyTkpKUlJSk7du3a+rUqWYvGTtx4oQWLFhQ4S5fOTk5ysnJUVpamv773/8qLi5Od955Z7VfZ3Fxca3WvvH19a32XdKCg4P13HPPKSAgoMbHhesg8ADVRdwBAOsQegCgRqKjo40fHzx4UFu2bNGtt97qdJc5bdmyRQUFBZo0aZI6dOigoqIiBQQEKDo6Wvfdd59OnDih999/X1LJpWajR4+WJJNAc/z4cS1ZskTFxcXy8fHRsGHD1K1bN4WEhKiwsFDHjx/XqlWrdPHiRe3du1dNmzbVb37zmwpz+emnn/TRRx+pqKhIISEhGj58uGJiYuTn56eMjAxt2bJFBw4cUHJysubNm6dnnnnGJKSlpqZq7ty5ys/Pl7e3twYPHqwePXqocePGys/P108//aSvvvpK586d0/r16+Xr66s77rijWl+vCxcu6KWXXqrJl1pS1WdemePr6ytfX98aHxOuhTV4gOog7gBA9bFGDwBUS3R0tLp06SKp5KyPFStW6M0339TXX3+ttLQ0k7VtHGnPnj2aMmWKevXqpZCQEDVo0ED+/v7y9fVVQECASVjw9vZWQECAAgIC5OfnZ3x88+bNxtdz//33a+jQoYqIiFBwcLDCwsLUq1cvPfLII8a4tXXrVuOduUoVFRVpyZIlKioqkq+vr5588kkNGDBAjRo1UkhIiK6//npNmTJF3bt3l1RyVlT5S8j+85//KD8/X15eXnrooYc0cuRIRUdHKyQkRI0aNVK/fv307LPPGi+ZW7dunc6dO2f7LypQC5zBA1iLuAMAtcMZPQBgtTFjxuhf//qXTp48KUlKS0vTypUrtXLlSgUGBio6Olpt2rRRu3btFB0dbfGyJXu67rrr1K5du1qN0axZM9WrV09ZWVmKjY01u0+LFi103XXXKTk5WTk5OTp79qyaN29u3J6UlKSzZ89Kknr37m2yrazbb79dBw8eVEBAgI4dO6abbrpJUsnZP8nJyZKkG2+8UV27djX7/KCgIA0fPlwLFy5UYWGhdu/ereHDh1v9Whs1alRhTSPAlgg8gDWIOwBgO4QeAKhSaGionnjiCcXHx2vLli0m69zk5ubqyJEjOnLkiCSpfv366tKli2655Ra1atWqzubYsWPHWo8xcuRIq/Zr3LixMcJkZ2ebbEtKSjJ+3KlTJ4tjXH/99frHP/5hcmmWJOPXUSoJPJXp1q2bvL29VVRUpCNHjlQr8AD2RuABqkLcAQD7IPQAQKV8fX1166236pZbbtHx48f1ww8/6Pjx40pJSTG5TMlgMGjv3r3au3evevbsqTFjxtTJoroNGza0+zFKlY0y5S/RKntL+CZNmlg9TqlffvnF+HFISEiFRZrLa9SokTIyMvTrr7+quLjY6dZGguci8ACVIe4AgP0RegCgUt7e3mrfvr3at28vqeTuUqdOndLx48d19OhR/fzzz8bokZiYqIyMDE2bNs3ui+uGhITYZJyCggJ9++23Onz4sM6ePausrCxlZ2dXCDmWXC6zbluQuXXeqlD2jKB33nnH6ufl5+crNzdX9evXr/YxAXsg8ACWEHcAoG4RegCnkJycrPnz52vXrl3KyMhQUFCQevTooYkTJ6pv375WjbFnzx6NHz++yv1eeeUV/f73vzd5LC8vT4sXL9a6det08uRJFRcXKzo6WsOHD9fYsWPl7+9fo9flTvz8/IzBZ9iwYcrMzNSGDRuUkJAgqWQR4R07duiWW26x+zxq65dfftFHH32k8+fP13iMsrdXr8laRLW5dXleXh6BB06DwAOYQ9wBAMch9AAOs3//fk2ePFkGg0GxsbEaOHCg0tPTlZCQoK1bt2rGjBkaO3as1eM1a9ZMQ4cOtbi9Q4cOJp8bDAY9+OCDSkxMVEREhOLi4iRJ8fHxevvtt/XNN99owYIFdXL5kSsJCwvT73//e9WrV0/btm2TJB06dMjugae2srKy9P777ysrK0uSFBUVpb59+6p9+/YKCgoyeZ+XLl2qffv2mR2nbGgyGAwKreZ/D8oe54033lBYWFi1nm+t4uLiWsUkX19f1atXz4Yzgrsh8ADlEXcAwDkQeoA6lZubq+nTp8tgMGjWrFkaMWKEcVtiYqImTJigmTNnqk+fPlbfOalVq1Z68cUXrZ7D3LlzlZiYqEGDBmnOnDnGs3Wys7M1efJkffvtt3r//ff19NNPV+u1eYqbb77ZGHguXrxY43FqEyGqY+fOnca4065dO/3pT3+yGDAquzV8aGio0tLSJFVcgNkaZS81y8rKslvguXDhgl566aUaP3/s2LHq16+fDWcEd1P399IDnBlxBwCcT2noWbxYGj9eMre+QmnoiY6W3nxTKrMeAwDrbNiwQampqRowYIBJ3JGknj17avTo0SooKNDChQvtcnyDwaAlS5bIx8dHr776qsmlWMHBwXr55ZclSYsXL65yEVxXdubMGX311Vf68MMP9c0331TruWXPZCl/llPZcFL2kqbysrKylFM+pttJ2cWNBw8eXOnZKSkpKRa3RUZGGj9OT0+v9JjJyck6efKkybFbtmxp1XEAZ8cZPEAp4g4AOLeantEDwCqbNm2SJONlUeUNHTpUixYt0ubNm/X666/b/PgJCQkyGAzq2bOnIiIiKmyPiYlRy5YtjevL3HbbbTafgzPIzMzUmjVrJEknTpxQ//79rb4k7ejRo8aPy98uvew6MRcuXLA4xnfffVed6dZK2TOFKlvH5vvvvzcJN+XP5unUqZO2bNkiSTpw4IBuuukms+OcO3dOb7/9tqSSW6ZPmzZNktS5c2fjn/89e/aof//+FudSVFSkr7/+Wm3atFF0dHS11vxp1KiR3nvvPav3B6qLM3gAibgDAK6kmmf0NJo/X941OGUf8DRHjhyRVPLLsjmdO3eWVBIgTp8+bfPjH772s1jpcSqbQ+lc3VGHDh10/fXXSyo5m+ajjz6SwWCo8nmpqan68ssvJZUsNDxgwACT7c2bNzd+fOjQIbN3qMrMzNT69evr7LbfZW+zfvLkSbP7pKSkaPHixWrQoIHxsdLLukq1b99ezZo1k1TyZ+OHH34wO9bGjRuNH/fq1cv4cdu2bY1n8Rw/flw7duywOOf169fryy+/1Lvvvmu8HA5wFpzBAxB3AMA1WXlGT9N//EPhn3wiPfssa/QAFuTn5xvPkDB39owkBQYGKiwsTJmZmUpOTlZUVJRVY2dlZembb74x3sq7ZcuWGjRokPEX8lKl0ahsiCivdG6nTp2y6tiuyMvLSxMnTtS7776rzMxMJSUl6ZVXXlHfvn0VExOjpk2bKjAwUAUFBbp8+bLOnz+vQ4cOaf/+/cZLr0aMGFHh/WnTpo0aNGigS5cu6cyZM/rkk080ZMgQNWrUSHl5eUpKStK6desUHBysqKgoJSUl2f213nDDDdq5c6ekkksEAwMD1alTJ/n5+SkjI0OJiYmKj49X27Zt1aNHDy1ZskRSydlebdq0kZ+fn4KCguTt7a3Ro0drzpw5Kioq0kcffaTf/OY36tGjhwIDA5WRkaH//ve/2r9/v6SSS7rKn+Uzbtw4/fWvf1VBQYGWLFmi5ORk9evXT02aNFFeXp7S09MVHx+vQ4cOSSr5c1o+ojmj/Pz8CjEvPz/f+HFRUZHZSx5ZyNw11Tjw1MU3fF3Izc2V5D6vB9bLzc1Vw7w8Faemqm7+jQIAYBdWhB6fS5ekF19U4dtv68LEibo4ZoyKgoMdNGHUFX7Os97lMutWpaSkWFzHxNfXV1LJpUDh4eEWx0tOTpYk/fjjj7r55puN70UpHx8fjRo1yuQW6WfOnJFUEoQsvWelZ7Kkp6db3KeyxXhdRaNGjfTcc89p2bJlOnjwoHJycrRlyxbjZUiWhIWFadSoUerZs2eFbfXq1dMf/vAH/etf/9LVq1e1f/9+Y/Aoe9wpU6Zo1apVtnw5FnXu3FmxsbHat2+f8vPztXTp0gr7tG/fXg8++KDy8vLk4+OjwsJCHTt2TP/3f/+ndu3a6cknnzTZb/HixcrNzdXq1au1evXqCuNdd911mjp1qnx8TH8VjoyM1OOPP64PP/xQly9f1o4dOyyeydO6dWtNnjzZ+P3gzN5//30dO3bM4vYTJ04YL1Ury1UvJcvNzXWLv/NjYmJq9DzO4IHHapiXp9Y5OcQdAHAXVoae0jN6CD3A/5RdC6X8L75llf5Ca+1dlgwGg+6++27ddtttatKkifESoNWrV2vZsmXy9/fXyJEjTcas7Pil2+rqLk+OFBoaqilTpujMmTM6cOCATpw4obNnzyo7O1v5+fmqV6+eAgICFB4erqioKHXu3FmdO3eu9OvXpUsXPfPMM9qyZYtOnDihrKwseXl5qUmTJurZs6cGDhyoIHOXvdrRhAkT1L59e+3evVtpaWnKy8tTYGCgWrZsqf79++uGG25QvXr1VL9+fU2aNElr1qzRuXPnFBgYqOjoaJOxbrjhBkVHRys+Pl6HDx/W+fPndeXKFeN4sbGx6tWrl8XFnK+//nq9+uqr2rFjh3744QelpaXJYDDIy8tLoaGhatWqlW688UZ17969zi5jA6rDq9gdEnctlNa9mhYyuKhff1Xx4cPEHQBwZ9nZli/dKhUezu3V3Rg/51nv4sWL6tu3r6SS9VnK3sGqrMGDBystLU1z5szRHXfcYXG87OxsnTx5UmFhYSZ3KCr1wQcf6G9/+5uCgoK0Y8cOBQYG6uGHH9bWrVv1yiuvmJzZU9Y///lPvffeexo8eLA++OADs/sEBgaaXHKydu1ai68HgHuJjIz06L/zWWQZnufamjvEHQBwc9xeHbBa2bM2KrtFdva1BctDQkIqHS84OFhdu3Y1G3ck6YEHHlBAQIBycnKMd20qnYMtjg8AnojAA8/CgsoA4HkIPUCV/Pz8FBkZKankbkzmZGVlGdfqKX9pTE2O16RJE0nS+fPnTcZMS0uz+LzSudX2+ADgjgg88BzEHQDwbIQeoFJdunSRJONdgso7cOCAJKlJkyaV3umqVHFxscUFj4uLi5WZmSlJxttfV3V8STp48KAkqVu3blUeHwA8DYEHnoG4AwAoVTb0jBtH6AGuiYuLk1Ryu2pz1q5dK0m68847qxxr4sSJ6tatm8Wxtm/frqysLPn4+Kh79+6SpP79+ys0NFSHDx/WL7/8UuE5u3fvVkZGhsLDw43rBQEA/ofAA/dH3AEAmBMcXHImD2f0AJKkIUOGKDo6Wvv27dOyZctMtm3btk2rV6823smo1ObNmxUXF6cpU6aY7N+rVy/l5+dr5syZOnXqlMm29PR0vfHGG5KkUaNGGc/g8fPz08SJE1VUVKQZM2aYLJScmZlpfI65W1wDALiLFndXcHfEHQCAtbjrltvh57zqO3LkiCZNmqTMzEzFxsaqbdu2On36tHbu3CkvLy/Nnj3beKaPJK1YsUIvvPCCoqOj9dVXXxkfz8vL04MPPqh9+/bJ19dXt9xyi5o2baqMjAzFx8crNzdXvXv31vz581W/fn3j8/Lz8/XII48oPj5eERER6t+/v65evart27frwoULGjp0qP72t79ZvM21xF20AE/m6XfRIvDwH373RdwBANQEocdt8HNezZw5c0bz5s1TfHy8zp49q9DQUMXGxurhhx+u8LW0FHgkqbCwUMuXL9fatWt17Ngx5eTkKCQkRB07dtTdd9+tu+++22yoKSws1NKlS7Vy5Ur9/PPPkqT27dvr3nvv1ahRo+TtXflFCAQewHMReAg8kvgPv9sh7gAAaovQ4/L4Oc8zEXgAz+XpgYc1eOB+iDsAAFvgrlsAAMCFEHjgXog7AABbI/QAAAAXQOCB+yDuAADsidADAACcGIEH7oG4AwCoK4QeAADghAg8cH3EHQCAIxB6AACAEyHwwLURdwAAjkboAQAAToDAA9dF3AEAOBNCDwAAcCACD1wTcQcA4KwIPQAAwAEIPHA9xB0AgCsg9AAAgDpE4IFrIe4AAFwNoQcAANQBAg9cB3EHAODKCD0AAMCOCDxwDcQdAIC7IPQAAAA7IPDA+RF3AADuiNADAABsiMAD50bcAQC4O0IPAACwAQIPnBdxBwDgSQg9AACgFgg8cE7EHQCApyL0AACAGiDwwPkQdwAAIPQAAIBqIfDAuRB3AAAwRegBAABWIPDAeRB3AACwjNADAAAqQeCBcyDuAABgHUIPAAAwg8ADxyPuAABQfYQeAABQBoEHjkXcAQCgdgg9AABABB44EnEHAADbIfQAAODRCDxwDOIOAAD2QegBAMAjEXhQ94g7AADYH6EHAACPQuBB3SLuAABQtwg9AAB4BAIP6g5xBwAAxyH0AADg1gg8qBvEHQAAnAOhBwAAt0Tggf0RdwAAcD6EHgAA3AqBB/ZF3AEAwLkRegAAcAsEHtgPcQcAANdB6AEAwKUReGAfxB0AAFwToQcAAJdE4IHtEXcAAHB9hB4AAFwKgQe2RdwBAMC9EHoAAHAJBB7YDnEHAAD3RegBAMCpEXhgG8QdAAA8A6EHAACnROBB7RF3AADwPIQeAACcCoEHtUPcAQDAsxF6AABwCgQe1BxxBwAAlCL0AADgUAQe1AxxBwAAmEPoAQDAIQg8qD7iDgAAqAqhBwCAOkXgQfUQdwAAQHUQegAAqBMEHliPuAMAAGqK0AMAgF0ReGAd4g4AALAFQg8AAHZB4EHViDsAAMDWCD0AANiUj6MnACdH3AEAAPZUGnruuUdauVL64gspJ8d0n9LQM3u2NG2a9NhjUmioY+brAZKTkzV//nzt2rVLGRkZCgoKUo8ePTRx4kT17du3WmOdOHFCCxYs0O7du3X27Fn5+fkpOjpacXFxGj9+vPz9/U32v/XWW5WamlrpmN27d9fy5cur/boAwN0ReGAZcQcAANQVQo9T2L9/vyZPniyDwaDY2FgNHDhQ6enpSkhI0NatWzVjxgyNHTvWqrE2btyoZ555Rvn5+erYsaP69eunS5cuaceOHXrnnXf01VdfadGiRQoyc/bWyJEjFRwcbHbcyMjIWr1GAHBXXsXFxcWOnoQjJSUlSZJiYmIcPBMnQ9wBAACOlJ1tOfSUCg+vNPTwc1715Obm6s4771RqaqpmzZqlESNGGLclJiZqwoQJKi4u1sqVK9WuXbtKx0pPT1dcXJwMBoOee+45PfDAA8ZtaWlpuu+++5SRkaFHHnlETzzxhHFb6Rk8W7ZsUVRUVI1eR2BgoK5cuWL8fO3atRXOFALgniIjIz3673zW4EFFxB0AAOBorNFT5zZs2KDU1FQNGDDAJO5IUs+ePTV69GgVFBRo4cKFVY61atUqGQwGde/e3STuSFKLFi304IMPSpI2bdpks/kDgKcj8MAUcQcAADgTQk+dKY0tcXFxZrcPHTpUkrR58+YqxxowYIBef/11PfXUU2a3X3/99ZKkM2fO1GSqAAAzCDz4H+IOAABwVjUIPd7Z2XU/Txd25MgRSVKnTp3Mbu/cubMkKTMzU6dPn650rM6dO+t3v/ud+vXrZ3b72bNnJUkNGzas6XQBAOUQeFCCuAMAAFxBNUJPmyFD1Gj+fM7osUJ+fr7S09MlSREREWb3CQwMVFhYmKSSO23VVHFxsT7//HNJls8WKi4u1p49ezRv3jy9/fbb+te//qUDBw7U+JgA4Am4ixaIOwAAwPVYcdctn0uX1PQf/5D+/W/uulWF7DJnO5m7q1Wp+vXrKzMzUzmWFr62wocffqgDBw4oLCxMU6ZMMbvPxIkTzZ4lFBsbq9mzZ6tZs2Y1Pj4AuKsaB57SuxK4utzcXEnu83qqK9RgUIuLF+Xl6IkAAADURDVur1749tu6MHGiLo4ZoyILt+D2VBkZGcaPjx8/Lm/vyk/0P3HiRI1+fl61apUWLlwoHx8fTZs2TWlpaUpLSzNuz8/PlySFhYVp6tSpateunYqLi5WYmKiPP/5Y+/bt0/jx4/XOO+/Ix8f8rzIefpNgwKPl5ua6xe/2Nb0TGGfweDDiDgAAcBvVOKMn/JNPCD3llL2NeGFhofz8/MzuV1BQUGF/axQXF+vjjz/W6tWr5evrq6efflpdu3atsN+LL76oq1evKjo62iQy3XTTTbr++uv1xBNP6NSpU4qPj9fgwYOrNQcAcHc1Djzucm/50rrnLq/Har/+KqWmOnoWAAAAtlWN0NOUS7eMSs+ckaSWLVsqPDzc7H55eXmSSn52tvbn57y8PE2fPl0bN25UaGio5syZo759+5rdt7IxY2JiNHz4cK1YsUI///yzHnnkEbP7eXnxz5eApwoMDPS83+3LYJFlT8SaOwAAwN1xe/Vq8fPzU2RkpCQp1cI/AmZlZenyta9RdHS0VePm5+dr6tSp2rhxo6KiorR06VKLcccaUVFRkqQLFy7UeAwAcFcEHk9D3AEAAJ6E0GO1Ll26SJIOHTpkdnvpXayaNGmi5s2bVzleUVGRpk+frl27dikmJkZLly5VmzZtrHqeJRcvXpQkNWjQoMpxAMDTEHg8CXEHAAB4KkJPlUpvWb5hwwaz29euXStJuvPOO60ab+7cufrqq6/Upk0bffzxx2rSpEml+y9btkx9+vTR1KlTzW7Py8vTli1bJEk9e/a0ag4A4EkIPJ6CuAMAAEDoqcSQIUMUHR2tffv2admyZSbbtm3bptWrV6t+/fqaNGmS8fHNmzcrLi6uwu3OT5w4ofnz58vX11dz585Vw4YNqzx+//79lZ2dre3bt+vTTz812Xb16lXNmjVLaWlpCg8P14gRI2r+QgHATXkVe/h9BD1ikWXiDgAAgHnZ2ZZvr14qPNxjFmM+cuSIJk2apMzMTMXGxqpt27Y6ffq0du7cKS8vL82ePdt4po8krVixQi+88IKio6P11VdfGR9/7rnntGrVKrVs2bLKu109+uijCgsLkyT95z//0Wuvvabi4mJ17txZXbt2VUFBgfbu3auUlBQ1aNBA77//vnr16mVxvMDAQF25csX4+dq1a6t91y8ArikyMtK9f7evAoHH3QMPcQcAAKBqhB6jM2fOaN68eYqPj9fZs2cVGhqq2NhYPfzwwxV+ZrYUeMaNG6e9e/dadbwtW7YYF0+WpO+++06LFi1SYmKizp8/L19fX0VFRWngwIEaP368mjVrVul4BB7AcxF4CDyS3DTwEHcAAACqh9Dj8gg8gOfy9MDDGjzuirgDAABQfazRAwBwUQQed0TcAQAAqB1CDwDAxRB43A1xBwAAwHYIPQAAF0HgcSfEHQAAAPsg9AAAnByBx10QdwAAAOyP0AMAcFIEHndA3AEAAKhbhB4AgJMh8Lg64g4AAIDjEHoAAE6CwOPKiDsAAADOgdADAHAwAo+rIu4AAAA4H0IPAMBBCDyuiLgDAADg3Ag9AIA6RuBxNcQdAAAA10HoAQDUEQKPKyHuAAAAuCZCDwDAzgg8roK4AwAA4PoIPQAAOyHwuALiDgAAgHsh9AAAbIzA4+yIOwAAAO6L0AMAsBECjzMj7gAAAHgGQg8AoJYIPM6KuAMAAOB5CD0AgBoi8Dgj4g4AAIBnI/QAAKqJwONsiDsAAAAoRegBAFiJwONMiDsAAAAwh9ADAKgCgcdZEHcAAABQFUIPAMACAo8zIO4AAACgOgg9AIByCDyORtwBAABATRF6AADXEHgcibgDAAAAWyD0AIDHI/A4CnEHAAAAtkboAQCPReBxBOIOAAAA7InQAwAeh8BT14g7AAAAqCuEHgDwGASeukTcAQAAgCMQegDA7RF46gpxBwAAAI5G6AEAt0XgqQvEHQAAADgTQg8AuB0Cj70RdwAAAOCsCD0A4Da8iouLix09CUdKSkqSJMXExNh+cOIOACeTX1io+Rs3at3+/Uo9f16S1LllSy195hkHzwxl7fnpJ43/xz8kSff06aOZ48c7eEb/s+voUU157z0VXL2qPw0bpsfuvNPmx8i5ckWjZ8/WT2lp6hgZqU+fflpBAQE2Pw4AM7KzpZUrpS++kHJyzO8THi5NmyY99pgUGlq387NCYGCgrly5Yvx87dq18vf3d+CMANSVyMhI+/xu7yJ8HD0Bt0XcAdzSlfx8bTxwQPFHjuintDSduXhROVeuyNvbW/X9/RXRsKE6REZqUOfOGnLDDfKtV8/RUzbx8pIlWrF7t8ljZy9dctBs4GpOnT2rJz76SAVXr2pI9+56dNiwKp9zyWDQwD//WVcKCiRJN7Zpo0+ffrrS5wQFBOj9qVM1atYs/ZiaqmmffKJ5U6fKy8vLJq8DQCVKz+i55x7Loaf0jJ7Zs5069ACALT3//PNauXKlyWOLFi1Snz59HDSjigg89kDcAdzShsREvfHZZ8owd2p6UZHyCwuVmZOjpNOntWrPHrVo2FBvT5ig2Hbt6n6yZmTn5urLvXslSfW8vfXWuHEaEBOjwqtXHTwzOMqvFy/q8507FRkerpH9+lW6b8HVq3r6//0/XTIY1LRBA70+ZoxVwWXl7t3GuCNJ+0+c0IkzZ9SmefNKn9eycWP93+9+p+kLF2rr999r0X//qwmDB1v3wgDUHqEHAFwOa/DYGnEHcEsrd+/WkwsWKOPyZfn6+Oje/v31wcMP6+tXX9W+v/5Vu2bN0poXX9TrY8ao83XXSZLSLl7Ug++9p++Tkx08+xKnL1zQ1aIiSVLvdu10d+/eahQSomZhYY6dGBzmm++/19z167Vyz54q9523YYMOp6RIkl6+/36FmVunw4ylCQmSpO6tW6uet7fJY1X5be/eGtyliyRp9pdf6tTZs1Y9D4ANsUYPALgMAo8tEXcAt5R95Yr+sny5JMnf11efPvWU3hgzRoO7dlXLxo0VWr++woOD1b5FC/2uf399Pn26Rg8YIEnKKyjQS0uWOHL6RpcNBuPHTRs0cOBM4Cy+PX7cqv1Sz5/XR19/LakkDt7evbtVz9t19KhOpqdLkn5/883q2769JOnLPXuUV+asnso8O3KkfLy9lVdQoJlffGHVcwDYAaEHgIe76aabNH78eJP/Na/ijOS6xiVatkLcAdzW9sOHZcjLkyTdFRurbq1bV7q/t7e3/nzvvdp04IAuZGfrxJkzOpqaqg6RkXUwW8vKrqnvzVomkPWB570NG4xB5vFqLKq8JD5eUkkYHdK9uwqLirTjxx91yWDQhsREjbDimvXrmzXTb3v31ordu7X1hx+U+PPP6nn99VbPAYCNcekWAA9111136a677nL0NCpF4LEF4g7g1k5fu9uUJEU1amTVc/x9fbXgscfk7+ur1k2bGi9NKTVn3TrNXb9ekvTW2LGVrn9y64wZSr1wQZJ09L33TLY9v2iR8fKafX/9q85nZend1au188cflVdQoEVPPqnlCQkVLsFZuWeP8bHI8HB989prJttTzp3TsoQE7T12TMkZGcrOzZWvj48ah4aqW6tWGtmvnwZYcYeC81lZWrVnj74+eFC/ZGToksGgkMBAdWrZUsN79dJdsbHyqWQh6pwrV7Ri927994cf9OPp07pkMCgoIEBNGzTQTR076t7+/dU2IqLKeTib//7wg5YmJOj7U6d0KTdXYUFBah8RoRF9+ui3vXtbPU5Nvz4dHn3U5PO9x44ZHyv/5+Hc5ctas2+fJKljZKTVa0plXLqkbw4dkiTd2rWrggMD9ZuePfXmZ5/JkJ+vpQkJVgUeSRp3yy3GxcE/2bKFwAM4A0IPADgdAk9tEXcAt+fn87+/Ko9cW4PEGp1atrTHdCy6mJ2tif/8p85kZhofKygsrPY4y3fs0GvLlyu/3HML8/OVcu6cUs6d07r9+3V37956a9y4CvGq1NcHD+q5RYuUXeZWtZJ0ITtbCUlJSkhK0n+2b9e8qVPVxMwlY/tPnNATCxYoo9xdvjJzcpSZk6Of0tL07//+V3+Mi6vRrbqLi4uNZ2bVhL+vb6VxypLXly/Xv7dtM3ks49IlZVy6pB0//qivDx7U72++ucpx7P31KbX222+Nfxbu6dvX6ud9tnOnCq4t4H1v//6SpOCAAA3r1Uuf79yp737+WT+lpal9ixZVjtWpZUu1b9FCP6WlacuhQ8rMybF6DSAAdkboAeAhuIuWuyPuAB6hR3S08ePNBw/q4y1bNPHWW53uls0LtmzRlYICzZ40Sf06dNDVoiIFBwSoR3S0Ztx3n749cUIPvf++pJJLzV4dPVpSySVlpb49flwvLVmi4uJi+fn46LFhw3Rbt25qFBKi/MJC7Tt+XO+sWqVfL17Ul3v3qnXTpnrkN7+pMJc9P/2kJz76SIVFRWoUEqInhg/XTTExqu/np+SMDH28ZYs2Hjig75OT9dC8eVr2zDMmIe1oaqomz50rQ36+fLy9NX7wYMX16KGWjRvLkJ+vvT/9pPe/+kop585pzvr18vP11UN33FGtr1fqhQu67aWXavKlllT1mVfmfLZzpzHuhAYG6snf/la3dO6soIAAnT5/Xqt279bi7duVVS6KlVfbr0/i7Nn69eJF3fn665JKbl3+4SOPSDL98yBJmw4cMH5s7do7RUVF+mzHDkklZwT179DBuO2+/v31+c6dkqRlCQmacd99Vo05pHt3/ZSWpsKiIn198KAxGgFwEoQeAHA4FlmuKeIO4DG6R0cb7+RTXFysmStW6Ldvvqn/9/XXOpaWZrK2jSOt2rNHc6ZM0fBevdQoJERNGzRQfX9/+fn6KiggQAG+vsZ9fby9FRQQoKCAAAX6+Rkf/3DzZuPrefn++zV16FC1jYhQw+BgNQsL0/BevfThI48Y49bCrVuNd+YqVVRUpJeWLFFhUZH8fX317yef1P0DBiiqUSOFh4Sox/XX659TpmjItVhwJCVFq8pdQvbif/4jQ36+vLy8NOehh/TcyJHqHh2t8JAQRTVqpJH9+unzZ59V5LVL5uasW6eUc+ds/0W1oatFRfrn2rXGz+c+9JDGDByoyEaNFBYUpC7XXaf/u+8+vTBqlHb++GOlY9X26xMUEKCAMu97PQt/Hq7k5+vgyZOSSi5PtPYSxf8ePqy0ixclSaP69zeJRt2jo41n7Xy5d69y8/OtGrP3tQWapZKACMBJsRgzADgMZ/DUBHEH8Divjxmjx/71L3137Zfdn9LSNGvlSs1auVKhgYHqHh2tXm3aKLZdO90QHW3xsiV76nLddept5foollzfrJl869XT+aws3RUba3afdi1aqOt11+lQcrIyc3J06uxZtSlzB4GEpCTj7azv7t3bZFtZD95+uzYfPKiggADtO3ZM9910k6SSX95Lby1/54036tauXc0+PywoSE8OH67pCxcqv7BQK3fv1uPDh1v9WqMaNaqwppE9fXv8uM5eu5yqT/v26lMmWJQ1btAg/WfbNiVnZJjdXldfH0k6nJKiwmsB74YyZ7JVZem1xZXreXvrXjNnOd130016/bPPlJWbq/X792uUFWdCdbnuOnl7eamouFiHrr1+AE6MM3oAoM5xBk91EXcAj9Q4NFSLnnhCL4wapWZhYSbbLufmKv7IEf1tzRr94d131e+55/TswoV1/kto/44daz3GcyNHau5DD2nJtGnyL3PGT3ktGzc2fnwxO9tkW3xSkvHjmzt1sjhGj+uv1/f/+IcSZ8/WXydOND6+/cgR48fDbryx0vne2q2bfK7FtLLPc0bf/fyz8ePKvi7e3t66rVs3i9vr8utTeotzSYpu1syq55w+f17x1441sFOnCt8vkvTb3r2Nf76WJSRYNW5wQIBxrJRz51R4bX0fAE6OM3oAoM4QeKqDuAN4ND9fX0289VZtfe01LXriCT1w223q2qqV8RfoUpcMBn25d69+9/bbenLBggqLDNtLi4YN6+Q4kunC0+Uv0fopNdX4casmTawep9ThX34xftw4JEQ5V65Y/J+XZLwM6fivvzrN5XLm/Fw2ljRtWum+HSIjLW6ry6/Pr9cus5Ks//O1PCFBRdeO87trZ2WV16B+fQ294QZJ0sFTp/RjmT8zlYkMD5dU8meu7GLiAFwAoQcA7I5LtKxF3AFwTT1vb5NLbHLz83Xw1Cl9e/y4dh89qsSffzZGjw2JifolI0NLp02TXyVnxNhCo5AQm4yTV1Cgdd9+q22HD+vk2bO6kJWlC9nZFUKOJefK/EBekzsdXShzRtB977xj9fNy8/OVlZur0Pr1q33MunDJYDB+XNXXpWEl2+vy63OpzOUUDax4L/MLC/X5rl2SpCYNGuiWa2tXmXPfTTdp9bXbry9LSNDL999f5fhl53DZYJCsXBMIgBPh0i0AsBsCjzWIOwAqEejnp77t26tv+/Z6bNgwpWdm6r0NG4yXnhxOSdHyHTs09pZb7DqPsovm1tThX37R4x99pNPnz9d4jLK3V6/JWkS5tbh1eU5entMGnitlFhM2d+ZSWZVtr8uvz5WCAuPHgVb8+dp84IDOZ2VJKrn1e6c//cmq46zeu1fTR4xQfX//SvcrOwdrF2cG4KQIPQDKSEtL03PPPae2bdtq7NixatOmjaOn5JIIPFUh7gCopmZhYfrL738vv3r1jLfE/vrQIbsHntq6kJWlh95/X+eu/YIeExWlkX37qk/79goLClJwQIBx35eXLtWaa2dflFc2NF0yGNS4mj+MB5U5zvY33jC7hostFBcXy1CLWOLv6yufevWqtX+pshHMnNwyYaW8uvr61MRSK9fTKS/7yhWt279fv+PW54DnqUboufLmm/J59ln5PPkkoQdwM8eOHdOZM2d05swZJSQkaMCAAYSeGiDwVIa4A6AWRt98szHwlF3LpLpyahEhquOznTuNcad3u3b6+E9/shgwKlvLpUloqH5KS5NUcQFma5S91OxCVpbdAkbqhQu67aWXavz8t8aO1Ugr7v5UKiQw0Phx2cu1zMm4drctc+rq6yNJAWWiVFVnzJw4c0Z7jx2TJPWIjtbUoUOrHD+voEBPf/yxrhYVaVlCQpWBp+wcrDmjCIALsSL0BOTkSC+/rOK//11ezzzDGT2AG0tISCD01ACBxxLiDgCV/NK66cABHUlJ0Y1t2mjirbda/dyyZ7KUPftFkkk4yavkbI7zWVnKLP8vmXZSdvHeCYMHV3p2ypGUFIvbOkRGasePP0oqWVi4V9u2Fvf9PjlZV4uK5FOvnrpcd50kqXPLlkq4dieuH1JSFNOyZbVeh7NqXWZh5eRrt5G3JOn0aYvb6vLrU3bNm0tV/Dlccu3W6JL0h4EDNdjC7dvLW7F7t7YdPqzvk5N1JCVFnSp5PZfLhDFnvRQPQC1ZEXq8Ll7k0i3AQxB6qofAYw5xB8A1ZzMz9fc1ayRJ+0+c0O/69ze5RKYyu48eNX7ctVUrk21lfzn99cIFi2Ns/O676ky3VsqeKdSgkl+et37/vckdoYrKnc0zsFMn/b8tWyRJmw4c0H0W7qSUcu6c7n37bUklt0xfOm1ayfM7d9b8TZskSV/u2VPpWR1Xi4q04OuvdWObNrohOrpaa/5ENWqko++9Z/X+tdWtzJ+BnUeP6oHbbze7X35hobYcOmRxHHt8fSydkRVR5s5ZaZWchZabn68v9+yRVBIz77h2hyxr3NO3r7Zd+2/u0oQE/eX3v7e4b+naUPW8vdXciS5NA2AHrNEDoAxCj3W4TXp5xB0AZfTt0EE9rr9eUsnZNI9/9JHJWQSW/Jiaqne+/FJSyS+jowcMMNnetnlz48dbDh1SkZk7VKVnZuq99evl5eVVm5dgtbK/zH938qTZfY6kpOiFxYvVtEED42MXrl3WVapP+/a6vlkzSVL8kSPa9sMPZseav3Gj8eO7evUyftyrbVt1vnYWx77jx7V8xw6Lc35v/XrN/vJL/eHdd/Wfa5fDOat+HToo9NplWglJSTp06pTZ/f61aZPOVnKJlq2+PmUvcbJ0vOhr76MknSwT9cpb9+23upybK0kaduON1Vrw+7auXY13FVv77bfKuXLF7H45V64o/dqt0aMaNarW+kcAXFgNbq8eUsllxABcW0JCgh5++GG9+uqrOnHihKOn43QIPGURdwCU4+XlpdkTJxrPFkhIStKQV17RrBUrlJCUpNTz53XZYNDZS5eUlJKiTQcO6LlFi3Tv228b15+ZPmKEOkZFmYx7Y5s2xkhy/MwZTfvkEyWlpOiywaBfL17U5zt36nd//asaBgfrpo4d6+S1Dilz1sW8DRu0JD5eqefP63xWlr77+We98fnnuv+ddxQTFaXHhg0z7rs0IUG/XrxovJTM29tbL48eLZ9rZ4v86aOPNH/jRp26dsv1737+WU/9v/+nz3bulFRySdfvyp3l8+a4ccZFiV9askQzPv1UB0+e1IXsbKWeP6/4I0f0yPz5em/DBkklwax8RHM2fr6+eujaujTFxcV6aN48fb5zp85c+9odSk7WS59+qjnr1mlI9+6VjmWLr0+jkBDVvxZikjMyNGfdOu0/cUJbv//e+Ge3c8uWxvfxoIUgJZlenjWyb99qfFVKvi7DbrxRUknEWfvtt2b3++GXX4xni3Vr3bpaxwDgBqoRepLy8vSCpJCKewBwE4Qe87hEqxRxB4AFkY0a6YvnntNfli3TpoMHlZmTo/+3ZYvxMiRLmoeF6flRo/Sbnj0rbPOpV0+v/eEPeuxf/1LB1atav3+/1u/fb7JPVKNGmjNliv66apUtX45Fgzp31m9jY7V63z4Z8vP1ytKlFfbp2769/vHgg8rJy5Ovj48KCgu199gx3fJ//6fe7drp308+adzv7w8+qBcWL1ZWbq7eXb1a765eXWG8Ltddp/enTq1wW/COkZH65PHH9fiHHyrj8mUt37HD4pkq3Vu31j8nT5ZfmQWBndUDt92mpJQUrdu/Xxezs/Xif/5TYZ9BnTvrkd/8RpsPHrQ4jq2+PqP69TMuBD53/XrNXb9ekrTq+efVMDhYAX5+6ta6tRJ//lkp584p9fx5RTZqZDLGD7/8oh+urd8U3ayZ8Yy36rinb199un27JGlZQoLuNxPrShdwlkr+fAHwUFZcutVI0puSnpF0q6QRI0bU2dmwAGrm6tWrNXpe+Uu3IiMjbTwz11KjwLO/3C8h7mC/wSCVuTwBAEw0bKgJzz6r21NTtW/fPh09elS//vqrsrKylJeXp3r16ikwMFCNGzdWq1at1KNHD91www3y8fGRpb8xQ26+Wa9ERWndunU6evSoLl26JC8vLzVv3lx9+/bVkCFDdCE4WJllfjHfX+7vqfP+/saPfwoJkU8lf4/9VObuS+f9/SuMJUn3P/mkmv33v9q+fbtSUlJ05coV1a9fX61bt9bgwYPVu3dvHbt2acxjf/qTli9frrNnzyowMFDNY2JMxgwfPFizevTQ119/re+++04ZGRnKzc1VUFCQWrdurf79++umm27S6Xr1ZHZJ4Rtv1Ntdumjr1q367rvvlJKSouzsbHl7e6tBgwZq06aN+vbtq9jYWKV6eSnV4it3LmOmTdP1u3Zp27ZtOnnypAwGg4KDgxUVFaX+/fvrlltu0S/nzhn3t/Re2eLrc+vEiTpXv7727dunixcvKjAwUBEREUqOiJDh2jE79e+vxJ9/liR9fOyYflNu0ex/ffaZ8eM+gwebn2tVGjZUVFSUTp8+rcMpKfrs4kVdXy4Urb52qV+9evXUZNAg7Q8Orv5xALiPhg2lxx9XvUmT1HTJEjX99FP5lLtzY7ikvpIOVnIzAwDuoTT0vPDCCxo1apRdjnH+2lqAZf3000/y8bHPeTM3XjvDuTq8iiu7160F7hh4AABARZcuXdLjjz+ugoICtW7dWm+++WadzyE5OVkvvPCCJKl379568tqZYgBQql5WllrOnKnwjRtV9lydhZImOmhOAOretGnT9PtKbtjgSmoSeGqUmmpyIGeVdO1WszExMdKlS9LPP0tmyhwAAJ7qt7166Ytdu3Tq1CkV79unXuXO4rG3z68tWC5JT918s3pWckcvAB5q927JzKXT6x0wFQB17/bbb9eECRN04403lvxu76FYg6esBg2kHj0IPQAAlPHIb36jtd9+q7yCAs1Zt04Ln3iizo596uxZrdm3T5J0S5cu6lmDNX4AuLndu6VXX5XKXYp14tlntegvf9EiB00LjvHjjz9KkjrW0U0qYBtffPGFxowZU+3n3X777Xr55Zc1YMAA48kbnozAYw6hBwAAo6hGjfTAbbdp3ldfafdPP2nr999rcNeudXLst1euVMHVq/Lz8dFzI0fWyTEBuBALcSf5z39W5siRalNmrTp4Br9rd4j05713Kb7VvFlG2bCD/+E26ZUpDT2xsVK5u4YAAOBJHvnNb9SpZUtJ0stLl+qSwWD3Y6799lttOXRIkjTt7rt1fbNmdj8mABdiIe5o/nydIwgDbun2229XfHy8Nm/eTNwxg8BjDUIPAMDD+fn46N1JkxQaGKj0zEz933/+oxrcp8FqKefO6S/LlkmSBnftqgmDB9vtWABcUCVxRw895Jg5AbAbwo51CDzVQegBAHiw6GbN9M8pU+Rbr542HTig99bbZ/nSnCtX9Mj8+bpkMKhjZKRmT5woLy+vqp8IwDMQdwCPQdipHo9Zg2f79u1aunSpDh48qMzMTNWvX19t27ZVr169NHTo0OoN1qCBDvv5adOOHerXtKn6tmtnn0kDAOBk+nXooB/++U+7HiMoIEBrXnzRrscA4KJsEHeSk5M1f/587dq1SxkZGQoKClKPHj00ceJE9e3b1w6TRm3Y4v3as2ePxo8fX+V+r7zyitvcYtvVla6xc9NNN+nf//63HnnkEeXl5WnRokXq06dPtcfzlO97jwg8b775phYuXChvb2/169dPUVFR+vXXX7Vr1y4lJiZq165d+vTTT40LclVl48aNevrpp1VcXKwf+vXToZwc9W3SRN0iI+38SgAAAAAPZSHu7J40SX2tjDv79+/X5MmTZTAYFBsbq4EDByo9PV0JCQnaunWrZsyYobFjx9pj9qgBW79fzZo1q/Qf9zt06GCLaaMGunXrpvDwcPXs2dO4ePK5c+f00EMPafv27bUa25O+790+8Hz99ddauHChgoKCtHDhQnUtc9ePH3/8Uffff7++//57ffrpp5o4cWKV4509e1Z//vOf5eXlpY8++kj9+vUzbtv11VcqOHpUAzt3tsdLAQAAADyThbjzaosW+mzvXq08dkztqjirPjc3V9OnT5fBYNCsWbM0YsQI47bExERNmDBBM2fOVJ8+faocC/Znj/erVatWepEzRJ1Shw4ddO7cOeMl2Tt37tQzzzyj8+fPa+zYsdq0aZPOnj1b7XE97fve7dfg+eyzzyRJDzzwgEnckaSOHTvqjjvukCRt2bLFqvGWLVum7OxsjRw50iTuSFK/uDgtPXpUv/vrX/VLTo4NZg8AAAB4uEouy/J55BEVFBRo4cKFVQ6zYcMGpaamasCAASa/5ElSz549NXr0aKvHgv3xfnmesuvtrVixQgUFBZo7d65mzJhR7duol/K0P0duH3j+9Kc/6b333tO9995rdntERIQkKcfKILNp0yZJUlxcnNntd9xxhw6dOqUnPvmExZgBAACA2qhizZ3Sy202b95c5VBV/RxfnbFgf7xfnq179+5auXKlhgwZUqtxPO3PkdsHni5duuj2229X8+bNzW4/c+aMJKlNmzZVjpWfn68TJ05Ikjp16mTxeJJ07Ngx5QcGctctAAAAoCasWFC587WlETIzM3X69OlKhzty5Igkyz/HV2cs2B/vl2cbN26coqKiaj2Op/05cvvAU5mtW7dq/fr18vX11ZQpU6rcPzU1VVevXlVgYKDCwsLM7lMakgoKCpSWllbyILdXBwAAAKxn5d2yyv5cnpycbHG4/Px8paenS/rfGfzlWTsW7M+e71dWVpa+/PJL/e1vf9Ps2bO1fPly47HgXjzx+97tF1kuKz09XR999JFycnKUlJSkI0eOqE2bNvrjH/+o9u3bV/n87OxsSVJQUJDFfcpuq3DZV2nouXRJ+vln6fz5mr0QAAAAwF1V81bo9evXV2ZmZqVLLpT+HC9V/rO8NWPB/uz1fh07dkyDBg2qsL+vr68eeughPf744zWbMJySJ37fu1Tgeeqpp5SUlGTVvs2aNauwUNKFCxe0aNEi4+dRUVG64YYb1KBBA6vGzMvLk6RKF3jy8vKSr6+vCgoKlJuba34nQg8AAABQkYW4UzRvnrwt3Ardz89Pkiz/7K3//RwvVf6zvDVjwf7s9X5lZ2frgQce0MiRI9WiRQudP39eixcv1ieffKL33ntPgYGBVl3ZAdfgid/3LhV4UlNTdfLkSav2zc/Pr/BYTEyMjh49qtzcXJ06dUqrV6/WwoULtW7dOi1YsEC9evWqdMyAgABJJZdfWVJcXGzcHhgYWPkkCT0AAABACQtxZ0bTpvq/SZPkb+FppT/3V/azd+nP8VLJz/L+/uZHs2Ys2J+t36/OnTvr888/V1hYmFq2bGl8PCIiQtOnT1dISIj+9re/ad68eRo7dizvv5vwxO97lwo8y5cvt8k4gYGBiomJUUxMjOrVq6cPP/xQzz77rL7++mt5e1telig4OFhS5XfcKnsaWEhIiHUTIvQAAADAk1USd5aHhempnByLv5yV/vxd2c/e5ZdRqM1YsD9bv1/BwcHq2rWrxe0PPPCA5s2bp5ycHH333Xfq379/DWYNZ+OJ3/cevciyJN12222SSs4OOnbsWKX7RkZGytfXV7m5ubpw4YLZfVJTUyVJ/v7+atGiRfUmw2LMAAAA8DSVrLmz49odbkp/xi4vKytLly9fliRFR0dbPISfn58iIyNtMhbsr67fLz8/PzVp0kSSdJ5/bHcbnvh979aBJycnR2+++aaefvppi9+oXl5e8vLykiRduXKl0vF8fX3VoUMHSdL3339vdp8DBw5IKrkNm49PDU+QIvQAAADAE1SxoHKXLl0kSYcOHTL79NKfvZs0aWK8m60lthwL9mfr96u4uFjFxcUWt2VmZkqS1euzwjV42ve9Wwee+vXra82aNVq3bp2++eYbs/scP35cxcXF8vLyMrke05KhQ4dKktavX292+9q1ayVJw4YNq+GsyyD0AAAAwF1ZcbesuLg4SdKGDRvMDlH6s/edd95Z5eFsORbsz5bv18SJE9WtWzeLY23fvl1ZWVny8fFR9+7dazhjOCNP+75368Dj5eWl+++/X5I0e/ZsHT161GR7RkaGFixYIEkaOHCgwsPDjdsWL16suLg4/d///Z/Jc+6//341bNhQa9as0bZt20y2LVu2TPv27VOzZs00atQo270QQg8AAADciZW3Qh8yZIiio6O1b98+LVu2zGTXbdu2afXq1apfv74mTZpkfHzz5s1mD1mTseA4NX3vH330Uf3lL38x2b9Xr17Kz8/XzJkzderUKZNt6enpeuONNyRJo0aN4gweF2Xpvfe073uvYkvnqbmJ/Px8PfLII4qPj5ePj4/69OmjqKgoZWRkaM+ePcrJyVHTpk21fPlyRUREGJ83Z84czZ07VwMGDDBGoFLx8fF69NFHVVhYqP79+ysqKkonTpzQ3r17Vb9+fX344YdV3pGrVliMGQAAAK7KyrhT6siRI5o0aZIyMzMVGxurtm3b6vTp09q5c6e8vLw0e/Zs47/SS9KKFSvUqlUrSdKNN95Yq7HgWDV571944QVFRkaaXMGRl5enBx98UPv27ZOvr69uueUWNW3aVBkZGYqPj1dubq569+6t+fPnq379+o54qSgjMzNT7733nsljX3zxhXJycjR06FA1a9bM+PjYsWPVqlUri++95Fnf9y51F62a8PPz07/+9S+tXr1aq1at0pEjR7Rnzx75+/urdevW6tatm4YPH24Sd6py8803a+XKlZo3b552796t3bt3q1GjRho5cqT++Mc/6rrrrrPjKxJ33QIAAIBrqmbckUrWtvzyyy81b948xcfH68CBAwoNDdWQIUP08MMPKyYmxurD23Is2J+t3i9/f3998sknWr58udauXWv8h/6QkBB1795dd999t+6++27Vq1fPzq8I1sjOztaiRYvMbtu4caPJ57fffrsx6FriSd/3bn8GT1WSkpIkybXfVEIPAAAAnF0N4k5N7d+/X1LFM3jg/tzi9zvUCO+9B5zB4xE4owcAAADOrA7jDgB4KgKPOyH0AAAAwNkQdwCgThB43BGhBwAAAM6AuAMAdYbA484IPQAAAHAU4g4A1CkCjycg9AAAAKAuEXcAoM4ReDwJoQcAAAD2RtwBAIcg8HgiQg8AAADsgbgDAA5D4PFkhB4AAADYCnEHAByKwANCDwAAAGqHuAMADkfgwf8QegAAAFBdxB0AcAoEHlRE6AEAAIA1iDsA4DQIPLCM0AMAAABLiDsA4FQIPKgaoQcAAABlEXcAwOkQeGA9Qg8AAACIOwDglAg8qD5CDwAAgGci7gCA0yLwoOYIPQAAAJ6DuAMATo3Ag9oj9AAAALg34g4AOD0CD2yH0AMAAOB+iDsA4BIIPLA9Qg8AAIB7IO4AgMsg8MB+CD0AAACui7gDAC6FwAP7I/QAAAC4FuIOALgcAg/qDqEHAADA+RF3AMAlEXhQ9wg9AAAAzom4AwAui8ADxyH0AAAAOA/iDgC4NAIPHI/QAwAA4FjEHQBweQQeOA9CDwAAQN0j7gCAWyDwwPkQegAAAOoGcQcA3AaBB86L0AMAAGA/xB0AcCsEHjg/Qg8AAIBtEXcAwO0QeOA6CD0AAAC1R9wBALdE4IHrIfQAAADUTBVxJzk5WfPnz9euXbuUkZGhoKAg9ejRQxMnTlTfvn2rfbgTJ05owYIF2r17t86ePSs/Pz9FR0crLi5O48ePl7+/v8n+t956q1JTUysds3v37lq+fHm15wIA7o7AA9dF6AEAALBeFXFn//79mjx5sgwGg2JjYzVw4EClp6crISFBW7du1YwZMzR27FirD7dx40Y988wzys/PV8eOHdWvXz9dunRJO3bs0DvvvKOvvvpKixYtUlBQUIXnjhw5UsHBwWbHjYyMrNbLBgBPQeCB6yP0AAAAVK6KuJObm6vp06fLYDBo1qxZGjFihHGXxMRETZgwQTNnzlSfPn3Url27Kg+Xnp6u559/Xvn5+Xruuef0wAMPGLelpaXpvvvu0w8//KCPPvpITzzxRIXnP/roo4qKiqrxywUAT+Tt6AkANlMaemJjpUaNHD0bAAAA52DFmjsbNmxQamqqBgwYYBJ3JKlnz54aPXq0CgoKtHDhQqsOuWrVKhkMBnXv3t0k7khSixYt9OCDD0qSNm3aVLPXBACogMAD90PoAQAAKGHlgsqloSUuLs7sMEOHDpUkbd682arDDhgwQK+//rqeeuops9uvv/56SdKZM2esGg8AUDUu0YL74tItAADgyapxt6wjR45Ikjp16mR2qM6dO0uSMjMzdfr06Sovn+rcubPxOeacPXtWktSwYcNKxwEAWI/AA/dH6AEAAJ6mGnEnPz9f6enpkqSIiAizwwUGBiosLEyZmZlKTk6u1fo4xcXF+vzzzyVZPmOouLhYe/bsUWJiorKyshQWFqbevXvrhhtuqPFxAcDd1TjwJCUl2XIeDpObmyvJfV4PqhAQoIAmTdTk8mUF5+U5ejYAAAC2ZyHu/PrKK8q8+Wap3M+9ly9fNn6ckpJijD3l+fr6SpKOHj2q8PDwGk/viy++0IEDBxQSEqJBgwaZ/Byen58vSRozZozZeXTu3FnTpk2z+vj8jO95+P3Oc7nTex8TE1Oj53EGDzzOFT8/pTRuLK+sLEXk5qpBQYGjpwQAAGAbFuLO7A4dtG7bNmnbNpPHw8PD9fjjjxs/9/Gx/OtBaeDJq8U/kq1atUqLFy+Wj4+Pnn32WYu3Qm/SpIkee+wxtWvXTsXFxUpMTNTHH3+sw4cP6y9/+YveeeedSucKAJ6oxn8r1rQoOZvSuucurwfWS0pKUlpIiBq0aMGlWwAAwPVZiDszmjbV8uJiKTXV7NO6du1q/Lht27by9/ev9DBt2rSp9s/OxcXFmjVrlj755BP5+flp9uzZuuOOOyrst2DBAhUWFiomJkbe3v+7H0zPnj11xx136K677tKpU6d04sSJCnf7Kmv//v2S+BnfE/H7nefivecMHoA1egAAgOurZM2d1x56SK9V8tTSy6IkKScnx2Lgyc7OliSFhIRUa2p5eXmaPn26Nm7cqNDQUM2ZM0d9+/Y1u2+HDh0sjnPddddp2LBhWrFihRISEioNPADgibhNOlCK26sDAABXVI0Flc3x8/NTZGSkJCnVwlk+WVlZxrV6oqOjrZ5afn6+pk6dqo0bNyoqKkpLly61GHesUbq484ULF2o8BgC4KwIPUB6hBwAAuIpaxp1SXbp0kSQdOnTI7PYDBw5IKlkbp3nz5laNWVRUpOnTp2vXrl2KiYnR0qVL1aZNG6ueZ8nFixclSQ0aNLBqDgDgSQg8gCWEHgAA4MxsFHek/92ufMOGDWa3r127VpJ05513Wj3m3Llz9dVXX6lNmzb6+OOP1aRJk0r3X7Zsmfr06aOpU6ea3Z6Xl6ctW7ZIKlmTBwBgisADVIXQAwAAnI0N444kDRkyRNHR0dq3b5+WLVtmsm3btm1avXq16tevr0mTJpls27x5s+Li4jRlyhSTx0+cOKH58+fL19dXc+fOVcOGDaucQ//+/ZWdna3t27fr008/Ndl29epVzZo1S2lpaQoPD2f9HQAwg0WWAWuxGDMAAHAGNo47Uskt0N99911NmjRJL730ktasWaO2bdvq9OnT2rlzp7y9vfXWW29VuDwrKytLJ0+erDDev/71LxUWFqply5ZasmRJpcd+9NFHFRYWppYtW+rPf/6zXnvtNb366qv6/PPP1bVrVxUUFGjv3r1KSUlRgwYNNGfOnGov9AwAnoDAA1QXoQcAADiKHeJOqU6dOunLL7/UvHnzFB8frwMHDig0NFRDhgzRww8/XK1bD6elpUmSUlJStGjRokr3nTBhgsLCwiRJY8aMUadOnbRo0SIlJibqiy++kK+vr6KiojR58mSNHz9ezZo1q/FrBAB35lVcXFzs6Ek4UlJSkiRV6z9YcA82e+8JPQAAoC7YMe64m/3790uSbrzxRgfPBHWN3+88F+89Z/AAtccZPQAAwN6IOwCAKhB4AFsh9AAAAHsg7gAArEDgAWyN0AMAAGyFuAMAsBKBB7AXQg8AAKgN4g4AoBoIPIC9EXoAAEB1EXcAANVE4AHqCqEHAABYg7gDAKgBAg9Q1wg9AADAEuIOAKCGCDyAoxB6AABAWcQdAEAtEHgARyP0AAAA4g4AoJYIPICzIPQAAOCZiDsAABsg8ADOhtADAIDnIO4AAGyEwAM4K0IPAADujbgDALAhAg/g7Ag9AAC4H+IOAMDGCDyAqyD0AADgHog7AAA7IPAArobQAwCA6yLuAADshMADuCpCDwAAroW4AwCwIwIP4OoIPQAAOD/iDgDAzgg8gLsg9AAA4JyIOwCAOkDgAdwNoQcAAOdB3AEA1BECD+CuCD0AADgWcQcAUIcIPIC7I/QAAFD3iDsAgDpG4AE8BaEHAIC6QdwBADgAgQfwNIQeAADsh7gDAHAQAg/gqQg9AADYFnEHAOBABB7A0xF6AACoPeIOAMDBCDwAShB6AACoGeIOAMAJEHgAmCL0AABgPeIOAMBJEHgAmEfoAQCgcsQdAIATIfAAqByhBwCAiog7AAAnQ+ABYB1CDwAAJYg7AAAnROABUD2EHgCAJyPuAACcFIEHQM0QegAAnoa4AwBwYgQeALVD6AEAeALiDgDAyRF4ANgGoQcA4K6IOwAAF0DgAWBbhB4AgDsh7gAAXASBB4B9EHoAAK6OuAMAcCEEHgD2RegBALgi4g4AwMUQeADUDUIPAMBVEHcAAC6IwAOgbhF6AADOjLgDAHBRBB4AjkHoAQA4G+IOAMCFEXgAOBahBwDgDIg7AAAXR+AB4BwIPQAARyHuAADcAIEHgHMh9AAA6hJxBwDgJgg8AJwToQcAYG/EHQCAGyHwAHBuhB4AgD0QdwAAbobAA8A1EHoAALZC3AEAuCECDwDXQugBANTGnj3EnUokJydr/vz52rVrlzIyMhQUFKQePXpo4sSJ6tu3r9Xj7NmzR+PHj69yv1deeUW///3vTR7Ly8vT4sWLtW7dOp08eVLFxcWKjo7W8OHDNXbsWPn7+1f7dQGAJyDwAHBNhB4AQHXt2SO98gpxx4L9+/dr8uTJMhgMio2N1cCBA5Wenq6EhARt3bpVM2bM0NixY6s1ZrNmzTR06FCL2zt06GDyucFg0IMPPqjExERFREQoLi5OkhQfH6+3335b33zzjRYsWKCAgIDqv0AAcHMEHgCujdADALAGcadSubm5mj59ugwGg2bNmqURI0YYtyUmJmrChAmaOXOm+vTpo3bt2lk9bqtWrfTiiy9avf/cuXOVmJioQYMGac6cOcazdbKzszV58mR9++23ev/99/X0009bPSYAeApvR08AAGyiNPTExkqNGjl6NgAAZ2Ip7nzwAXHnmg0bNig1NVUDBgwwiTuS1LNnT40ePVoFBQVauHCh3eZgMBi0ZMkS+fj46NVXXzW5FCs4OFgvv/yyJGnx4sW6cuWK3eYBAK6KwAPAvRB6AABlVRZ3pk51yJSc0aZNmyTJeElUeaWXWW3evNluc0hISJDBYFC3bt0UERFRYXtMTIxatmypnJwc7dixw27zAABXReAB4J4IPQAA4o7Vjhw5Iknq1KmT2e2dO3eWJGVmZur06dN2mcPhw4dNjlXZPErnCwD4H9bgAeDeWKMHADwTccdq+fn5Sk9PlySzZ85IUmBgoMLCwpSZmank5GRFRUVZPX5WVpa++eYb/fzzzyoqKlLLli01aNAgNWvWzGS/0nDUvHlzi2OVzu/UqVNWHx8APEWNA09SUpIt5+Ewubm5ktzn9cB6vPceKCBAAU2aKDwzUw0KChw9GwCAvViIO7++/LIyBw6U+G+/icuXLxs/TklJMcae8nx9fSVJR48eVXh4eKVjJicnS5J+/PFH3Xzzzcafu0r5+Pho1KhRJrdIP3PmjKSSIGTp5zODwSBJSk9Pt+pnOH7O8zz8jO+53Om9j4mJqdHzOIMHgEe54uenEyEhql9YqKi8PAXn5Tl6SgAAW6os7tx/v2PmVMfeeecdnTx50qp9w8PD9fjjjxs/9/Gx/OtBaeDJq8Z/Ow0Gg+6++27ddtttatKkiTIzM7V+/XqtXr1ay5Ytk7+/v0aOHGkybmVzKN1WnTkAgKeoceCpaVFyNqV1z11eD6zHe++5kpKSVCwpuHdvLt0CAHdSyWVZEVOnyvzFR+4nKytLqampVu/ftWtX48dt27Y1uXuVOW3atKny56eWLVsqJiZGYWFhatmypcm2gQMHqnXr1vrb3/6mL774Qk8//bQCAwPVuHFjSVLjxo0tjh8WFiZJatSoUaVz2L9/vyR+zvNE/IzvuXjvOYMHgKdjjR4AcA+VnLkT4WFr7ixfvrxa++fn5xs/zsnJsRh4srOzJUkhISFVjhkcHGwSjsp74IEHNG/ePOXk5Oi7775T//79FRQUZJyDJdWZAwB4Gu6iBQASd90CAFfGZVm14ufnp8jISEmyeOZPVlaWca2e6OhomxyzSZMmkqTz1/5xpXTctLQ0i88rnZ8t5gAA7obAAwBlEXoAwLVUclkWccd6Xbp0kSQdOnTI7PYDBw5Ikpo0aVLpXa7KKi4uVnFxscVtmZmZkqQGDRpYNQdJOnjwoCSpW7duVs0BADwJgQcAzCH0AIDz41boNhMXFydJ2rBhg9nta9eulSTdeeedVo03ceJEdevWzeJ427dvV1ZWlnx8fNS9e3dJUv/+/RUaGqrDhw/rl19+qfCc3bt3KyMjQ+Hh4erbt69V8wAAT0LgAYDKEHoAwDkRd2xqyJAhio6O1r59+7Rs2TKTbdu2bdPq1atVv359TZo0yWTb5s2bFRcXpylTppg83qtXL+Xn52vmzJk6deqUybb09HS98cYbkqRRo0YZz+Dx8/PTxIkTVVRUpBkzZujKlSvG52RmZhqfM3Xq1ErvtAUAnoq/GQHAGizGDADOg7hjc76+vnr33Xc1adIkvfTSS1qzZo3atm2r06dPa+fOnfL29tZbb71V4fKsrKwss7dknzJlinbv3q19+/Zp+PDhuuWWW9S0aVNlZGQoPj5eubm56t27t55//vkKz/vuu+8UHx+vuLg49e/fX1evXtX27dt14cIFDR06VOPGjbPr1wIAXBWBBwCqg9ADAI5F3LGbTp066csvv9S8efMUHx+vAwcOKDQ0VEOGDNHDDz9crVsP+/v765NPPtHy5cu1du1a7dmzRzk5OQoJCVH37t1199136+6771a9evVMnufn56cPPvhAS5cu1cqVK42XeLVv315PP/20Ro0aJW9vLkIAAHO8ii2tfOYhkpKSJKla/8GCe+C991w2fe8JPQBQd6oZd/hvvefav3+/JOnGG2908ExQ1/i+91y895zBAwC1wxk9AFA3OHMHAIBKEXgAwBYIPQBgP8QdAACqROABAFsi9ACAbRF3AACwCoEHAOyB0AMAtUfcAQDAagQeALAnQg8A1AxxBwCAaiHwAEBdIPQAgPWIOwAAVBuBBwDqEqEHACpH3AEAoEYIPADgCIQeAKiIuAMAQI0ReADAkQg9AFCCuAMAQK0QeADAGRB6AHgy4g4AALVG4AEAZ0LoAeBpiDsAANgEgQcAnBGhB4AnIO4AAGAzBB4AcGaEHgDuirgDAIBNEXgAwBUQegC4E+IOAAA2R+ABAFdC6AHg6og7AADYBYEHAFwRoQeAKyLuAABgNwQeAHBlhB4AroK4AwCAXRF4AMAdEHoAODPiDgAAdkfgAQB3QugB4GyIOwAA1AkCDwC4I0IPAGdA3AEAoM4QeADAnRF6ADgKcQcAgDpF4AEAT0DoAVCXiDsAANQ5Ag8AeBJCDwB7I+4AAOAQBB4A8ESEHgD2QNwBAMBhCDwA4MkIPQBshbgDAIBDEXgAAIQeALVD3AEAwOEIPACA/yH0AKgu4g4AAE6BwAMAqIjQA8AaxB0AAJwGgQcAYBmhB4AlxB0AAJwKgQcAUDVCD4CyiDsAADgdAg8AwHqEHgDEHQAAnBKBBwBQfYQewDMRdwAAcFoEHgBAzRF6AM9B3AEAwKkReAAAtUfoAdwbcQcAAKdH4AEA2A6hB3A/xB0AAFwCgQcAYHuEHsA9EHcAAHAZBB4AgP0QegDXRdwBAMClEHgAAPZH6AFcC3EHAACXQ+ABANQdQg/g/Ig7AAC4JAIPAKDuEXoA50TcAQDAZRF4AACOQ+gBnAdxBwAAl0bgAQA4HqEHcCziDgAALo/AAwBwHoQeoO4RdwAAcAsEHgCA8yH0AHWDuAMAgNsg8AAAnBehB7Af4g4AAG6FwAMAcH6EHsC2iDuwIDk5WfPnz9euXbuUkZGhoKAg9ejRQxMnTlTfvn2tHmfcuHHau3evVftu2bJFUVFRkqRbb71Vqample7fvXt3LV++3Oq5AICnIPAAAFwHoQeoPeIOLNi/f78mT54sg8Gg2NhYDRw4UOnp6UpISNDWrVs1Y8YMjR071qqxhg4dqo4dO1rcXlBQoKVLl8rX11fBwcEVto8cOdLs45IUGRlp3QsCAA9D4AEAuB5CD1AzxB1YkJubq+nTp8tgMGjWrFkaMWKEcVtiYqImTJigmTNnqk+fPmrXrl2V41UVgj744AMVFxfrgQceUFhYWIXtjz76qPGsHgCAdbwdPQEAAGqsNPTExkqNGjl6NoBzI+6gEhs2bFBqaqoGDBhgEnckqWfPnho9erQKCgq0cOHCWh/r9OnT+uCDD9SiRQs9/PDDtR4PAFCCwAMAcH2EHqByxB1UYdOmTZKkuLg4s9uHDh0qSdq8eXOtj/X6668rNzdXzz//vAIDA2s9HgCgBIEHAOA+CD1ARcQdWOHIkSOSpE6dOpnd3rlzZ0lSZmamTp8+XePjxMfHa+vWrerdu7cxGgEAbIM1eAAA7oc1eoASxB1YIT8/X+np6ZKkiIgIs/sEBgYqLCxMmZmZSk5OrtH6OMXFxXr33XclSU8//XSV++7Zs0eJiYnKyspSWFiYevfurRtuuKHaxwUAT1HjwJOUlGTLeThMbm6uJPd5PbAe773n4r33MAEBCmjSRE0uX1ZwXp6jZwPUHQtx59eXX1bmwIGSB/wdyN/31rl8+bLx45SUFGPsKc/X11eSdPToUYWHh1f7OHv37tWRI0fUvXt3BQQEmH1f8vPzJUljxowxO4/OnTtr2rRpVh+f997z8H3vudzpvY+JianR8ziDBwDg9q74+SmlcWN5ZWUpIjdXDQoKHD0lwL4qizv33++YOaHOvPPOOzp58qRV+4aHh+vxxx83fu7jY/nXg9LAk1fDWL5q1SpJ0m9/+9sq923SpIkee+wxtWvXTsXFxUpMTNTHH3+sw4cP6y9/+YveeeedSucKAJ6oxn8r1rQoOZvSuucurwfW4733XLz3nispKUlpISFq0KIFl27BfVVyWVbE1KkyfwGOe/LUv++zsrKUmppq9f5du3Y1fty2bVv5+/tXun+bNm2q/TU9duyYjhw5ooiICI0ZM0ZeXl5m91uwYIEKCwsVExMjb+//LRfas2dP3XHHHbrrrrt06tQpnThxosLdvsrav3+/JM977+G53/fgvZc4gwcA4IlYowfuijV3IGn58uXV2r/0sihJysnJsRh4srOzJUkhISHVnlPp2TvDhg2zGHckqUOHDha3XXfddRo2bJhWrFihhISESgMPAHgi7qIFAPBc3HUL7oS4gxry8/NTZGSkJFk88ycrK8u4Vk90dHS1j1F6e/VbbrmlZpO8pnRx5wsXLtRqHABwRwQeAAAIPXB1xB3UUpcuXSRJhw4dMrv9wIEDkkrWxmnevHm1xk5JSVFycrICAgKsugtWUVGRxW0XL16UJDVo0KBacwAAT0DgAQCgFKEHroi4AxuIi4uTJG3YsMHs9rVr10qS7rzzzmqPXRqH2rRpIz8/P4v7LVu2TH369NFUC39u8/LytGXLFkkla/IAAEwReAAAKI/QA1dB3IGNDBkyRNHR0dq3b5+WLVtmsm3btm1avXq16tevr0mTJpls27x5s+Li4jRlyhSLYx87dkyS1Lp160rn0L9/f2VnZ2v79u369NNPTbZdvXpVs2bNUlpamsLDw1l/BwDMYJFlAAAsYTFmODPiDmzI19dX7777riZNmqSXXnpJa9asUdu2bXX69Gnt3LlT3t7eeuuttypcnpWVlVXlLdnPnDkjqeSW7JVp2bKl/vznP+u1117Tq6++qs8//1xdu3ZVQUGB9u7dq5SUFDVo0EBz5syp0ULPAODuCDwAAFSF0ANnQ9yBHXTq1Elffvml5s2bp/j4eB04cEChoaEaMmSIHn744RrfejgrK0uSVL9+/Sr3HTNmjDp16qRFixYpMTFRX3zxhXx9fRUVFaXJkydr/PjxatasWY3mAQDujsADAIC1CD1wBsQd2FHz5s316quvWr3/yJEjNXLkyEr3mTdvXrXm0KNHD/Xo0aNazwEAEHgAAKg+Qg8chbgDAAAsIPAAAFBThB7UJeIOAACoBIEHAIDaIvTA3og7AACgCgQeAABshdADeyDuAAAAKxB4AACwNUIPbIW4AwAArETgAQDAXgg9qA3iDgAAqAYCDwAA9kboQXURdwAAQDUReAAAqCuEHliDuAMAAGqAwAMAQF0j9MAS4g4AAKghAg8AAI5C6EFZxB0AAFALBB4AAByN0APiDgAAqCUCDwAAzoLQ45mIOwAAwAYIPAAAOBtCj+cg7gAAABsh8AAA4KwIPe6NuAMAAGyIwAMAgLMj9Lgf4g4AALAxAg8AAK6C0OMeiDsAAMAOCDwAALgaQo/rIu4AAAA7IfAAAOCqCD2uhbgDAADsiMADAICrI/Q4P+IOAACwMwIPAADugtDjnIg7AACgDhB4AABwN4Qe50HcAQAAdYTAAwCAuyL0OBZxBwAA1CECDwAA7o7QU/eIOwAAoI4ReAAA8BSEnrpB3AEAAA5A4AEAwNMQeuyHuAMAAByEwAMAgKci9NgWcQcAADgQgQcAAE9H6Kk94g4AAHAwAg8AAChB6KkZ4g4AAHACBB4AAGCK0GM94g4AAHASBB4AAGAeoadyxB0AAOBECDwAAKByhJ6KiDsAAMDJEHgAAIB1CD0liDsAAMAJEXgAAED1eHLoIe4AAAAnReABAAA142mhh7gDAACcGIEHAADUjieEHuIOAABwct6OngAAAHATpaEnNlZq1MjRs6laRoaUmlr1fsQdAADgAgg8AADAtlwh9Fy9Kj3+uDR5srRzp+X9iDsAAMBFEHgAAIB9OHPoOXhQOneuJNy89pr5yEPcAQAALoTAAwAA7MsZQ8+2bf/72FzkIe4AAAAXQ+ABAAB1w1lCz9Wr0o4dpo+VjTzEHQAA4IK4ixYAAKhbjr7r1sGDJccurzTylH5cFnEHAAA4OQIPAABwDEeFnrKXZ5VXPuxIxB0AAOASCDwAAMCx6jL0mLs8qzLEHQAA4CIIPAAAwDnUReixdHmWOT4+UkSE7ecAAABgByyyDAAAnIs9F2Ou7PKs8goLpXvvlVavtu0cAAAA7IDAAwAAnJOtQ091L8+SpIICIg8AAHAJBB4AAODcbBV6qnN5VllEHniY4uJiLVq0SN26dVOHDh20Z8+eGo+VnJysP//5zxo8eLC6dOmiPn366OGHH9bu3bstPicvL08LFizQyJEj1aNHD91www265557tGDBAuXl5dV4LgDg7liDBwAAuIbartFTncuzyiuNPImJUpcuNR8HcHLnzp3TCy+8oO3bt9d6rP3792vy5MkyGAyKjY3VwIEDlZ6eroSEBG3dulUzZszQ2LFjTZ5jMBj04IMPKjExUREREYqLi5MkxcfH6+2339Y333yjBQsWKCAgoNbzAwB3Q+ABAACupSahpyaXZ5Xn7y95edVuDMCJ7dy5U88884zOnz+vsWPHatOmTTp79myNxsrNzdX06dNlMBg0a9YsjRgxwrgtMTFREyZM0MyZM9WnTx+1a9fOuG3u3LlKTEzUoEGDNGfOHPn7+0uSsrOzNXnyZH377bd6//339fTTT9fqtQKAO+ISLQAA4Jqqc+lWTS/P8veX7r5b+s9/pNRUqXPnms0VcAErVqxQQUGB5s6dqxkzZsjX17fGY23YsEGpqakaMGCASdyRpJ49e2r06NEqKCjQwoULjY8bDAYtWbJEPj4+evXVV41xR5KCg4P18ssvS5IWL16sK1eu1HhuAOCuOIMHAADYXH5+vj799FNt3rxZx48fV1ZWlq5evWrc/tZbb2nkyJEmzyksLNTdd9+t48ePGx/75JNP1K9fP+Pnzz//vFauXGnyvEWLFqlPnz4mZ/T8fc0azfvqK+M+94WG6jVrJ+/vL8XFSffdJw0fLoWGWv/CARfWvXt3Pfnkk4qKiqr1WJs2bZIk4yVW5Q0dOlSLFi3S5s2b9frrr0uSEhISZDAY1LNnT0VERFR4TkxMjFq2bKmUlBTt2LFDt912W63nCQDuhMADAABsKjs7W+PHj9fhw4er9bxPP/3UJO50797dJO5UqcylW+N9ffXJN98oNz9fkvT5pUv6g7+/Yiwt0ErUATRu3DibjXXkyBFJUqdOncxu73ztbLjMzEydPn1aUVFRxr8zOldyplznzp2VkpKiI0eOEHgAoBwu0QIAADb14YcfVjvuGAwGffDBByaPPfTQQzWbQIMGCh80SL8rc4ZQkZeX/l7+Mi5/f2nEiJLLr86elVatkv7wB+IOUEv5+flKT0+XJLNn4khSYGCgwsLCJJXcaUuSTp8+LUlq3ry5xbFLxzt16pSNZgsA7qPGZ/AkJSXZch4Ok5ubK8l9Xg+sx3vvuXjvPRfvfd1Yu3Zthcdat26tjh07ysen5EePevXqmbwPq1at0vkyiyU3a9ZMLVq0qPBetW7dWsOHDzd5LCcnx+x7etPgwVq0dKnx8/8GB+v74GC17tNHl4cOVfYtt6goOLhkY2pqyf/gVvier538a2fAJScnK7Qa4fPy5cvGj1NSUoyxp7zSNX6OHj2q8PBwnTlzRpKUlZVl8T0zGAySpPT0dKveV957z8P3vedyp/c+JiamRs/jEi0AAGBT5X+ZCwgI0Ntvvy0/Pz+z+1+9elXr1q0zeezmm2+Wl5k7Vg0aNEiDBg2yah7N/n97dxMS1f7HcfxzJxtCayof0tBSSRJFU5BIXCiFmtROkyKn0kVUuwjuKgriEi3+PUAPZESLgiBrERUllhAmmOAVtYgwsMJUMEktR0Kiuov+M3k6M16tczse5/3a6O97zu9h/DEuvvwe4uOVnp6u7u7uQOxsZaX2//nntOoDTnX8+HG9evVqWu9GR0frr7+mfULVtExM2grpT+oG40/w+N/3/5yqjv/ZRKjtlgAQxn46wfOzGaXZxp/dmyufB9PH3Icv5j58Mfe/x6dPnwzlmJgY5eTkhHy/qalJQ0NDhtiuXbu0evXqXx5LZWVl4ABXSXr899/6X2LijFYjwLnC9Ts/Njam/hmsSAv19/EnZZOTk2f0N5y8xSotLc1wG1Ywq1atUkZGhmJjYyVJsbGxIfvzb+uKiYmZckzt7e2Swm/uEb7fezD3Eit4AACABc6cOaOzZ88Gfdbf36/09HRDbPKqmnv37hmepaSkhEzuTHmLVhClpaWGBM/ExIQaGxtNN3gBc8n169dt7T8qKirw+/j4eMgEj8/nkyQtWrTIUG98fDxk2z/WAQB8xyHLAADAVq2trYZybm6uZW3Hx8cHVgWE6g+AtdxutxITEyUp5EqisbGxwFk9qamphp8DAwMh2/a3538XAPAdCR4AAGCbN2/eBA5W9VuzZo2lffy4Gqitrc3S9gGYZWVlSZKePHkS9HlnZ6ckKS4uLrCl69/qSFJXV5ck6/9PAMBcwBYtAADwy3JycrRz505J37ZMTRYVFaWKioqg9To6OkyxzMxMS8eWmpqqlpaWQHlgYECDg4OKj4+3tB8A35WVlamhoUH19fWqqqoyPffftrd58+ZArKCgQB6PR8+ePVNvb69WrlxpqNPa2qqhoSFFR0crPz//v/0AAOBAJHgAAMAvKywsVGFhoSRzgmfJkiU6ePBg0Hpv3741xaKjoy0d2+LFi4P2S4IH+HUPHjzQiRMntGLFCl28eDEQLykpUWpqqtra2lRXV6etW7cGnjU1Nen27duKjIxUTU1NIO52u1VdXa3Tp0/r0KFDunDhghYsWCBJGh0d1dGjRyVJe/bsmfKmLQAIV/xnBAAAtnn37p0p5r8lxyrBDmMdHh62tA/A6UZHR3Xu3DlTTJKuXr2qxsbGQNzr9So5OVnSt7N0gl3JPn/+fJ08eVI1NTU6fPiw7ty5o7S0NPX19amlpUUul0vHjh0z3LglSbt371ZHR4eam5tVVlamgoICff78WY8ePdLw8LA2btyoHTt2WPzpAWBuIMEDAABsMzY2ZopNvoHHCpGRkaaY/3BXAN/4fD7T6ju/hoYGQ7m4uDiQ4JlKZmambt26pfPnz6u5uVmdnZ3yeDwqKSnR3r17g15l7Ha7VVtbq2vXrunmzZuqr6+X9O0srQMHDqiiokIuF8eIAkAwJHgAAIBtgq2u8fl8lq7iCXblssfjsax9YC5ISkpSd3f3jOuVl5ervLw85POEhAQdOXJkRm1GRETI6/XK6/XOeDwAEM5IfwMAANssXbrUFHv//r2lffh8vmn1CwAA4GQkeAAAgG2WLVtmill9Pk6whBEHLAMAgLmGBA8AALBNbm6uKfb8+XNL+3j58qWhvHz5chI8AABgziHBAwAAbJOSkqK4uDhD7OnTp5b28eLFC0N57dq1lrYPAAAwG5DgAQAAtlq3bp2h3NXVZVnbg4ODpqvY8/PzLWsfAABgtiDBAwAAbLVp0yZDuaenRz09PZa0ff/+fUPZ7XarpKTEkrYBAABmExI8AADAVkVFRUpISDDE7t69a0nbP7ZTWlrKFekAAGBOIsEDAABsFRERIa/Xa4iFSvB8+fLFFJs3b17Qd/v6+tTR0WGIVVdX/9wgAQAAZrkIuwdgt4yMDLuHAJsw9+GLuQ9fzP3v0d3dPeM627dv16VLlzQyMiJJev36tR4+fKj169cb3hsdHTXVXbhwYdA2L1++bCgXFRUpOzt7xmODc/GdB8IP3/vwxdyzggcAAMwCUVFR2rdvnyFWW1trKI+MjJhW5LhcLiUlJZnaGx4e1o0bNwzv7d+/37oBA5jV8vLylJeXZ/cwAOC3CvsVPAAAYHaoqqpSXV1d4IDlzs5OPX78WO3t7ert7VVLS4s+fPhgqJOVlRV0Bc+VK1f08ePHQHnLli3KzMz8bz8AAACAjf74+vXrV7sHAQAAEMqGDRvU398f9NmpU6dMt3ABAACEI7ZoAQAAR6qqqiK5AwAA8H9s0QIAAI7gcrnk8XiUnZ2tbdu2qbi42O4hAQAAzBps0QIAAAAAAHA4tmgBAAAAAAA4HAkeAAAAAAAAhyPBAwAAAAAA4HAkeAAAAAAAAByOBA8AAAAAAIDDkeABAAAAAABwOBI8AAAAAAAADkeCBwAAAAAAwOFI8AAAAAAAADgcCR4AAAAAAACHI8EDAAAAAADgcCR4AAAAAAAAHI4EDwAAAAAAgMOR4AEAAAAAAHA4EjwAAAAAAAAO9w9rBueyblzEGwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 305, + "width": 572 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# base d'origine\n", + "vector([1,0], text='i')\n", + "vector([0,1], text='j')\n", + "plt.fill([0,1, 1, 0],[0,0,1,1], '#bbbbbb')\n", + "plt.text(0.5, 0.5, 'Surface = 1', horizontalalignment='center', size=16)\n", + "# base transformée\n", + "vector([-2,1], 'r', 'f(i)')\n", + "vector([-1,-1], 'r', 'f(j)')\n", + "plt.fill([0,-2, -3, -1],[0,1,0,-1], '#ffbbbb')\n", + "plt.text(-1.5, 0, 'Surface = det(A)', horizontalalignment='center', size=16)\n", + "plt.gca().spines[:].set_position('zero')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.0" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy.linalg as lin\n", + "\n", + "A = np.array([[-2, -1], [1, -1]])\n", + "lin.det(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "* si det(A) = 0 alors cela veut dire que $\\bf f(i)$ et $\\bf f(j)$ sont colinéaires, donc qu'on a perdu une dimension (on regarde la tranche du plan).\n", + "* si det(A) < 0 alors cela veut dire que $\\bf f(i)$ est après $\\bf f(j)$ dans le sens trigonométrique (on a retourné le plan)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Si vous n'êtes pas à l'aise avec l'algèbre linéaire, je vous invite à regader [les vidéos de 3 bleus, 1 marron](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Normes\n", + "\n", + "### Norme d'un vecteur\n", + "\n", + "Il existe différentes normes, la plus connue étant la norme euclidienne ou la norme 2. Sa définition est :\n", + "\n", + "$$\n", + "|| {\\bf v} ||_2 = \\sqrt{\\sum_{i=1}^n v_i^2} = \\sqrt{\\bf v . \\bf v}\n", + "$$\n", + "\n", + "On a aussi la norme 1 (dites aussi Manhattan) :\n", + "\n", + "$$\n", + "||{\\bf v}||_1 = \\sum_{i=1}^n |v_i|\n", + "$$\n", + "\n", + "La norme n :\n", + "\n", + "$$\n", + "|| {\\bf v} ||_n = \\left( {\\sum_{i=1}^n v_i^n} \\right)^{1/n}\n", + "$$\n", + "\n", + "et donc la la norme infinie est le max (il faut utiliser les limites pour comprendre pourquoi)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v = [ 0.1 1. 4. 10. 50. ]\n", + "v¹⁰⁰ = [1.000e-100 1.000e+000 1.607e+060 1.000e+100 7.889e+169]\n", + "Σ v¹⁰⁰ = 7.888609052210118e+169\n", + "ǁvǁ₁₀₀ = 50.00000000000001\n" + ] + } + ], + "source": [ + "v = np.array([0.1, 1, 4, 10, 50])\n", + "print(\"v =\", v)\n", + "print(\"v¹⁰⁰ =\", v**100)\n", + "print(\"Σ v¹⁰⁰ =\", (v**100).sum())\n", + "print(\"ǁvǁ₁₀₀ =\", (v**100).sum()**0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Norme d'une matrice\n", + "\n", + "La norme qui dérive du produit scalaire est la **norme de Frobenius** :\n", + "\n", + "$$\n", + "|| A ||_F = \\sqrt{\\textrm{trace}(A A^*)} = \\sqrt{ \\sum_{1 \\le i\\le m \\atop 1 \\le j\\le n}|A_{ij}|^2 }\n", + "$$\n", + "\n", + "avec $A^*$ la matrice adjointe (ou la matrice transposé si on est dans R).\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 1]\n", + " [2 3]]\n", + "ǁAǁ = 3.872983346207417\n" + ] + } + ], + "source": [ + "A = np.array([[1, 1], [2, 3]])\n", + "print(A)\n", + "print(\"ǁAǁ = \", np.linalg.norm(A))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "La **norme subordonnée** est induite par la norme vectorielle :\n", + "\n", + "$$\n", + "||B||_n = \\sup_{\\bf v} \\frac{||B\\, {\\bf v}||_n}{||\\textbf{v}||_n} = \\sup_{\\textbf{v} \\, t.q. ||\\textbf{v}||_n = 1} ||B\\, {\\bf v}||_n = \\sup_{\\textbf{v} \\, t.q. ||\\textbf{v}||_n \\le 1} ||B\\, {\\bf v}||_n\n", + "$$\n", + "\n", + "C'est la norme qu'on utilise par défaut dans ce cours." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ǁAǁ₂ = 3.8643284505408246\n" + ] + } + ], + "source": [ + "print(\"ǁAǁ₂ = \", np.linalg.norm(A,2))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Propriétés\n", + "\n", + "Dans notre cas où l'espace d'arrivée et l'espace de départ sont $\\mathbb{R}^n$ ou $\\mathbb{C}^n$, ces\n", + "normes ont les propriétés suivantes :\n", + " \n", + "$$\n", + "\\begin{array}{l}\n", + "|| A B || \\le ||A|| \\; ||B|| \\\\\n", + "|| A {\\bf v} || \\le ||A|| \\; ||{\\bf v}||\n", + "\\end{array}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma21 Transformations isometriques.ipynb b/PVCM/cama/fr/ma21 Transformations isometriques.ipynb new file mode 100644 index 0000000..56bb6b1 --- /dev/null +++ b/PVCM/cama/fr/ma21 Transformations isometriques.ipynb @@ -0,0 +1,458 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Transformations isométriques\n", + "\n", + "Dans le monde du calcul vectoriel (ou matriciel) on parle d'automophisme orthogonal plutôt que de transformation isométrique comme on\n", + "le verra à la fin." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0. 0.5 0.866 1. 0.866 0.5 0. -0.5 -1. -1. -1. -0.5 0. ]\n", + " [-1. -0.866 -0.5 0. 0.5 0.866 1. 1. 1. 0.5 0. -0.5 -1. ]]\n" + ] + } + ], + "source": [ + "angle = np.array([θ for θ in np.linspace(-np.pi/2,np.pi/2,7)])\n", + "shape1 = np.concatenate([np.array([np.cos(angle), np.sin(angle)]), \\\n", + " np.array([[-0.5, -1, -1, -1], [1, 1, 0.5, 0]]), \\\n", + " np.array([[-0.5, 0], [-0.5, -1]])], axis=1)\n", + "print(shape1)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 300, + "width": 606 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(shape1[0], shape1[1], '-or')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Matrice de rotation centrée en (0,0)\n", + "\n", + "R = \n", + "$\n", + "\\begin{bmatrix}\n", + "cos(θ) & -sin(θ) \\\\\n", + "sin(θ) & cos(θ) \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "### Propriétés\n", + "\n", + "* Effectue une rotation de centre (0,0) et d'angle θ\n", + "* Déterminant = 1\n", + "* Matrice orthogonale $\\rightarrow$ pas de déformation ni d'agrandissement de la forme (automorphisme orthogonal)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0.707 -0.707]\n", + " [ 0.707 0.707]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 300, + "width": 606 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "θ = np.pi / 4\n", + "\n", + "R = np.array([[np.cos(θ), -np.sin(θ)], [np.sin(θ), np.cos(θ)]])\n", + "print(R)\n", + "\n", + "shape2 = R @ shape1\n", + "\n", + "plt.plot(shape2[0], shape2[1], '-ob')\n", + "plt.axis('equal');\n", + "\n", + "np.save(\"mouse.npy\", shape2) # pour le prochain cours" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Matrice orthogonale donc (par définition) $R.R^T = \\textrm{Id}$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 0.],\n", + " [0., 1.]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "R @ R.T" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Donc la transposée est la rotation d'angle -θ ce qui est logique puisque sinus est une fonction impaire." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Symétrie axiale\n", + "\n", + "La symétrie horizontale, qui transforme (a,b) en (a,-b), est \n", + "\n", + "Sx = \n", + "$\n", + "\\begin{bmatrix}\n", + "1 & 0 \\\\\n", + "0 & -1 \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "On voit donc que pour avoir une symétrie axiale par rapport à une droite qui passe par (0,0) il suffit de \n", + "\n", + "* faire une rotation pour mettre l'axe de symétrie à l'horizontale\n", + "* appliquer la symétrie horizontale\n", + "* faire la rotation inverse\n", + "\n", + "Ainsi la symétrie axiale par rapport à la droite qui passe en (0,0) et qui a un angle d'alpha est :\n", + "\n", + "$S = R_{-α}^{-1}\\; Sx\\; R_{-α} = R_α\\;Sx\\; R_{-α}$\n", + "\n", + "Notez que l'ordre des matrices est l'inversé puisqu'on applique les points **x** à droite de $S$. " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-0.766 0.643]\n", + " [ 0.643 0.766]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 383 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def Rα(α):\n", + " return np.array([[np.cos(α), -np.sin(α)], [np.sin(α), np.cos(α)]])\n", + "\n", + "Sx = np.array([[1, 0],[0,-1]])\n", + "\n", + "θ = 70 * (2 * np.pi)/360 # 70 degrés\n", + "\n", + "shape2 = Rα(θ) @ Sx @ Rα(-θ) @ shape1\n", + "\n", + "print(Rα(θ) @ Sx @ Rα(-θ))\n", + "\n", + "plt.plot(shape1[0], shape1[1], \":\")\n", + "plt.plot(shape2[0], shape2[1])\n", + "plt.plot([-np.cos(θ),np.cos(θ)],[-np.sin(θ),np.sin(θ)],\"-.\") # axe de symétrie\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0., 1.],\n", + " [ 1., -0.]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "θ = np.pi / 4\n", + "Rα(θ) @ Sx @ Rα(-θ)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Je ne sais pas s'il y a une formule directe plus simple pour avoir la symétrie axiale par rapport à une droite quelconque qui passe par (0,0)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Translation\n", + "\n", + "On ne peut pas exprimer la translation avec un produit matriciel car ce n'est pas une application linéaire :\n", + "\n", + "$T(2\\;\\textbf{x}) \\ne 2\\; T(\\textbf{x})$\n", + "\n", + "Ce n'est pas non plus une transformation isométrique car la distance d'un point à (0,0) change après une translation.\n", + "\n", + "D'un point de vue vectoriel une translation est une addition :\n", + "\n", + "$T(\\textbf{x}) = \\textbf{x} + \\textbf{v}_t$ \n", + "\n", + "Il existe un truc pour exprimer les translations sous forme de produit matriciel : on change la représentation des points :\n", + "\n", + "$\\textbf{x} = (x_1, x_2)$ devient $\\textbf{x} = (x_1, x_2, 1)$\n", + "\n", + "Ainsi la translation par le vecteur $(v_1, v_2)$ est \n", + "\n", + "$T(X) = \n", + "\\begin{bmatrix}\n", + "1 & 0 & v_1\\\\\n", + "0 & 1 & v_2 \\\\\n", + "0 & 0 & 1 \\\\\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "x_1 \\\\\n", + "x_2 \\\\\n", + "1 \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "On peut vérifier que $T$ est bien une application linéraire puisque $T(2\\;\\textbf{x}) = 2\\; T(\\textbf{x})$ mais à l'arrivée\n", + "le nouveau point ne respecte pas la convention $(x_1, x_2, 1)$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Translate matrix:\n", + " [[1. 0. 1.]\n", + " [0. 1. 2.]\n", + " [0. 0. 1.]]\n", + "Shape1 3d:\n", + " [[ 0. 0.5 0.866 1. 0.866 0.5 0. -0.5 -1. -1. -1. -0.5 0. ]\n", + " [-1. -0.866 -0.5 0. 0.5 0.866 1. 1. 1. 0.5 0. -0.5 -1. ]\n", + " [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. ]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "v = np.array([1,2])\n", + "\n", + "T = np.identity(3)\n", + "T[0:2,2] = v\n", + "print(\"Translate matrix:\\n\", T)\n", + "\n", + "shape1_3d = np.concatenate([shape1, np.ones((1, len(shape1[0])))], axis=0)\n", + "print(\"Shape1 3d:\\n\", shape1_3d)\n", + "\n", + "shape2 = T @ shape1_3d\n", + "\n", + "plt.plot(shape1[0], shape1[1], \":\")\n", + "plt.plot(shape2[0], shape2[1])\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "La matrice inverse de notre matrice de translation est celle qui remet la forme orange à sa place d'origine, donc qui applique la transaltion $-\\textbf{v} = (-1,-2)$.\n", + "\n", + "$T^{-1} = \n", + "\\begin{bmatrix}\n", + "1 & 0 & -1\\\\\n", + "0 & 1 & -2 \\\\\n", + "0 & 0 & 1 \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "ce qui n'est pas la transposée de T donc T n'est pas orthogonale.\n", + "\n", + "Le piège est qu'il y a 2 types d'isométries :\n", + "\n", + "* l'isométrie vectorielle ou automorphisme orthogonal qui veut que $\\forall\\, \\textbf{x}, \\;||\\textbf{f}(\\textbf{x})|| = ||\\textbf{x}||$ ainsi que la conservation des angles\n", + "* l'isométrie géométrique qui veut que $\\forall\\, \\textbf{a}, \\textbf{b}, \\; ||\\textbf{f}(\\textbf{a}) - \\textbf{f}(\\textbf{b})|| = ||\\textbf{a} - \\textbf{b}||$.\n", + "\n", + "La translation est bien une isométrie géométrique mais pas vectorielles d'où le fait qu'on préfère parler\n", + "d'automorphisme orthogonal plutôt que d'isométrie pour ne pas prêter à confusion." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Exercice 1.1\n", + "\n", + "Écrire sous forme d'un produit matriciel la symétrie axiale par rapport à un axe qui ne passe pas par (0,0).\n", + "On prendra l'axe qui passe par (2,0) et qui a un angle de π/3 par rapport à l'horizontale.\n", + "\n", + "Est-ce un automorphisme orthogonal ? Le montrer." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma22 Changement de repere.ipynb b/PVCM/cama/fr/ma22 Changement de repere.ipynb new file mode 100644 index 0000000..f57bf47 --- /dev/null +++ b/PVCM/cama/fr/ma22 Changement de repere.ipynb @@ -0,0 +1,697 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "hide_input": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt\n", + "from scipy import linalg as lin\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid']) #,'data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "hide_input": true + }, + "outputs": [], + "source": [ + "matplotlib.rcParams['figure.figsize'] = (12.0, 8.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Matrice de passage\n", + "\n", + "On a vu qu'une matrice représente une application linéaire qui déplace les points qu'on lui donne.\n", + "\n", + "On va voir qu'une matrice sert aussi à représenter un changement de repère à savoir quelle est la valeur\n", + "d'un point par rapport à un autre repère." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "hide_input": true + }, + "outputs": [], + "source": [ + "def arrow2D(a,b, color='k', **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "hide_input": true, + "tags": [ + "hide-input" + ] + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 462, + "width": 693 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# beaucoup de code pour un petit dessin\n", + "\n", + "δx = np.array((0.1, 0))\n", + "δy = np.array((0, 0.1))\n", + "\n", + "O = np.array((0,0))\n", + "I = np.array((1,0))\n", + "J = np.array((0,1))\n", + "plt.annotate(\"O\", O - δx -δy , size=20, color='k')\n", + "plt.annotate(\"I\", I + δx, size=20, color='k')\n", + "plt.annotate(\"J\", J - δx, size=20, color='k')\n", + "\n", + "A = np.array((0,0))\n", + "B = np.array((2,1))\n", + "C = np.array((-1.5,1))\n", + "plt.annotate(\"A\", A - 1.5* δy, size=20, color='r')\n", + "plt.annotate(\"B\", B + δy, size=20, color='r')\n", + "plt.annotate(\"C\", C + δy , size=20, color='r')\n", + "\n", + "arrow2D(O,I)\n", + "arrow2D(O,J)\n", + "arrow2D(A,B, 'r')\n", + "arrow2D(A,C, 'r')\n", + "\n", + "plt.xticks(np.arange(-3,3,1))\n", + "plt.yticks(np.arange(0,2,1))\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hide_input": true + }, + "source": [ + "La matrice de passage d'un repère à un autre l'ensemble des vecteurs de la seconde base exprimés dans la première base.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 2. , -1.5],\n", + " [ 1. , 1. ]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P = np.array([(B-A), (C-A)]).T # matrice de passage : déformation sans la translation\n", + "P" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Vecteurs dans le nouveau repère\n", + "\n", + "Cette déformation permet de passer d'une représentation de l'espace à une autre (d'un repère à un autre). \n", + "\n", + "Regardons ce que valent certains vecteur dans chacune des bases :\n", + "\n", + "| | base départ (O,I,J) | base d'arrivée (A,B,C) |\n", + "| --:| :-: | :-: |\n", + "AB | [2,1] | [1,0] |\n", + "AC | [-1.5, 1] | [0,1] |\n", + "OI | [1,0] | ? |" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-1.5, 1. ])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P @ [0,1] # donne AC, [0,1] de base d'arrivée, exprimé dans la base de départ" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "C'est logique puisqu'il s'agit de la 2e colonne de la matrice de passage. On a donc\n", + "\n", + "$$ \\mathbf{v}_{(d)} = P \\; \\mathbf{v}_{(a)} $$\n", + "\n", + "avec :\n", + "\n", + "* $ \\mathbf{v}_{(d)}$ : le vecteur __v__ exprimé dans la base de départ\n", + "* $ \\mathbf{v}_{(a)}$ : le vecteur __v__ exprimé dans la base d'arrivée\n", + "\n", + "et on a aussi \n", + "\n", + "$$ \\mathbf{v}_{(a)} = P^{-1} \\; \\mathbf{v}_{(d)} $$\n", + "\n", + "Cela nous permet de calculer la case qui nous manque à savoir OI exprimé dans la base d'arrivée :" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.286, -0.286])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xa = lin.inv(P) @ [1,0]\n", + "xa" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "c.a.d. OI = 0.286 AB - 0.286 AC." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Matrice de passage vue comme une transformation\n", + "\n", + "En tant que matrice, une matrice de passage représente aussi une application linéaire. Elle prend un vecteur et le déforme.\n", + "\n", + "Ainsi le vecteur OI est déformé par P pour devenir AB. On peut donc écrire :\n", + "\n", + "$$ AB = P\\; OI $$\n", + "\n", + "Dans ce cas, tout est exprimé en fonction du repère de départ. On a \n", + "\n", + "$$ \\mathbf{w}_{(d)} = P \\; \\mathbf{v}_{(d)} $$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hide_input": true + }, + "source": [ + "### Points dans le nouveau repère\n", + "\n", + "Lorsqu'on pense en point, alors l'orgine des deux repères peut être différente.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "hide_input": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 462, + "width": 693 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.annotate(\"O\", O - 4*δx, size=20, color='k')\n", + "plt.annotate(\"I\", I + δx, size=20, color='k')\n", + "plt.annotate(\"J\", J - 3*δx, size=20, color='k')\n", + "\n", + "A = np.array((3,3))\n", + "B = np.array((5,4))\n", + "C = np.array((1.5,4))\n", + "plt.annotate(\"A\", A - 3*δy, size=20, color='r')\n", + "plt.annotate(\"B\", B + δx, size=20, color='r')\n", + "plt.annotate(\"C\", C - 4*δx , size=20, color='r')\n", + "\n", + "arrow2D(O,I)\n", + "arrow2D(O,J)\n", + "arrow2D(A,B, 'r')\n", + "arrow2D(A,C, 'r')\n", + "\n", + "arrow2D([1,1], [2.5,3], 'b')\n", + "plt.annotate(\"p\", (1.3,2), size=30, color='b')\n", + "plt.yticks(np.arange(0,5,1))\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Si on veut travailler sur les points il faut prendre en compte la translation d'un repère vers l'autre soit de O vers A.\n", + "\n", + "La bonne facon de faire en mathématique est de séparer la déformation de la translation ce qui permet de rester\n", + "dans l'espace 2D.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([5., 4.])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P2D = P\n", + "A + P2D @ I # passage de I en B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Mais on a vu qu'on peut intègrer la translation dans une matrice d'une dimension supérieure." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 2. , -1.5, 3. ],\n", + " [ 1. , 1. , 3. ],\n", + " [ 0. , 0. , 1. ]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P = np.identity(3) # defines the size and set the last line (others will be overwritten)\n", + "P[:2, :2] = P2D # deformation\n", + "P[:2, 2] = A # translation\n", + "P" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "hide_input": false + }, + "outputs": [], + "source": [ + "def to3D(x):\n", + " \"\"\" Transform 2D point(s) to 3D point(s) with 1 as third value \"\"\"\n", + " if type(x) == list:\n", + " x = np.array(x)\n", + " if len(x.shape) == 1:\n", + " return np.array([*x,1])\n", + " elif len(x.shape) == 2:\n", + " return np.array([*x,np.ones(len(x[0]))])\n", + " else:\n", + " raise Exception('Erreur de dimension')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notre matrice de passage P qui inclu la translation de l'origine permet de calculer la position d'un point\n", + "dans le nouveau repère." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1.5, 4. , 1. ])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P @ to3D([0,1]) # C expressed in start basis including translation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Notre souris dans le nouveau repère\n", + "\n", + "A quoi ressemble la souris exprimée dans le repère d'arrivée vue depuis le repère de départ." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 476, + "width": 707 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "mouse = np.load('data/mouse.npy')\n", + "\n", + "dmouse = P2D @ mouse\n", + "\n", + "plt.plot(mouse[0,:], mouse[1,:], color='r', label=\"repère d'arrivée\")\n", + "plt.plot(dmouse[0,:], dmouse[1,:], color='k', label='repère de départ')\n", + "plt.title('Déformation sans la translation')\n", + "plt.legend()\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On peut aussi voir la souris noire comme la transformée de la souris rouge par la matrice de passage.\n", + "\n", + "Si on ajoute la translation, alors on a :" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 476, + "width": 693 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "ε = 0.03 # pour voir les 2 repères qui sont supperposés\n", + "\n", + "pmouse = P @ to3D(mouse)\n", + "\n", + "arrow2D(O+ε,I+ε, 'k')\n", + "arrow2D(O+ε,J+ε, 'k')\n", + "arrow2D(O,I, 'r')\n", + "arrow2D(O,J, 'r')\n", + "arrow2D(A,B, 'g')\n", + "arrow2D(A,C, 'g')\n", + "\n", + "plt.plot(mouse[0,:], mouse[1,:], 'red')\n", + "plt.plot(pmouse[0,:], pmouse[1,:], 'black')\n", + "plt.axis(\"equal\")\n", + "plt.title('Changement de repère de la souris avec en vert affichage du repère ABC exprimé dans la base de départ (noire)');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercice -- Et l'inverse ?\n", + "\n", + "À quoi ressemble la souris du repère de départ vue depuis le repère d'arrivée ?" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 476, + "width": 698 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "pmouse = lin.inv(P) @ to3D(mouse)\n", + "\n", + "arrow2D(O+ε,I+ε, 'k')\n", + "arrow2D(O+ε,J+ε, 'k')\n", + "arrow2D(O,I, 'r')\n", + "arrow2D(O,J, 'r')\n", + "arrow2D(A,B, 'g')\n", + "arrow2D(A,C, 'g')\n", + "\n", + "plt.plot(mouse[0,:], mouse[1,:], 'k')\n", + "plt.plot(pmouse[0,:], pmouse[1,:], 'r')\n", + "plt.axis(\"equal\")\n", + "plt.title('Changement de repère de la souris avec en vert affichage du repère ABC exprimé dans la base de départ (noire)');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Une application linéaire transposée dans le nouveau repère\n", + "\n", + "Combinons les deux usages qu'on a vu de la multiplication matricielle.\n", + "\n", + "Choisissons une rotation comme exemple d'application linéaire. Elle prendre un point et le fait tourner dans le sens trigonométrique de θ autour de (0,0).\n", + "\n", + "Que fait cette rotation dans notre nouveau repère ?\n", + "\n", + "Pour le voir \n", + "\n", + "* on fait tourner point (1,0) autour du centre du repère de départ (le cercle noir),\n", + "* on déforme le cercle avec l'inverse de la matrice de passage P (la forme rouge) \n", + "* on applique plusieurs fois la rotation du depuis le repère d'arrivée au point $I$ vu depuis le repère d'arrivée (la forme violette pointillée)\n", + "\n", + "La rotation dans le repère de départ est $R_{(d)}$.\n", + "L'application qui correspond à cette rotation vue du repère d'arrivée est $Q_{(a)}$ : \n", + "\n", + "$$Q_{(a)} = P^{-1} \\, R_{(d)} \\, P$$\n", + "\n", + "En effet (de droite à gauche), \n", + "\n", + "* $P$ permet d'exprimer un point du repère d'arrivée dans le repère de départ,\n", + "* ce qui permet d'y effectuer la rotation $R_{(d)}$\n", + "* puis on repart dans le nouveau repère avec $P^{-1}$.\n", + "\n", + "On espère que la *rotation* $Q_{(a)}$ du point $I$ vu depuis le repère d'arrivé va donner la même chose que le changement de repère du cercle noir." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "def Rot(θ):\n", + " return np.array([[np.cos(θ), -np.sin(θ)], [np.sin(θ), np.cos(θ)]])\n", + "\n", + "def Rot3D(θ):\n", + " return np.array([[np.cos(θ), -np.sin(θ), 0], [np.sin(θ), np.cos(θ), 0], [0, 0, 1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1.145, -0.546, -0.157],\n", + " [ 0.84 , 0.473, 1.348],\n", + " [ 0. , 0. , 1. ]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 462, + "width": 707 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# plusieurs rotation qui donnent le cercle bleu :\n", + "cercle = np.array([Rot(α) @ I for α in np.linspace(0, 2*np.pi, 10)]).T\n", + "\n", + "# le cercle exprimé dans le nouveau repère (noir)\n", + "p_cercle = lin.inv(P) @ to3D(cercle)\n", + "\n", + "# construction de Q\n", + "Q = lambda θ: lin.inv(P) @ Rot3D(θ) @ P # définition de Q en fonction de θ (c'est une fonction)\n", + "display(Q(2*np.pi/10))\n", + "# calcul de inv(P) @ I puis on applique Q pour faire tourner B autour de A (orange)\n", + "Ia = lin.inv(P) @ to3D(I)\n", + "p_rot_A = np.array([Q(α) @ Ia for α in np.linspace(0, 2*np.pi, 10)]).T \n", + "\n", + "# on affiche les repères\n", + "ε = 0.01\n", + "arrow2D(O+ε,I+ε, 'k')\n", + "arrow2D(O+ε,J+ε, 'k')\n", + "arrow2D(O,I, 'r')\n", + "arrow2D(O,J, 'r')\n", + "plt.annotate(r\"$I$\", I+δx , size=20, color='black')\n", + "plt.annotate(r\"$I_{(a)}$\", Ia[:2]+δx , size=20, color='purple')\n", + "\n", + "# et voici nos rotations\n", + "plt.plot(cercle[0,:], cercle[1,:], 'o-k', \n", + " label=\"cercle dans le repère de départ\") \n", + "plt.plot(p_cercle[0,:], p_cercle[1,:], 'o-r', lw=2, \n", + " label=\"même cercle vu depuis le repère d'arrivée\")\n", + "plt.plot(p_rot_A[0,:], p_rot_A[1,:], 'o:', lw=3, color='purple', \n", + " label=r\"point $I_{(a)}$ transformé plusieurs fois par $Q_{(a)}$\")\n", + "plt.legend(fontsize=14)\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma24 Vectors propres.ipynb b/PVCM/cama/fr/ma24 Vectors propres.ipynb new file mode 100644 index 0000000..fb29cb8 --- /dev/null +++ b/PVCM/cama/fr/ma24 Vectors propres.ipynb @@ -0,0 +1,807 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# $A^n \\textbf{x}$\n", + "\n", + "Soit A une matrice qui représente une application linéraire quelconque. Que se passe-t-il si on l'applique $n$ fois ?" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def arrow2D(a,b, color='k', **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 300, + "width": 606 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "mouse = np.load('data/mouse.npy')\n", + "\n", + "plt.plot(mouse[0], mouse[1], ':ob')\n", + "plt.plot([0,mouse[0][0]], [0,mouse[1][0]], 'r') # le point 0\n", + "plt.plot([0,mouse[0][3]], [0,mouse[1][3]], 'g') # le point 3 pour voir comment ils évoluent\n", + "plt.axis(\"equal\");" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.707, 0.966, 0.966, 0.707, 0.259, -0.259, -0.707, -1.061, -1.414, -1.061, -0.707, -0. , 0.707],\n", + " [-0.707, -0.259, 0.259, 0.707, 0.966, 0.966, 0.707, 0.354, 0. , -0.354, -0.707, -0.707, -0.707]])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mouse" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[3, 1],\n", + " [0, 2]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# on prend une matrice de transformation au hasard (donc probablement pas orthoganale)\n", + "A = np.array([[3,1], [0,2]])\n", + "A" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1.414, 2.639, 3.157, 2.828, 1.742, 0.189, -1.414, -2.828, -4.243, -3.536, -2.828, -0.707, 1.414],\n", + " [-1.414, -0.518, 0.518, 1.414, 1.932, 1.932, 1.414, 0.707, 0. , -0.707, -1.414, -1.414, -1.414]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "as1 = np.dot(A, mouse) # autre facon d'écrire le produit matrice vecteur\n", + "as1" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 599 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(as1[0], as1[1], ':ob')\n", + "plt.plot([0,as1[0][0]], [0,as1[1][0]], 'r')\n", + "plt.plot([0,as1[0][3]], [0,as1[1][3]], 'g')\n", + "plt.title(\"Transformation de la souris par A\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On constate que la transformation n'est pas une isométrie donc que la matrice n'est pas orthogonale.\n", + "\n", + "Appliquons plusieurs fois de suite la transformation pour voir." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAABKgAAAJ8CAYAAADaopkmAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAABYlAAAWJQFJUiTwAAChWElEQVR4nOzdd3hTZf/H8U9LB5QCZc+yFEoZshQQUFkCKiiIIPCwRFDBiT7+BH0UfRQVlQcVEBAQRPYQUJCh7FH2kiGyKXsWWlo68/vj2LRpk9KR5HS8X9eVC5qcnHxPc5o2n9z39/awWCwWAQAAAAAAACbxNLsAAAAAAAAA5G0EVAAAAAAAADAVARUAAAAAAABMRUAFAAAAAAAAUxFQAQAAAAAAwFQEVAAAAAAAADAVARUAAAAAAABMRUAFAAAAAAAAUxFQAQAAAAAAwFQEVAAAAAAAADAVARUAAAAAAABMRUAFAAAAAAAAUxFQAQAAAAAAwFQEVADgAhEREfr000/VqlUr1a5dW3Xr1tWQIUPMLitX2bZtm4KCghQUFKShQ4eaXY5b9e7d23rsZ8+eNa2OxBpatWplWg15WatWrazPQXYQFxen559/XkFBQXrooYd0+fJls0vKNbLysxYfH69+/fopKChILVq04HkBAGRbXmYXACB72LZtm/r06ZPl/ZQvX15r1qxxQkU526BBg7R9+3br17Gxsbp69aqJFQGAa3366afatGmTvL29NW7cOJUqVcrskiApX758+vrrr9WlSxedPXtWgwYN0qxZs+Tr62t2aTnKV199pUmTJlm/njZtmh588EETK5KOHz+uxx9/3Pr1k08+qS+//DJd942JidFPP/2kn3/+WWfOnJGXl5eCgoLUvXt3derUyUUVmycrz9/q1as1c+ZM/f333woLC1PRokXVuHFjvfzyy6pSpYqrSgbyJAIqAHCyY8eOWcMpf39/ffXVV6pbt64SEhJMrizn+e677xQfH69XX3011W3333+/du/eLUny9vZ2d2mA6ZYtW5ZtXldWrVqlmTNnSpJee+013XfffSZXlLskvtZ5emZu8kNAQIBGjhyp3r1768CBAxo1apTeffddZ5aYq8XExGjhwoU2182dO9f0gGr27Nk2X69cuVL/+c9/VKRIkTTvFxMTo969e2vv3r0qUaKEmjVrprCwMO3Zs0d79uzRxYsX9dJLL7mydIciIiI0depUFSpUSP369XPKPrPy/H3//fcaNWqUPDw8VL9+fdWuXVsHDx7Ur7/+qnXr1unnn39WxYoVnVInAAIqAP9I/mbfntdff10bN26UZPyyvv/+++1ul9k/nnOT06dPW//fvn17tWzZ0sRqcq5jx47pm2++kSS7AVW+fPlUsGBBd5cFZBsFChQwuwRJ0vXr1/X+++9LkmrVqqXnn3/e5IpyH2e81t1///3q2bOnZsyYoenTp+vRRx/VAw884ITqcr+VK1fq+vXrkqQGDRpo9+7d+uOPP3Tt2jUVL17clJqioqK0ZMkSm5qio6O1aNGiuwY7EyZM0N69e9W0aVNNmDDBOppu7ty5+uCDDzRx4kT1799fPj4+rj6MVHbt2qWxY8eqfPnyTguoMvv8Xbx4UV9//bU8PT01bdo0NW7cWJIReHXv3l0HDx7UnDlz9H//939OqRMAPagA/CPxzb6jS758+azb5s+f3+F22eUNk5lu3bpl/T9TXDJvx44dZpcAIB2++eYbhYWFSZKGDh1q8/sC2csrr7yiwoULy2Kx6JNPPsk2I/Cyuzlz5kiSKlSooH//+9+SjKn7KUfluNOyZcusf28MGTJElStXliTNmzfvrveNjIxUixYt9MYbb9hM9ezQoYP19mvXrjm/6HRwxe/+zD5/Hh4eev/99/XBBx9YwylJ8vHxUZMmTSRJ0dHRTq8XyMsIqADAySwWi/X/jCjLvJ07d5pdAoC7OHv2rObPny9Jaty4sRo1amRyRUhL0aJF1bdvX0nSX3/9pWXLlplcUfZ39OhR6++jJ554Qg0aNFC5cuUkSfPnz7f5ne9OidP7Spcurfvvv1+PPfaYJKMv1d1CnqFDh2rixImqW7euzfXnzp2TZIzYM2tkmLN/92fl+StdurR69OihHj162Fx//vx5rVq1SpL06KOPOrVeIK9jih8Al/j55581bNgwSdK4cePUuHFjjRkzRsuWLVNYWJhef/11vfDCCzb3iYiI0Pz587V+/XodO3ZMt27dUkJCggICAlSjRg21a9dOnTp1cthvqFWrVjp37pxq1KihJUuWKDo6WgsXLtSiRYt07NgxxcTEqEiRIqpVq5aeffZZtWnTxmH958+f19y5cxUSEqLTp08rIiJC+fLlU/HixRUUFKRHH31UHTt2tBn+3rt3b5vG6JI0duxYjR07VpLUqFEj/fTTTza337x5U3PmzNGmTZt04sQJ3bx5U76+vipRooQaNGigjh07qmnTpnZrTN7YftiwYerZs6e+//57LViwQFeuXFHXrl314YcfSjL+GF20aJEkKSQkRIULF9bChQs1d+5cHT9+XJ6enipTpozatm2r5557TgEBAZKMqTs//vijVq9ebf3DtUqVKnryySfVu3fvNEdKhIaGau7cudq+fbv1e+jt7a0SJUrovvvu09NPP63mzZunup+972PyVcpWr16tChUq2Bx/586d9fnnn9utw5nf4379+unMmTOaPn261q5dq0uXLilfvnwqXbq0HnzwQT3//PNZ7kURFhamKVOmaO3atTp37pw8PDxUunRpPfzww+rdu7cqVKiQ7n3t379fCxYs0K5du3ThwgXFxcWpWLFiqlatmtq1a6ennnrK5f27rly5onnz5mnz5s06efKkwsPD5enpqWLFiqlmzZrq2LGj2rdvLw8Pjyw9zrFjxzRv3jzt3LlToaGhun37try9vVWyZEnVrFlTjz/+uNq2bZtmaHzp0iXNmjVLISEhCg0NVXh4uPz8/FSqVCk1bNhQzzzzjOrUqWP3vslf81555RW701ITJT/HE8/nRGPGjLG+ZixevFjFixfX6NGjtWbNGkVEROiLL77QE088ISnpNU+Sjhw5kupxIiMjtWDBAq1du1ZHjx7VzZs3ZbFYVLhwYVWpUkUPPfSQunXrpmLFiqX1rU3Tjz/+qPj4eElK10IbN27c0Lx587Rx40YdO3ZMERER8vf3V7ly5fTwww+rW7du1jePKaX83gQHB2vHjh366aeftGvXLoWFhcnX11eVKlVS69at1a9fP/n7+2fquBKfo0KFCmnnzp2Kj4/X0qVLtWDBAh0+fFhRUVHy9/dX9erV1alTJz399NNpnsNxcXFasmSJVq9erUOHDunGjRvy8PBQQECAatWqpVatWumpp56Sl5f9P80TXwPtLUSS8nffpk2bNGbMGB0+fFienp7au3evzfbPPvusJkyYoNjYWE2dOlUdO3bM1Pco+e+VlStXqlKlSlqwYIGWLFmiEydO6NatW9bj69atm1q3bp3m/rL6WpH4PWrdurW+++47LV26VBMnTtTJkydVqVKlTIdxiaNvJOmpp56Sh4eHOnfurHHjxunMmTPasmWLmjVrlql9Z9aBAwd04MABSVLHjh3l6empLl26aMKECbJYLJozZ06Gp2/GxMTo448/liQNGDAg09P7YmJitHTpUv3+++86ePCgrl+/rvz586tEiRJq3LixOnfurHr16qW6X/LXM8kIy5L/7rf3Gpceznr+IiMjNWTIEN26dUt//vmnSpUqpZEjR1pHUgFwDgIqAG4xZMgQaw8rKfWQ6P3792vw4MG6cuVKqvteuXJFV65c0caNGzVr1ixNnjz5rp/sXb9+XS+++KL2799vc/21a9e0YcMGbdiwQYMHD9brr7+e6r6//fabhg4dmqrGuLg4nT9/XufPn9fatWs1bdo0TZkyJdPT+FavXq3/+7//U0REhM31sbGxioiI0KlTp/Tzzz+rVatWGjVqlPz8/NLc34gRI2z+ELtz547d7WJjY/XKK69o7dq1NtefOHFCEyZM0Lp16zRz5kxdunRJzz//vC5cuGCz3cGDB3Xw4EH99ddfDkOhefPm6eOPP1ZMTIzN9XFxcQoNDVVoaKiWLVump556Sp999pnLpgQ5+3u8bt06DRkyRJGRkTb7On36tE6fPq1ly5Zp+vTpqlmzZqbqPXbsmPr27ZtqxccTJ07oxIkT+vnnn61v0NOS+EbD3lSPCxcu6MKFC9qwYYOmTZumsWPHWqeGONuaNWv09ttvp/r+J69j9erVatasmcaNG5fpKcJTp07Vl19+aQ1KEsXHx1vPt5UrV6pRo0aaMGGC3X4+c+bM0YgRI1Kdszdv3tTNmzd19OhRzZkzR88++6yGDx/ulmlsMTExeuGFF3T48GHrdemdTvL3339r4MCBunjxYqrbrl27pmvXrmnnzp2aOnWqxowZk6mRT3Fxcfrll18kGU24W7Rokeb2f/zxh955551U58ONGzd048YNHTx4UNOmTdO7776rbt263fXxkwdWyWs6dOiQDh06pBUrVmjOnDmZDqkSRUVF6fXXX9f69ettrg8LC9P27dutl5EjR9q9/8mTJzVo0CCdPHnS7r4vXLigP/74Q5MmTdLEiRNVqVKlTNe6c+dOvfjii4qLi3O4TcmSJdW8eXOtXbtWBw8e1JEjR2yCgMy4efOmXnrpJa1bt87m+itXrmjdunVat26dnn32Wf33v/+1e39nv1b89ttveuutt6xfR0VFZfygZIQSiX2e6tevr3vuuUeS1KVLF40fP14JCQmaO3eu2wOq5M3Ru3TpIkkKDAxUkyZNFBISolWrVunGjRsqWrRouvZ35coVDRkyRDt27FDLli0z3SD9+PHjevnll1Od67GxsQoPD9fJkyc1d+5cdevWzS2vo858/uLi4qznt4eHh0qVKuUwUAaQecw9AeByGzZs0ObNm/Xqq69q7dq12rp1q/71r39Zbw8LC9NLL71kDaeeeeYZ66eoISEhmjZtmrUp+6FDh2z+6LTHYrHo3//+t06cOKG33npLK1as0Pbt27V8+XINGjTI+unr+PHjdfz4cZv7njlzRu+8846io6NVqFAhDRs2TMuWLVNISIjWr1+vH374Qe3bt5dkvAF8++23rfedNGmSdu/erY8++sh63Ysvvqjdu3dr9+7dNssbb9++Xa+88op1VNFLL72kxYsXa9u2bdqwYYPGjh1rDTnWrFmjN998M81jPnHihObOnatevXpp5cqV2r59u8Pv04QJE7R161a9/fbbWr16tbZt26Zp06apWrVqkoxpHzNmzNBrr70mHx8fffPNN9qyZYs2bdqkL774wvpmb9GiRakCQMl4g/TBBx8oJiZGPj4+evPNN7Vs2TJt3bpVGzZs0KhRo1S2bFlJ0pIlSzRx4kSb+yd+H5OPokj8Hu7evVvly5dP83vhqu/xqVOn9MYbb6hKlSoaN26cNm3apK1bt2rGjBnWT6rDw8Ntnv+MiImJ0aBBg6zhVMuWLTV79mxt3bpV69at06hRo1S8eHG99dZb1n4/jvznP/+xhlNBQUEaPXq0Vq1apa1bt2revHnWN/9Hjx5Vv379rM1jnen06dMaMmSIIiIi5OHhoQEDBmjx4sUKCQnRpk2b9N1336l69eqSpM2bN+uTTz7J1OPs3LlTn3/+ueLj41WmTBl9/PHHWrFihbZt26Y1a9bou+++s67UtH37druPs3jxYg0fPlwxMTHy9/fXW2+9pWXLlmn79u1as2aNvvjiC+vIuLlz5+rTTz/N5HclYxYuXKiTJ0/qgw8+0MaNG7Vly5Y0R34mSlz58uLFi/Lw8FC/fv00f/586z7mz5+vgQMHysvLS2FhYXr11Vdteuel144dO6znYqtWrdJ8s7Z582a99tprioiIkJ+fn15//XUtWrRIW7du1cqVK/X++++rePHiioqK0gcffHDX0S6//PKLxo4dq/bt22vmzJnaunWrNm7cqG+++cb6+nL06NFUry+Z8cknn2jLli168cUX9csvv2j79u36448/NGzYMOsok8WLF9t8CJPo+vXr6t27t/UN+2OPPaYZM2Zoy5YtCgkJ0cyZM9WuXTtJRpDVp0+fTD0Xib788ktVq1ZN06dP17Zt27R69Wq72yWflrRixYpMP16ib7/9VuvWrVPPnj21cOFC62O/99571uB/7ty5mjFjRqr7Ovu1Ij4+XiNHjtSDDz6o+fPna/v27dYVJjNq2bJlCg8Pl2T8bZKofPny1lBj9erVdj9cc5Xw8HD99ttvkozG91WrVrXelvjaHhMTYx3ddjdbtmxRp06dtGPHDvXo0UNjx47NVHuCS5cuqW/fvtZzvUuXLpo5c6Y2b96sDRs26JtvvlFwcLAsFovmzp2bKqxctmyZzWI95cqVs/ndnxnOfP4KFy6sI0eOaNeuXfrhhx907do1vfXWW5o2bVqmagPggAUA0uGFF16wVK9e3VK9enXL1q1b77r9woULrdvXqVPHMmbMGIfbTp482brt22+/bXebqKgoS8uWLa3bHTp0KNU2ibcHBQVZateubfnzzz/t7uvdd9+17mfcuHE2t3333XfW25YuXeqw5vfee8+63d9//+3w2L/99ttU942Pj7e0adPGus2qVavsPsbt27ctHTp0sG73+++/29y+detWm+/x0KFDHdb7zjvvWLetUaOGZf369am2+euvv6zbBAUFWZo2bWq5evVqqu2mT59u3W706NGpbk9+rsyfP99uPX///bclKCjIUr16dUujRo0scXFxqbZJ/nzbk/z433nnHZvbXPE9DgoKsvTs2dNy586dVPsJDw+3PPDAA9ZtL1y4YPfx0jJr1izr/fv06WOJj49Ptc2NGzcsrVu3tm5XvXp1S2hoqM02a9eutd7Wo0cPu/VaLBbL1KlTrdu9//77Ga7XYrFY79+yZctUt3300UfW27/++mu797969aqlfv361vPy+vXrGa4h+c/inj177G4THx9v6d+/v6V69eqWmjVrWm7evGm9LTw83NKwYUPrbfv27bO7jytXrliaNm1qPRdSvgbd7ec+uV69ejl8/r799lubn+tFixY53I+jn5GdO3em67ldsmSJdbsZM2akWbM9//vf/6z3T6vO6Ohoy0MPPWSpXr265b777nP4PT5z5ozl/vvvt1SvXt3SpEkTS3h4uM3tyb83QUFBls8//9zufnbs2GHdrk2bNhk+Losl6TkKCgqyBAUFWdasWWN3u3Hjxlkf69133011+9ChQ623f/zxxw4fL/l2I0aMSHV7Wj9riedBnTp1LE2aNLFcu3btrsd35swZm9eJzEj+e6V69eqW7777zu52GzdutG7z4IMPWmJiYmxud9ZrRfKfm/bt21uio6MzdVzJde7c2VK9enVL/fr1Lbdv37a5beXKldbHHD9+fJYfK72S/w5O+XMXHR1tady4saV69eqWtm3b3nVf3377rSUoKMjSoEEDy6+//pqlul599dW7vp7cuXPH8swzz1i327VrV6pt0jrXM8qVz1/i3wctWrTIcp0AkjCCCoDLJX6C70jhwoX12GOPqVGjRurevbvdbfLnz29tACpJe/bscbg/i8WiXr16qXbt2nZvb9u2rfX/f//9t81tyaezJX5ia8+bb76pmTNnat26ddYh4+m1ceNGnTlzRpLUvHlzhw02E0cZJFqwYIHDfUZHR2vQoEHpevymTZvq4YcfTnV9UFCQSpcuLcn4Hj733HN2p1Imv++JEydS3V61alU9+uij1v5O9lSrVs3ayycsLEynTp1KV+3p5YrvscVi0fDhw21WPErk7+9vHaUjZa5XRuIn4pLRw8jeJ9gBAQF65ZVX0tzPlClTJBk/d5988ondeiWjX1Di1L4lS5bYTFt0hjJlyqhdu3Zq2LChdQpKSsWLF7eeTwkJCXZH5N1Nen5mPT099cknn2ju3Llas2aNChUqZL3tl19+sX7C3qVLF913331291GiRAlr3zyLxZLmueIsxYsX15NPPpnh+yX/nqQ1datDhw768ccftXLlSnXt2jXDj5P8+UrZbDm5pUuX6tKlS5Kkvn37OvweBwYGqn///pKMkUcrV650uM+SJUs6HPV4//33W/tqnTlzJtPTuyTjuW7btq1atmxp9/a0fp/cvHnTOhKscOHCaY7+ffvtt60j0JYsWaLY2NgM1xodHa1nn302XT3FAgMDrdsdPHgwzSmB6VGqVCkNHDjQ7m3NmzdX/fr1JRnTS3ft2mVzu7NfK6Kjo9W/f/9M91BKtH//fh08eFCS8bOScgp4y5YtVaJECUnGtHZ3rYg4d+5cScY5lTiiO5GPj486deokyRj1u3XrVrv7sFgsevfddzV27FhVqlRJ8+fPt67glxmhoaHWpuH169e3GSWfnK+vr4YOHZrqWFzBGc/fmjVrNGzYMLsj/xKnmZq12iGQWxFQAXC5unXrptkDpGvXrvr666/1008/qUGDBg63CwwMtP7/xo0baT5m8jArpeRTxFJOpUj8Y0WSZs2a5XB1l2LFiun+++9X2bJlMzwUPiQkxPr/lH9cpvTwww9bm1jv2LHDYT0VKlRId3PutPrElClTxuax77ZN4hv75N555x2NHTtWs2fPdhiOSBl7PjPKFd/je++9N83QMq3z6m4SEhK0b98+ScbqSWn9HLRp08bhORcREWGdChEcHGwz9SMlT09Pa3B3584dpy/t/cILL+jbb7/VrFmz0mzsntXzIPnPbFrTeMqWLat69eqpdOnSNk2Wk58rab1uSLJp8pyykb8rNGnSJFNTbZJ/TxYvXmy3r49knANNmjRR5cqVM/VmPnEqj5eXV5qvPxs2bLD+//HHH09zn8kDn+T3S6lNmzZpNvjPys9jSpn9fbJr1y5rz7AWLVqk2TepWLFi1p/7sLCwVGFXemWkF1Li68OdO3dS9RrMqDZt2qQ5xTP5ghgpwyVXvFY4oydU8j5P9nqieXt7q3PnzpKMht6bNm3K8mPezY4dO3T06FFJ0pNPPqn8+fOn2iZ52OwoAPr++++1cOFCVahQQbNnz07zd0V6bNy40fq7824/4w0bNlTJkiUlpf0znlXOeP5iY2P1888/a8yYMTp9+rT1eovFop9//llS2h8CAMg4AioALudoRaaMSv4G6m6fVKY1qin5H3QpP6VOvjLfrFmz9NRTT2nq1KmpelVlRfKGx3f7w8bHx8c6yiUiIkLnz5+3u11GvsdpvZFMHiglfzPgaJusfOqe/PlM2dw6q1zxPb7bSLnkbz4zOvrh3Llz1jeyFStWTLNxbOKKZ/b89ddf1uekTJkyun37dpqXKlWqWO+b2TfEWZWRn2t7unTpYg2cvvrqK/Xo0UNz5sxRaGhouu6fkXOlQoUK1k/hT5w44fTzNqXMvnbef//91nN6//79at++vb788kvt2bMnUyNz7ImLi9Ply5clGUuxp3XOJo5ikIwgJq1zsnTp0tZzIvGNuD2u/HnMyGOl9TgZObckWfsASpn/eUzsv5UeycM1R6976XW3hSGSN34/e/Zsph4jva8ViavSZsWtW7e0fPlyScaxORqR3bVrV+vrjytHAyVKvhCKo1GP99xzjxo2bChJ+v333+32GBw/frwk4+f45ZdfVo8ePVJdUi6kkpbkP+MlSpS46++exJ+p69evu2QEkrOevzZt2qhx48YKCwvTE088of79+2vIkCHq0KGDZs+eLW9v77v2rwSQMSw9AMDl0ruE+caNG7Vy5UodPnzYuspUyhW10sveKl3pUaVKFY0ePVpvv/22IiMjdeTIEX3++ef6/PPPVaxYMTVt2lStWrVSixYtMv0YyT/5vdtqhJJsVuEJCwuz2yQ8I8vE2/vE1Z7MrqgmGVMsli1bpvXr1+vkyZO6fv26rl+/7vI39Ilc8T2+2wp/WZG86XmRIkXuun3RokXtvslLftxr1qxJcyRWSolhgzPFx8fr999/1+rVq3Xs2DFdvXpVN27ccFpIIkmNGjXSBx98oE8//VSxsbE2DXXLli2rpk2bqnXr1nrooYfsjhJK/J55enqma8WrokWLKjIyUnFxcQoPD1dAQIDTjiWljPxcJ+fl5aXx48frpZde0unTp3XlyhVNnjxZkydPVoECBXT//ffrkUceUdu2ba3TejMqIiLC+vN8t3M2+Rvkhx56KN2PkdY56cqfR2c9VlZfhzIjPY+TKPnzltVRZnc7V+/2WM58rQgICMjUyMPkFi1aZJ0amry5dkqVKlVSo0aNtG3bNq1bt06XL1/O9Mq+d5N82mudOnVUo0YNh9t269ZNu3btso4AGjBggM3ticd28eJFuyt9Skq1muzdaks0ZMiQdN9PMn7OM3Lepoeznr98+fJp8uTJmjlzppYuXao9e/YoOjpaRYsWVdu2bTVw4ECHU5YBZA4BFQCXu1vQcePGDb3xxhsOeyW4W5s2bbRmzRrNnDlTP//8s86dOyfJ+ANs6dKlWrp0qQoVKqTnnntOgwYNyvAfwsn7oaQnLEo+YunOnTt2t8lKmORsBw8e1GuvvZbpT8mdwRXfY1dKHD0lKV1TrRxtk5U+Urdv3870fe0JDQ3Vq6++ajOKxFV69uypVq1aaerUqVq2bJl1RaYLFy5o4cKFWrhwoUqWLKnBgwerZ8+eNvdNPFd8fHxspv45kvxcSf68uUJWfq6rVq2qZcuWacmSJZo9e7YOHjwoi8WiqKgobdy4URs3btRnn32mjh07atiwYRkO2pIf+91+xjLbA8rZ56S7JT/utKY729sms69DGTlnkgdvWenTlXJf9iSfjpnygydnv1Y44/dh8pFK//3vf1OtOGdPXFycFixYoMGDB2f58e1ZsGCBNbD7888/0z21bN68eXr++edtXt8y0ycxLVk5f1zxc+7M58/Hx0fPPfecnnvuOafXCSA1AioApnv99de1bds2SUbj227duumhhx5S6dKlVbhwYesfVb/++quGDx/ulpqKFi2qV155Ra+88oqOHz+ujRs3KiQkRNu3b1dkZKTCw8P17bff6vjx4/rf//6XoX1n9E1B8jcqmR215S7Xr1/XCy+8YP3kNTg4WE8//bQaN26sgIAAm15kw4cP16+//uqSOnLa9zh54JSeEQOO3rwmr71bt276+OOPs15cJsTExOiFF16wNtGvWLGiunbtqmbNmql48eLy9/e3/lxPnDhREydOzPJjlilTRsOGDdPQoUN16NAhbdq0SSEhIdq5c6diY2N15coVffTRR7pw4YJNs2o/Pz+Fh4crOjpaFovlriFV8u+9O0fxZIa3t7eeeeYZPfPMM7py5Yo2bdqkzZs3KyQkRFevXlV8fLwWL16svXv3auHChWn2CsyKggUL6tatW/L29taBAwdc8hjZUfLzIz2BU046t1K622jn5K9ryQNNM14r7mbbtm12FwBJjwULFuill17K8giulBISEjI9hfD06dPaunWrzUIezpb8d8/s2bMzNHrX2bLj8wcg/QioAJhqz5491nCqWLFiWrhwocMpJ+kZ3eAK99xzj+655x7169dP0dHR+uWXXzRy5EiFh4dr2bJl6tKlS4YasiafCnHt2rU0m8JKtkPn0zMFyUzz58+3hlONGjXS1KlTHTbOddSM3Bly2vc4+apyN2/evOv2jqY+JW+ObebKQqtWrbK+Qahatarmz5/vsvAjJQ8PD9WqVUu1atXSiy++qIiICM2ZM0dff/21YmNjNWXKFHXq1MnaA6VYsWIKDw+XxWLRtWvXbL6HKVksFuvUK29v70wfkxkjg0qWLKnOnTurc+fOslgs2rJli0aMGKHjx4/r1KlTmjRpUoam5mRktE/x4sV169YtxcbG6tatWypcuHCmjyMnSf46lJ7pUslfhzI7vTMjko+4zOqoo7s1LU9+bMlH65n5WuFI8uba77//vt0p3yktXrxYK1as0Llz57Rx40Y98sgjTq1p48aN1lHJbdq0SXPaWqJLly5ZP9SbM2eOSwOq5FP07PW8cqfs+PwBSD8CKgCmSt5Ys0OHDmn2Qzl06JA7SkqTr6+vunbtKj8/P2tjzPXr12cooKpZs6a2bNkiyTimtJZnv3PnjnXlmOLFi2e6X4y7JH8++/btm+aqTq58PnPa97hChQry9vZWbGyszpw5o4SEBIef4F67ds06hS2loKAgeXl5KS4uztSfl+TnwbPPPpvmG05X1+nv768BAwYoISFBo0aNUnx8vDZt2mQNqGrWrGl9/g8dOuRw9UpJOnPmjPVNfY0aNWxC8+TnelpT/+Lj43Xq1KmsHFKWeXh4qFmzZvrhhx/UunVrxcXFaf369RkKqPz9/ZUvXz7Fx8ffNVStVauWdcW/gwcPuvSNcnaSvHF4eqavJZ92FRwc7JKakkveCyqroeHdmronXwEt+UId2em1QjKCxD/++EOSVLlyZfXq1Std9ytevLhWrFghyQiDnB1wJJ+y1r9/f2sT9LuZMWOGjh49qtWrV+vq1atpBvBZUatWLev/Dxw4oDZt2rjkce4muz5/ANKP8YsATJV8JEFajXYvX75sMx0sM6t93U1kZKTWr1+vCRMmpFoGO6XkzUkz2sQ1+XLbiX8QObJmzRrrqmxNmzbN0OOYIb3P59q1a22G4N/t+czoaKuc9j329va2nlMRERH6888/HW6b1vEUKFBADzzwgCSj/9Ld+rqFhIRo8eLFDgOvzEp+HqTV2+ivv/7S5s2brV9n9Oc6LCxMf/zxh8aMGXPXVfsc/cwmD5fvdq4kNihOeT/J9ny/cOGCw31s2rTJ5SOoduzYoenTp2vZsmVpblemTBnr85PR1zEvLy9rM+FLly6luQBC8tBv8eLFae43IiJC33//vbVnVk7WsGFD61S99evXp9kj7tKlS9q7d68ko7l/1apVXV5f8j6BWV1td/Xq1Wk+X8l/zpNP/3LXa0V6Je/z1Llz53Tf77777rOuwrh+/XpdunTJaTVduHBB69evl2SELukNpySpU6dOkmRtlu4qDz30kPVDlWXLlt11hd8ff/xRW7ZsSXNqaGZ+/rPj8wcgYwioAJgq+ZLYe/bssbvNjRs39PLLL9v0OHDF9KXIyEgNGjRIo0eP1meffZbmKIjEaYlS+pYPT+7BBx9U9erVJUlbt261ftqXUnh4uL755hvr1+n9JNBM6Xk+Dx06pGHDhtmslGNvSkDyPiUZ/WMxJ36P27VrZ/1/4hLgKV25csXhbYn69Olj/f8nn3zicHWu8+fPa9iwYXrnnXfUuXPnTK+YaU/y8yBxRb2UQkND9dprr9l8op/RqSGhoaF6+eWXNXbsWH311Vdpvml19DPbsWNH63SqJUuWOAwHL168qClTpkgyAsVnn33W5vbEEVmS8WbcXhgRHh6uL774wuXTlT/66CONGDFCH330kc6fP+9wu6NHj1pfSzP6OiYZq55KRnPhtALCxx57TCVLlpQk/fLLL9q4caPd7RISEjRixAiNGjVKTz/9tNasWZPhmrITf39/65vk27dva/To0Xa3s1gs+vzzz63nb8+ePd3SAydxVFv+/PltfmYz49SpUzajfJJbv3699u3bJ0kqX768ateubb3NXa8V6ZGQkKB58+ZJMlb1TAx30itx+/j4eM2fP99pdc2bN88aAGckdJGkp556Svny5bPux1Whb7ly5ayjps6cOaMxY8Y43HbhwoX69NNP9dxzz2nUqFGpbk/83X/9+vUMBefZ9fkDkDEEVABM1bx5c2vvi02bNunTTz/V8ePHFRYWpqNHj2rKlCnq0KGDLly4oG+//dZ6v9WrV+vQoUNODapKlCihbt26STL+UO7Ro4cWLVpkrefq1av6888/NXr0aH3++eeSpNKlS6tDhw4ZfqwRI0ZYVzUaMmSIxowZo6NHj+rWrVs6f/68li1bpu7du1unAvXu3Vv16tVzynG60qOPPmr9//jx4zV79mydO3dO165d0549ezRixAg9++yzCg4O1iuvvGLdds6cObpw4YLN0urJ+0aNGDFC27dv15YtW3Ts2LF01ZLTvsc9evSwvgFbu3atXn/9de3fv19hYWE6f/68Fi9erO7duysuLi7NT9BbtWplPSePHj2qp59+WosWLdK5c+d048YNHTlyRJMmTVLXrl2tI33efvvtdK0emF5t2rSxhjDz58/XxIkTdebMGd24cUMHDx7UN998o06dOsnHx0cfffSR9X6LFy/WyZMn0/3ms06dOtbROStWrNBzzz2nFStW6NSpU7p586YuX76sXbt26b///a9++OEHScbUqeQj5fLnz29d4SkuLk79+/fXtGnTdOrUKd26dUtnzpzR/Pnz9eyzz1rPz7feeivViJMKFSpYlxu/ceOGBg8erD179igsLEyXL1/W8uXL1a1bN4WFhWXqNSMjElehunnzprp166bJkyfrr7/+0tWrV3Xjxg0dP35cM2bM0IABA2SxWJQvXz7169cvw4+TfHn1xNE/9vj4+OjTTz+Vp6enEhISNGjQIH355Zc6fPiwwsLCdObMGf3+++/q06ePdZTHgw8+qNatW2e4puzmjTfesJ4r06dP17///W/reXH16lWFhIToxRdf1G+//SbJmCrljtXCzp49a/39WbNmzTSnY6dHy5Yt9fHHH+uLL76wPq9nz57V9OnT9cYbb1i3e+2112zCN3e9VqTHhg0brKv2Nm3aVGXKlMnQ/ZOHQfPnz081qjAoKMh6Sa+4uDhrWJKZ0KVkyZLWEcWhoaE2o9Cc7T//+Y+1h+OECRP02muvadu2bbp27ZouXryo7du3a9iwYXrvvfestb344oup9pP4u//OnTsaMWKEdu7cafPcOOLq5w+Ae9CDCoCpihUrpnfffVcffPCBLBaLfvzxR/34448225QvX17jx49X9erVVa1aNR09elRXr161fpLozOWS3333XV2/fl0rV67UwYMHNXToUIfbli9fXt99912mGrred999mjBhgt58803dvHlTY8eO1dixY1Nt5+HhoT59+uidd97J8GOY4ZFHHtGTTz6pX375RZGRkfrwww9TbdOkSRN98803un37trXv0vbt29WiRQs1atRIP/30kyTpmWeesU5rWLVqlVatWiVJGjZsmO6999671pLTvsf+/v4aO3asBgwYoIiICK1YsSLVlDM/Pz99++23d/109/PPP5evr68WLlyo0NBQh+exr6+v3n77bT311FNOOw5Jqlatml566SWNHz9eCQkJ+t///pdqtcsaNWpowoQJKlKkiIoVK6br16/r+PHjat++vcqXL5/u0TNfffWVXn75Ze3YsUNbt25Nc1pjUFCQvvvuO+ubkESPPvqoRo4cqeHDh+vWrVv67LPP9Nlnn6W6v7e3t15//XWHAcLw4cPVp08f3b59WyEhIQoJCbG5PSAgQBMmTLCGEa7y+OOP69y5cxo9erSuXLmiL7/8Ul9++aXdbf38/PTRRx/ZhE3p1bhxY02YMEGSMUItrTfPDz/8sMaMGaN33nlHERERmjx5siZPnmx320ceeURfffVVhuvJjgoXLqzp06dr8ODB+vvvv/Xrr786XL20SZMm+vrrr63Buitt377d5nGzqm/fvvL29taUKVOsIw1T6t+/f6pzxJ2vFXeTfATY008/neH7J4ZB69ev18WLF7V+/Xq1atUqSzWtXr3aOgU7M6GLZIy6SvxdOnfuXJsp8M5UunRpzZw5U4MHD9apU6e0cuVKm2nRyVWuXFljx461uxjAM888Y/0QcPbs2dam5+PGjUuz4Xl2fP4AZBwBFQDTdevWTZUqVdK0adO0b98+3bx5Uz4+PqpSpYo6duyoLl26WBu4jh49Wh999JEOHjwoT09Pm8aczuDj46Nvv/1WISEh+vXXX/Xnn3/q/PnzioyMlLe3t4oXL66goCC1bt1aTz75pM1KVhnVvHlz/fHHH5ozZ442bNig48ePKzw83DrdolGjRurWrVumpt6Y6YsvvlCjRo20aNEi/f3334qMjFShQoVUs2ZNde3aVW3btpWXl5cKFy6s0aNH6+uvv9aZM2dUqFAhmxFMbdu21X//+1/9+OOPCg0Nlbe3t8qXL6/KlSunu5ac9j2uX7++fvvtN02ZMkUbNmzQxYsX5eHhoVKlSqlZs2bq06ePKleufNfeQt7e3vr000/VvXt3LViwQDt37tSlS5d0584d+fv7q3LlymratKm6du2a5d4zjrzxxhuqVauWZs2apUOHDik8PFx+fn6qVq2aOnfurCeffNI6lWPMmDHW0ZO+vr7WPlrpUaRIEU2fPl2rV6/WihUrdPDgQeux+vr6qmTJkgoODla7du3Uvn37VOFUok6dOqlp06aaOXOmtmzZojNnzigiIkL+/v4qX768mjRpoh49eigwMNBhLbVr19aiRYs0efJkhYSE6NKlS7JYLCpfvrzatGmj3r17q0yZMi4PqCRp4MCBat26tebPn6+dO3daj8fDw0OFCxfWPffco6ZNm6pLly42020zolGjRgoICFBYWJjWrFmj+Ph4h99fyRgts3r1as2ZM0cbN27UiRMndOvWLfn4+KhUqVKqV6+ennrqqRzRby8jAgMDtWjRIi1dutT64ceNGzfk5eWl4sWLq27duurYsaNatGjhtpp+//136//bt2+f5f15enpqzJgx+uWXX7RkyRIdOXJEYWFhCggIUO3atdWzZ0+HCxC467UiLefPn7eGOIULF850k++nn37aJgyyF3BkZPpm8hXpMhO6SFLr1q1tfk4vX76c6Z/5u7nnnnu0dOlS/fLLL/r999916NAh6wqPxYoVs74Wd+jQwWEQ26dPH925c0c///yzLly4oAIFCigwMDDNBUzc+fwBcC0PS07vQAkAAABTjBgxQtOnT5ckfffdd7liWl5ud+3aNbVo0UIxMTGqVatWpptnDx06VIsWLZJkTF9s3LixM8vMlQYPHqzt27dr586dZpcCANkSPagAAACQKX369LGOmkqcnovsbfbs2dZFEdzR7wpJDh06pIoVK5pdBgBkWwRUAAAAyJTAwEA988wzkqSQkBBGhmRzYWFh1hFvQUFBeuKJJ0yuKO8ICQnRhQsX1KxZM7NLAYBsi4AKAAAAmfbGG2+oSJEikowG/QkJCSZXBEfGjRunmzdvysPDQ++9916G+iEh8ywWi0aPHq38+fOrZ8+eZpcDANkWv5UAAACQacWKFdN///tfSdKff/7pcBU3mGvnzp2aMWOGJKlXr170jHIjDw8PzZs3T/v27VPZsmXNLgcAsi0CKgAAAGRJ+/btrSNDvvnmG+3fv9/kipBcWFiYhg4dqoSEBNWuXVtvv/222SUBAJAKARUAAACy7L333lPz5s0VGxurl19+WZcvXza7JEiKj4/XkCFDFBoaqjJlymj8+PHy9fU1uywAAFLxsFgsFrOLAAAAAAAAQN7FCCoAAAAAAACYioAKAAAAAAAApiKgAgAAAAAAgKm8zC7ADLt27TK7BAAAAAAAgFypYcOGGb4PI6gAAAAAAABgqjw5gipRZhK97Obw4cOSpODgYJMrQXbBOQF7OC+QEucE7OG8QEqcE7CH8wIpcU4gUVZmrDGCCgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKbyMruA48ePa8qUKdq6dasuX74sHx8fValSRe3bt1efPn3k6+trs310dLRmzJihZcuW6eTJk7JYLKpSpYo6dOigXr16pdoeAAAAAAAA2ZupAdXKlSv173//WzExMapRo4YefPBB3bx5U5s3b9ZXX32lFStWaPr06SpYsKAkKTIyUs8//7x2796tsmXLqn379pKkjRs36osvvtCaNWs0ZcoU5c+f38zDAgAAAAAAQAaYFlBdunRJQ4cOVUxMjN555x3179/fetv58+fVrVs3HThwQJMnT9brr78uSRo7dqx2796tRx55RGPGjLGOloqIiNCAAQO0c+dOfffdd3rzzTdNOSYAAAAAAABknGk9qBYvXqzIyEjVrVvXJpySpHLlyun555+XJK1atUqSMXpq9uzZ8vLy0kcffWQzlc/f31/Dhw+XJM2YMUN37txx01EAAAAAAAAgq0wbQdW8eXMVK1ZMFSpUsHt71apVJUkXL16UJG3atEmRkZFq0KCBypYtm2r74OBgBQYGKjQ0VJs3b1br1q1dVzwAAAAAAACcxrSAqlatWqpVq5bD2y9fvixJKlq0qCTp4MGD1vultc/Q0FAdOnSIgAoAAAAAACCHMG2KX1osFosWLFggSdZG6GfPnpUklSlTxuH9EkdWnTp1yrUFAgAAAAAAwGlMXcXPkUmTJmnv3r0KCAjQwIEDJRmN0CVZV/Szx8/PT5J0+/btdD3O4cOHs1ip+aKioiTljmOBc3BOwB7OC6TEOQF7OC+QEucE7OG8QEqcE3CGbDeC6ocfftD//vc/eXt765tvvlGRIkUkydr43Nvb2+F9fXx8bLYFAAAAAABA9pdtRlBZLBaNHDlSU6dOlY+Pj0aNGqUmTZpYby9QoIAkKTY21uE+YmJiJEn58+dP12MGBwdnoeLsITGhzg3HAufgnIA9nBdIiXMC9nBeICXOCdjDeYGUOCeQaNeuXZm+b7YIqKKjo/X2229r5cqVKly4sMaMGWMTTklJU/vSmr6XOA2wUKFCrisWAAAAAAAATmV6QBUTE6MXX3xRISEhqlChgr7//nvdc889qbarUqWKJOn8+fMO93Xu3DmbbQEAAAAAAJD9mRpQJSQk6O2331ZISIiCg4M1adIklSxZ0u62tWvXliTt37/f4f727dsnSbrvvvucXywAAAAAAABcwtQm6WPHjtWKFSt0zz33aOrUqQ7DKUlq2rSpChcurIMHD+rMmTOpbt+6dauuXLmiYsWKpZoeCAAAAAAAgOzLtIDq+PHjmjhxory9vTV27FgVLVo0ze19fHzUr18/JSQk6P3337dZqS8sLEwjRoyQJL344ovy8jJ95iIAAAAAAADSybQk5/vvv1dcXJwCAwM1e/bsNLd9+eWXFRAQoIEDB2rPnj3auHGj2rdvr6ZNmyo+Pl4bNmzQ9evX1a5dO/Xu3dtNRwAAAAAAAABnMC2gSmx2HhoaqunTp6e5bd++fRUQECAfHx9NmDBBc+bM0aJFi7R8+XJJUvXq1fXmm2+qS5cu8vQ0ddYiAAAAAAAAMsi0gOqnn37K1P28vLzUq1cv9erVy8kVAQAAAAAAwAwMNwIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKYioAIAAAAAAICpCKgAAAAAAABgKgIqAAAAAAAAmIqACgAAAAAAAKbyMrsASbJYLPrpp5/01VdfKTo6WtOnT1fjxo1TbdeqVSudO3cuzX3VrVtX8+bNc1WpAAAAAAAAcDLTA6qrV69q2LBh2rBhQ7rv8/TTT8vf39/ubeXLl3dWaQAAAAAAAHADUwOqLVu26N///reuXbumXr16adWqVbp8+fJd7/fyyy+rQoUKbqgQAAAAAAAArmZqD6qff/5ZsbGxGjt2rN5//315e3ubWQ4AAAAAAABMYOoIqrp16+qNN95gNBQAAAAAAEAeZmpA1bt3bzMfHgAAAAAAANmA6U3SM8NisWjbtm3avXu3wsPDFRAQoEaNGqlevXpmlwYAAAAAAIAMypEBVb9+/XT27NlU1z/wwAMaNWqUSpcuna79HD582NmluV1UVJSk3HEscA7OCdjDeYGUOCdgD+cFUuKcgD2cF0iJcwLOYGqT9MwqV66cpk+frj179mjXrl36+uuvVbZsWe3YsUMDBw5UbGys2SUCAAAAAAAgnXLUCKrx48crLi5OwcHB8vRMytYee+wx1apVSx07dtSRI0e0bNkyderU6a77Cw4OdmG17pGYUOeGY4FzcE7AHs4LpMQ5AXs4L5AS5wTs4bxASpwTSLRr165M3zdHjaAKCgpSrVq1bMKpRBUrVtTjjz8uSdq0aZO7SwMAAAAAAEAm5aiA6m4qVKggSbp+/brJlQAAAAAAACC9clxAlZCQ4PC2GzduSJKKFCnirnIAAAAAAACQRTkmoJo7d64aN26sF1980e7t0dHRWr16tSSpQYMG7iwNAAAAAAAAWZBjAqqmTZsqIiJCGzZs0KxZs2xui4+P18iRI3X+/HkVK1YsXQ3SAQAAAAAAkD2YtopfWFiYxo0bl+o6SZo5c6b++OMP6/W9evVSpUqV9O677+rjjz/WRx99pAULFqhOnTqKjY3V9u3bFRoaqiJFimjMmDEqVKiQOw8FAAAAAAAAWWBaQBUREaHp06fbvW3lypU2X7dp00aVKlXSv/71L9WsWVPTp0/X7t27tXDhQnl7e6tChQoaMGCA+vTpo9KlS7ujfAAAAAAAADiJaQFVhQoVdOTIkQzfr379+qpfv74LKgIAAAAAAIAZckwPKgAAAAAAAOROBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBU2SKgslgsmj59uu677z4FBQVp27ZtDreNjo7WlClT9PTTT6t+/fqqV6+eOnfurClTpig6OtqNVQMAAAAAAMAZvMwu4OrVqxo2bJg2bNhw120jIyP1/PPPa/fu3Spbtqzat28vSdq4caO++OILrVmzRlOmTFH+/PldXTYAAAAAAACcxNSAasuWLfr3v/+ta9euqVevXlq1apUuX77scPuxY8dq9+7deuSRRzRmzBj5+vpKkiIiIjRgwADt3LlT3333nd588013HQIAAAAAAACyyNQpfj///LNiY2M1duxYvf/++/L29na4bWRkpGbPni0vLy999NFH1nBKkvz9/TV8+HBJ0owZM3Tnzh2X1w4AAAAAAADnMDWgqlu3rhYtWqRHH330rttu2rRJkZGRuu+++1S2bNlUtwcHByswMFC3b9/W5s2bXVEuAAAAAAAAXMDUgKp3796qUKFCurY9ePCgJKlWrVoOt0m87dChQ1kvDgAAAAAAAG6RLVbxS4+zZ89KksqUKeNwm8SRVadOnXJHSQAAAAAAAHAC01fxS6+IiAhJUsGCBR1u4+fnJ0m6fft2uvZ5+PDhrBdmsqioKEm541jgHJwTsIfzAilxTsAezgukxDkBezgvkBLnBJwhx4ygSmx8nlYjdR8fH5ttAQAAAAAAkP3lmBFUBQoUkCTFxsY63CYmJkaSlD9//nTtMzg4OOuFmSwxoc4NxwLn4JyAPZwXSIlzAvZwXiAlzgnYw3mBlDgnkGjXrl2Zvm+OGUGVOLUvrel7idMACxUq5JaaAAAAAAAAkHU5JqCqUqWKJOn8+fMOtzl37pzNtgAAAAAAAMj+ckxAVbt2bUnS/v37HW6zb98+SdJ9993nlpoAAAAAAACQdTkmoGratKkKFy6sgwcP6syZM6lu37p1q65cuaJixYqpSZMmJlQIAAAAAACAzMgxAZWPj4/69eunhIQEvf/++zYr9YWFhWnEiBGSpBdffFFeXjmm9zsAAAAAAECeZ1qSExYWpnHjxqW6TpJmzpypP/74w3p9r169VKlSJQ0cOFB79uzRxo0b1b59ezVt2lTx8fHasGGDrl+/rnbt2ql3797uPAwAAAAAAABkkWkBVUREhKZPn273tpUrV9p83aZNG1WqVEk+Pj6aMGGC5syZo0WLFmn58uWSpOrVq+vNN99Uly5d5OmZYwaFAQAAAAAAQCYGVBUqVNCRI0cyfD8vLy/16tVLvXr1ckFVAAAAAAAAcDeGGwEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwlZfZBQAAAADIfW7elE6fNi6nTkkXLkjx8WZXBWe4dq2kJKl4cZMLyaaKFJFatpQaNZLy5TO7GiDnIKACAAAAkCEWi3TlSlIAlRhCJf/65k2zq4TrlDC7gByhWDGpXTvp8ceNf0uWNLsiIHsjoAIAAABgIz5eOn9e2rWrgM6f99aiRbYB1JkzUlSU2VUC2dv169Ls2cbFw8MYUfXYY0Zg1bCh5EnDHcAGARUAAACQx0RHS6GhtiOeko+COntWiouTpMrmFgrkEhaLtG2bcfnwQ2M01WOPGZe2bY3RVkBeR0AFAAAA5DIREanDp+Qh1MWLxhtmV/L1lSpWlCpVMi6BgVL+/K59TLjH5cuXJUmlSpUyuZLsx2KR9u2TVq6UbtxwvN2VK9L06cbF01N68EFjZNXjj0t16xojroC8hoAKAAAAyEEsFuONb8qeT8kv1665vo5ChZLCp0qVpMqVbb8uVYopTLnV4cPGCRYcTEDlSFyctH279NtvxmXPHsfbJiRImzcbl/fek8qWTZoK2KaN0XQdyAsIqAAAAIBsJCFBunQp7QAqIsL1dZQoIZUuHaVy5WJVu3bhVEFUQACjPABHvLykpk2NyyefGD3dVqyQli+XVq2Sbt1yfN8LF6QffjAuXl5Ss2ZJo6tq1eLnDrkXARUAAADgRrGx0rlzjle/O3NGiolxbQ0eHlK5crYjnlJeChaUDh8+JUkKDi7s2oKAXK5cOal/f+MSGytt2WKMrFq+XPrzT8f3i4uT1q83Lu+8Y0yVTRxd1bq15O/vvmMAXI2ACgAAAHCiqCgjZHIUQJ07Z4ySciUvL9v+TykvgYGSj49rawBgn7e39MgjxmXkSGPBguXLjcDqjz+k27cd3zc0VPr+e+Pi4yM9/HBSYBUUxOgq5GwEVAAAAEAG3LzpePW706elf/pHu1SBAvb7PiVeypaV8uVzfR0Asi4wUHrhBeMSHS1t2pTUu+qvvxzfLybGCLT++EN66y2pShUjqHrsMallS8nPz33HADgDARUAAADwD4vFWF3L0ep3p08bAZWrBQQ4bj5eqZLRH4qREkDu4+trTN1r3VoaNUo6eTJpdNWaNcYITUdOnpTGjTMuvr5GSJUYWN17r/uOAcgsAioAAADkGfHxRrNiR83HT59O+w2gs5QunfYKeIVp+QRAxqiowYONS1SUtGGDEVYtWyYdP+74ftHRRlP2FSuMr6tVS2q0/vDDUv787qkfyAgCKgAAAOQa0dFGjxZH4VNoqNF02JU8PaUKFVKPekoMoQIDjSl6AJARBQpI7doZl2++kY4eTWq0vm6d8frnyNGjxn2++caY+teqVdLoqsqV3XUEQNoIqAAAAJBj3L5tv/F44uXCBWOaniv5+jpuQF65slS+vNGkHABcqVo16fXXjcvt29LatUm9q06fdny/yEhp6VLjIkk1ayY1Wm/enAUUYB5+dQIAACBbsFikGzccr353+rR07Zrr6/D3T7sBeenSxigpAMguChaUOnQwLhaL0Vw9MazauFGKjXV830OHjMuoUcbr36OPGoHVY48Zo0EBdyGgAgAAgFskJEiXLqUdQEVEuL6O4sXTDqCKFqUBOYCcy8NDCg42Lm+9JYWHS6tXJwVW5845vm9EhLRokXGRpPvuS5oK+OCDkre3e44BeRMBFQAAAJwiLk46e9b+ynenT0tnzhjLoruSh4dUtqzj5uMVKxojBAAgryhUSOrUybhYLNKBA0lh1ebNxuIRjuzfb1w+/1wqUkRq29YIrNq3l8qUcdcRIK8goAIAAEC6REUZIVPKUU+JIdS5c8YoKVfy8jKajDtqQF6hgtEjCgCQmoeHVKeOcXnnHSksTPr9d6PR+m+/GaNcHbl5U5o/37hIUoMGSSsDFiok5cvnlkNALkZABQAAAElSeLinzp/31rFj9kOoy5ddX0OBAvan3SWGUGXL8iYIAJwlIEDq2tW4JCRIe/cmrQy4dWvaHzrs3m1cPvlEKlKkmpo3v63u3Y1VBkuWdNcRIDchoAIAAMgDLBbp6lXHq9+dOiXdvBnk8jqKFHHc+6lyZalECfo/AYAZPD2NUVENGkj/+Y+xKMWqVUZgtWKF8TvEkZs3vbRsWREtW2a8hjdqlLQyYMOGLCyB9CGgAgAAyAXi46ULFxwHUKdPG1P0XK1UKccBVKVKRkAFAMj+iheXevQwLvHx0q5dSb2rduxwfD+LRdq2zbh8+KExmipxVcC2baVixdx2CMhhCKgAAABygJgYKTTU8ep3oaFGk3JX8vSUypd3vAJexYrGFD0AQO6SL58xKqpRIyN0unxZWrnSCKtWrpRu3HB83ytXpOnTjYunp7EaYOLKgPXqMWoWSQioAAAAsoHbtx2vfnf6tDE6ymJxbQ3e3gkqWzZO1ar52A2hypdniXEAgDFatndv4xIXJ82de0obN/pr+/YS2rPH8f0SEoyVAzdvlt57z+grmDgVsE0bRtnmdQRUAAAALmaxGJ8uO1r97vRpo9eHq/n7O179rlIl6fr1I/L0lIKDg11fDAAgV/Dykho0iFKDBlEKDi6h8+eNnlXLlxs9rG7dcnzfCxekH34wLl5eUrNmSSsD1qrF6Kq8hoAKAAAgixISjKW50wqgIiJcX0fx4o6bj1eqJBUtmvYf+2Fhrq8RAJC7lSsn9e9vXGJjpS1bknpXHTjg+H5xcdL69cblnXekwMCk0VWtWxsfsiB3I6ACAAC4i7g46exZx6vfhYZK0dGur6Ns2bQbkPPHOwAgO/H2lh55xLiMHGn8vly+3Air/vjDmN7uSGio9P33xsXHR3r44aTAKiiI0VW5EQEVAADI86KipDNnHK9+d/asMUrKlby8pAoVHAdQgYGSr69rawAAwJUCA6UXXjAu0dHSpk1Jo6v++svx/WJijEDrjz+kt96SqlRJarTesqXk5+e+Y4DrEFABAIBc79Ytx6vfnT5tTM9ztfz57fd9SryUK2eskgQAQF7g62tM3WvdWho1Sjp5Mml01Zo1xodHjpw8KY0bZ1x8fY2QKjGwuvde9x0DnIuACgAA5BqXLhn9Lf78M+nfv/92T2+lIkUcNx+vVEkqWZLpCAAAOFKlijR4sHGJijJ6US1fLi1bJh0/7vh+0dFGU/YVK4yva9eWxo+Xmjd3T91wHgIqAACQ44SHSwcP2gZRBw5IV6647jFLlUp7BTyWxgYAwDkKFJDatzcu33wjHT2aNBVw/fq0+z4eOCD17GmMmvb0dFvJcAICKgAAkG3FxEhHjqQeFXXqlHMfx9NTKl/e8Qp4FSsafywDAAD3q1ZNev1143L7trR2bVJgdfp06u3Dwhi1nBPlqIBq27Zt6tOnz123+/DDD9WjRw83VAQAAJwhIcEInVIGUUeOGCvoZZWPjxEyOVr9rkIFY6UhAACQvRUsKHXoYFwsFqO5eocO0okTSds89RQBVU6UowKqRKVLl1a7du0c3h4UFOTGagAAQEbY6xN18GDaS02nV/78Us2aRv+JOnWMf2vVMkZHMcwfAIDcxcPDWGAkeTglSa++ak49yJocGVBVqlRJ7733ntllAACANLiyT5SnpzHcP3kQVaeOdM89rIQHAEBeMm6c7deNGhkX5Dw5MqACAADZh6v7RJUvbxtC1a4tBQfTEwoAgLwuPFyaOtX2OkZP5VwEVAAAIF1c3ScqICB1EFW7tlS0aNb3DQAAcp/p042QKlGpUlLXrubVg6whoAIAAKm4u09UnTpSuXI0NAUAAOmTkCCNHWt73YsvSr6+5tSDrMuxAVV4eLjWrFmjEydOKCEhQYGBgXrkkUdUunRps0sDACDHoE8UAADIif74w1jBL5GXl/TSS+bVg6zzsFgsFrOLSK9t27apT58+Klq0qGJiYnQ7xce43t7eeuGFF/Taa6+luZ9du3ZJkvz8/FxWq7tERUVJkgrQiAP/4JyAPZwXiImRTp3y1dGjvvr7b18dOeKlY8cK6Px553zMWKZMrO69N1rVq0erWrVoVat2R1Wrxih//hzzZwbEawVS45yAPZwXSMmMc2Lw4Apat66Q9evHH7+pr74677bHh32RkZGSpIYNG2b4vjlyBFVERIT69++vp59+WuXKldO1a9c0Y8YMTZs2TePGjVOBAgU0cOBAs8sEAMDtEhKkc+e8rUHUsWPGv6dO+SouLuvz5woXjv8ngIpW9ep3VK1atO69N1pFiiQ4oXoAAIC7Cw311vr1/jbX/etfN0yqBs6So0ZQRURE6OTJkwoICFBgYGCq2ydMmKDRo0erYMGC2rx5s8P0NnEEVWYSvezm8OHDkqTg4GCTK0F2wTkBezgvcif6RMHZeK1ASpwTsIfzAim5+5x46y3pf/9L+rpBA2nnTv5GyQ6ykrfkqBFU/v7+qlOnjsPb+/fvr/Hjx+v27dvas2ePmjZt6sbqAABwDfpEAQAAGCIipClTbK979VXCqdwgRwVUd+Pj46OSJUsqNDRU165dM7scAAAyJCZGOnIk9aioU6ecs/8KFZICqGLFzqtatTt6/PGqooUIAADIKWbMkG7eTPq6RAmpe3fz6oHz5LiAKnFGooedeNRisSgsLEySVKRIEXeWBQBAuiUkGKFTyiDqyBEpLi7r+w8IsB0NVaeOVKuWVLRo0jaHDxt/2RFOAQCAnMJikcaOtb3uhReM1gTI+XJUQNWvXz/t2rVLI0eO1OOPP57q9g0bNig8PFxeXl6qW7euCRUCAGCLPlEAAADOsXat8XdUonz5pEGDzKsHzpWjAqr7779fISEh+vzzz1WzZk1VrlzZetulS5c0YsQISVKXLl0YQQUAcCv6RAEAALjWmDG2X3fubLQwQO6QowKqgQMHauvWrdqxY4c6dOigFi1aqFSpUrpy5Yo2btyoqKgoNWrUSEOHDjW7VABALuXOPlGJ/9aowVQ8AACQt50+Lf3yi+11r75qTi1wjRwVUPn6+mratGmaN2+eli5dqm3btun27dsqVKiQ6tatq6eeekpPPfWU8vFxMgAgi9zVJyp5EJWyTxQAAAAM331n/H2W6L77pIceMq8eOF+OCqgkycvLSz179lTPnj3NLgUAkEu4o09U8iCqdm36RAEAAKRXZKQ0aZLtda++yt9SuU2OC6gAAMgs+kQBAADkPLNmSTduJH1dtKjEmJXch4AKAJDr0CcKAAAgd7BYUjdHHzhQ8vMzpx64DgEVACDHok8UAABA7rZxo7R/f9LXnp7S4MHm1QPXIaACAOQI9IkCcqcrt69oz8U92n1ht/VyIeKC2WWZwjefrx6u9LCeq/ecHq/2uLzzeZtdEgCYLuXoqSeflCpVMqcWuBYBFQAgW6FPFJA7WSwWnQs/p90XdmvPhT3afdEIo87eOmt2adlGZGyklhxZoiVHlqikX0n1uq+Xnqv3nOqUrmN2aQBgitBQadEi2+tefdWcWuB6BFQAAFPQJwrIvSwWi07cOJE0KuqiEUpdiXRC0pxHXIm8otFbR2v01tFqWLah+tXrp551eqpYgWJmlwYAbjN+vBQfn/R1rVpSy5bm1QPXIqACALgUfaKA3C0uIU5Hrh6xmaa35+Ie3Yq+ZXZpucauC7u068IuvbXqLT0V9JT61euntve0lZcnf8oDyL3u3JEmTbK97pVXaL+Qm/FbDQDgNPSJAnK36LhoHbxy0Gaa3r6L+xQVF5XpfXp7eqtO6TqqX6a+GpRtoAZlG6hGiRry9sx7/ZcOXD6gaXunafaB2boZfTPV7THxMZp/aL7mH5qvsv5l1aduH/Wr1081StQwoVoAcK05c6SrV5O+LlJE6t3bvHrgegRUAIAMc0efqJRBFH2iAPe6HXNb+y/tt5mmd/DyQcUmxGZ6nwW8CqhemXpqULaBNZCqVaqWfPL5OLHynKtxhcZqXKGx/tfuf1r812JN2zdNvx//XRZZUm17IeKCRm4eqZGbR6pJhSZ6rt5zerbWsyqSv4gJlQOAc1ksqZujP/+8VLCgOfXAPQioAAAOmdEnKjjYGC0FwH3C7oRpz4U9WnFkhQ7dOKTja47ryLUjSrAkZHqfRXyLqH7Z+mpQxhgVVb9sfQUVD1I+T5LmuyngXUA96vRQjzo9FHozVNP3Tde0fdN07Poxu9tvPbtVW89u1esrXtfTwU/ruXrPqVWVVvL08HRz5QDgHCEh0u7dSV97eEgvv2xePXAPAioAAH2igDzk8u3LNr2idl/YrRM3TmRpnyX9SqphuYY20/SqBFSRB/NvsyywSKDee/g9vfvQu9ocullT90zVvEPzFBETkWrbO3F3NOvPWZr15ywFFg5U37p91a9eP91T7B4TKgeAzEs5euqJJ6SqVc2pBe5DQAUAeQx9ooC8wWKxKPRWqNErKtlKeufCz2Vpv4GFA60hVGIgVa5QOcIoF/Pw8FDzis3VvGJzffvYt1p4eKGm7p2qdafW2d0+9FaoPtn4iT7Z+IkervSw+tXtp661usrfx9+9hQNABp0/Ly1YYHvdq6+aUwvci4AKAHKp5H2iNmworaNHfXXiBH2igNwowZKg49eP24yK2n1ht65FXcvSfqsVq5Zqml4JvxJOqhqZVdCnoPrU7aM+dfvoxI0TxhTAvdN0+uZpu9tvOL1BG05v0KvLX1XXWl31XL3n9FDFhwgVAWRLEybYjuAPCpLatDGvHrgPARUA5HDp6xNVLNP7p08UkL3EJcTpr6t/JTUvv7Bbey/uVXhMeKb36enhqZola+qeAvcouGiwHqv3mOqVqafCvoWdWDlcoWrRqvqwxYf64JEPtO7UOk3dO1ULDy20u7Li7djbmrZ3mqbtnaaqRauqX91+6luvryoWqWhC5QCQWnS0NHGi7XWvvmp8OIrcj4AKAHII+kQBec+duDs6cPmAzTS9/Zf2607cnUzv0yefj+qUqmMzTa9O6Try8/bT4cOHJUnBlYKddQhwE08PT7Wq0kqtqrTSuMfHad7BeZq6d6q2hG6xu/2JGyf0wboPNHzdcLWq0krP1XtOnYM7y8/bz82VA0CS+fOly5eTvi5USOrTx7x64F4EVACQDdEnCsh7ImIitO/iPptpegevHFRcQuYT6ILeBVWvTD2b5uXBJYPlk8/HiZUjuynsW1gDGgzQgAYD9Pe1vzVt7zRN3zfdbv8xiyxafXK1Vp9crcK/FVb3Wt3Vr14/NanQhCmAANwuZXP0554zQirkDQRUAGCi5H2ikgdSzu4TVbr0FVWvHq327SvQJwrIBsLuhNlM0dtzcY+OXD0iiyyZ3mdA/gAjhCpj9IpqULaBqhWrpnye/MDnZdWLV9enrT/Vxy0/1h8n/tDUvVO1+K/Fio6PTrXtrehb+n739/p+9/eqUaKG+tXtpyZ+TVSqQCkTKgeQ12zbJm3fbnvdyy+bUwvMQUAFAG6Qvj5RmXe3PlGHD1+VJFWv7pzHA5AxCZYE7b24V8uPLtdvx37T1rNblWBJyPT+ShcsbR0RlXipVKQSI17gUD7PfGp3bzu1u7edbkTd0JwDczR171TtOL/D7vZ/Xf1LQ1cPlbentz5+4GMFBzPtE4BrpRw91b49f7vmNQRUAOBE9IkCkOhG1A2tOr5Ky48t14pjK3Tp9qVM7adSkUrWXlGJYVTZQmWdXC3ykqIFimrQA4M06IFBOnD5gKbtnaaf9v+ky7cvp9o2NiFW/9v/P/1fu/8jAAXgMhcvSvPm2V736qvm1ALzEFABQCbRJwpAcs4YJVW9eHWbaXr1y9RXcb/iLqoYkGqXqq2v2n6lz1p/phXHVmjq3qn69e9fbXqfXY66rOj4aOX3YvlWAK7x/fdSbGzS1/fea4ygQt5CQAUAd+GuPlHJgyj6RAE5Q1ZGSQWXCFaj8o2so6Lqlq6rQr50goU5vPN5q2NQR3UM6qgrt6/o3jH36lb0Levt4dHhBFQAXCImRpowwfa6V14x/k5G3kJABQD/cEefqJRBVPI+UQCyv6yMkvL38Vebqm30+L2Pq/297RVYJNDF1QKZU7JgSRXNX9QmoIqIiVDJgiVNrApAbvXzz9KFC0lfFywo9etnWjkwEQEVgDzHnX2iEoOo2rWN6wHkPFkZJVW7VG09du9jeuzex9SsYjP55PNxYaWA8/j7+Nt8HR4TblIlAHK7b7+1/bpvX6lIEXNqgbkIqADkavSJApBRjJIClGq6aURMhEmVAMjNdu2SQkJsr3vlFXNqgfkIqADkCvSJApAVjJICbKUaQRXNCCoAzjdmjO3XbdoYLTCQNxFQAchR6BMFwBmSj5Jafmy5Qs6GMEoKSKaQDyOoALjWlSvSnDm21736qjm1IHsgoAKQLdEnCoCzMUoKSD96UAFwtUmTpOjopK+rVJGeeMK8emA+AioApqNPFABXYJQUkHkpR1AxxQ+AsyQkSMuXp57e9/LLtM/I6wioALgNfaIAuBqjpJzkzh3p5EnjXYQzlSollSzp3H3CJVKOoGKKH4Csun5dmjpV+u476cQJ29v8/KT+/c2pC9kHARUAp6NPFAB3YZSUE4WHq/Bvv6nQqlXSpk1SZKRrHqdtW+ndd6WHH2YoazaWchU/pvgByKy9e6WxY6VZs6SoKPvb9OkjFS3q1rKQDRFQAcg0+kQBMMONqBv6/cTvWn5suZYfXc4oqay4fl365Rdp4ULp999VPnkzEFdZtcq4NGtmBFWPPUZQlQ3RJB1AVsTESD//bARTmzenve0jj0gff+yeupC9EVABSBf6RAEwC6OknOziRWnxYiOUWrtWio83p47Nm41uuHXrGkFVly7Myc5GaJIOIDPOn5cmTpS+/974deOIj4/UvbvRd6pRI/fVh+yNgAqADfpEAcgOGCXlZKdPS4sWGaHU5s2SxXL3+5QuLRUv7rwa7txJ3XREkvbtk5591vgFMXSo1KuX8c4Fpko5xY8RVAAcsViknTsLaNasYvrjj7RnUgQGSoMGSQMG0JIQqRFQAXmUO/pEJYZQ9IkCcDeMknKBv/825lcsXCjt3Jmuu8QEBir80UdV/IUXpAceMD5ZcKaNG6XPPjOWb0rp6FHp+eel4cOlt9823r34+Tn38ZFuqUZQsYofgBRu35ZmzpTGjZP276+c5ratW0uvvCJ16CB5kULAAU4NIJdzZ5+oxECqVi2aHAK4O0ZJOZnFYrzAJ4ZSBw6k7361aklPPy116aLj3t6Sh4eKBwe7psaHHjIue/YYQdWCBalHc509K73+utGQZMgQafBgmg+aIGUPKqb4AUh07JixEt8PP0g3bzrezt9f6tvXeBmvWdN99SHnIqACcpFLl6SQED8dPeqrK1foEwUge2GUlAtYLNKuXUbQs3Ch8a4hPRo2tIZSCgpKuv7wYdfUmVL9+tK8ecanJSNHSj/9lPpTk6tXpffeM25/+WXpjTekUqXcUx9SjaBiih+QtyUkGINfx42zPwg2uRo1jNFSvXtLhQu7pz7kDgRUQA6Udp+oSlnaN32iADgTo6RcxGKR1qyRPvxQ2rTp7tt7eEhNmxqBVOfOUuXKrq4wfYKCjI/gP/xQ+uoradIko1dVcrduGaOtJk6UNmwwRnzB5VL2oGKKH5A3Xb8uTZ1qjJiy10YwkaenRS1bRmjYsEJq1YoPsJE5BFRANubOPlGJ/9InCkBWMErKxTISTOXLJ7VoYYRSnTpJZcu6ocBMqlhR+vZb6T//kb7+2viI/tYt222uX5dGjJBmzTKlxLyGEVRA3rZ3rzR2rPGSGxXleLsSJaSBA6XWrY+pXLk4BbtqijjyBAIqIBugTxSAnIxRUm6Q3mDKx0d69FEjlOrY0XjnkJOUKiV9+qn0f/9nfFw/erQx1S/R4sVGcMWcEZejBxWQ98TEGG0Mx441FnxNywMPGNP4unUzPtw+fNgJb1qQ5xFQAW526VLqIMqZfaKqVo1S9erRatYsgD5RAFyCUVJulN5gql07oxPtE0/kjvAmIEB6912j71RwsHTmjHF9VJTRa+u558ysLk/w8/aThzxkkdHE/k7cHcUlxMnLk7cPQG5z/rwxi/r776WLFx1v5+Mjde9utAVs1Mh99SHv4DcM4CJp94nKmrT6RP399ylJUnBwQNYfCAD+wSgpN0tvMPXYY9Lw4VLjxm4rza38/IwuuyNGJF33008EVG7g4eEhfx9/m5FTETERCsgfYF5RAJzGYjF+vYwda4yaSmvWRmCgNGiQNGCAVLKk+2pE3kNABWQRfaIA5EbOGCWVGEoxSioD3BxM3bp1S7t27VJsbKwk6cw/I5VCQ0MlSQEBAWrQoIG8vEz8kzFlQLV2rXT6tFQpa4uCIG0Wi0V+3n42AVV4dDgBFZDD3b4tzZxptPrbvz/tbVu3NqbxdeggmflrAHkHpxmQTvSJApDb3Yi6oVXHV2n5seVacWwFo6Tcyc3BVGRkpL788kuNHDlSUWl1v5VUpUoVjRo1Sp06dZKHGfPFg4KMuSTbtyddN3OmMQUQLhEVG6WXlr2U6jUgMjbSpIoAZNWxY0Zrvx9+kG7edLydv78xY3zwYKlmTffVB0gEVIBdru4TVbNm6ul59IkC4G4JlgTtvrCbUVJmcnMwZbFYNG/ePL399tvWUVJ3c/LkST399NNq1aqVvv76a9WpUydLNWRKnz62AdVPP0nDhvGL0wVCb4aq89zO2nVhl831hXwKqWKRiiZVBSAzEhKk5cuN0VLLl6e9bY0axmip3r1zRytD5EwEVMjTzOoTlS9f1vcPAJmROEpqzq452nhxo67duZbu+zJKyolM6DG1e/duvf7669qU1uOlYc2aNapXr55efPFF/fe//1UJd64Q+Oyz0pAh0j9TEfXXX9LOncYyUnCa9afWq+v8rroSafuHUEGvgprfdb4KeBcwqTIAGXH9ujR1qjFi6sQJx9t5ekpPPmkEU61akfnDfARUyBPoEwUgr6KXVDZjQjB1584dDRkyRBMnTpTFYkl1e4kSJVS/fn1J0u1/hgoXLFhQcXFx2rBhg+Lj463bJiQkaPz48Zo9e7YmTpyobt26Zbm+dClRQnr8cWnJkqTrpk8noHISi8WiMdvH6M2VbyreEm9zW5VCVTSm2Ri1u7edSdUBSK+9e42m57NmGYueOlKihDRwoPTSS1JFBkYiGyGgQq5CnygAoJdUtmTSqnx37txR586dtWLFilS3eXl56bXXXtP777+vgIAASdLhw4clScHBwZKkgwcPasiQIfr9999t7hsWFqYePXqocuXKauSutcb79LENqObMkUaNMtY9R6Yl9puavm96qts6Vu+o/9T8jwr5FDKhMgDpERNjrMI3dqy0eXPa2z7wgDFaqls3PkhH9kRAhRyLPlEAYGCUVDZmUjAlpR1OPfHEExo1apSCgoLS3EetWrW0cuVK/frrr3rrrbd07Ngx620JCQl67bXXtGXLFnl6ejqtboeeeML4ROjGDePrq1elFSuM+SnIFEf9piRp+CPD9cEjH+jIX0dMqAzA3Zw/L02cKH3/vXTxouPtfHyk7t2ll1821psAsjMCKmR79IkCgNSyOkqqUdFGeqjsQ+rZvCejpFzBxGBKchxO3XPPPRozZowee+yxdO/Lw8NDTz75pNq1a6dRo0bpvffes962bds2zZo1S7169XJa7Q75+hrvssaPT7pu+nQCqkxy1G+qkE8h/dT5Jz1V4ymTKgPgiMVi/EoZO9YYNZXWDJHAQGnQIGnAAKlkSffVCGRFjg2oTp8+rYkTJyokJERXrlxRwYIFVb9+ffXr109NmjQxuzxkAn2iAMCx5KOkfjv2m7ae3ZqlUVKJU7kIp5zM5GBKchxO1axZU2vWrFHp0qUztV9fX1+9++672rFjhxYvXmy9/p133lGnTp3k7++flbLT5/HHbQOqNWtc/5i5TFr9poKKB2lx98WqUaKGSdUBsOf2bWnmTGM1vv370962dWtjGl+HDpJXjn23j7wqR56yu3bt0oABAxQZGakHHnhADz/8sC5duqRNmzZp7dq1ev/9993zSR4yhT5RAJA+9JLKQbJBMCW5LpxK7quvvtJvv/2mmJgYSdL58+c1cuRIffzxx1ne913Nnm379b33uv4xc5G79Zv6qfNPKpK/iAmVAbDn2DFjJb4ffpBu3nS8nb+/1LevNHiw0aYEyKlyXEAVFRWlt99+W5GRkRo5cqQ6depkvW337t3q27evPv/8czVu3FjVqlUzr1BIok8UAGSEs0dJwQ2ySTAluSeckoxpgkOGDNHIkSOt13355Zd6/vnnVblyZac8hl1//ZU6oPq//3Pd4+Uy6ek35enhhl5iANKUkCAtX26Mllq+PO1ta9QwRkv17i0VLuye+gBXynEB1fLly3Xu3Dk1b97cJpySpAYNGqh79+6aPn26fvzxR33yySfmFJkH0ScKADKHUVI5VDYKpiT3hVOJ3nvvPf3444+6+E9n3ujoaH399df6+uuvnfo4Nj7+2Pi+J6pdW3r6adc9Xi5Cvykg+7t+XZo61RgxdeKE4+08PY3We6+8IrVqxQfzyF1yXEC1atUqSVL79u3t3t6uXTtNnz5dv//+OwGVC9AnCgCyhlFSOVw2C6Yk94dTklSoUCF9+OGHeumll6zX7b9bY5SssDd6avhw450aHKLfFJD97d1rND2fNUuKinK8XYkS0sCB0ksvSRUruq08wK1yXEB16NAhScYfXfbUqlVLkhQWFqazZ8+qQoUKbqstN9q2TfrjD/pEAUBWJFgStOSvJVpyZAmjpHKydeuk99/PNsGUZE44lcitrRQYPZVh9JsCsq+YGGMVvrFjpc2b0972gQeM0VLduvGhPXK/HPWxU0xMjC5dMv6oL1u2rN1tChQooICAAEnGSn95Qc2awfLwkPXiyPffy2a7F15wvG3DhsY2TZpI//mPNGeOMYUvo+FU/vxSgwZG077kf6uHhUm9ehlzqwcNkpo3tw2nktfp7GNKvOxK3YJBknF98u0aNnS8zxdesN32++8db8sxcUxmHlPNmsHW14rcckw56XnK5+mpp2t21o9TfByHUx9abC4TO0zUmTfO6M9Bf+qLR79Qyyot5ZPPJ9scU258ntI8pnnzpFat5LFpozxksV6sHntM2rpV+u03qXFjtx3TK6+8YjecatBgh8qUKZ3h56lmzWCH26U8pv/9L8glx5TKP6OnXtDEpO/9gT/1/WTHf8bmqnMvk8fk51NA0zv/KP0y0eb24Y8M1+Lui1Ukf5F0H9PBg/mzxTHlxueJY8pbx3T+vDEKytdX6tHDcTjl4yP16SM99ZS0Y4fxXqpAgex5TJJxffK/NXP685R4TGaee3lVjhpBFRERYf1/wYIFHW7n5+ensLAw3b5LJ+7EJbZzsig740AdHdeFCwGSkoK9sLAbOnz4ot1t79ypLKlAhuspVCheffpcV/Xq0apWLVqBgTHWPlHDh5fRtm1Fk9VzQYcPhznYk+0fyK44ppMnT8rP706q7U6ezC+pSrL7Renw4VN29xkWVkZS9jqmqlWjUu0/px9TbnyeOKbU8sIxOVKtSDUdTXHdQ34PKeJ8hA6ftz02Zx1T4u+Pw4cP8zyl45gqjB+vQslH8Pwj4qGHdGXwYN2pW9e44p9jdNcxzZw502ab/Pnza9y4cfruu2hJfmkeUxLb5ykqKsruc5XymMLDI2xuj4yMtN7Pmc9TubffVhE73/u8cu4lSd8xhfwdJunBVNcX9Cqozxt/rtalW+vIX0f+qa2y7nZMUVFRio623RevERxT8t8hSfsIUE4+JnuccUwWi7RrVwHNmlVMf/xRSHFxjlOJMmVi1b37DT3zTJiKFYvX8OHZ85hSyg3PU0pmH1NelaMCquhkvx29vb0dbufjY0x/sBfeIOuKF49TcPAdVa8eLT+/BI0dW9J6W2BgjF5++aqJ1QFAzuCbz1fv1H1Hj5R7RGX9yopVobO3qLp1VWjdulTXnx8xQvElSri/oH/UqVNHO3bssH59584dff755/L3n2VaTc7kc+KECv/2m9ll5AgWi0Uzjs7Qj39fV8qAqkqhKhrTbIyqFq5qTnFAHnTnjjR/foBmzSqqI0fSnpvXpMlt9ex5XS1aRMgrR71DB5wrR53++ZNNuo2NjZWvr6/d7WJiYiQZ0/3SEhzseBh7TmEvcXV0XClnRQYEFFVwsP1P9tOa31ytmpeWLfNX4cL+2rXLmDuddL8CDh//n5mXyeopq+Bg+1M1U3LFMVWpUkX2dhsZmfJ+OeuYChS4k2r/Of2YcuPzxDGllheOKbno+Ggdjz2uD+p/oHyeqZckdfUxJf7+CA4O5nkKSFmPnWP6/HPp77+lFEt+V3/xRWntWilFryd3HdOCBQvUokULnTx50nr9ypUrVaXKbklt0j4mBwoUsP+9SnlMhQr523zt5+dnvZ/TnqdPPrHtPWVTTx459xxIvk+bflOWgTbbVSxSSXsG77Hbbyo9x3T48GH5+tpuyGsEx5T8d0jSPlI+Rs46JnuyckyDBlVRRITdTW3UrCmFhBSUlHqGUHY7ptz4PGXXY8rJdjmaN5kOHhaLg9/62VBMTIzq1KkjSQoJCVGxYsXsbvfAAw/o1q1bmjZtmh58MPUQ58RvWMO0JpLmEPZ+OTjTrVtSu3ZGW43kmjSRVq6UChd2ycMiC1x9TiBn4rww34kbJ9Tyx5Y6c/OMzfX/qvMv/djpR7shlStxTmTCnTtGY+7lKVKq4GC7IZW7nDlzJlVIJUldu3bVzJkz0xx1nlJGzouff/5ZXbp0sX7dsmVLrVmzJt2PdVd//WW8c0v+p+r8+dIzzzjvMXKB0Juh6jy3s3ZdSP2GYPgjw/XBIx/I0yPzbWd5rYA9nBe2EhKkFSuMD+5T/opIqUYNo+l57965670U5wQSZSVvyVFN0n18fFS+fHlJ0rlz5+xuEx4erlu3bkky0lBkTeHCRhDVpInt9Vu3GsHVP99qAMBdVC1aVWv7rlXFIrZrQ8/8c6b6Lu6r+IR4B/dEtpE/v7Hs0mOP2V5/+LDUsqX0z0Iu7laxYkWtW7cu1d898+fP17/+9S/FxsY6/THj4+P18ccf21wXGBjo3Adh5b67Wn9qvRp+3zBVOFXIp5AWP7tYH7b4MEvhFIC0Xb8ujRolVasmPfGE43DK01Pq1MlYHf3QIenll3NXOAU4S477jVW7dm1J0v79++3evnfvXklSyZIlVaZMGXeVlasRUgGAcxBS5QKEVJKkqVOnWv/mSjRw4ED7G2fGPyv32Rg+3HiXB1ksFn277Vu1nt5aVyKv2NwWVDxI2wdu11M1njKpOiD327vXWI2vQgXp3/+WTpywv12JEtKwYdLJk9KiRVLr1qzcBqQlx/2Wb9++vSRpuYN4eunSpZKkJ554wm015QWEVADgHIRUuUAeD6lu3rypd9991+a67t27q3nz5k7Zv06elHr1YvSUA1GxUeq3pJ9eX/G64i22rxcdq3fUtgHbVKNEDZOqA3KvmBhpzhypeXOpfn1p8mTJ0ZpcDzwg/fijFBoqffqpVLGi/e0A2MpxAdWjjz6qKlWqaMeOHZo7d67NbevXr9cvv/wiPz8/PffccyZVmHsRUgGAcxBS5QJ5OKT6+OOPdeVK0qidAgUKaOTIkVneryRp3jypXj0pZYNVRk9JMvpNPTT1IaMZegrDHxmuxd0X222GDiDzzp+XPvxQqlRJ6tFD2rzZ/nY+PlKfPtK2bdL27cb/01p4CkBqOWoVP0ny9vbW//73Pz333HP64IMP9Ouvv+ree+/V2bNntWXLFnl6euqzzz5jep+LJIZUKRunJ4ZUNE4HgPRJDKlSNk6f+edMSTKlcToyKDGkStk4PTGkMqlxemJIlbJx+vz587Vs2TJ5pbGGeUJCgiTJ00EYdMvOp1HvvPOOKmZ1eEBkpPTGG9KkSalva9qU0VMy+k11nd811ZS+Qj6F9FPnn5jSBziRxSJt2mQ0Pf/5ZykuzvG2gYHSoEHSgAFSyZLuqxHIjXLkR1E1a9bUkiVL1L17d50/f14LFizQoUOH9Oijj2rBggXWaYBwDUZSAYBzMJIqF0hrJFWrVtluJFVkZKRu3brl8BIREaGIiAiHt9vz9ttvZ63YAweM+TD2wqmOHaVff83To6foNwW4z+3bxktRvXrSww8bgzodhVOtWxt9pU6cMPpMEU4BWZfjRlAlKlOmjD766COzy8izGEkFAM7BSKpcwNFIqkOHjJBqzZpsNZLKmT788EP5+fll7s4WizRxojRkiHTnju1tPj7Sl19Kr76apzsKR8VG6aVlL9md0texekf91PknpvQBTnDsmPTdd9LUqVJYmOPt/P2lvn2lwYOlmjXdVh6QZ+Tdj6OQZYykAgDnYCRVLuBoJFViSGXySKrGjRu7ZP8ffPBB5u5444bUtasxLyZlOFWtmvHHxGuv5elwin5TgGslJEi//SY9/rjxsjN6tONwqkYNY7rfuXPGv4RTgGvk2BFUyB4YSQUAzsFIqlwgG4+k2rp1qyIiIhQfn3bYeeTIEUlSUFCQw20sFov8/Pzk4+OTuYK2bDE6DZ85k/q2vn2Nd3/+/pnbdy6QYEnQ0r+XasAvA+g3BbjA9evGSKnvvjOm5zni6Sk9+aT0yivGS3gezssBtyGgQpYRUgGAcxBS5QLZNKSSJP90hD6FChWSJBUp4oKROfHx0siR0gcfGP+3LU4aP17q1cv5j5tDnL11VlP3TNWUPVN0+ubpVLcHFQ/S4u6LVaNEDROqA3K+vXulceOkmTOlqCjH25UoIQ0cKL30kpTV9R8AZAxT/OAUTPcDAOdgul8ukE2n+5nqwgWpbVvpvfdSh1MNGki7d+fJcCo2PlaL/1qsDrM6qNLXlfTBug/shlMdq3fUtgHbCKeADIqJkebMkZo3l+rXlyZPdhxOPfCA9OOPUmio9OmnhFOAGQio4DSEVADgHIRUuQAhVZLly6W6dY3RYykNGWJM+atWzf11mejY9WMa9scwVfy6ojrP7axlR5cpwZJgd1v6TQEZd/689OGHUqVKxozizZvtb+fjI/XpI23bJm3fbvw/f363lgogGab4wamY7gcAzsF0v1wgG0/3c4uYGOndd6VRo1LfVqKENG2a9MQTbi/LLHfi7mjR4UWatHuS1p5am+a2+b3yq2vNrnql0StqVL6RmyoEcjaLRdq0yWhj9/PPUlyc420DA401GgYMkEqWdF+NANJGQAWnI6QCAOcgpMoF0gqpWraUunUzrzY7Slz5pyl3Vt+xnTgh/fST/dtatpRmzJDKlcvaY+QQBy4f0KRdk/TT/p90486NNLetW7quBjYYqH/d9y8F5A9wT4FADnf7tjRrlhFM7d+f9ratWxtNzzt0kLx4JwxkO/xYwiUIqQDAOQipcgFHIdXhw9JHH5lXlx0uHUiQL59xvEOHGv/PxSJiIjT3wFxN2j1J285tS3PbQj6F1LNOTw1oMEANyzaUB0uFAely7JixEt/UqVJYmOPt/P2NBUIHD5Zq1nRbeQAygYAKLkNIBQDOQUiVCzgKqfKKwEBp9mypWTOzK3EZi8WiHed3aPLuyZp9YLYiYiLS3P7BCg9qYIOB6lqrq/x97r7CIgApIUFascIYLXW3l9IaNYzRUr17854DyCkIqOBShFQA4ByJIVWLaS0UeivUej0hVQ6Sl0OqvXulYsXMrsIlrkdd18z9MzVp9yT9efnPNLctXqC4+tTto+frP69apWq5qUIg57t+3Rgp9d13xgxiRzw9pSefNIKpVq0kBiQCOQsBFVyOkAoAnKNq0apa128dIVVOlj+/9Msvxrrnx46ZXU0qV/7pQVUyqz2oLl6Uli6VXnxR+s9/ct27RIvFovWn12vy7slacGiBouOj09y+dZXWGthgoDrV6CRfL183VQnkfHv3SuPGSTNnSlFRjrcrUUIaOFB66SWpYkXH2wHI3gio4BaEVADgHIRUuYCXl9Srl9lV2HX18GFJUsngYJMryZ4uRVzStL3TNHnPZB27nnbAWNa/rJ6r95yeb/C8qhat6qYKgZwvJsYYbDp2rLR5c9rbPvCAMVqqWzcj/weQsxFQwW0IqQDAOQipAPeJT4jXyuMrNXn3ZP3696+KS3C8dr2nh6eeqPaEBjQYoMerPS4vT/7UBtLr/Hnp+++liRONQZiO+PhI3btLL78sNWrkvvoAuB6/NeFWhFQA4ByEVIBrnQ47rR/2/KAf9v6gs7fOprltlYAqer7+8+pXr5/KFy7vpgqBnM9ikTZtMkZL/fyzFOc4/1VgoDRokPT881KpUu6rEYD7EFDB7QipAMA5CKkA54qJj9GvR37VpN2TtOr4KllkcbitTz4fda7RWQMaDFCrKq3k6eHpxkqBnO32bWnWLCOY2r8/7W1btTKm8XXsaMyQBpB78SMOUxBSAYBzEFIBWXfk6hFN3j1ZP+77UVcir6S5bXCJYA1sMFC96/ZWCb8SbqoQyNksFmP1vc2bpY0bpQULpLAwx9v7+0t9+0qDB0s1a7qtTAAmI6CCaQipAMA5CKmAjIuMjdTCQws1afckbTyzMc1t/bz99GytZzWgwQA9WOFBeeSyVQkBZ4uNlfbsMQKpxEtafaUSBQUZo6X69OF9AJAXEVDBVIRUAOAchFRA+uy9uFeTd0/WjP0zdDP6ZprbNizbUAMbDFSPOj1U2Jc/SABHwsKkkJCkMGrbNikqKn339fSUnnzSCKZatZLIf4G8i4AKpiOkAgDnIKQC7LsVfUuz/5ytSbsnadeFXWluW8S3iHrd10vP139e9cvWd1OFQM5hsUhnz3pr9+4C+vZbo8n5wYPG9RlRvLg0cKD00ktSpUquqRVAzkJAhWyBkAoAnIOQCjBYLBaFnA3R5N2TNffgXEXGRqa5/UMVH9LABgPVpWYX+Xn7ualKIPuLjZX27TNGRm3aZPx74cK9Gd6Pn5/UuLHUrJlxadFCyp/f+fUCyLkIqJBtEFIBgHOkJ6QCcqurkVf1076fNHnPZB26cijNbUv6lVS/ev30fP3nFVQiyE0VAtnbzZvG39+JgdS2bVJk2vmuXWXLJoVRzZtLdetK3t7OrxdA7kFAhWyFkAoAnONuIdXQoKGMpEKukWBJ0JqTazR592Qt+muRYuJjHG7rIQ+1vaetBjYYqI5BHeWTz8eNlQLZi8UinTljOzrqzz8zPl3Pw0OqVSspjGrWTKpcmX5SADKGgArZDiEVADhHWiHVzZs39Vmjz0ysDsi68+HnNXXPVE3ZM0Unw06muW2FwhXUv15/9a/fX5UCaHiDvCkuTtq/PymM2rxZOncu4/vJnz9BdepEqW3bgmrWTHrwQSkgwOnlAshjCKiQLRFSAYBzOAqplp5ZKklaHLyYkVTIUeIS4vTb0d80efdkLTu6TAmWBIfbenl6qWP1jhrQYIDa3dOOcx15zq1bSdP1Nm82/n/7dsb3U7p00sioZs2k/PmPyNtbCg4Odn7RAPIsAipkW4RUAOAcaYVUfRf3pXE6coQTN05oyu4pmrp3qi5EXEhz23uL3asB9Qeob72+KuNfxk0VAuZLnK6XeNm/X0pwnOE6VLOmbSBVtartdL3Dh51XMwAkIqBCtkZIBQDOkdZ0v7O3zqpK0SomVofsIiwsTJIU8HeAqXUkt+PcDh28cvCu2/nm89UzNZ/RgAYD9EilR+RB8xvkcvHxRgCVPJAKDb37/VLKn19q1CgpjHrwQalYMefXCwB3Q0CFbI+QCgCcw1FItf70eq0/vd7EyoDMq1OqjgY2GKh/3fcvFSvAu2rkXhERqafrhYdnfD+lSiWFUc2aSQ0aSD6sFQAgGyCgQo5ASAUAzpEYUjWb3EwXIy+aXQ6QKf4+/upRu4cGNBigB8o9wGgp5Epnz9qOjtq7N3PT9YKDbQOpe+9ldT0A2RMBFXIMQioAcI6qRavqxxY/qv/6/jp3OxPLNwEm8fP207ftv1W3Wt1UyLeQ2eUAThMfLx04kBRGbdpk9JPKKF9f6YEHksKopk2l4sWdXy8AuAIBFXIUQioAcI5A/0AtartIp/KdUkRMhNnlIJs4f+G8JKlc2XImV5IkPCZc289t1/P1n1fLKi3NLgdwitu3pW3bksKorVuNFfcyqkSJpDCqeXNjup6vr/PrBQB3IKBCjkNIBQDO4e/tr67BXc0uA9nI4fzG0lwsHQ841/nzSWFU4nS9+PiM7ycoKCmMatZMqlaN6XoAcg8CKuRIhFQAAADIjhISpIMHbQOpU6cyvh8fH+n++5PCqKZNjRFTAJBbEVAhxyKkAgAAgNkiI6Xt25MCqZAQ6ebNjO+neHEjhEoMpBo2lPLnd369AJBdEVAhRyOkAgAAgDtdvGg7OmrPHikuLuP7qVYtKYxq1syYvsd0PQB5GQEVcjxCKgAAALhCQoJ0+HBSGLV5s3TiRMb34+1tTNdLvrpeqVLOrxcAcjICKuQKhFQAAADIqqiopOl6mzdLW7ZIYWEZ30/RoklhVLNmRjhVoIDTywWAXIWACrkGIRUAAAAy4tKlpDBq82Zp924pNjbj+7n3XttAqkYNydPT+fUCQG5GQIVchZAKAAAA9iQkSH/9ZRtIHTuW8f14eRkNzJMHUqVLO79eAMhrCKiQ6xBSAQAA4M4daccO2+l6169nfD8BAUbPqMQw6oEHJD8/p5cLAHkeARVyJUIqAACAvOXKFdvRUTt3Zm66XtWqSWFU8+ZScDDT9QDAHQiokGsRUgEAAOROFot05EhSGLVpk3T0aMb34+Ul1a+fFEY1bSqVLev8egEAd0dAhVyNkAoAACDnu3NH2rUrKYzaskW6di3j+ylSRHrwQSOMatZMatSI6XoAkF0QUCHXI6QCAADIWa5eNUKoxEBq504pJibj+6lcOSmMatZMqlWL6XoAkF0RUCFPIKQCAADIniwWY3peYhi1ebMxfS+j8uVLmq6XeClXzvn1AgBcg4AKeQYhFQAAgPmio6Xdu5PCqC1bjAbnGVW4sDFdLzGMatRI8vd3fr0AAPcgoEKeQkgFAADgXteuJU3X27xZ2rHDCKkyqlIl29FRtWsbo6YAALkDARXyHEIqAAAA17BYpGPHksKozZulw4czvh9PT6lePdtAqkIFp5cLAMhGCKiQJxFSAQAAZF1MjDFdL3kgdflyxvfj7287Xa9xY6lQIefXCwDIvnJMQLVt2zb16dPnrtt9+OGH6tGjhxsqQk5HSAUAAJAxN27YTtfbvl26cyfj+wkMTAqjmjeX6tRhuh4A5HU5JqBKVLp0abVr187h7UFBQW6sBjkdIRUAAIB9Fot05oy39uzx09dfG4HUwYMZ34+np3TffUlhVLNmRkAFAEByOS6gqlSpkt577z2zy0AuQkgFAAAgxcZKe/bYTte7ePHeDO+nYEGpSZOkMKpxY/6WAgDcXY4LqABXIKQCAAB5TViYFBKSFEZt2yZFRWV8P+XLJ4VRzZoZo6W8eJcBAMggfnUA/yCkAgAAuZXFIp06lRRGbdpkTNezWDK2Hw+PpOl6iZeKFY3rAQDICgIqIBlCKgAAkBvExkr79iWFUZs3SxcuZHw/BQok6L77otS2bUE1a2ZM3StSxPn1AgCQIwOq8PBwrVmzRidOnFBCQoICAwP1yCOPqHTp0maXhlyAkAoAAOQ0N28af6skBlLbtkmRkRnfT7lytqOjfHyOyNtbCg4Odn7RAAAk42GxZHRgrzm2bdumPn36qGjRooqJidHt27dtbvf29tYLL7yg11577a772rVrlyTJz8/PJbW6U9Q/jQIKFChgciW5T0SEpwYODNS+fbbnSd26kZo0KVT+/gkmVZY2zgnYw3mBlDgnYA/nRc5gsUjnz3tpzx4/7d7tpz17Cujvv31lsWRsnp2Hh0XVqkWrfv0o1a8fqQYNolS+fKzNdD3OCdjDeYGUOCeQKPKfT0caNmyY4fuaMoJqyJAhOnz4cLq2LV26tH788Ufr1xEREerfv7+efvpplStXTteuXdOMGTM0bdo0jRs3TgUKFNDAgQNdVTryEH//BE2aFJoqpNq3z08DBwZm65AKAADkHnFx0t9/59euXQW0Z48RSF265J3h/eTPb0zXSwyk6tWLUuHC/C0DAMgeTBlB1a1bN+3bty9d25YvX15r1qxRRESETp48qYCAAAUGBqbabsKECRo9erQKFiyozZs3p5ncJo6gykyil90kBn0Mu3adW7dST/eTjB4M2XG6H+cE7OG8QEqcE7CH8yJ7uHUrabre5s3G/1NMHkiXMmWSpuo1by7Vqyd5ZzDX4pyAPZwXSIlzAomykreYMoJq3rx5Gb6Pv7+/6tSp4/D2/v37a/z48bp9+7b27Nmjpk2bZqVEwIqeVAAAwJXOnEkKozZvlvbvlxIyMbCpVq2kMKpZM6lKFVbXAwDkHDmySbo9Pj4+KlmypEJDQ3Xt2jWzy0EuQ0gFAACcIT7eCKCSB1KhoRnfT/78UqNGSYHUgw9KRYs6v14AANwlRwVUibMRPex8FGSxWBQWFiZJKsLat3ABQioAAJBRERGpp+uFh2d8P6VK2Y6Oql9f8vFxfr0AAJglxwRU/fr1065duzRy5Eg9/vjjqW7fsGGDwsPD5eXlpbp165pQIfICQioAAJCWs2dtR0ft3Zu56XrBwUlhVLNm0j33MF0PAJC75ZiA6v7771dISIg+//xz1axZU5UrV7bedunSJY0YMUKS1KVLF0ZQwaUIqQAAgGRM1ztwICmM2rTJ6CeVUb6+SdP1mjUzpusVL+78egEAyM5yTEA1cOBAbd26VTt27FCHDh3UokULlSpVSleuXNHGjRsVFRWlRo0aaejQoWaXijwgrZDqnnvMDahiY++RlPFVepC7cV4gJc4J2MN5kT6RkdLFi5m/f8mSSWFUs2ZSgwZGSAUAQF6WYwIqX19fTZs2TfPmzdPSpUu1bds23b59W4UKFVLdunX11FNP6amnnlK+fPnMLhV5hKOQ6upV42IeGlLAHs4LpMQ5AXs4L1yhRg3bQKpaNabrAQCQUo4JqCTJy8tLPXv2VM+ePc0uBZDkOKQCAAB5k4+P9MADSWFU06ZSiRJmVwUAQPaXowIqIDtKDKmeeUb6/XezqwEAAO7WsaPR0Lx5c6lhQ6brAQCQGQRUgBMkhlQXLxp9Kcx07NgxSdK9995rbiHIVjgvkBLnBOzhvEg/i0XKl0+qXJnpegAAOAMBFeAkHh5S2bJmVyHFxMRKMpq1A4k4L5AS5wTs4bwAAABm8TS7AAAAAAAAAORtBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAAAAAAAATEVABQAAAAAAAFMRUAEAAAAAAMBUBFQAAAAAAAAwFQEVAPx/e/ce5FVd/w/8CcKKiHipBtElIm11BUEqRJGxyTToNlNa2YyLaerg5NSko5YXakhzsonKETMzdFwxyRIcy8ELai7iJQMvM4DklBdYU0BbhV2EFT6/P36z+3Vhwb2xx919PGaccc/7fT77PvN58f6c93PP5xwAAAAKJaACAAAAoFACKgAAAAAKJaACAAAAoFCFB1SlUinV1dUZO3ZsDjvssDz55JO77L958+bMmTMnJ598csaPH5+jjjoqX/va1zJnzpxs3ry5m0YNAAAAQFcZUOQvX79+fS655JLU1NS0qX9DQ0POOuusLFu2LMOHD8/UqVOTJIsXL84vfvGLPPTQQ5kzZ04GDRq0O4cNAAAAQBcqLKB67LHHcuGFF+aNN95IVVVV7r///qxdu3aX+8yePTvLli3LZz7zmVx77bXZc889kyQbN27M2WefnX/+85/57W9/mwsuuKA7DgEAAACALlDYV/zmz5+fxsbGzJ49OzNmzMjAgQN32b+hoSG33357BgwYkJkzZzaHU0kyZMiQ/OQnP0mSzJ07N++8885uHTsAAAAAXaewgGrcuHFZsGBBTjrppDb1f/TRR9PQ0JCxY8dm+PDhO7RXVlZmxIgRqa+vz5IlS7p6uAAAAADsJoUFVNOmTUt5eXmb+y9fvjxJMnr06J32aWpbsWJF5wYHAAAAQLcp/Cl+bbVmzZokyYEHHrjTPk1XVr300kvdMSQAAAAAukChT/Frj40bNyZJ9t577532GTx4cJKkvr6+Ta+5cuXKzg+sYJs2bUrSO46FrqEmaI26YHtqgtaoC7anJmiNumB7aoKu0OmA6vzzz29zEQ4bNiy33HJLh35P043Pd3Uz9bKyshZ9AQAAAPjg63RAVVtbmxdffLFNfbds2dLh37PXXnslSRobG9/39QcNGtSm16ysrOzweD4omsLB3nAsdA01QWvUBdtTE7RGXbA9NUFr1AXbUxM0Wbp0aYf37XRAdccdd3T2Jdqk6at9u/r6XtPXAPfZZ59uGRMAAAAAnddjbpI+atSoJMmrr7660z61tbUt+gIAAADwwddjAqoxY8YkSZ577rmd9nn22WeTJGPHju2WMQEAAADQeT0moJo0aVKGDh2a5cuX55VXXtmh/Yknnsi6detywAEH5JhjjilghAAAAAB0RI8JqMrKynLGGWdk27ZtmTFjRosn9dXV1eVnP/tZkmT69OkZMKDTt9YCAAAAoJsUkuTU1dXluuuu22Fbktx2221ZtGhR8/aqqqqMHDkySXLOOefk6aefzuLFizN16tRMmjQpW7duTU1NTd58881MmTIl06ZN67bjAAAAAKDzCgmoNm7cmOrq6lbb7rvvvhY/n3jiic0BVVlZWX73u99l3rx5WbBgQRYuXJgkqaioyAUXXJBTTjkl/fv3mIvCAAAAAEhBAVV5eXlWrVrVoX0HDBiQqqqqVFVVdfGoAAAAACiCy40AAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKNSAogdQKpVy66235pe//GU2b96c6urqTJw4sdW+J5xwQmpra3f5euPGjcsdd9yxO4YKAAAAwG5QaEC1fv36XHLJJampqWnXfieffHKGDBnSatvBBx/cFUMDAAAAoJsUFlA99thjufDCC/PGG2+kqqoq999/f9auXdumfc8777yUl5fv5hECAAAA0B0KuwfV/Pnz09jYmNmzZ2fGjBkZOHBgUUMBAAAAoECFXUE1bty4/OAHP3AlFAAAAEAfV1hANW3atKJ+NQAAAAAfIIU/xa8jSqVSnnzyySxbtiwbNmzIfvvtl6OPPjpHHXVU0UMDAAAAoJ16ZEB1xhlnZM2aNTtsnzBhQmbNmpVhw4a16XVWrlzZ1UPrdps2bUrSO46FrqEmaI26YHtqgtaoC7anJmiNumB7aoKu0OmA6vzzz29zEQ4bNiy33HJLZ39lDjrooFx11VU58sgjs23btixevDhXX311nnrqqZxzzjm588473XQdAAAAoIfodEBVW1ubF198sU19t2zZ0qnfdf311+fdd99NZWVl+vf/vwcQfuELX8jo0aPzla98JatWrco999yTr371q+/7epWVlZ0azwdBUzjYG46FrqEmaI26YHtqgtaoC7anJmiNumB7aoImS5cu7fC+nQ6o7rjjjs6+RJsddthhO2376Ec/mi9+8YuZP39+Hn300TYFVAAAAAAUr//7d+k5ysvLkyRvvvlmwSMBAAAAoK16XEC1bdu2nbb973//S5Lsu+++3TUcAAAAADqpxwRUf/rTnzJx4sRMnz691fbNmzfnwQcfTJJ88pOf7M6hAQAAANAJPSagmjRpUjZu3Jiampr88Y9/bNG2devWXH311Xn11VdzwAEHuP8UAAAAQA/S6Zukd0RdXV2uu+66HbYlyW233ZZFixY1b6+qqsrIkSMzYsSIXHrppbniiisyc+bM/OUvf8mRRx6ZxsbG/OMf/8jq1auz77775tprr80+++zTnYcDAAAAQCcUElBt3Lgx1dXVrbbdd999LX4+8cQTM3LkyCTJaaedliOOOCLV1dVZtmxZ7rzzzgwcODDl5eU5++yzc/rpp2fYsGG7ffwAAAAAdJ1CAqry8vKsWrWqQ/uOHz8+48eP7+IRAQAAAFCUHnMPKgAAAAB6JwEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQKAEVAAAAAIUSUAEAAABQqH6lUqlU9CC629KlS4seAgAAAECv9KlPfard+7iCCgAAAIBC9ckrqAAAAAD44HAFFQAAAACFElABAAAAUCgBFQAAAACFElABAAAAUCgBFQAAAACFGlD0AOi8hx9+OOeee26SpLq6OhMnTtyhz+bNmzN37tzcc889efHFF1MqlTJq1Kh8+ctfTlVVVfbcc8/uHjZdqKamJvPmzcuzzz6burq6DB48OIceemi+/OUv59RTT82AATv+U9+wYUPmzJmTRYsWZfXq1dljjz1SUVGRU045JSeffHL22GOPAo6ErvTvf/87c+bMyRNPPJG1a9emrKwso0aNytSpU3P66ae3+u/eXNH7lUql3HrrrfnlL3+ZzZs37/Rzo4ma6Btefvnl3HDDDXn88cezbt267L333hk/fnzOOOOMHHPMMUUPj92sPfOCOaH3a+/5g5roG9q73rDWoCP6lUqlUtGDoOPefvvtfOlLX8ratWuTtB5QNTQ05KyzzsqyZcsyfPjwHHvssUmSxYsXZ926dfn0pz+dOXPmZNCgQd0+fjrvqquuyi233JL+/fvn2GOPTXl5ef773//m8ccfT2NjY4455pjceOONKSsra95n/fr1mTZtWv7zn/9k1KhRmTBhQhoaGrJ48eK89dZbmTp1an7zm9+kX79+BR4ZnXHfffflwgsvzJYtW3L44YdnzJgxeeutt7JkyZI0NDRkzJgxqa6uzt577928j7mi91u/fn0uueSS1NTUNG/b1UJUTfQNS5cuzdlnn52GhoZMmDAhhxxySF5//fU8+uijaWxszIwZM1JVVVX0MNlN2jMvmBN6v/aeP6iJvqG96w1rDTqsRI928cUXlyoqKkoTJ04sVVRUlJ544okd+lx99dWlioqK0jnnnFN65513mrdv2LChdOqpp5YqKipKs2bN6s5h00UeeOCBUkVFRWn8+PGl5557rkXbypUrS0cddVSpoqKidPPNN7do+/73v1+qqKgoXX755aV33323efu6detKJ510UqmioqI0b9687jgEdoPXXnut+b2fM2dOi7ba2trScccdV6qoqCj95je/adFmrujdlixZUjr22GNLFRUVpZ/+9KelyZMn7/Rzo4ma6P0aGhpKn/3sZ0sVFRWlBQsWtGhbunRpacyYMaXRo0eX/vWvfxUzQHar9s4L5oTerSPnD2qi9+vIesNag45yD6oe7JFHHsldd92Vz3/+8/nEJz7Rap+GhobcfvvtGTBgQGbOnNniEtshQ4bkJz/5SZJk7ty5eeedd7pl3HSdP//5z0mS73znOznyyCNbtB1++OH55je/mSR58MEHm7evXr069957b/bdd99ceumlLS6v/fCHP5yLL744STJnzpzdPXx2k7vuuisNDQ0ZN25cvvOd77RoO+igg3LWWWclSe6///7m7eaK3m/+/PlpbGzM7NmzM2PGjAwcOHCX/dVE37Bw4cLU1tZm8uTJ+epXv9qi7ZOf/GS+9a1vpbGxMbfccksxA2S3as+8YE7o/dp7/qAm+ob2rjesNegMAVUPtWHDhsyYMSNDhw7N5ZdfvtN+jz76aBoaGjJ27NgMHz58h/bKysqMGDEi9fX1WbJkye4cMrvB9773vVx33XX5+te/3mr7yJEjkyT19fXN2xYtWpQkOf7447PXXnvtsM/xxx+fQYMG5eWXX87zzz+/G0bN7jZ58uRceeWVOf/881tt//jHP54kee2115q3mSt6v3HjxmXBggU56aST2tRfTfQNTQvNqVOntto+ZcqUJMkDDzzQbWOi+7RnXjAn9H7tPX9QE31De9cb1hp0hoCqh7rqqqvy+uuv50c/+lGGDRu2037Lly9PkowePXqnfZraVqxY0bWDZLcbM2ZMTjzxxBx44IGttq9evTpJcsghhzRve7+aKCsra74iT030TKNHj843vvGN5vtAbK/pnnX7779/8zZzRe83bdq0lJeXt7m/mugbmt67I444otX2pve4rq4ua9as6bZx0T3aMy+YE3q/9p4/qIm+ob3rDWsNOkNA1QPV1NRk/vz5mTx5ck455ZRd9m06mdzZhJKk+S8eL730UpeNkeI9/PDDmTt3bsrKynLOOec0b29PTbz88su7d5B0u1KplL/85S9JWl4xYa5ge2qi99uyZUtef/31JGn16ock2WuvvbLffvsl8ZnQ15kT+rbWzh/UBK2tN6w16Iwdnz3PB9rGjRvz4x//OEOGDMmVV17Zpv5JWjypa3uDBw9O0vJrYPQ8r7/+ev7whz+kvr4+K1euzIoVKzJ69OjMnDkzFRUVzf3URN9244035plnnsl+++3XIrhUF2xPTfR+Te9x8v7vc11dnfe5jzMn9G2tnT+oib6nLesNdUFnCKgKcv7552flypVt6jts2LDmm5P+/Oc/z3//+9/89Kc/3elfO9+r6YaEu7rpZdPjQN28sFgdrYkmb775Zqqrq5t/Li8vz3HHHZcPf/jDLfq1pyY2bdrUpvGw+3S2Lt7rpptuyq9+9asMHDgw11xzTfbdd9/mNnNFz9GVNbEraqL327x5c/P/+0zg/ZgT+q6dnT+oib6nLesNaw06Q0BVkNra2rz44ott6rtly5YkyZIlS/LnP/85xx57bE499dQ27dt0Y7rGxsb3ff1Bgwa16TXZPTpSE+9VWVmZVatWZdOmTXnppZdy991356abbsrcuXNz44035tOf/nSS9tVEazc2pHt1ti6S/39Z/tVXX52bb745ZWVlmTVrVo455pgWfcwVPUdX1ERbqIne773vW2NjY4sncL2XzwQSc0Jf9H7nD2qi72nLesNag84QUBXkjjvuaFf/jRs35vLLL8/ee+/dpq/2NWm6tHJXl082XYa5zz77tGtMdK321sTO7LXXXqmsrExlZWUOPvjgXHHFFbn44ouzaNGi9O/fv101MWTIkC4ZEx3X2brYvHlzLrrootx3330ZOnRorr322h3CqcRc0ZN01VzxftRE7/fer1/U19fvNKDyPpOYE/qatpw/qIm+a1frDWsNOkNA1UPMmzcvr776akaMGJFf/OIXO7S/8MILSZJrr702t912WyZOnJjTTjsto0aNSpK8+uqrO33t2traJGnuS+9x8skn54orrkhtbW1eeOGFHHbYYRk1alSefvppNdEHbNmyJdOnT8/jjz+e8vLy/P73v2/xRMf3MlewPTXR+5WVleXggw9ObW1tamtrc8ABB+zQZ8OGDXn77beTeJ/7OnNC39HW8wc1QbLjesNag84QUPUQTd/PXb16dfOjPFvz1FNPJfm/G8+NGTMmSfLcc8/tdJ9nn302STJ27NguGSvdo76+Ptdcc03Wr1+fyy67LB/60Id26NOvX7/069cvpVKp+fvgY8aMyfz583daEw0NDc2Bp5roubZt25aLLroojz/+eCorK3PjjTfmIx/5yE77myvYnproG8aMGZPa2to899xzOfLII3dof+aZZ5IkH/nIR3b5RCZ6P3NC39Ce8wc10ft1ZL1hrUFn9C96ALTN9773vaxatWqn/x199NFJkurq6qxatSo///nPkySTJk3K0KFDs3z58rzyyis7vO4TTzyRdevW5YADDmj1az98cA0ePDh//etfc8899+Shhx5qtc/y5ctTKpXSr1+/jBgxIkly4oknpn///qmpqWnxBKcmCxcuzLvvvpsjjjjCXzV6sNmzZ+fee+/NIYcckptvvnmX4VRirmBHaqJvaHpc/MKFC1tt/9vf/pYk+dKXvtRtY+KDyZzQN7Tn/EFN9H4dWW9Ya9AZAqperqysLGeccUa2bduWGTNmtHiCRl1dXX72s58lSaZPn54BA1xQ15P069ev+Wb5s2bNyqpVq1q0r1u3rvn9Pf7445u/ujFs2LB87WtfS0NDQ2bOnJmtW7c271NbW5tf//rXSZLzzjuvOw6D3eDf//53brjhhgwcODCzZ8/O/vvv/777mCvYnproG0466aSMGjUqTz31VP70pz+1aHvkkUdy9913Z/DgwTnzzDMLGiEfFOaE3q+95w9qovfryHrDWoPO6FcqlUpFD4LOmzZtWv7xj3+kuro6EydObNG2ZcuWfPe7383ixYszfPjwTJo0KVu3bk1NTU3efPPNTJkyJb/+9a+zxx57FDR6Ouq97+2AAQMyceLElJeXZ926dXnyySdTX1+fgw8+OLfddluGDx/evN9bb72VM888M8uXL8+oUaNy9NFHZ+PGjfn73/+e+vr6nH766bnssssKPDI644c//GHuuuuujBgxIp/97Gd32fe8887Lfvvtl8Rc0ZvV1dXluuuua7HtzjvvTH19faZMmZJhw4Y1b6+qqsrIkSOTqIm+YsWKFTnzzDNTV1eXCRMm5NBDD82aNWvy2GOPpV+/fpk1a1bzlVb0Hh2ZF8wJvVtHzh/URO/XkfWGtQYdJaDqJXYVUCXJu+++m3nz5mXBggX5z3/+kySpqKjI17/+9Zxyyinp39/FdD3Vtm3bcvfdd+euu+7K888/nw0bNmTPPffMxz72sZxwwgn59re/3eqTUzZt2pSbb745CxcuzMsvv5yBAwdm9OjROe200zJlypQCjoSu0jQftMWDDz6Y8vLy5p/NFb3TmjVr8rnPfa5Nfbf/HFETfcNrr72W66+/PosXL87atWszdOjQTJgwIeeee24qKyuLHh67QUfnBXNC79XR8wc10ft1ZL1hrUFHCKgAAAAAKJQ4GwAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKJSACgAAAIBCCagAAAAAKNT/AwHPdyQoovuyAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 596 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "aas1 = A @ A @ mouse\n", + "aaas1 = A @ A @ A @ mouse\n", + "\n", + "plt.plot(mouse[0], mouse[1], 'k')\n", + "plt.plot(as1[0], as1[1], 'r')\n", + "plt.plot(aas1[0], aas1[1], 'g')\n", + "plt.plot(aaas1[0], aaas1[1], 'b')\n", + "plt.plot([-40,36], [0,0], ':b')\n", + "plt.title(\"Transformation de la souris (en noir) par A, A² et A³\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On note \n", + "\n", + "* que la souris est de plus en plus grosse (donc le det(A) > 1)\n", + "* que sa pointe (son point le plus à gauche) reste toujours sur l'axe horizontal\n", + "* qu'elle est de plus en plus écrasée" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Évolution du point 0 transformé par A et A³\n", + "[ 1.414 -1.414] et normé [ 0.707 -0.707]\n", + "[ 5.657 -5.657] et normé [ 0.707 -0.707]\n", + "\n", + "Évolution du point 3 transformé par A et A³\n", + "[2.828 1.414] et normé [0.894 0.447]\n", + "[32.527 5.657] et normé [0.985 0.171]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 589 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "print('Évolution du point 0 transformé par A et A³')\n", + "print(as1[:,0], \" et normé \", as1[:,0] / lin.norm(as1[:,0]))\n", + "print(aaas1[:,0], \" et normé \", aaas1[:,0] / lin.norm(aaas1[:,0]))\n", + "print('\\nÉvolution du point 3 transformé par A et A³')\n", + "print(as1[:,3], \" et normé \", as1[:,3] / lin.norm(as1[:,3]))\n", + "print(aaas1[:,3], \" et normé \", aaas1[:,3] / lin.norm(aaas1[:,3]))\n", + "\n", + "plt.plot([0,mouse[0][0]], [0,mouse[1][0]], '-or') # vecteur (0,0) -- point 0 de la souris\n", + "plt.plot([0,mouse[0][3]], [0,mouse[1][3]], '-og') # vecteur (0,0) -- point 3 de la souris\n", + "plt.plot([0,as1[0][0]], [0,as1[1][0]], '--or')\n", + "plt.plot([0,as1[0][3]], [0,as1[1][3]], '--og')\n", + "plt.plot([0,aaas1[0][0]], [0,aaas1[1][0]], ':or')\n", + "plt.plot([0,aaas1[0][3]], [0,aaas1[1][3]], ':og')\n", + "plt.title(\"Transformation des point 0 et 3 de la souris A et A³\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Les transformations du point 0 de la souris par A et A³ sont sur la droite qui passe par (0,0) et le point 0 de la souris (en rouge) !" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Vecteurs propres et valeurs propres\n", + "\n", + "Calculons les valeurs propres et vecteurs propres de A.\n", + "\n", + "Par définition les valeurs propres et vecteurs propres respectent cette propriété :\n", + "\n", + "$$ A \\, {\\bf v_i} = \\lambda_i \\, {\\bf v_i} $$\n", + "\n", + "pour tout couple de valeur propre / vecteur propre $(\\lambda_i, {\\bf v_i})$. \n", + "\n", + "Cela veut dire que si un vecteur ${\\bf w}$ est sur la droite générée par ${\\bf v_i} $ alors appliquer $A \\, {\\bf w}$ le laisse sur la même droite. Ci-dessus on a déjà trouvé les vecteurs propres de A (avec pas mal de chance)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de A : [3.+0.j 2.+0.j] \n", + "\n", + "Vecteurs propres de A (chaque vecteur propre est écrit verticalement):\n", + " [[ 1. -0.707]\n", + " [ 0. 0.707]]\n" + ] + } + ], + "source": [ + "val_propre, vec_propre = lin.eig(A)\n", + "print(\"Valeurs propres de A :\", val_propre,\"\\n\")\n", + "print(\"Vecteurs propres de A (chaque vecteur propre est écrit verticalement):\\n\", vec_propre)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Le premier vecteur propre (1,0) correspond à la valeur propre 3\n", + "* Le second vecteur propre (-0.07, 0.707) correspond à la valeur propre 2\n", + "\n", + "Le point 0 de la souris est sur l'axe du second vecteur propre et on a donc\n", + "\n", + "$$A³ \\, s[0] = 2 \\times 2 \\times 2 \\times s[0]$$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " A³ s[0] = [ 5.657 -5.657] \n", + "8 A s[0] = [ 5.657 -5.657]\n" + ] + } + ], + "source": [ + "print(' A³ s[0] = ', aaas1[:,0], \"\\n8 s[0] = \", 2*2*2*mouse[:,0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Les vecteurs propres sont des sortes d'attracteurs qui vont capturer tous les points si on fait un nombre infini\n", + "de multiplication par A." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Les 12 points de la souris multipliés par A¹⁰ puis normés :\n", + "[[ 0.707 1. 1. 1. 1. 1. -0.707 -1. -1. -1. -1. -1. ]\n", + " [-0.707 -0.006 0.004 0.009 0.014 0.024 0.707 0.009 0. -0.004 -0.009 -0.018]]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 322, + "width": 599 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "A10 = np.linalg.matrix_power(A,10)\n", + "a10s1 = np.array([x/lin.norm(x) for x in (A10 @ mouse).T]).T\n", + "print(\"Les 12 points de la souris multipliés par A¹⁰ puis normés :\")\n", + "print(a10s1[:,:-1])\n", + "\n", + "plt.plot(a10s1[0], a10s1[1], 'ob')\n", + "plt.title(r\"Transformation des points de la souris par $A^{10}$ puis normés\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Tous les points sont alignés sur le premier vecteur propre sauf ceux qui ont commencé alignés sur le second vecteur propre." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Nombre de points proche du 1er vecteur propre : 40\n", + "Nombre de points proche du 2e vecteur propre : 0\n" + ] + } + ], + "source": [ + "N = 100\n", + "cercle = np.array([[np.cos(i * 2*np.pi/N), np.sin(i * 2*np.pi/N)] for i in range(N)]).T\n", + "a10c = np.array([x for x in (A10 @ cercle).T]).T\n", + "a10cn = np.array([x/lin.norm(x) for x in a10c.T]).T # a10c normé\n", + "nb1 = np.sum([lin.norm(a10cn[:,i] - vec_propre[:,0]) < 0.01 for i in range(N)]) \\\n", + " + np.sum([lin.norm(a10cn[:,i] + vec_propre[:,0]) < 0.01 for i in range(N)])\n", + "nb2 = np.sum([lin.norm(a10cn[:,i] - vec_propre[:,1]) < 0.01 for i in range(N)]) \\\n", + " + np.sum([lin.norm(a10cn[:,i] + vec_propre[:,1]) < 0.01 for i in range(N)])\n", + "print(\"Nombre de points proche du 1er vecteur propre : \", nb1)\n", + "print(\"Nombre de points proche du 2e vecteur propre : \", nb2)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 572, + "width": 1164 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(2,2, figsize=(20,10))\n", + "ax[0,0].plot(cercle[0], cercle[1], '.', label='cercle' )\n", + "ax[0,1].plot((A @ cercle)[0], (A @ cercle)[1], '.', label='A cercle' )\n", + "ax[1,0].plot((A @ A @ A @ cercle)[0], (A @ A @ A @ cercle)[1], '.', label='A³ cercle' )\n", + "ax[1,1].plot(a10c[0], a10c[1], '.' , label=r'$A^{10}$ cercle')\n", + "for x in ax.flat:\n", + " x.axis(\"equal\")\n", + " x.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On voit que les points du cercles s'alignent dans l'axe du premier vecteur propre." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Le cas des matrices de rotation\n", + "\n", + "On sait bien que si on applique plusieurs fois une rotation tous les points ne vont pas s'aligner dans une direction.\n", + "On a donc un comportement totalement différent. Qu'en est-il des vecteurs propres d'une matrice de rotation ?" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de R : [0.809+0.588j 0.809-0.588j] \n", + "\n", + "Norme des valeurs propres de R : 1.0 et 1.0 \n", + "\n", + "Vecteurs propres de R :\n", + " [[0.707+0.j 0.707-0.j ]\n", + " [0. -0.707j 0. +0.707j]]\n" + ] + } + ], + "source": [ + "def Rot(θ):\n", + " return np.array([[np.cos(θ), -np.sin(θ)], [np.sin(θ), np.cos(θ)]])\n", + "\n", + "R = Rot(2*np.pi/10)\n", + "\n", + "R_valp, R_vecp = lin.eig(R)\n", + "print(\"Valeurs propres de R :\", R_valp,\"\\n\")\n", + "print(\"Norme des valeurs propres de R :\", lin.norm(R_valp[0]), \" et \", lin.norm(R_valp[1]), \"\\n\")\n", + "print(\"Vecteurs propres de R :\\n\", R_vecp)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de R : [0.+1.j 0.-1.j] \n", + "\n", + "Vecteurs propres de R :\n", + " [[0.707+0.j 0.707-0.j ]\n", + " [0. -0.707j 0. +0.707j]]\n" + ] + } + ], + "source": [ + "# regardons un autre angle\n", + "R = Rot(np.pi/2)\n", + "\n", + "R_valp, R_vecp = lin.eig(R)\n", + "print(\"Valeurs propres de R :\", R_valp,\"\\n\")\n", + "print(\"Vecteurs propres de R :\\n\", R_vecp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On constate que\n", + " \n", + "* les valeurs propres et vecteurs propres sont des complexes\n", + "* les valeurs propres sont de norme 1 (normal puisque c'est une isométrie)\n", + "* l'angle de rotation θ se retrouve dans les valeurs propres $ v_p = e^{\\pm \\,i\\, θ}$\n", + "\n", + "C'est le second point qui fait qu'aucun des vecteurs propre ne peut prendre l'ascendant et qu'on ne retrouve pas\n", + "l'alignement des points de notre figure le long du premier vecteur propre." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0.9510565162951535+0.3090169943749474j),\n", + " (0.9510565162951535+0.3090169943749474j),\n", + " (0.9510565162951535-0.3090169943749474j))" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "θ = np.pi / 10\n", + "R = Rot(θ)\n", + "R_valp, R_vecp = lin.eig(R)\n", + "np.e**(0+1j * θ), R_valp[0], R_valp[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Symétrie axiale horizontale\n", + "\n", + "Sx = \n", + "$\n", + "\\begin{bmatrix}\n", + "1 & 0 \\\\\n", + "0 & -1 \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "Là c'est simple puisque la matrice est diagonale, donc ses valeurs propres sont les valeurs de la diagonales.\n", + "Elles ont la même norme donc pas d'alignement des points dans la direction du premier vecteur propre." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de Sx : [ 1.+0.j -1.+0.j] \n", + "\n", + "Vecteurs propres de Sx :\n", + " [[1. 0.]\n", + " [0. 1.]]\n" + ] + } + ], + "source": [ + "Sx = np.array([[1, 0], [0, -1]])\n", + "\n", + "Sx_valp, Sx_vecp = lin.eig(Sx)\n", + "print(\"Valeurs propres de Sx :\", Sx_valp,\"\\n\")\n", + "print(\"Vecteurs propres de Sx :\\n\", Sx_vecp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Une matrice diagonale ne modifie que la i-ième coordonnée de **x** par la i-ème valeur de sa diagonale. Aussi ses vecteurs propres sont ceux de la base d'origine." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4, 0, 0, 0, 0],\n", + " [0, 7, 0, 0, 0],\n", + " [0, 0, 9, 0, 0],\n", + " [0, 0, 0, 8, 0],\n", + " [0, 0, 0, 0, 6]])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D = np.diag(np.random.randint(10,size=5))\n", + "D" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de D : [4.+0.j 7.+0.j 9.+0.j 8.+0.j 6.+0.j] \n", + "\n", + "Vecteurs propres de D :\n", + " [[1. 0. 0. 0. 0.]\n", + " [0. 1. 0. 0. 0.]\n", + " [0. 0. 1. 0. 0.]\n", + " [0. 0. 0. 1. 0.]\n", + " [0. 0. 0. 0. 1.]]\n" + ] + } + ], + "source": [ + "D_valp, D_vecp = lin.eig(D)\n", + "print(\"Valeurs propres de D :\", D_valp,\"\\n\")\n", + "print(\"Vecteurs propres de D :\\n\", D_vecp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Diagonalisation d'une matrice\n", + "\n", + "On voit l'importance des valeurs et vecteurs propres pour caractériser une application linéaire. En fait ils sont tellement\n", + "important qu'en appliquant le bon changement de repère, l'application est représentée par une matrice diagonale\n", + "contenant les valeurs propres. \n", + "\n", + "$$\n", + "\\exists P \\; / \\; A = P\\, \\Lambda \\, P^{-1} \\quad \\textrm{avec } \\Lambda \\textrm{ la matrice diagonale des valeurs propres } \\lambda_i\n", + "$$\n", + "\n", + "La matrice de passage $P$ représente la nouvelle base donc sans surprise il s'agit des vecteurs propres. \n", + "\n", + "Vérifions le avec A :" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A :\n", + " [[3 1]\n", + " [0 2]] \n", + "\n", + "𝑃 Λ inv(𝑃) :\n", + " [[3.+0.j 1.+0.j]\n", + " [0.+0.j 2.+0.j]]\n" + ] + } + ], + "source": [ + "print('A :\\n', A, '\\n')\n", + "print('𝑃 Λ inv(𝑃) :\\n', vec_propre @ np.diag(val_propre) @ lin.inv(vec_propre))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ainsi la formule pour obtenir la diagonalisation de A est $\\; \\Lambda = P^{-1} \\, A \\, P\\;$ lorsqu'on connait ses\n", + "vecteurs propres (en pratique si on a les vecteurs propres on a aussi les valeurs propres et donc la diagonalisation de A)." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P :\n", + " [[ 1. -0.707]\n", + " [ 0. 0.707]] \n", + "\n", + "inv(𝑃) A 𝑃 :\n", + " [[3. 0.]\n", + " [0. 2.]]\n" + ] + } + ], + "source": [ + "print('P :\\n', vec_propre, '\\n')\n", + "print('inv(𝑃) A 𝑃 :\\n', lin.inv(vec_propre) @ A @ vec_propre)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On retrouve nos 2 valeurs propres sur la diagonale." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Matrice inversible** Notons que si une des valeurs propres est nulle alors $\\Lambda$ n'est pas inversible et comme il s'agit de\n", + "la même application que A (dans un autre repère) alors A n'est pas inversible non plus.\n", + "\n", + "**Matrice non diagonalisable** Si l'ensemble des vecteurs propres ne génère pas un espace de la même dimension que d'origine (c.a.d. que 2 vecteurs propres sont colinéaires), alors on ne peut pas diagonaliser la matrice.\n", + "\n", + "**Matrice symétrique de réels** Dans ce cas il existe une matrice de passage orthogonale et la matrice diagonale des valeurs propres a toutes ses valeurs réelles.\n", + "\n", + "**Matrice symmétrique réelle définie positive** (c.a.d. $\\forall {\\bf x} \\in ℝ^n, \\; {\\bf x}^T\\, A \\, {\\bf x} > 0$) a toutes ses valeurs propres strictement positives." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma25 Drones -- Exercice.ipynb b/PVCM/cama/fr/ma25 Drones -- Exercice.ipynb new file mode 100644 index 0000000..019ce93 --- /dev/null +++ b/PVCM/cama/fr/ma25 Drones -- Exercice.ipynb @@ -0,0 +1,295 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5, + "cells": [ + { + "cell_type": "markdown", + "id": "3235ec05", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Spectacle de drones\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "630fb2b1", + "metadata": { + "lang": "fr" + }, + "source": [ + "Le but est de faire un joli spectacle nocturne. \n", + "\n", + "On a un ensemble de 100 drones qui forment l'image d'un bateau en 3D. Pour nous il s'agit d'un ensemble de points 3D (centre de gravité de chaque drone) qu'on range dans un tableau Numpy 3 par 100. Le bateau tient dans un cube de 20x20x20. \n", + "\n", + "Initialement \n", + "\n", + "* l'ensemble des drones est centré en (0,0,0) donc si on veut positionner le bateau en (10, 20, 200) il faut faire une translation d'autant sur l'ensemble des drones.\n", + "* l'axe principal du bateau est l'axe de x c.a.d que l'avant du bateau est en x=10 et l'arrière en x=-10." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "58dcf259", + "metadata": { + "ExecuteTime": { + "end_time": "2024-03-25T09:43:59.562566Z", + "start_time": "2024-03-25T09:43:59.487939Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-20., 20., 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 0., 0., 0., -10., 10.],\n", + " [ 0., 0., -5., 5., 0., 0., 0.]])" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "#boat = np.random.randint(-100, 100, size=(3,10)) / 10 # with a little luck...\n", + "\n", + "# A formation that allows for easier debugging\n", + "\n", + "boat = np.array([[-20., 0., 0.],\n", + " [ 20., 0., 0.],\n", + " [ 0., 0., -5.],\n", + " [ 0., 0., 5.],\n", + " [ 0., 0., 0.],\n", + " [ 0., -10., 0.],\n", + " [ 0., 10., 0.],\n", + " ])\n", + "boat = boat.T\n", + "boat" + ] + }, + { + "cell_type": "markdown", + "id": "311abaaa", + "metadata": { + "lang": "fr" + }, + "source": [ + "On désire déplacer le bateau dans le ciel en lui faisant faire des figures (les unités utilisées sont le mètre et la seconde). Tous les mouvements sont décomposés seconde par seconde c.a.d. qu'on donne la position de tous les drones à chaque seconde (un autre programme se débrouille pour déplacer les drones à leur position suivante).\n", + "\n", + "### Figure 1\n", + "\n", + "Faire tourner le bateau (donc l'ensemble des drones) à l'horizontal autour du point (0,0,80) à une distance de 100 m. Il fait un tour complet en 5 minutes. \n", + "\n", + "On fera attention à ce que l'orientation du bateau suive le mouvement, c.a.d. que l'avant du bateau soit toujours bien orientée. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4818926d", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def circle(boat, t):\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "35cc29f4", + "metadata": {}, + "outputs": [], + "source": [ + "# Code to display\n", + "# Do not touch this unless you know what you are doing\n", + "import matplotlib.animation\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.patches import Circle\n", + "from matplotlib.transforms import Affine2D\n", + "import mpl_toolkits.mplot3d.art3d as art3d\n", + "matplotlib.rcParams['animation.embed_limit'] = 256 # 256mb max animation size\n", + "\n", + "plt.rcParams[\"animation.html\"] = \"jshtml\"\n", + "plt.rcParams['figure.dpi'] = 100 \n", + "plt.ioff()\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(projection='3d')\n", + "\n", + "# 5min -> 300 sec;\n", + "FRAMEPERSEC = 1.\n", + "\n", + "def animate(t):\n", + " boat_prime = circle(boat_start, t/FRAMEPERSEC)\n", + " plt.cla()\n", + " p = Circle((0, 0), 100, fill=False)\n", + " ax.add_patch(p)\n", + " art3d.pathpatch_2d_to_3d(p, z=80, zdir=\"z\")\n", + " plt.plot(boat_prime[0,:], boat_prime[1,:], boat_prime[2,:], '.b')\n", + " ax.set_xlim([-120, 120])\n", + " ax.set_ylim([-120, 120])\n", + " ax.set_zlim([0, 120]) # alternative\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_ylabel(\"y\")\n", + " ax.set_zlabel(\"z\")\n", + " ax.set_title(f\"t: {t} sec\")\n", + "\n", + "\n", + "matplotlib.animation.FuncAnimation(fig, animate, frames=int(300*FRAMEPERSEC))" + ] + }, + { + "cell_type": "markdown", + "id": "2318d7f5", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Figure 2\n", + "\n", + "On désire faire tourner le bateau sur son axe principal (l'axe des x) jusqu'à revenir à la position d'origine. En aviation on appelle cela faire un tonneau (rotation de 360 sur l'axe du roulis). Écrire la fonction `barrel_roll(boat, T, t)` qui retourne la position de chaque drone, à l'instant `t` si un tour complet dure `T`seconds." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3bbdb81d", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def barrel_rool(boat, T, t):\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3861ca65", + "metadata": {}, + "outputs": [], + "source": [ + "# Code to display\n", + "# You can change this\n", + "Tcomplete = 20\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(projection='3d')\n", + "\n", + "# Do not touch this unless you know what you are doing\n", + "def animate2(t):\n", + " boat_prime = barrel_roll(boat, Tcomplete, t)\n", + " plt.cla()\n", + " plt.plot(boat_prime[0,:], boat_prime[1,:], boat_prime[2,:], '.b')\n", + " ax.set_xlim([-60, 60])\n", + " ax.set_ylim([-60, 60])\n", + " ax.set_zlim([-60, 60])\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_ylabel(\"y\")\n", + " ax.set_zlabel(\"z\")\n", + " ax.set_title(f\"t: {t} sec\")\n", + "\n", + "# One frame per second for 2 complete rolls\n", + "matplotlib.animation.FuncAnimation(fig, animate2, frames=2*Tcomplete)" + ] + }, + { + "cell_type": "markdown", + "id": "65cfd841", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Figure 3\n", + "\n", + "Combiner les figures 1 et 2 pour que le bateau fasse un tonneau en 10 secondes toutes les 30 secondes." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fc7aed8e", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def combined_move(boat, t):\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d2265fd3", + "metadata": {}, + "outputs": [], + "source": [ + "# Code to display\n", + "# Do not touch this unless you know what you are doing\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(projection='3d')\n", + "\n", + "def animate3(t):\n", + " boat_prime = combined_move(boat, t/FRAMEPERSEC)\n", + " plt.cla()\n", + " p = Circle((0, 0), 100, fill=False)\n", + " ax.add_patch(p)\n", + " art3d.pathpatch_2d_to_3d(p, z=80, zdir=\"z\")\n", + " plt.plot(boat_prime[0,:], boat_prime[1,:], boat_prime[2,:], '.b')\n", + " ax.set_xlim([-120, 120])\n", + " ax.set_ylim([-120, 120])\n", + " ax.set_zlim([0, 120])\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_ylabel(\"y\")\n", + " ax.set_zlabel(\"z\")\n", + " ax.set_title(f\"t: {t} sec\")\n", + "\n", + "# 5min -> 300 sec\n", + "matplotlib.animation.FuncAnimation(fig, animate3, frames=int(300*FRAMEPERSEC))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7c2da47f", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2f9122e6-899e-4afa-a49a-992e48e99647", + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma26 Vecteurs propres -- Exercices.ipynb b/PVCM/cama/fr/ma26 Vecteurs propres -- Exercices.ipynb new file mode 100644 index 0000000..88d82df --- /dev/null +++ b/PVCM/cama/fr/ma26 Vecteurs propres -- Exercices.ipynb @@ -0,0 +1,305 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Cas d'utilisation des valeurs et vecteurs propres" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fibonnacci\n", + "\n", + "La suite de Fibonnacci est $x_n = x_{n-2} + x_{n-1}$ avec $x_0 = 1, x_1 = 1$.\n", + "\n", + "Quelle est la complexité pour calculer $x_n$ ?\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Comme on a 2 termes à droite du signe égal, écrivons Fibonnacci sous forme d'un système matriciel $2\\times 2$ :\n", + "\n", + "$\n", + "\\begin{align}\n", + "x_{n-1} &= x_{n-1} \\\\\n", + "x_n &= x_{n-2} + x_{n-1} \\\\\n", + "\\end{align}\n", + "$\n", + "ce qui donne\n", + "$\n", + "\\begin{bmatrix}\n", + "x_{n-1}\\\\\n", + "x_n \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1 \\\\\n", + "1 & 1 \\\\\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "x_{n-2}\\\\\n", + "x_{n-1} \\\\\n", + "\\end{bmatrix}\n", + "$\n", + "\n", + "Écrire la matrice F ci-dessous et vérifier que le 6e élément de la suite de Fibonacci est 8 en n'utilisant que \n", + "la matrice F et les valeurs initiales de la suite. La fonction `numpy.linalg.matrix_power` pourra vous être utile." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calculer n produits matriciels n'est pas rentable, par contre sachant que\n", + "$F = P\\, D\\, P^{-1}$ avec\n", + "\n", + "* P la matrice des vecteurs propres\n", + "* D la matrice diagonale des valeurs propres\n", + "\n", + "on peut faire quelque chose car il va avoir des simplification lors du calcul de de $F^n$. \n", + "\n", + "* Ecrire la formule matriciel de la suite de Fibonnacci en fonction de P et D. \n", + "* Expliquer pourquoi le calcul du n-ème élément de la suite peut se faire en temps constant." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Écrire la fonction `fibo(n)` qui calcule le n-ème élément de la suite de Fibonnacci en temps constant." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vérifier que votre fonction est en temps constant en chronométrant `fibo(5)` et `fibo(1000)` avec la commande \n", + "`%timeit` de Jupyter." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Google page rank\n", + "\n", + "Soit N pages web numérotées qui font référence les unes aux autres. Disons que si la page 3 est référencée par les pages 8 9 et 13 j'écris $x_3 = x_8 + x_9 + x_{13}$. On voit qu'on peut écrire ces référencements dans une\n", + "matrice avec le i-ième ligne qui décrit par qui est référencée la i-ème page web. Cette matrice a un 1 dans\n", + "la j-ième colonne si la page j cite la page i et sinon un 0." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0, 1, 0, 0, 0, 1, 0, 0],\n", + " [0, 0, 0, 0, 0, 0, 1, 0],\n", + " [1, 1, 0, 0, 1, 0, 1, 1],\n", + " [1, 1, 1, 0, 1, 1, 0, 0],\n", + " [1, 1, 1, 0, 0, 0, 0, 0],\n", + " [0, 0, 1, 1, 1, 0, 1, 0],\n", + " [1, 1, 0, 1, 0, 1, 0, 1],\n", + " [1, 0, 0, 0, 0, 0, 0, 0]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.random.seed(42)\n", + "N = 8\n", + "A = np.random.randint(2,size=(N,N))\n", + "for i in range(len(A)):\n", + " A[i,i] = 0 # on ne compte pas les auto-référencements\n", + "A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Cet article](https://www.math.upenn.edu/~wilf/website/KendallWei.pdf) indique que Google à l'époque de l'écriture de l'article (2001) basait son classement des pages web \n", + "en utilisant les vecteurs propres de cette matrice (vous n'avez pas besoin de lire cet article pour faire l'exercice).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Approche itérative\n", + "Une bonne introduction qui va un peu plus loin peut-être trouvé [ici](https://pi.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html).\n", + "\n", + "Dans un premier temps on procède de la manière suivant pour trouver l'importance d'une page:\n", + "Étant donné N page à évaluer \n", + "* On initialise un vecteur __v__ de taille N avec 1 partout -> Correspond à une distribution uniforme de l'importance initialement\n", + "* On calcule le produit matrice vecteur A __v__\n", + "* On normalise le résultat pour que la norme 1 soit égale au nombre de pages (N)\n", + "* On répète ces étapes jusqu'à un point fixe\n", + "\n", + "De cette manière l'entrée i du vecteur __v__ correspond à l'importance de la page i -> Discutez pourquoi." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.774 0.387 1.419 1.419 1.032 1.29 1.548 0.129]]\n", + "[[0.542 0.5 1.25 1.583 0.833 1.75 1.292 0.25 ]]\n", + "[[0.742 0.426 1.127 1.608 0.756 1.636 1.526 0.179]]\n", + "[[0.672 0.497 1.183 1.527 0.748 1.635 1.496 0.242]]\n", + "[[0.694 0.487 1.19 1.542 0.766 1.613 1.489 0.219]]\n", + "[[0.683 0.484 1.189 1.545 0.771 1.622 1.481 0.226]]\n", + "[[0.686 0.482 1.187 1.546 0.767 1.624 1.485 0.222]]\n", + "[[0.686 0.484 1.186 1.546 0.767 1.624 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n", + "[[0.686 0.484 1.187 1.545 0.767 1.623 1.485 0.223]]\n" + ] + } + ], + "source": [ + "v = np.zeros((N,1))\n", + "vprime = np.ones((N,1))\n", + "\n", + "while (np.absolute(np.max(vprime - v)) > 1e-5): # which norm is used here?\n", + " v = vprime\n", + " vprime = \n", + " vprime *= \n", + " print(vprime.T)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Un autre approche\n", + "\n", + "Vous constatez que A.__v__ = α * __v__ pour une constante α. Est-ce que ça vous rappelle quelque chose ?\n", + "\n", + "* On considère que les composantes du premier vecteur propre représentent la valeur de chaque page. Calculez les valeurs des pages. Comparez avec le résultat obtenue auparavant.\n", + "* Calculez le nombre de citations pour chaque page." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma30 ACP.ipynb b/PVCM/cama/fr/ma30 ACP.ipynb new file mode 100644 index 0000000..273e13b --- /dev/null +++ b/PVCM/cama/fr/ma30 ACP.ipynb @@ -0,0 +1,461 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Analyse en composantes principales (ACP)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import numpy.linalg as lin\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib\n", + "\n", + "def arrow2D(a,b, color='k', **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Nuage de points\n", + "\n", + "Lorsqu'on a un nuage de points on peut étudier sa forme par une **analyse en composantes principales** (ACP). Cela revient\n", + "à chercher les vecteurs propres de la matrice de covariance (ou de corrélation qui est la matrice de covariance normalisée par les écarts types). Ces vecteurs propres nous décrivent le nuage de points.\n", + "\n", + "Pour le vérifier fabriquons\n", + "un nuage de points avec une corrélation forte entre $x$ et $y$ :\n", + "\n", + "$$ y = 0.2 \\, x + 1.45 + U(-1,1) \\quad \\textrm{avec U la loi uniforme qui simule du bruit.}$$\n", + "\n", + "Cette relation linéaire entre $x$ et $y$ permet de savoir que l'on a :\n", + "\n", + "* une pente de 0.2\n", + "* un décalage vertical de 1.45 en x=0\n", + "\n", + "Le but est de \n", + "voir si, avec seulement le nuage de points, on peut retrouver la corrélation entre $x$ et $y$ malgré le bruit. \n", + "\n", + "$$ y = α x + β$$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "N = 50\n", + "x = 10 * np.random.rand(N) - 5\n", + "nuage = np.array([x, 0.2 * x + 1.45 + (2 * np.random.rand(N) - 1)])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 589 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.title('Un nuage de points')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Graphiquement on cherche la droite qui minimise la distance entre les points et leur projection sur la droite.\n", + "\n", + "\n", + "On peut aussi construire la **matrice de covariance** (cf ci-dessous) et voir que la pente du premier vecteur propre est \n", + "égale à ce coefficient 0.2 qui relie x à y. \n", + "\n", + "Ensuite la moyenne du nuage de point dans un point de la droite qu'on cherche ce qui fait qu'avec le vecteur directeur qu'est le premier vecteur propre, on a notre droite." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[9.107, 1.925],\n", + " [1.925, 0.764]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov = np.cov(nuage.copy())\n", + "cov" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Profitons de l'occasion pour rappeler que si une matrice est symétrique alors\n", + "\n", + "* ses valeurs propres sont réelles\n", + "* ses vecteurs propres sont orthogonaux" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de la matrice de covariance : [9.53 0.341] \n", + "\n", + "Vecteurs propres de la matrice de covariance :\n", + " [[ 0.977 -0.215]\n", + " [ 0.215 0.977]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_26870/3419464211.py:2: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " val = val.astype('float') # on convertit puisqu'on sait que ce sont des réels\n" + ] + } + ], + "source": [ + "val, vec = lin.eig(cov)\n", + "val = val.astype('float') # on convertit puisqu'on sait que ce sont des réels\n", + "print(\"Valeurs propres de la matrice de covariance :\", val,\"\\n\")\n", + "print(\"Vecteurs propres de la matrice de covariance :\\n\", vec)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 595 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "arrow2D((0,0), val[0] * vec[:,0], 'r') # vecteur propre multiplié par sa valeur propre\n", + "arrow2D((0,0), val[1] * vec[:,1], 'g')\n", + "plt.title('Un nuage de points et les vecteurs propres de sa matrice de covariance')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Vérifions que la pente du premier vecteur propre est proche de 0.2 :" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "La pente est de 0.21963615318288862 \n", + "\n", + "Le points moyen du nuage est [-0.152 1.327]\n" + ] + } + ], + "source": [ + "pente = vec[1,0] / vec[0,0] \n", + "print(\"La pente est de\", pente, '\\n')\n", + "moyenne = nuage.mean(axis=1)\n", + "print(\"Le points moyen du nuage est\", moyenne)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Le décalage verticale est de 1.360408912029785\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 589 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "eq_droite = lambda x: pente * (x - moyenne[0]) + moyenne[1]\n", + "\n", + "print(\"Le décalage verticale est de \", eq_droite(0))\n", + "\n", + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.plot([nuage[0].min(), nuage[0].max()], [eq_droite(nuage[0].min()), eq_droite(nuage[0].max())]) \n", + "plt.title(\"Un nuage de points et sa droite d'approximation\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "On a donc α = 0.220 et β = 1.360 sachant que le nuage a été généré avec 0.2 et 1.45\n" + ] + } + ], + "source": [ + "print(f'On a donc α = {pente:.3f} et β = {eq_droite(0):.3f} sachant que le nuage a été généré avec 0.2 et 1.45')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Matrice de covariance\n", + "\n", + "La covariance entre deux jeux de données __x__ et __y__ indique à quel point il sont liés (c.a.d. si la i-ème valeur de __y__ peut se déduire de la i-ème valeur de __x__ ou pas). Si leur covariance est grande \n", + "en valeur absolue alors ils sont fortement liées, si elle est proche de 0, elles sont soit indépendantes \n", + "soit liée par une relation plus compliquée qu'une simple relation linéaire.\n", + "\n", + "La covariance mesure la relation linéaire entre 2 variables (cf [cette vidéo](https://www.youtube.com/watch?v=UM-AOmT2RWk)\n", + "pour une présentation rapide et complète de la covariance et de ses propriétés).\n", + "\n", + "$$\n", + "\\textrm{cov}(\\textbf{x},\\textbf{y}) = \\frac{1}{N} \\sum_{i=1}^N (x_i - \\overline{\\textbf{x}}) (y_i - \\overline{\\textbf{y}})\n", + "$$\n", + "\n", + "avec $N$ le nombre de points du nuage, $\\overline{\\textbf{x}}$ et $\\overline{\\textbf{y}}$ les moyennes de $\\textbf{x}$ et de $\\textbf{y}$.\n", + "\n", + "Si on place l'orgine des axes à la moyenne $(\\overline{\\textbf{x}},\\overline{\\textbf{y}})$ alors la formule indique que pour avoir corrélation il faut qu'il y ait plus de point dans 2 quadrans diagonalement opposés. \n", + "\n", + "Si à l'inverse on a tire des points aléatoire, donc pas de relation entre x et y, alors on aura des points répartit uniforméments autour de la moyenne donc une\n", + "covariance nulle.\n", + "Enfin si toutes les valeurs de $\\textbf{y}$ valent une même valeur, alors elles ne dépendent pas de x et $y_i - \\overline{\\textbf{y}} = 0 \\; \\forall i$ donc la covariance est nulle.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 708 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.plot([moyenne[0], moyenne[0]], [nuage[1].min(), nuage[1].max()],'k')\n", + "plt.plot([nuage[0].min(), nuage[0].max()], [moyenne[1], moyenne[1]],'k')\n", + "plt.title('La covariance indique une direction privilégiée et donc plus de points dans les quadrans traversés')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Ici on voit bien que la grande majorité des points sont dans 2 quadrans opposés, dont nos 2 variables sont liées.\n", + "\n", + "La matrice de covariance exprime toutes les covariances possibles entre les variables. Dans notre cas où \n", + "le nuage a 2 dimensions, on a :\n", + "\n", + "$$\n", + "\\textrm{Cov(nuage 2D)} = \n", + "\\begin{bmatrix}\n", + "\\textrm{cov}(\\textbf{x},\\textbf{x}) & \\textrm{cov}(\\textbf{x},\\textbf{y}) \\\\\n", + "\\textrm{cov}(\\textbf{y},\\textbf{x}) & \\textrm{cov}(\\textbf{y},\\textbf{y}) \\\\\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[8.925, 1.887],\n", + " [1.887, 0.749]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov = lambda x,y : np.dot((x - x.mean()), (y - y.mean())) / len(x)\n", + "\n", + "Cov = lambda x,y : np.array([[cov(x,x), cov(x,y)], [cov(y,x), cov(y,y)]])\n", + "\n", + "Cov(nuage[0], nuage[1]) # par défaut Numpy divise par (N-1), avec bias=True il divise par N et donne ce résultat" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Ce résultat montre que x est très liés avec lui-même ce qui est une évidence. Par contre il semble que y soit\n", + "moins lié avec lui-même. En fait les variation de y sont plus petites (entre 0 et 3 alors que x varie entre -5 et 5) ce qui explique cette plus petite valeur. Le fait que cov(x,y) soit plus grand que cov(y,y) est déjà un\n", + "indicateur que x et y sont liés.\n", + "\n", + "Le calcul des valeurs et vecteurs propres de la matrice de covariance est encore plus intéressant avec\n", + "une grande dimension car il fait ressortir lesquelles sont les plus importantes. Ainsi l'exemple de l'article\n", + "de Wikipédia sur l'['analyse en composantes principales](https://fr.wikipedia.org/wiki/Analyse_en_composantes_principales)\n", + "sur la pollution de l'eau du Doubs montre que le premier vecteur propre est celui des polluants connus : nitrates (nit), phosphates (pho), ammoniaque (amm)\n", + "et le second est celui du PH. On notera l'anti-corrélation entre la teneur en oxygène et les polluants.\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Pour bien comprendre cette figure et voir un cas d'utilisation, je vous invite à regarder cet\n", + "[exemple d'ACP avec Excel](https://www.youtube.com/watch?v=GNBeWpkHFJw)." + ] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma31 Syst\303\250me d'\303\251quations.ipynb" "b/PVCM/cama/fr/ma31 Syst\303\250me d'\303\251quations.ipynb" new file mode 100644 index 0000000..2d5453a --- /dev/null +++ "b/PVCM/cama/fr/ma31 Syst\303\250me d'\303\251quations.ipynb" @@ -0,0 +1,799 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Systèmes matriciels\n", + "\n", + "Un système de plusieurs équations à autant d'inconnues peut s'écrire sous forme d'un système matriciel de la forme $A {\\bf x} = {\\bf b}$ c.a.d.\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "a_{11} a_{12} \\ldots a_{1n} \\\\\n", + "a_{21} a_{22} \\ldots a_{2n} \\\\\n", + " \\vdots \\\\\n", + "a_{n1} a_{n2} \\ldots a_{nn} \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "\\vdots \\\\\n", + "x_{n} \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "b_{1} \\\\\n", + "b_{2} \\\\\n", + "\\vdots \\\\\n", + "b_{n} \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Ainsi si votre épicier ne vous donne pas le prix des pommes, poires et bananes mais que vous en achetez 3 fois des quantités différentes, vous pouvez retrouver le prix de chaque fruit. Il suffit de résoudre les 3 équations\n", + "qui correspondent aux 3 achats ou le système matriciel 3x3 correpondant. Pour résourdre ce dernier la facon intuitive est d'inverser A et de calculer $A^{-1}\\, {\\bf b}$ :" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.8, 0.9, 0.6])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# A est la quantité de chaque fruit achetée\n", + "# x est le prix de chaque fruit\n", + "# b est la somme qu'on a payé pour chaque course\n", + "\n", + "A = np.array([[6,5,4], [5,3,2], [7,3,2]])\n", + "b = np.array([11.7, 7.9, 9.5])\n", + "\n", + "x = lin.inv(A) @ b\n", + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Les systèmes matriciels sont probablement l'application la plus importante des matrices car quoi de plus important que de connaitre le prix des bananes ?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Résolution d'un système matriciel\n", + "\n", + "On regardera les méthodes suivantes :\n", + "\n", + "* Méthode du pivot de Gauss (rendre la matrice triangulaire)\n", + "* Décomposition LU (effet de bord de la résolution par le pivot de Gauss)\n", + "* Méthode de Gauss-Jordan (rendre la matrice diagonale)\n", + "\n", + "**Note :** Si vous trouvez la suite difficile, faites une pause et regardez cette [explication sur une matrice 3x3](https://www.youtube.com/watch?v=VoMsTiJOUE4). Elle commence par triangulariser la matrice comme le fait\n", + "la méthode du pivot de Gauss, puis elle continue pour diagonaliser la matrice comme le fait Gauss-Jordan et\n", + "finalement elle arrive à l'inverse de la matrice. C'est très bien pour comprendre ou faire les calculs à la main\n", + "sur une petite matrice, c'est horrible à programmer. Ce que je vous montre c'est la transformation de l'intuition\n", + "qu'offre cette vidéo en un calcul matriciel rapide et simple à programmer." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Méthode du pivot de Gauss\n", + "\n", + "On transforme A en une matrice triangulaire qui permet ensuite de résoudre le système en O(n²) opérations.\n", + "\n", + "Pour cela on commence à mettre des 0 sur la première colonne en dessous de la diagonale. Pour cela il\n", + "suffit de multiplier A par la matrice $E_1$ suivante :\n", + "\n", + "\n", + "$$\n", + "E_1 = \n", + "\\begin{bmatrix}\n", + "\\;1 \\quad 0\\; 0 \\ldots 0 \\\\\n", + "\\frac{-a_{21}}{a_{11}} \\, 1\\; 0 \\ldots 0 \\\\\n", + "\\frac{-a_{31}}{a_{11}} \\, 0\\; 1 \\ldots 0 \\\\\n", + "\\vdots \\\\\n", + "\\frac{-a_{n1}}{a_{11}}\\; 0\\; 0 \\ldots 1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "$E_2$ sera la matrice équivalente avec des termes $\\frac{-a_{k2}}{a_{22}}$ sous la diagonales afin des 0 dans la 2e colonne de A sous la diagonale, etc.\n", + "\n", + "Si vous ne connaissez pas cette méthode, je vous conseille de vérifier à la main sur une matrice 4x4 que\n", + "$E_1 \\, A$ met bien des zéros là où il faut. Ensuite faites le travail sur la 2e colonne.\n", + "\n", + "Bien sur si on multiplie A par $E_1$, il faut aussi multiplier ${\\bf b}$ par $E_1$ pour que le système matriciel soit\n", + "équivalent. Cette multiplication $E_1 \\, \\bf b$ peut se calculer nettement plus rapidement qu'avec un \n", + "produit matrice vecteur. Donnez la bonne formule et vérifiez dans le code ci-dessous.\n", + "\n", + "#### Système matriciel avec matrice triangulaire\n", + "\n", + "Pour finir il faut résoudre U x = c avec U une matrice triangulaire supérieur. Cela se fait en partant\n", + "de la dernière ligne qui donne directement `x[-1] = c[-1] / U[-1,-1]`. Une fois `x[-1]` connu, on en\n", + "déduit la valeur de `x[-2]` avec l'avant dernière ligne, etc.\n", + "\n", + "On faisant les calculs on constate qu'il faut environ n²/2 additions et multiplications.\n", + "\n", + "Là encore, si vous ne vous rappelez pas comment on fait, faites le à la main avec une matrice 3x3. Vous pouvez aussi ajouter des `print` dans le code qui suit pour voir les matrices intermédiaires." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Cf analyse du code ci-dessous\n", + "\n", + "def solve_gauss(A, b):\n", + " A = A.astype(np.float64) # si A a des entiers, on va avoir des erreurs de calculs\n", + " for i in range(len(A)-1):\n", + " coefs = - A[i+1:,i] / A[i,i] # Normalement il faut tester que A[i,i] != 0\n", + " A[i+1:, i:] += np.outer(coefs, A[i, i:]) # ou np.einsum('i,j -> ij', coefs, A[i, i:])\n", + " b[i+1:] += coefs * b[i]\n", + " # A est maintenant triangulaire surpérieur\n", + " res = np.zeros(len(b), dtype=b.dtype)\n", + " res[-1] = b[-1] / A[-1,-1]\n", + " for i in range(len(A)-1)[::-1]:\n", + " res[i] = (b[i] - A[i,i+1:] @ res[i+1:]) / A[i,i]\n", + " return res\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Analyse du code\n", + "\n", + "Comme **E** = **Id** + **Coefs**, on a **E A** = **A** + **Coefs A** et donc **A** += **Coef A**. Ici **Coefs** est la matrice **E** ci-dessus sans les 1 sur la diagonale.\n", + "\n", + "Le problème est que `Coef @ A` fait n³ opérations ce qui est beaucoup trop et surtout inutile sachant que **Coef** est un vecteur dans une matrice de zéros. Si ce vecteur est dans la colonne $i$ alors seuls les termes de la ligne $i$ de A serviront pour générer ce produit matriciel (à faire sur un papier). De plus on a `res[j,k] = Coef[j,i] * A[i,k]` ce qui s'écrit en Numpy `res = np.outer(coefs, A[i,:])` si `coefs` est la colonne $i$ de `Coefs`.\n", + "\n", + "Comme la matrice **Coefs** n'a des valeurs non nulles qu'en dessous de la diagonale, cela veut dire que le résultat `res` de la multiplication n'a que des zéros au dessus de la ligne $i$. Donc autant ne faire que le calcul pour ce qui est en\n", + "dessus de la ligne $i$ : `A[i+1:, i:] += np.outer(coefs, A[i, i:])` avec `coefs` un vecteur de taille $n-i$. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A\n", + " [[2.878 0.086 7.04 4.388 7.731]\n", + " [1.997 0.405 9.546 0.681 3.954]\n", + " [9.664 5.849 3.799 5.096 8.049]\n", + " [7.136 3.182 6.452 1.741 3.594]\n", + " [1.064 3.951 8.733 7.093 9.787]] \n", + "b\n", + " [22.122 16.584 32.457 22.105 30.627]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1., 1.])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = 10 * np.random.random(size=(5,5))\n", + "b = A.sum(axis=1)\n", + "print(f\"A\\n {A} \\nb\\n {b}\")\n", + "solve_gauss(A, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Complexité du pivot de Gauss\n", + "\n", + "#### Exercice 10.1\n", + "\n", + "Calculer la complexité de `solve_gauss`. Vous devez trouver n³/3 multiplications et autant d'additions\n", + "plus des termes de degrés inférieurs. Pour compter les opérations je vous suggère de faire un dessin \n", + " et d'imaginer votre dessin en 3 dimensions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Décomposition LU (Lower, Upper)\n", + "\n", + "Si on a besoin de résoudre plusieurs systèmes matriciels avec A, alors il est préférable de décomposer\n", + "A en un produit d'une matriciel triangulaire inférieur et d'une matrice triangulaire supérieure.\n", + "\n", + "$A = L\\, U$\n", + "\n", + "Pour cela il suffit de relancer le pivot de Gauss mais au lieu de modifier **b** à chaque itération, on\n", + "fabrique à la volée l'inverse de la matrices $E_n \\ldots E_2\\, E_1$ : \n", + "\n", + "$$\n", + "E_n \\ldots E_2\\, E_1 \\, A\\, x = E_n \\ldots E_2\\, E_1 \\, b \\quad \\textrm{donc} \\\\\n", + "(E_n \\ldots E_2\\, E_1)^{-1} \\, E_n \\ldots E_2\\, E_1 \\, A\\, x = b \\\\\n", + "E_1^{-1} \\, E_2^{-1} \\ldots E_n^{-1} \\; E_n \\ldots E_2\\, E_1 \\, A\\, x = b \\\\\n", + "$$\n", + "\n", + "Ce calcul est très simple car ces matrices inverses ont la\n", + "même forme que les $E_k$ avec simplement le valeurs opposées sous la diagonale :\n", + "\n", + "$$\n", + "E_1^{-1} = \n", + "\\begin{bmatrix}\n", + "\\;1 \\quad 0\\; 0 \\ldots 0 \\\\\n", + "\\frac{a_{21}}{a_{11}} \\, 1\\; 0 \\ldots 0 \\\\\n", + "\\frac{a_{31}}{a_{11}} \\, 0\\; 1 \\ldots 0 \\\\\n", + "\\vdots \\\\\n", + "\\frac{a_{n1}}{a_{11}}\\; 0\\; 0 \\ldots 1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "et le produit $E^{-1} = E_1^{-1} \\,E_1^{-1} \\,E_2^{-1} \\,E_3^{-1} \\, \\ldots \\,E_n^{-1}$ est simplement la concaténation\n", + "des colonnes (je vous laisse vérifier) :\n", + "\n", + "$$\n", + "E^{-1} = \n", + "\\begin{bmatrix}\n", + "\\;1 \\quad 0\\; \\; 0 \\ldots 0 \\\\\n", + "\\frac{a_{21}}{a_{11}} \\; \\; 1\\; \\; 0 \\ldots 0 \\\\\n", + "\\frac{a_{31}}{a_{11}} \\, \\frac{a_{32}}{a_{22}} \\; 1 \\ldots 0 \\\\\n", + "\\vdots \\\\\n", + "\\frac{a_{n1}}{a_{11}}\\; \\frac{a_{n2}}{a_{22}}\\; \\frac{a_{n3}}{a_{33}} \\ldots 1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "et ainsi on a $L = E^{-1}$ et $U = E_n \\ldots E_2\\, E_1 \\, A$ puisque tout le travail fait sur A est\n", + "justement pour mettre des 0 sous la diagonale et donc en faire une matrice triangulaire supérieure.\n", + "\n", + "Une fois la décomposition LU faites, résoudre $L\\, U \\, {\\bf x} = {\\bf b}$ se fait en 2 étapes :\n", + "\n", + "* on résoud $L\\, {\\bf y} = {\\bf b}$ ce qui donne ${\\bf y}$ \n", + "* puis on résoud $U\\, {\\bf x} = {\\bf y}$ et on a notre solution ${\\bf x}$\n", + "\n", + "en O(n²) opérations à chaque fois puisqu'il s'agit de matrices triangulaires." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def LU(A):\n", + " L = np.diag([1.,] * len(A))\n", + " for i in range(len(A)-1):\n", + " E = np.diag([1.,] * len(A))\n", + " E[i+1:,i] = - A[i+1:,i] / A[i,i]\n", + " L[i+1:,i] = -E[i+1:,i]\n", + " A[i:, i:] = E[i:,i:] @ A[i:,i:]\n", + " return L, A" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A\n", + " [[7.512 7.513 5.909 4.879 0.641]\n", + " [8.468 6.44 4.16 1.435 4.431]\n", + " [6.661 4.823 2.936 3.073 4.768]\n", + " [5.927 6.654 1.168 9.273 0.706]\n", + " [0.631 1.075 2.517 6.229 7.547]]\n", + "L\n", + "[[ 1. 0. 0. 0. 0. ]\n", + " [ 1.127 1. 0. 0. 0. ]\n", + " [ 0.887 0.906 1. 0. 0. ]\n", + " [ 0.789 -0.358 122.023 1. 0. ]\n", + " [ 0.084 -0.219 -40.943 -0.357 1. ]]\n", + "U\n", + "[[ 7.512 7.513 5.909 4.879 0.641]\n", + " [ 0. -2.029 -2.502 -4.066 3.708]\n", + " [ 0. 0. -0.036 2.432 0.838]\n", + " [ 0. 0. 0. -292.814 -100.761]\n", + " [ 0. 0. 0. 0. 6.662]]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[ 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 0., -0., 0.],\n", + " [ 0., 0., 0., 0., 0.],\n", + " [ 0., 0., 0., -0., -0.],\n", + " [ 0., 0., 0., -0., -0.]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = 10 * np.random.random(size=(5,5))\n", + "print(\"A\\n\",A)\n", + "L,U = LU(A.copy()) # Attention, notre fonction modifie A donc si on veut le réutiliser il faut une copie\n", + "print(f\"L\\n{L}\\nU\\n{U}\")\n", + "A - (L @ U)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Gauss Jordan\n", + "\n", + "L'idée est de diagonaliser A par des multiplications matricielles similaires à celles de Gauss mais qui\n", + "annulent aussi les termes au dessus de la diagonale :\n", + "\n", + "$$\n", + "E_3 = \n", + "\\begin{bmatrix}\n", + "1 \\; 0\\; \\frac{-a_{13}}{a_{33}} \\; 0 \\ldots 0 \\\\\n", + "0 \\; 1\\; \\frac{-a_{23}}{a_{33}} \\; 0 \\ldots 0 \\\\\n", + "0 \\; 0\\quad 1 \\quad 0 \\ldots 0 \\\\\n", + "0 \\; 0\\; \\frac{-a_{43}}{a_{33}} 1 \\ldots 0 \\\\\n", + "\\vdots \\\\\n", + "0 \\; 0\\; \\frac{-a_{n3}}{a_{33}} 0 \\ldots 1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "\n", + "Cette méthode est plus compacte à écrire que Gauss car il n'y a pas remonté finale, mais elle est plus lente car on modifie tout A et b à\n", + "chaque itération." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def solve_gauss_jordan(A,b):\n", + " for i in range(len(A)):\n", + " d1 = np.diag([1.,] * len(A))\n", + " d1[:,i] = - A[:,i] / A[i,i]\n", + " A = d1 @ A\n", + " b = d1 @ b\n", + " return b / np.diag(A)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1., 1.])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = 10 * np.random.random(size=(5,5))\n", + "b = A.sum(axis=1)\n", + "solve_gauss_jordan(A, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparaison de la vitesse de méthodes" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "n = 500\n", + "A = 10 * np.random.random(size=(n,n))\n", + "b = A.sum(axis=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.63 s ± 218 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" + ] + } + ], + "source": [ + "%timeit solve_gauss_jordan(A, b)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "101 ms ± 3.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" + ] + } + ], + "source": [ + "%timeit solve_gauss(A, b) # 2.5 fois plus rapide que Gauss-Jordan" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "16.4 ms ± 227 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%timeit B = lin.inv(A) # 6 fois plus rapide que mon pivot de Gauss" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "14.2 ms ± 277 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + ] + } + ], + "source": [ + "%timeit lin.solve(A, b) # un peu plus rapide" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pour n=5000, `lin.solve` est 3 fois plus rapide que `lin.inv` sur ma machine. Et plus on augmente $n$ et plus\n", + "l'écart se creuse \n", + "\n", + "**Note**: Les calculs utilisent tous les processeurs de ma machine, Numpy sait paralléliser et utilise\n", + "les bonnes bibliothèques (BLAS et Lapack) s'il est bien installé.\n", + "\n", + "#### Morale\n", + "\n", + "* Une bonne méthode est mieux qu'une mauvaise (et oui !).\n", + "* Une bonne bibliothèque fait toute la différence (vous ne ferez pas mieux que BLAS et Lapack)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Erreurs d'arrondi" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "finfo(resolution=1e-06, min=-3.4028235e+38, max=3.4028235e+38, dtype=float32)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.set_printoptions(precision=20, linewidth=150, suppress=True)\n", + "\n", + "np.finfo(np.float32)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A\n", + " [[0.000001 1. ]\n", + " [1. 2. ]] \n", + "b\n", + " [1. 3.]\n" + ] + } + ], + "source": [ + "e = 1E-6\n", + "A = np.array([[e, 1], [1, 2]], dtype='float32')\n", + "b = np.array([1., 3.], dtype='float32')\n", + "print(f\"A\\n {A} \\nb\\n {b}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [1.013279 0.999999]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([1. , 3.013277], dtype=float32)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = solve_gauss(A.copy(),b)\n", + "print(\"x =\", x)\n", + "A @ x # on ne retrouve pas exactement b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Il y a un problème d'arrondi évident sachant que la solution est [1 + 2*e, 1 - e] :" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "La solution est : [1.000002 0.999999]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([1., 3.], dtype=float32)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([1 + 2*e, 1 - e], dtype='float32')\n", + "print(\"La solution est :\", x)\n", + "A @ x # on retrouve b" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Le problème est qu'on divise les valeurs de la première colonne de A par le premier pivot : 1E-6.\n", + "\n", + "Aussi on multiplie par 1E6 ce qui va faire des grandes valeurs or la précision est au niveau du 6e chiffre,\n", + "on pert les suivants comme le montre la simple addition qui suit :" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1000000.], dtype=float32)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.array([1E6], dtype='float32') # 1 million\n", + "y = np.array([1E-2], dtype='float32') # 0.01\n", + "x+y # résultat : 1 million sans rien après la virgule" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**À mélanger des grands nombres avec des petits, on fait des erreurs d'arrondi.**\n", + "\n", + "C'est vrai pour les calculs matriciels qu'on fait, c'est toujours vrai et c'est pour cela qu'on aime normaliser\n", + "les données sur lesquelles on travaille lorsqu'on le peut." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution au problème d'arrondi dans le cas du pivot de Gauss\n", + "\n", + "Il suffit d'échanger les lignes (ou colonnes mais c'est plus compliqué) pour avoir la plus grande valeur,\n", + "en valeur absolue, comme pivot. C'est la méthode du pivot partiel.\n", + "\n", + "La méthode du pivot total consiste à prendre comme pivot la plus grande valeur parmis la ligne et la colonne concernées.\n", + "\n", + "#### Exercice pour le TP\n", + "\n", + "Programmer la méthode du pivot partiel et vérifier ce que cela donne sur l'exemple ci-dessus qui pose\n", + "des problèmes d'arrondi." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "A = np.array([1,2,3])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "np.isin?" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(False)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.isin(5,A)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "B = np.array([1,5,6])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ True, False, False])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.isin(B,A)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma32 Conditionnement d'une matrice.ipynb b/PVCM/cama/fr/ma32 Conditionnement d'une matrice.ipynb new file mode 100644 index 0000000..9ff805a --- /dev/null +++ b/PVCM/cama/fr/ma32 Conditionnement d'une matrice.ipynb @@ -0,0 +1,589 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conditionnement d'une matrice\n", + "\n", + "Soit la matrice A suivante :" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[10, 7, 8, 7],\n", + " [ 7, 5, 6, 5],\n", + " [ 8, 6, 10, 9],\n", + " [ 7, 5, 9, 10]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.array([[10, 7, 8, 7], [7, 5, 6, 5], [8, 6, 10, 9], [7, 5, 9, 10]])\n", + "A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Une matrice symétrique qui n'a rien de méchant a priori. Son déterminant est 1." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9999999999999869" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lin.det(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Construisons **b** de telle sorte que la solution du système matriciel A **x** = **b** soit [1,1,1,1] :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[32 23 33 31]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1.])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b = A.sum(axis=1)\n", + "print(b)\n", + "x = lin.solve(A, b)\n", + "x" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Perturbons légèrement **b**. Dans le cas d'une expérience cela s'appelle une erreur de mesure. En informatique\n", + "cela peut être le résultat d'erreurs d'arrondi." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0033319453118976702" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bp = [32.1, 22.9, 33.1, 30.9]\n", + "eb = lin.norm(b - bp) / lin.norm(b) # une erreur se mesure par rapport à la valeur de la donnée\n", + "eb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On a une erreur sur **b** de l'ordre de 0,3 %. On la note $ ||{\\bf \\delta b}|| \\, / \\,||{\\bf b}||$.\n", + "\n", + "On pourrait espérer une erreur sur le résultat du même ordre de\n", + "grandeur.\n", + "Regardons la solution **x** de notre système matriciel perturbé :" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 9.2, -12.6, 4.5, -1.1])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xp = lin.solve(A, bp)\n", + "xp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Cette solution n'a rien à voir avec [1, 1, 1, 1]." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8.19847546803699" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ex = lin.norm(x - xp) / lin.norm(x)\n", + "ex" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "L'erreur est de l'ordre de 8 pour 1.\n", + "\n", + "L'erreur est 2460 fois plus grande que l'erreur sur **b**." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2460.567236431514" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ex / eb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Pourquoi ?\n", + "\n", + "On a \n", + "\n", + "$$\n", + "\\begin{align}\n", + "& A ({\\bf x} + {\\bf \\delta x}) = {\\bf b} + {\\bf \\delta b} \\quad \\textrm{et donc} \\\\\n", + "& A \\, {\\bf \\delta x} = {\\bf \\delta b} \\; \\textrm{ puisque } A {\\bf x} = {\\bf b} \\quad \\textrm{et finalement}\\\\\n", + "& {\\bf \\delta x} = A^{-1} \\, {\\bf \\delta b}\n", + "\\end{align}\n", + "$$\n", + "\n", + "Comme A et son inverse sont des applications linéaires on a\n", + "\n", + "$$\n", + "\\begin{align}\n", + "& ||{\\bf b}|| \\le ||A|| \\, ||{\\bf x}||\n", + "\\quad \\textrm{et} \\quad ||{\\bf \\delta x}|| \\le ||A^{-1}|| \\, ||{\\bf \\delta b}||\n", + "\\end{align}\n", + "$$\n", + "\n", + "donc \n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{||{\\bf \\delta x}||}{||{\\bf x}||} \\le ||A^{-1}|| \\, \\frac{||{\\bf \\delta b}||}{||{\\bf x}||}\n", + "\\le ||A^{-1}|| \\, ||A|| \\, \\frac{||{\\bf \\delta b}||}{||{\\bf b}||}\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3009.5787080586942" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lin.norm(lin.inv(A)) * lin.norm(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Le problème est là.\n", + "\n", + "On appelle cela le conditionnement de A :\n", + " \n", + "cond(A) = $||A^{-1}|| \\, ||A||$\n", + "\n", + "**Une matrice mal conditionnée va générer des erreurs de calcul lors de la résolution du système matriciel.**" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2984.0927016757555" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.linalg.cond(A) # scipy n'a pas le conditionnement mais numpy l'a. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Bizarre cette différence avec le calul ci-dessus qui a donné 3009." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Perturbons la matrice\n", + "\n", + "Que ce passe-t-il si on perturbe A et non b ?" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.098, 0.43 , 0.206, 0.09 ],\n", + " [-0.153, 0.292, -0.125, 0.784],\n", + " [ 0.927, -0.233, 0.583, 0.058],\n", + " [ 0.136, 0.851, -0.858, -0.826]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Erreur relative sur A : 0.06868857112100454\n" + ] + } + ], + "source": [ + "np.random.seed(0)\n", + "\n", + "dA = 2 * np.random.random(size = A.shape) - 1\n", + "display(dA)\n", + "ea = lin.norm(dA) / lin.norm(A)\n", + "print('Erreur relative sur A :', ea)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[10.098, 7.43 , 8.206, 7.09 ],\n", + " [ 6.847, 5.292, 5.875, 5.784],\n", + " [ 8.927, 5.767, 10.583, 9.058],\n", + " [ 7.136, 5.851, 8.142, 9.174]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Ap = A + dA\n", + "Ap" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-12.365, 15.574, 10.146, -5.94 ])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xp = lin.solve(Ap, b)\n", + "xp" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "11.432687335993894" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ex = lin.norm(xp - x) / lin.norm(x)\n", + "ex" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "166.44235204505293" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ex / ea" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On note que l'erreur est nettement moins grande. La raison est qu'on n'a pas trouvé l'erreur sur A qui\n", + "perturbera le plus possible le résultat. En fait ce n'est pas que le conditionnement de A qui compte,\n", + "l'erreur est aussi importante. Deux erreurs de même norme pertuberont différemment le résultat.\n", + "\n", + "\n", + "Notons aussi que dans ce cas les maths sont un peu différente mais on retrouve le conditionnement de A :\n", + "\n", + "$$\n", + "\\begin{align}\n", + "& (A + \\Delta A) \\, ({\\bf x} + {\\bf \\delta x}) = {\\bf b} \\quad \\textrm{et donc} \\\\\n", + "& A \\, {\\bf \\delta x} + \\Delta A \\, ({\\bf x} + {\\bf \\delta x}) = 0 \\; \\textrm{ puisque } A {\\bf x} = {\\bf b} \\quad \\textrm{et finalement}\\\\\n", + "& {\\bf \\delta x} = -A^{-1} \\,\\Delta A \\, ({\\bf x} + {\\bf \\delta x}) \\quad \\textrm{et} \\\\\n", + "& ||{\\bf \\delta x}|| \\le ||A^{-1}|| \\, ||\\Delta A|| \\, ||{\\bf x} + {\\bf \\delta x}||\n", + "\\end{align}\n", + "$$\n", + "\n", + "Ainsi\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{||{\\bf \\delta x}||}{||{\\bf x} + {\\bf \\delta x}||} \n", + "\\le ||A^{-1}|| \\, ||\\Delta A|| = ||A^{-1}|| \\, ||A|| \\, \\frac{||\\Delta A||}{||A||}\n", + "\\end{align}\n", + "$$\n", + "\n", + "ou\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{||{\\bf \\delta x}||}{||{\\bf x} + {\\bf \\delta x}||} \n", + "\\le cond(A) \\, \\frac{||\\Delta A||}{||A||}\n", + "\\end{align}\n", + "$$\n", + "\n", + "L'erreur ne se mesure pas par rapport à **x** mais par rapport à ${\\bf x} + {\\bf \\delta x}$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Propriétés\n", + "\n", + "* $cond(A) \\ge 1$ car $Id = A\\, A^{-1}$ et donc $1 \\le ||A||\\, ||A^{-1}||$ (pour les normes subordonnées car $||Id||_F = \\sqrt{n}$)\n", + "* $cond(A) = cond(A^{-1})$ par définition du conditionnement\n", + "* $\\displaystyle cond_2(A) = \\frac{\\max_i |\\lambda_i|}{\\min_i |\\lambda_i|}$ si la matrice est normale \n", + " où le 2 indique qu'on utilise la norme 2 et $\\lambda_i$ sont les valeurs propres de A" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2984.092701676269+0j)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vp = lin.eigvals(A)\n", + "vp.max() / vp.min() # et voici la différence avec le calcul ||A|| ||inv(A)|| ci-dessus\n", + " # ca sent l'erreur numérique" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* si A est unitaire ou orthogonale alors $cond_2(A) = 1$ (une rotation ou symétrie ne va pas agrandir l'erreur)\n", + "* le conditionnement n'est pas modifié par transformation unitaire " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Préconditionnement\n", + "\n", + "Si le conditionnement n'est pas modifié par une transformation unitaire, il l'est par d'autres transformations.\n", + "Ainsi\n", + "\n", + "$$\n", + "\\forall A, \\exists B \\; \\textrm{appelée matrice de préconditionnement t.q.} \\quad cond(B\\, A) \\le cond(A)\n", + "$$\n", + "\n", + "aussi on lieu de résoudre $A {\\bf x} = {\\bf b}$ on résoud $B\\, A {\\bf x} = B\\, {\\bf b}$\n", + "\n", + "Toute la difficulté consiste à trouver une matrice de préconditionnement B qui soit simple à calculer.\n", + "\n", + "#### Exercice 11.1\n", + "\n", + "Quelle est la meilleure matrice de préconditionnement de A ? Pourquoi ?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma34 ACP -- Exercice.ipynb b/PVCM/cama/fr/ma34 ACP -- Exercice.ipynb new file mode 100644 index 0000000..9cd80ca --- /dev/null +++ b/PVCM/cama/fr/ma34 ACP -- Exercice.ipynb @@ -0,0 +1,295 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "import plotly.graph_objects as go\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.random.seed(0)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Exercice : Nuage de points en 3D\n", + "\n", + "On a des résultats de mesures et on sait qu'on doit avoir une relation\n", + "quadratique entre x et z :\n", + "\n", + "$$ z = \\alpha \\, x^2 + \\beta \\, x + \\gamma $$\n", + "\n", + "Comment trouver ces 3 coefficients ?\n", + "\n", + "Bien sûr on va faire une analyse en composante principale mais attention, cela\n", + "ne marche que pour les relations linéaires (ca nous donne un vecteur). Aussi\n", + "il faut introduire une nouvelle variable pour que notre équation soit linéaire.\n", + "\n", + "Comment écrire notre équation pour qu'elle soit linéaire suivant 2 variables ?\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### réponse :\n", + "\n", + "..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Données de l'expérience\n", + "\n", + "Fabriquer un nuage de point 2D avec l'équation \n", + "\n", + "$$ z = -1.3 \\, x^2 + 0.2 \\, x + 1.45 + U(-1,1)$$ \n", + "\n", + "où U est la loi uniforme qui simule du bruit." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "N = 50\n", + "x = ... # x varie entre -3 et 3\n", + "z = ...\n", + "nuage = np.array([x,z])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.title('Un nuage de points')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Calculs pour trouver les caractéristiques de notre nuage\n", + "\n", + "Fabriquer à partir de notre nuage de points 2D un nuage de points 3D en introduisant la nouvelle\n", + "variable qu'on a choisit.\n", + "\n", + "Le nouveau nuage s'appelle `nuage3D`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=nuage3D[0], y=nuage3D[1], z=nuage3D[2], mode='markers')])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Calculer la matrice de covariance de notre nuage et ses vecteurs propres (on stockera les vecteurs propres dans la variable `vec`)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=nuage3D[0], y=nuage3D[1], z=nuage3D[2], mode='markers'),\n", + " go.Scatter3d(x=[0,-5*vec[0,0]], y=[0,-5*vec[1,0]], z=[0,-5*vec[2,0]]),\n", + " go.Scatter3d(x=[0,vec[0,1]], y=[0,vec[1,1]], z=[0,vec[2,1]])])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Que peut-on déduire de notre premier vecteur propre ?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### réponse\n", + "\n", + "..." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Créer un nuage de point en 2D qui ne prend plus en compte l'impact du coefficient\n", + "que l'on vient de trouver.\n", + "\n", + "On appelle ce nouveau nuage `nuage2D` (ce n'est pas le même que notre `nuage` initial)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.plot(nuage2D[0], nuage2D[1], 'x')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Que peut-on en déduire ?\n", + "\n", + "#### réponse\n", + "\n", + "...." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(\"Les coefficients de z fonction polynomiale de degré 2 en x sont :\\n\")\n", + "print(f\"alpha = {alpha}\")\n", + "print(f\"beta = {beta}\")\n", + "print(f\"gamma = {gamma}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Vous pouvez tout relancer en changer la valeur de la graine de l'aléatoire. Vous allez voir que parfois le\n", + "bruit perturbe bien plus les résultats." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma35 Syst\303\250me matriciel -- Exercices.ipynb" "b/PVCM/cama/fr/ma35 Syst\303\250me matriciel -- Exercices.ipynb" new file mode 100644 index 0000000..2107be6 --- /dev/null +++ "b/PVCM/cama/fr/ma35 Syst\303\250me matriciel -- Exercices.ipynb" @@ -0,0 +1,190 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "__Programmation vectorielle__\n", + "\n", + "Le but des exercices est\n", + "\n", + "* d'avoir un programme qui donne la bonne réponse\n", + "* qui soit le plus rapide possible (et pour cela on utilise massivement Numpy)\n", + "\n", + "En règle général si vous avez des `for` imbriqués c'est mauvais signe." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "np.set_printoptions(precision=10, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Méthode du pivot de Gauss partiel\n", + "\n", + "L'ennoncé est dans le cours. On verifiera sur le cas qui génère des\n", + "erreurs d'arrondis." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Factorisation de Choleski\n", + "\n", + "Il s'agit de décomposer A en $A = B\\, B^T$ avec B une matrice triangulaire inférieure. Cela n'est possible\n", + "que si la matrice A est symétrique et définie positive (c'est d'ailleurs un facon de vérifier qu'une\n", + "matrice est définie positive).\n", + "\n", + "Écrire l'algorithme de Choleski qui prend A et retourne B (pour deviner l'algorithme, essayez de trouver les \n", + "coefficients de B à partir des coefficients de A sur une matrice A 4x4)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Rappel : pas de boucles `for` imbriquées mais des opérations vectorielles et matricielles (sur des sous-matrices).\n", + "\n", + "Créer une matrice symétrique définie positive et vérifier que sonprogramme marche bien." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Amméliorer Jacobi\n", + "\n", + "Lorsqu'on écrit une itération de la méthode de Jacobi avec l'ensemble des coefficients, on constate que\n", + "si on calcule la nouvelle valeur de **x** élément par élement alors lorsqu'on veut mettre à jour `x[1]`, \n", + "on connait déjà `x[0]`. Idem lorsqu'on met à jour `x[2]` on connait déjà `x[0]` et `x[1]`, etc.\n", + "\n", + "L'idée de la version amméliorée de Jacobi est d'utiliser la nouvelle valeur de `x[0]` et non pas l'ancienne\n", + "comme c'est le cas dans l'algorithme du cours. Ainsi en utilisant des valeurs mise à jour on peut espérer\n", + "converger plus vite.\n", + "\n", + "Dans ce cas, chaque itération demande un calcul ligne par ligne et donc une boucle `for` dans la boucle `for` sur\n", + "les itérations." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Test d'arrêt\n", + "\n", + "On ajoutera un argument `error` à la fonction qui indique la précision désirée du résultat. Malheureusement pour connaitre la précision de notre calcul il faut connaitre la solution. On pourrait aussi calculer \n", + "${\\bf A \\, x}^t - {\\bf b}$ mais ce n'est pas non plus l'écart entre ${\\bf x}^t$ et la solution (en plus\n", + "c'est un calcul en n² donc lourd).\n", + "\n", + "Aussi on va regarder quand la\n", + "convergence ralentit et donc on s'arrête lorsque\n", + "$||{\\bf x}^{t+1} - {\\bf x}^t|| < \\texttt{error}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Bonus\n", + "\n", + "Réécrire la méthode sans la boucle `for` mais en prenant bien le nouvelles valeurs de `x`. Pour cela on va découper la matrice **A** en deux matrices triangulaires." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# les méthodes de Numpy triu et tril seront utiles\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma40 M\303\251thodes it\303\251ratives.ipynb" "b/PVCM/cama/fr/ma40 M\303\251thodes it\303\251ratives.ipynb" new file mode 100644 index 0000000..ae66062 --- /dev/null +++ "b/PVCM/cama/fr/ma40 M\303\251thodes it\303\251ratives.ipynb" @@ -0,0 +1,417 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "np.random.seed(123)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## La simulation numérique\n", + "\n", + "Si le prix des bananes est important, le secteur qui a les plus gros besoins en résolution de systèmes\n", + "matriciels est la simulation numérique.\n", + "Cela comprend ceci\n", + "\n", + "
\"simulation
\n", + "\n", + "et tout ce qu'on simule numériquement à savoir tout ce qui touche le transport, l'énergie, la construction, tout\n", + "ce qu'on fabrique, qui coûte cher et qui doit avoir un comportement physique bien précis. Mais ce n'est pas tout,\n", + "comprendre notre environnement (météo, réchauffement de la planète, chimie...) revient aussi à résoudre des\n", + "systèmes matriciels ainsi que d'autres domaines. Cela étant il existe des méthodes de simulation numérique\n", + "qui ne passent pas par des systèmes matriciels.\n", + "\n", + "Pour faire l'image ci-dessus, on transforme des équations physique comme [Navier-Stokes](https://fr.wikipedia.org/wiki/%C3%89quations_de_Navier-Stokes) en un système matriciel où les inconnues sont définies en chaque point\n", + "d'un maillage à définir. Dans notre cas l'inconnue est la pression et le maillage est l'intérieur d'une\n", + "boite imaginaire qui comprend l'avion et l'air qui circule autour.\n", + "\n", + "Si la boite est un cube avec 1000 points dans chaque direction, on a 1 milliard de points dans la boite (moins\n", + "ce qui est à l'intérieur de l'avion mais restons sur 1 milliards). Alors la matrice a 1 trillion d'éléments (un milliard au carré).\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "a_{11} \\; a_{12} \\ldots a_{1,10^9} \\\\\n", + "a_{21} \\; a_{22} \\ldots a_{2,10^9} \\\\\n", + " \\vdots \\\\\n", + "a_{10^9,1} a_{n2} \\ldots a_{10^9,10^9} \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "p_{1} \\\\\n", + "p_{2} \\\\\n", + "\\vdots \\\\\n", + "p_{10^9} \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "f_{1} \\\\\n", + "f_{2} \\\\\n", + "\\vdots \\\\\n", + "f_{10^9} \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Inverser une matrice se fait en $O(n³)$ opérations soit $O(10^{27})$ dans notre cas. \n", + "\n", + "Si vous avez [l'ordinateur le plus puissant du monde](https://www.top500.org/)\n", + "vous pouvez faire 1 Eflops soit $10^{18}$ opérations par seconde en pic (en 2024). Aussi il vous faudra $10^{9}$ secondes soit un peu plus de 30 ans. C'est trop.\n", + "\n", + "**Inverser une matrice ou résoudre par une méthode directe n'est pas la bonne solution pour résoudre un grand système matriciel.**\n", + "\n", + "#### Exercice 1\n", + "Pour une telle simulation il faut aussi calculer la vitesse de l'air en chacun des 1 milliard de points de notre maillage. Une vitesse c'est 3 variables qu'il faut ajouter à la pression. Combien de temps faut-il pour inverser\n", + "la matrice qui intègre aussi la vitesse de l'air ?" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# ceci est une calculatrice, vous pouvez donc écrire la réponse ici\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Estimer le temps d'un gros calcul avant de le lancer est une bonne idée. \n", + "\n", + "D'ailleur avec des temps si longs, il ne\n", + "faut pas rester aux ordres de grandeurs mais préciser avec la formule exacte. Ainsi avec Choleski c'est $n^3/3$\n", + "opérations, donc 3 fois moins, mais bon..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Méthodes itératives\n", + "\n", + "Les méthodes itératives sont des méthodes qui s'approchent pas à pas de la solution recherchée. Elles permettent\n", + "de trouver une approximation de ${\\bf x}$, la solution de $A\\, {\\bf x} = b$.\n", + "\n", + "En général on\n", + "arrête le calcul lorsqu'on estime qu'on est à une distance choisie de la solution (qu'on appelle l'erreur) plutôt\n", + "que d'attendre d'être à la solution exacte.\n", + "De toute facon la solution exacte sur un ordinateur qui est limité en nombre de chiffres après la virgule peut\n", + "être inatteignable. Donc **on cherchera jamais à avoir une erreur plus petite que notre précision maximale**.\n", + "\n", + "L'idée fondamentale de l'algorithme itératif est d'avoir une formule du type $\\; {\\bf x}^{t+1} = B \\, {\\bf x}^t + {\\bf c}\\;$ ou en Python:\n", + "\n", + "```\n", + "x = np.random(size = c.size)\n", + "while np.square(x - old_x) > seuil:\n", + " old_x = x\n", + " x = B @ x + c\n", + "```\n", + "\n", + "La magie c'est si **x** converge. Dans ce cas on a atteint un point fixe c.a.d. que ${\\bf x}^{t+1} = {\\bf x}^t$\n", + "et donc \n", + "\n", + "$${\\bf x}^t = B \\, {\\bf x}^t + {\\bf c} \\quad \\textrm{c.a.d.} \\quad (Id -B) \\, {\\bf x}^t = {\\bf c}$$\n", + "\n", + "On retrouve notre $A \\; {\\bf x} = {\\bf b}$ cela étant en pratique on ne découpe pas A en Id et B car\n", + "ca ne converge pas (sauf cas particuliers). Regardons comment fait la méthode de Jacobi." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Méthode de Jacobi\n", + "\n", + "La méthode de Jacobi découpe la matrice A en M et N avec\n", + "\n", + "* M la matrice diagonale qui comprend les éléments de la diagonale de A\n", + "* N = M - A (donc 0 sur la diagonale et l'opposé des éléments de A ailleurs)\n", + "\n", + "Ainsi le système à résoudre est $\\; (M - N) \\, {\\bf x} = {\\bf b}$.\n", + "\n", + "La formule itérative est donc pour l'itération k+1 exprimée en fonction de l'itération k :\n", + "\n", + "$$\n", + "M \\; {\\bf x}^{k+1} = N\\; {\\bf x}^k + {\\bf b}\n", + "$$\n", + "\n", + "et comme M est une matrice diagonale on a :\n", + "\n", + "$$\n", + "\\begin{array}{l}\n", + "a_{11} x_1^{k+1} = \\qquad -a_{12} \\, x_2^k - a_{13} \\, x_3^k \\ldots - a_{1n} \\, x_n^k + b_1 \\\\\n", + "a_{22} x_2^{k+1} = -a_{21} \\, x_1^k \\qquad - a_{23} \\, x_3^k \\ldots - a_{2n} \\, x_n^k + b_2 \\\\\n", + "a_{33} x_3^{k+1} = -a_{31} \\, x_1^k - a_{32} \\, x_2^k \\qquad \\ldots - a_{3n} \\, x_n^k + b_3 \\\\\n", + " \\vdots \\\\\n", + "a_{nn} x_n^{k+1} = -a_{n1} \\, x_1^k - a_{n2} \\, x_2^k \\ldots - a_{n-1,n-1} \\, x_{n-1}^k \\qquad + b_n \\\\\n", + "\\end{array}\n", + "$$\n", + "\n", + "On voit en filigramme $A \\; {\\bf x} = {\\bf b}$.\n", + "\n", + "Pour calculer $x_1^{k+1}$ il faut diviser le terme de droite de la première ligne par $a_{11}$ il faut donc que $a_{11} \\ne 0$.\n", + "\n", + "Pour calculer les termes suivants $x_i^{k+1}$ il faut aussi que $a_{ii}$ soient non nul donc **il\n", + "faut que A n'ait pas pas de zéro sur sa diagonale**.\n", + "\n", + "Cela se retrouve dans l'écriture suivante qui reprend la formule initiale :\n", + "$ {\\bf x}^{k+1} = M^{-1} \\;(N\\; {\\bf x}^k + {\\bf b})$ \n", + "\n", + "> On voit que pour être efficace, il faut que M soit facilement inversible, sinon autant inverser A directement.\n", + "Ici c'est bien le cas puisque M est diagonale.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Programmons Jacobi" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A:\n", + " [[2 2 6 1]\n", + " [3 9 6 1]\n", + " [0 1 9 0]\n", + " [0 9 3 4]] \n", + "b:\n", + " [11 19 10 16] \n", + "\n", + "M:\n", + " [[2 0 0 0]\n", + " [0 9 0 0]\n", + " [0 0 9 0]\n", + " [0 0 0 4]]\n", + "N:\n", + " [[ 0 -2 -6 -1]\n", + " [-3 0 -6 -1]\n", + " [ 0 -1 0 0]\n", + " [ 0 -9 -3 0]]\n", + "\n", + "x_0 = [0.398 0.738 0.182 0.175]\n", + "x_1 = [4.127 1.837 1.029 2.203]\n", + "x_2 = [-0.526 -0.195 0.907 -0.906]\n", + "x_3 = [3.427 1.782 1.133 3.759]\n", + "x_4 = [-1.56 -0.204 0.913 -0.86 ]\n", + "x_5 = [3.395 2.118 1.134 3.775]\n", + "x_6 = [-1.907 -0.196 0.876 -1.616]\n", + "x_7 = [3.877 2.342 1.133 3.784]\n", + "x_8 = [-2.133 -0.357 0.851 -2.12 ]\n", + "x_9 = [4.364 2.49 1.151 4.165]\n", + "x_10 = [-2.525 -0.574 0.834 -2.467]\n", + "x_11 = [4.804 2.671 1.175 4.665]\n", + "x_12 = [-3.027 -0.792 0.814 -2.89 ]\n", + "x_13 = [5.293 2.898 1.199 5.17 ]\n", + "x_14 = [-3.581 -1.027 0.789 -3.421]\n", + "x_15 = [5.87 3.159 1.225 5.719]\n", + "x_16 = [-4.194 -1.298 0.76 -4.026]\n", + "x_17 = [6.531 3.45 1.255 6.35 ]\n", + "x_18 = [-4.891 -1.608 0.728 -4.704]\n", + "x_19 = [7.277 3.779 1.29 7.073]\n" + ] + } + ], + "source": [ + "A = np.random.randint(10, size=(4,4))\n", + "b = A.sum(axis=1) # ainsi la solution est [1,1,1,1]\n", + "print('A:\\n', A, \"\\nb:\\n\", b, \"\\n\")\n", + "\n", + "M = np.diag(A) # attention, c'est un vecteur\n", + "N = np.diag(M) - A # np.diag d'une matrice donne un vecteur, np.diag d'un vecteur donne une matrice\n", + "print(f\"M:\\n {np.diag(M)}\\nN:\\n {N}\\n\")\n", + "\n", + "x = np.random.random(4)\n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = (N @ x + b) / M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Ca ne converge pas vraiment... (si vous relancez et voyez des `NaN` c'est qu'il y a un zéro sur la diagonale)\n", + "\n", + "2e essai :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A:\n", + " [[24 2 4 8]\n", + " [ 0 24 9 3]\n", + " [ 4 6 16 5]\n", + " [ 6 2 1 32]] \n", + "b:\n", + " [38 36 31 41] \n", + "\n", + "M:\n", + " [[24 0 0 0]\n", + " [ 0 24 0 0]\n", + " [ 0 0 16 0]\n", + " [ 0 0 0 32]]\n", + "N:\n", + " [[ 0 -2 -4 -8]\n", + " [ 0 0 -9 -3]\n", + " [-4 -6 0 -5]\n", + " [-6 -2 -1 0]]\n", + "\n", + "x_0 = [0.766 0.777 0.028 0.174]\n", + "x_1 = [1.456 1.468 1.4 1.088]\n", + "x_2 = [0.865 0.839 0.683 0.873]\n", + "x_3 = [1.109 1.135 1.134 1.045]\n", + "x_4 = [0.951 0.944 0.908 0.967]\n", + "x_5 = [1.031 1.039 1.043 1.015]\n", + "x_6 = [0.984 0.982 0.973 0.99 ]\n", + "x_7 = [1.009 1.011 1.014 1.005]\n", + "x_8 = [0.995 0.994 0.992 0.997]\n", + "x_9 = [1.003 1.003 1.004 1.002]\n", + "x_10 = [0.998 0.998 0.998 0.999]\n", + "x_11 = [1.001 1.001 1.001 1. ]\n", + "x_12 = [1. 0.999 0.999 1. ]\n", + "x_13 = [1. 1. 1. 1.]\n", + "x_14 = [1. 1. 1. 1.]\n", + "x_15 = [1. 1. 1. 1.]\n", + "x_16 = [1. 1. 1. 1.]\n", + "x_17 = [1. 1. 1. 1.]\n", + "x_18 = [1. 1. 1. 1.]\n", + "x_19 = [1. 1. 1. 1.]\n" + ] + } + ], + "source": [ + "A = np.random.randint(10, size=(4,4))\n", + "A = A + np.diag(A.sum(axis=0))\n", + "b = A.sum(axis=1) # ainsi la solution est [1,1,1,1]\n", + "print('A:\\n', A, \"\\nb:\\n\", b, \"\\n\")\n", + "\n", + "\n", + "M = np.diag(A) # attention, c'est un vecteur\n", + "N = np.diag(M) - A # np.diag d'une matrice donne un vecteur, np.diag d'un vecteur donne une matrice\n", + "print(f\"M:\\n {np.diag(M)}\\nN:\\n {N}\\n\")\n", + "\n", + "x = np.random.random(4)\n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = (N @ x + b) / M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Magie !" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Pourquoi le 2e cas marche ?\n", + "\n", + "Pour qu'une méthode itérative du type ${\\bf x} = B\\; {\\bf x} + {\\bf c}$ converge il faut au choix\n", + "\n", + "* $\\rho(B) < 1\\quad$ avec $\\rho$ le rayon spectral (qui est la plus grande valeur propre en valeur absolue)\n", + "* $||B|| < 1\\quad$ avec une norme matricielle est subordonnée à une norme vectorielle.\n", + " \n", + "\n", + "#### Cas de la méthode de Jacobi\n", + "\n", + "Pour la matrice B de Jacobi, on respecte ces conditions si A est à **diagonale dominante** à savoir que chaque\n", + "élément de la diagonale est plus grand en module que la sommes tous les autres éléments en module de sa ligne ou colonne ($|a_{i,i}| \\ge \\sum_{j \\ne i} |a_{i,j}|$).\n", + "\n", + "Jacobi converge aussi si A est symétrique, réelle et définie positive \n", + "(c.a.d. $\\forall {\\bf x}, \\; {\\bf x}^T \\, A \\, {\\bf x} > 0$)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Temps calcul\n", + "\n", + "Si on converge en 10 itérations alors\n", + "on utilise 10 multiplications matricielles, 10 additions vectorielles et 10 divisions vectorielles soit 180 opérations\n", + "à comparer aux $4^3 / 3 = 22$ opérations d'une méthode directe. Zut !\n", + "\n", + "Quelques raisons qui font qu'on y perd sont\n", + "\n", + "* La matrice A est trop petite, les méthodes itératives sont intéressantes pour les grandes matrice\n", + "* La méthode de Jacobi n'est pas la meilleure (mais elle est très facilement parallélisable)\n", + "* Le rayon spectral de la matrice est trop grand. Plus le rayon spectral est\n", + " petit et plus on converge vite." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma41 Convergence de Jacobi avec inertie.ipynb b/PVCM/cama/fr/ma41 Convergence de Jacobi avec inertie.ipynb new file mode 100644 index 0000000..7735898 --- /dev/null +++ b/PVCM/cama/fr/ma41 Convergence de Jacobi avec inertie.ipynb @@ -0,0 +1,1182 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Dans ce cours on regarde 2 points :\n", + " \n", + "* comment améliorer Jacobi\n", + "* la convergence des algorithmes itératifs (comment la comprendre et bien l'exploiter)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Ajouter de l'inertie à Jacobi\n", + "\n", + "La méthode de Jacobi mène au système itératif suivant\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = M^{-1} \\, ( N\\; {\\bf x}^k + {\\bf b})\n", + "$$\n", + "\n", + "On a vu que cette méthode ne converge que si la matrice B a son rayon spectral inférieur à 1, $\\rho(M^{-1}\\,N) < 1$.\n", + "\n", + "On peut modifier cette méthode pour qu'elle ait un plus grand rayon de convergence\n", + "et donc converge pour plus de matrices. Pour cela on ajoute de l'inertie :\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = w \\, M^{-1} \\, (N\\; {\\bf x}^k + {\\bf b}) + (1-w) \\, {\\bf x}^k\n", + "$$\n", + "\n", + "avec $0 < w \\le 1$.\n", + "\n", + "Si $w = 1$ alors on a Jacobi classique et si $w = 0$ alors on ne bouge pas, ${\\bf x}^{k+1} = {\\bf x}^k$.\n", + "\n", + "On parle d'inertie car on voit qu'on avance moins vite puisque la nouvelle valeur de ${\\bf x}^{k+1}$\n", + "est comprise entre l'ancienne valeur de ${\\bf x}^{k+1}$ et ${\\bf x}^k$.\n", + "\n", + "\n", + "Note : $w \\, {\\bf a} + (1-w) \\, {\\bf b}$ représente le segment $[{\\bf b}, {\\bf a}]$ lorsque $w$ varie entre 0 et 1.\n", + "\n", + "L'idée est qu'avec l'intertie on va peut-être entre dans la zone de convergence alors que sans on aurait sauté\n", + "par dessus.\n", + "\n", + "Cette méthode s'appelle la **surrelaxation** (*over-relaxation* en anglais), je ne sais pas pourquoi." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Programmons l'inertie pour Jacobi\n", + "\n", + "On commence par un Jacobi simple pour vérifier qu'on diverge." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A:\n", + " [[5 7 6 0]\n", + " [1 7 2 5]\n", + " [5 6 5 1]\n", + " [0 6 3 7]] \n", + "b:\n", + " [18 15 17 16] \n", + "\n", + "M:\n", + " [[5 0 0 0]\n", + " [0 7 0 0]\n", + " [0 0 5 0]\n", + " [0 0 0 7]]\n", + "N:\n", + " [[ 0 -7 -6 0]\n", + " [-1 0 -2 -5]\n", + " [-5 -6 0 -1]\n", + " [ 0 -6 -3 0]]\n", + "\n", + "x_0 = [0.062 0.652 0.185 0.852]\n", + "x_1 = [2.465 1.472 2.384 1.647]\n", + "x_2 = [-1.322 -0.067 -1.161 0.002]\n", + "x_3 = [5.088 2.662 4.803 2.841]\n", + "x_4 = [-5.89 -1.986 -5.451 -2.055]\n", + "x_5 = [12.921 6.009 12.084 6.324]\n", + "x_6 = [-19.314 -7.672 -17.997 -8.044]\n", + "x_7 = [35.937 15.79 33.53 16.575]\n", + "x_8 = [-58.741 -24.41 -54.8 -25.618]\n", + "x_9 = [103.534 44.49 96.557 46.694]\n", + "x_10 = [-174.554 -73.588 -162.861 -77.23 ]\n", + "x_11 = [302.056 128.775 281.706 135.159]\n", + "x_12 = [-514.732 -218.038 -480.218 -228.824]\n", + "x_13 = [885.114 376.327 825.542 394.983]\n", + "x_14 = [-1513.908 -642.302 -1412.303 -674.084]\n", + "x_15 = [2597.587 1103.419 2422.887 1158.103]\n", + "x_16 = [-4448.651 -1888.411 -4149.91 -1981.882]\n", + "x_17 = [7627.267 3238.983 7114.521 3399.456]\n", + "x_18 = [-13068.402 -5548.37 -12190.539 -5823.066]\n", + "x_19 = [22399.965 9511.401 20894.459 9982.548]\n" + ] + } + ], + "source": [ + "np.random.seed(799)\n", + "\n", + "A = np.random.randint(10, size=(4,4))\n", + "b = A.sum(axis=1) # ainsi la solution est [1,1,1,1]\n", + "print('A:\\n', A, \"\\nb:\\n\", b, \"\\n\")\n", + "\n", + "M = np.diag(A) # attention, c'est un vecteur\n", + "N = np.diag(M) - A # np.diag d'une matrice donne un vecteur, np.diag d'un vecteur donne une matrice\n", + "print(f\"M:\\n {np.diag(M)}\\nN:\\n {N}\\n\")\n", + "\n", + "x0 = np.random.random(4)\n", + "x = x0\n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = (N @ x + b) / M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Ajoutons maintenant l'inertie à Jacobi :" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x_0 = [0.062 0.652 0.185 0.852]\n", + "x_1 = [1.264 1.062 1.284 1.25 ]\n", + "x_2 = [0.918 0.882 0.948 1.037]\n", + "x_3 = [1.072 0.941 1.082 1.08 ]\n", + "x_4 = [1.028 0.925 1.032 1.048]\n", + "x_5 = [1.047 0.939 1.042 1.049]\n", + "x_6 = [1.041 0.943 1.029 1.042]\n", + "x_7 = [1.043 0.949 1.024 1.039]\n", + "x_8 = [1.042 0.954 1.017 1.036]\n", + "x_9 = [1.043 0.959 1.011 1.034]\n", + "x_10 = [1.044 0.962 1.005 1.032]\n", + "x_11 = [1.045 0.966 1. 1.031]\n", + "x_12 = [1.046 0.969 0.995 1.03 ]\n", + "x_13 = [1.048 0.971 0.99 1.03 ]\n", + "x_14 = [1.05 0.973 0.986 1.029]\n", + "x_15 = [1.053 0.974 0.981 1.029]\n", + "x_16 = [1.056 0.976 0.977 1.03 ]\n", + "x_17 = [1.059 0.977 0.972 1.03 ]\n", + "x_18 = [1.063 0.977 0.968 1.031]\n", + "x_19 = [1.067 0.978 0.963 1.032]\n" + ] + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = w * (N @ x + b) / M + (1-w) * x" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "La solution recherchée étant [1,1,1,1] ca semble bien marcher !\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Étudions la convergence\n", + "\n", + "Pour bien comprendre une méthode itérative il faut étudier sa convergence et donc tracer une courbe\n", + "de l'erreur absolue (lorsqu'on connait la solution), ou de l'erreur relative (entre 2 ${\\bf x}^i$ successifs)\n", + "ou du résidu ($||A \\, {\\bf x}^i - {\\bf b}||$) ou de toute autre mesure qui a du sens.\n", + "\n", + "Regardons :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 248, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "error = [np.square(x - np.ones(4)).sum()]\n", + "for i in range(20):\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error.append(np.square(x - np.ones(4)).sum())\n", + "plt.plot(range(len(error)), error);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "A priori cela semble bien, sauf qu'en fait on ne voit rien car l'échelle empêche de voir ce qui se passe à\n", + "la fin.\n", + "\n", + "Regardons en échelle logarithmique :" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(range(len(error)), error)\n", + "plt.semilogy();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Oula, la fin fait peur...\n", + "\n", + "Moralité : **Il faut toujours regarder une erreur en échelle logarithmique.** \n", + "\n", + "Puiqu'on mesure quelque chose \n", + "qui doit tendre vers 0, avec une echelle normale on est vite écrasé et donc on ne voit pas si on est à \n", + "$10^{-3}$ ou $10^{-6}$ alors que c'est très très différent.\n", + "\n", + "De même si on diverge on ne verra pas le début car un échelle linéraire s'ajustera sur les dernières valeurs qui \n", + "peuvent être très grandes." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Reprenons notre calcul sur plus d'itérations." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 375 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "error = [np.square(x - np.ones(4)).sum()]\n", + "for i in range(200):\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error.append(np.square(x - np.ones(4)).sum())\n", + "plt.plot(range(len(error)), error)\n", + "plt.title('Erreur absolue')\n", + "plt.semilogy();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Donc on s'est approché de la solution puis on a divergé ce qui est mieux que de diverger directement.\n", + "\n", + "#### Erreur relative \n", + "\n", + "Aurait-on pu le voir si on n'avait pas connu la solution ? Regardons l'écart entre 2 ${\\bf x}^k$ successifs." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "lang": "fr" + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "error2 = []\n", + "for i in range(200):\n", + " old_x = x\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error2.append(np.square(x - old_x).sum())\n", + "plt.plot(range(len(error2)), error2)\n", + "plt.title('Ecart entre 2 x successifs')\n", + "plt.semilogy();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Il semble bien qu'il y ait une relation forte entre l'écart entre deux **x** successif et l'erreur absolue.\n", + "Vérifions :" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération présentant le minimum : 12 14\n", + "Erreur absolue minimum : 0.004062676542953207\n", + "Erreur absolue minimum devinée à partir du minimum de l'écart : 0.004333899458825818\n" + ] + } + ], + "source": [ + "k_min = np.argmin(error)\n", + "k2_min = np.argmin(error2)\n", + "print('Itération présentant le minimum : ', k_min, k2_min)\n", + "print('Erreur absolue minimum : ', min(error))\n", + "print(\"Erreur absolue minimum devinée à partir du minimum de l'écart : \", error[k2_min])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "L'écart entre 2 **x** successifs est une facon simple et relativement efficace de savoir quand arrêter un algorithme\n", + "itératif." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Résidu\n", + "\n", + "Enfin on peut calculer le résidu à savoir $||A \\, {\\bf x} - {\\bf b}||$ mais c'est $n^2$ opérations :" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvAAAAIQCAYAAADn4lr4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOzdeXxU9b3/8VcSCPu+KiIK6BdQFqUudalrra1WRUVsb2+vXa/tbStUrVpttVbrUhfsr622trX3trcK7mutVeu+VWoAWb6IoAiIIMi+hCTz+2OGa+AQIJDkzExez8cjjzMznzNnPvmK8M4353xPSSaTQZIkSVJhKE27AUmSJEk7zgAvSZIkFRADvCRJklRADPCSJElSATHAS5IkSQXEAC9JkiQVEAO8JEmSVEAM8JIkSVIBMcBLkiRJBcQAL0mSJBUQA7wkSZJUQAzwkiRJUgExwEuSJEkFpEXaDUiSskIIVwCX7+DulcBqYCEwGZgYY3yonp9XArwBDM+99DBwWoyxpj7HqcfnZXIP340x7rWTxzga+Efu6U9ijFfsemeSVFicgZekwlQOdAX2B/4NeDCE8FQIoUM9jnEWH4f3fwFfaKzwLklqOM7AS1J+mgDctY16W6Af8DngiNxrx+be97ntHTyEUAb8JPf0PeDkGOOane5WktRkDPCSlJ9mxhgf2IH9rgkh/AfwB7K/Vf1sCOHTMca/b+d9XwYCsBI4Kcb4/q61u30xxpLG/gxJag4M8JJU4GKM/x1COAr4Su6lc4BtBvgY4x3AHY3cmiSpEXgOvCQVh9oXsIbUupAkNTpn4CWpOGRqPW5T104hhEOBrwJHA7sDJWRXsnkGuD3G+Nq2PiSE0A34T7Ln2Q8BOgDLgXeAp4Dfxhjn1PHe7a5Ck7sI99vAGbnjlwBzgbuBm7bT2165fQGejTEevY19r+DjFX++EmP847aOLUn5xAAvScXh2FqPZ25ZDCG0An5L9tz3LQ3MfX09hPA74L9ijJVbOcZhZGf6u21R6p77+gRwfgjh4hjjjfX9BkII+wOPAX23KO2X+zoHuKq+x5WkYmOAl6QCF0I4BPhGrZf+d4t6GfAIcHzupSXAfwMVuefDyZ4/3x34OtAzhHBajDFT6xjdgAfIhvcM2Rnxp4BlQA/gOOB0sv+u3BBCeDPG+Ld6fA/9geeBzrmXJud6XAgMyPW1N/DLHT2mJBUrA7wkFZgQQjnQCRgMfB74Lz4+beZR4P4t3nIxH4f3vwNnxRiX16r/bwjhGrIB/VPAKcC5wK219vkS2aAO8KMY49VbfMatIYSvAb/LPf8+sMMBHhjPx+H9t8C3Y4zVm4ohhJuBicDJ9TimJBUlA7wk5afLQwg7elfWTe4CvrbFzHl74ILc00XA6THG1Vu+Mcb4UQjhC0AE2gMXhxB+WytED6q1+1bv+Bpj/H0I4TtAFdmZ8x0SQhhC9gcRgGlkT+Gprr1PjHFdCOGLwAygz44eW5KKkavQSFJhe4/sGvCHxxi/EGNcu0X9RD6e2f7L1sL7JjHGhXwczvcEDqhVXlLr8QW5c+q3dowDYowHxRi/srV6HT5f6/FtMcaqOo69CritHseVpKLkDLwk5act78RaRvYc9dFkzzcHeBv4Zozx6W0c5/Baj9uHEE7bzufWDs+HAK/X6udSshM/XwY+HUJ4CHgCeHqLU3Lq67Baj5/fzr7/2IXPkaSiYICXpPxU151YfxNCOBf4NdmLO58MIXw3xvirOo5Te0WXb+a+dlTPTQ9ijNNCCGPJnqteCuxGdjnJ/wSqQwj/JLuCzN0xxsQqONvRu9bjedvZ9616HluSio6n0EhSgYkx3sbHa5iXAL8IIZxZx+6dduGjOm7xuf8POBS4B1hXq1SWe/1KYEYI4dEQwh71+JwutR5veQrQllbW47iSVJScgZekwnQVcBTZ02lKgd+HEF6PMb6zxX61A/FnY4yP78qHxhj/CYwOIbQFjiG7us2xwFCyP0xA9iZPT4UQRsQY1239SJtZVutxO2DDNvbd6rn3O6F1Ax1HkpqcM/CSVIByK818BViVe6kj8N8hhJItdl1U63GDrd4SY1wbY3w0xjguxjg8d+wL+Hhmfl/g33fwcLVXrOm/nX23NbNfU+vx9iaoOm+nLkl5ywAvSQUqxvgecEmtlz5F9m6ltb1S6/GxbEcI4YIQwv+EEK4MIQzNvVYaQhgdQrgshPDTOnp5P3f31YtqvXzA1vbditoXrh5X515Zn9pGrfbMfcc698oaup26JOUtA7wkFbZbgX/Wen59CKFrreePAutzj88MIexb14FCCLuTPY/934Efkb3jKjHGGuB64KfAD0MIves6BvBhrcer6txrc/ds+izgWyGEdnX01xL49jaOsxTYtH78wBDCVkN8CGEAcNAO9iZJeccAL0kFLBeuv8XHp490B66tVV8M3J57Wg48FEJInKYSQuhMdg34TXd0fSTG+GatXTYtaVlK9lSdxLnoufPiz6/10g4t+Zj7TcLvc0/7AXeGENrU3ieEUEb2h5X9t3GcKmBS7mkb4Mdb6bF37ntpuSO9SVI+8iJWSSpwMcZJIYTb+Hh2+ushhDtijC/nnl8EHEH2lJYAvBlC+BPwEtngvx/wdaBbbv8PyP5QUNvPyZ6e0xs4AZgdQvgjMDtXHwh8Fdg99/wfMca/1uPbuIDsKT79yd7YaVoI4Xaya93vkfvsocBiai1vuRW/AQ7OPT4/hLAfcD/Zi3lHAv9BdtWbV8iunCNJBccAL0nF4VLgTLLhtgS4NYQwMsZYHWNcF0I4Bvgf4BSys9N1rQk/HRgVY5xf+8UY47IQwonAI2QD9R7AZXX08neyN5zaYTHGFSGEw8j+FuBgYG/gZ1vstgQYw7Zn9u/Ivf8/c89PzH3V9iey6+i/jCQVIE+hkaQikLsT6oW1XhoOfK9WfUWM8VTgaOAPwCxgNbCR7Eo1j5Fd1WZEjHFWHZ8xGRgMnAc8mXtfJdnZ7TnAn4GTY4wnxBhX7MT38AHZO8d+A3iW7JrvG8jOwt8CDAMqtnOMTIzxXLLLW04ku8JNJfA+2R8OTo4xfpnN7zgrSQWlJJPJbH+vPBVC6ANMBc6KMT65Re0YsrM3w8iuMXwHcGXuHElJkiSpIBXsDHwIoS/ZX9N22UrtEOCvwHvAGcCvgIuBG5qyR0mSJKmhFdw58CGEUuDLZMP4ljcs2eQnwAxgTO5mJ4+HEDYAPw8hXB9jXFjH+yRJkqS8Vogz8MOA28hejJW4y19uabNjgPty4X2TiUAZyYuZJEmSpIJRiAF+HjAwxvh9shdObak/2bWOY+0XY4wLyN7ie3CjdyhJkiQ1koI7hSbGuIzsRal16ZTbrtxKbRXbv722JEmSlLcKcQZ+e7b3PRXusjuSJElq9ooxwC/PbTtspdYBqPfaxJIkSVK+KMYA/zZQTfa23v8nt2Z8G7Kr00iSJEkFqegCfIxxA/AMcHpuyclNziJ7572n0+hLkiRJaggFdxHrDvop2aB+bwjhdrJLT14J3BpjnJdqZ5IkSdIuaLQAn5v9fhkYEGPsvo39ugCXA6OA3YAlwOPAlTHGd3fms2OMz4YQTiMb2u8HPgCuyT3fpkmTJnmRqyRJkprEyJEj67oxaZ1KMpnGyashhJ8BlwBL6wrwufD+EjCI7BKPs8iu496F7MWoR8UYpzRKg3UwwEuSJKmp7EyAb/AZ+BBCCdkZ9Ut2YPfbyYb3x4CzY4yrQgitgVuBc4C7QghDY4zVDd3n9owcObJJP2/GjOy1tYMHe5+pHeWY1Y/jVX+OWf04XvXnmNWP41U/jlf9NeWYTZo0aaff26Az8CGE3sBtwKm1Xt7qDHwIYRAwHVgD9MvdoGlTrQyYSvauqaNjjPc0WJPbsWkGvm3btk31kQCsW7cOgDZt2jTp5xYyx6x+HK/6c8zqx/GqP8esfhyv+nG86q8px2zt2rXAzs3AN9gqNCGEE8ieAnMqsIjtz8B/CSgBHq4d3gFyM+535J6OaageJUmSpELXkKfQDAHaA38CxgFDt7P/IbntS3XUX8ltj9z11uqvqX/d5K+56s8xqx/Hq/4cs/pxvOrPMasfx6t+HK/6K5RTaBpyHfjXgANjjF+OMS7dgf033Whpbh31TSvQ9AohtN/l7iRJkqQi0GAz8DHGumbS69Ijt60r7Nc+raY7sLreTUmSJElFJs07sW66OmBdHfXar3v1hSRJkkS6AX57S0PW7s212SVJkiTSDfBrctvWddRb1Xpc1yy9JEmS1KykGeA3nfvetY56t1qPlzRyL5IkSVJBSDPAz8xt96qj3i+3fT/GuLbx25EkSZLyX5oB/vXc9tA66ptef7UJepEkSZIKQpoB/r7c9rQQwman0YQQyoBzck//3JRNSZIkSfkstQAfY5wCPAp0BO4JIXQDCCG0Bn4HDAYicH9aPUqSJEn5psFu5LSTzgVeAI4B5oUQZgD9gS7ACmBUjLEmxf4kSZKkvJLmKTTEGOcDI4FfkF1pZhhQBdwJHBRjnJFie5IkSVLeabQZ+BjjM0DJDuy3FDgv9yVJkiQ1ieVrK/nbtEV0blvOcYN6pt3ODkv7FBpJkiSpyT098wN+cM8UPlxdCcD3jh3IZ/um3NQOSvUUGkmSJKkpraus5rIHpvLVP77+f+Ed4PnZH6bYVf04Ay9JkqRmYer8FZw34Q3mLFmTqB29b0+yl2LmP2fgJUmSVNSqazL86h+zGfXrFxPhvay0hHHH78t3jh2YUnf15wy8JEmSitZ7y9by/YkV/POdjxK1vbq15eYxIzhgzy4pdLbzDPCSJEkqOplMhvvfWMCPH5zG6g3JU2O+cHBfLjtpCO1aFV4cLryOJUmSpG1YvraSSx94k0envJ+odW1XzrWnD+WE/Xqn0FnDMMBLkiSpaLw4+0POnziZRSvXJ2pHhx5cf+YwenZonUJnDccAL0mSpIK3oaqaG/4Wuf35uYlaqxalXHrSYP790H6UlGz3PqN5zwAvSZKkgjZz0UrG3lXBzEWrErX9du/ILWePYGDPDil01jgM8JIkSSpINTUZ7njpHa57fCaVVTWb1UpK4NyjBjDu+H0pb1FcK6cb4CVJklRwFq1YzwV3T+aFrdxBtU/nNtx01nAO6d8thc4anwFekiRJBeWxqe9zyX1TWbFuY6I26oA+/OTU/ejYumUKnTUNA7wkSZIKwqr1G/nJw9O5Z9L8RK1j6xZcNWoopwzfPYXOmpYBXpIkSXnv9XeWMW5iBe8tW5eoHdq/KzedNYLdO7dJobOmZ4CXJElS3tpYXcMvnnqLX/1jNjWZzWsty0q48DOBrx/Rn9LSwl8eckcZ4CVJkpSX5ixZzdgJFUyZvyJR26dne8afPYL9du+UQmfpMsBLkiQpr2QyGf7y2jyuemQG6zZWJ+pfOXwvLjpxEK1blqXQXfoM8JIkScobH67ewMX3TuHJGYsTtZ4dWnHD6OF8at8eKXSWPwzwkiRJygtPz/yAH9wzhQ9XVyZqJ+7Xm2tOH0qXduUpdJZfDPCSJElK1brKaq5+bDp/fmVeotauvIzLT9mP0SP3oKSk+Vyoui0GeEmSJKVmyvzljJ1QwZwlaxK1A/fszM1jRtCvW7sUOstfBnhJkiQ1ueqaDLc9+zY3/30WVVusD1lWWsJ5x+3Dt48eQIuy0pQ6zF8GeEmSJDWp95atZdyECl5/96NEba9ubbl5zAgO2LNLCp0VBgO8JEmSmkQmk+H+Nxbw4wensXpDVaL+hYP7ctlJQ2jXyoi6LY6OJEmSGt3ytZVc+sCbPDrl/USta7tyrj19KCfs1zuFzgqPAV6SJEmN6sXZH3L+xMksWrk+UTs69OD6M4fRs0PrFDorTAZ4SZIkNYr1G6u54W+R370wN1Fr1aKUy04azJcO7efykPVkgJckSVKDm7loJWPvqmDmolWJ2v59OjJ+zAgG9uyQQmeFzwAvSZKkBlNTk+EPL87l+scjldU1m9VKSuDcowYw7vh9KW/h8pA7ywAvSZKkBrFoxXouuHsyL8z+MFHr07kNN501nEP6d0uhs+JigJckSdIue2zq+1xy31RWrNuYqI06oA8/OXU/OrZumUJnxccAL0mSpJ22av1GrnhoOvf+a36i1rF1C64aNZRThu+eQmfFywAvSZKknfLPd5YxbkIF8z9al6h9sn83bjxrOLt3bpNCZ8XNAC9JkqR62Vhdwy1PvsWvn5lNTWbzWsuyEi78TODrR/SntNTlIRuDAV6SJEk77O0lqxk3oYIp81ckavv2as/4MQcwZPeOKXTWfBRtgA8hfAMYC+wFzANuBX4ZY6zZ1vskSZKUlMlk+Mtr87jqkRms21idqH/l8L246MRBtG5ZlkJ3zUtRBvgQwjeB3wD/D3gQOBIYD7QBrkuxNUmSpILz4eoNXHTPFJ6auThR69mhFTeMHs6n9u2RQmfNU1EGeOBrwAsxxu/lnj8VQgjAdzDAS5Ik7bCnZnzARfdO4cPVlYnaifv15prTh9KlXXkKnTVfxRrg2wBb3kFgKeCdAyRJknbA2soqrn50Bv/76rxErV15GZefsh+jR+5BSYkXqja1Yg3w44HfhhC+BDwMHAr8B/CnVLuSJEkqAFPmL2fsXRXM+XBNonbgnp25ecwI+nVrl0JnguIN8H8me9577cD+BPDddNqRJEnKf9U1GW59Zjbjn3yLqi3WhywrLeG84/bh20cPoEVZaUodCoo3wG+6cPUi4FVgKHAFcG8I4VRXopEkSdrce8vWMm5CBa+/+1Gitle3tow/+wBG9O2cQmfaUtEF+BDCYcCJwLdijLflXn42hDAHeBQ4BXggrf4kSZLySSaT4b5/LeDyh6axekNVov6Fg/ty2UlDaNeq6GJjwSrG/xL9ctsXt3j9udx2PwzwkiRJLF9byaX3v8mjU99P1Lq2K+fa04dywn69U+hM21KMAX5mbnskMLXW64fntnOath1JkqT888JbH3L+3RV8sHJDonZ06MH1Zw6jZ4fWKXSm7Sm6AB9jfCOEcC/w8xBCB7LnwO9H9hz4CuDeFNuTJElK1fqN1fz8b5HfvzA3UWvVopTLThrMlw7t5/KQeSzVAB9CKAVeBgbEGLtvY78uwOXAKGA3YAnwOHBljPHdrbzli8BlwLnAlcA84I+5/ZN3IZAkSWoGZi5aydi7Kpi5aFWitn+fjowfM4KBPTuk0JnqI+0Z+KuAg8neZGmrcuH9JWAQsAqYAvQHvgqcHkI4KsY4pfZ7ciH9x7kvSZKkZq2mJsMfXpzL9Y9HKqs3X4yvpAS+ddQAxh6/L+UtXB6yEKQS4EMIJWRn1C/Zgd1vJxveHwPOjjGuCiG0Bm4FzgHuCiEMjTFWN1a/kiRJher9Feu44O7JvDg7OV/ap3Mbbh4zgoP37ppCZ9pZJZlMZvt7NaAQQm/gNuDUWi8v3dopNCGEQcB0YA3QL8a4rFatjOxFqoOB0THGexqiv0mTJmUA2rZt2xCH22Hr1q0DoE2bNk36uYXMMasfx6v+HLP6cbzqzzGrH8erftatW8dL763jtkkrWV2ZvAXOsf3b8+1DutOu3Fn3TZryz9jatWsBGDlyZL0vNmjS/2IhhBOAWWTD+yK2PwP/JaAEeLh2eAfIzbjfkXs6poFblSRJKlhrKmv4xavLueHl5Ynw3r68lIs+1ZMLj+xpeC9QTX0KzRCgPfAnYBzZO6RuyyG57Ut11F/JbY/c9dY2N3jw4IY+5DbNmDEjlc8tZI5Z/The9eeY1Y/jVX+OWf04Xjvmn+8sY9xDFcz/aF2i9sn+3bjxrOHs3tnfYmxNU/4ZmzRp0k6/t6kD/GvAgTHGCoAQwvb2H5jbJtc5ytq0Ak2vEEL7GOPqXW9RkiSp8GysruGWJ9/i18/MpmaLM6TLy0q58DOBrx2xN6WlLg9Z6Jo0wMcY65pJr0uP3LauVWpqn1bTHTDAS5KkZuftJasZN6GCKfNXJGr79mrP+DEHMGT3jil0psaQ9jKS27Pp9zvJ3wElX/d3QZIkqVnJZDL876vzuOrR6azfmLxQ9dTBHbnui4fRumVZCt2pseR7gK9m2xfa1q417XI6kiRJKVqyagMX3TuFp2cuTtR6dmjF9w7pwsg+bQ3vRSjfA/waoDPQuo56q1qP65qllyRJKipPTv+Ai+6dwtI1yRvMn7hfb645fSiL5r2dQmdqCvke4JeSDfB13V2gW63HSxq/HUmSpPSsraziqkdn8JdX5yVq7crLuOKU/Thz5B6UlJSwKIX+1DTyPcDPBAYAe9VR75fbvh9jXNskHUmSJKVgyvzljL2rgjkfrknURvbrws1njWDPbk17I0qlI98D/OvAScChwK1bqR+a277aZB1JkiQ1oeqaDLc+M5vxT75F1RbrQ5aVljD2uH341tEDaFHmTZmai3z/L31fbntaCGGz02hCCGXAObmnf27KpiRJkprCe8vWMuY3L3PDE7MS4X3v7u2491uH8d3j9jG8NzN5/V87xjgFeBToCNwTQugGEEJoDfwOGAxE4P7UmpQkSWpgmUyGeybN57O3PM/r736UqH/h4D155LtHMKJv5xS6U9ry/RQagHOBF4BjgHkhhBlAf6ALsAIYFWNMLnwqSZJUgD5aU8mlD0zlsanJy1C7tivnujOG8ekhvVLoTPkir2fgAWKM84GRwC/IrjQzDKgC7gQOijHOSLE9SZKkBvPCWx9y4i3PbTW8HxN68PjYIw3vSncGPsb4DFCyA/stBc7LfUmSJBWV9Rur+fnfIr9/YW6i1rplKZeeNIQvHbInJSXbjU1qBgrhFBpJkqSiNeP9lYy9q4L4wapEbf8+HRk/5gAG9myfQmfKVwZ4SZKkFNTUZPjDi3O5/vFIZfXml/OVlMC3jhrA2OP3pbxF3p/xrCZmgJckSWpi769Yx/kTJ/PS20sTtT6d23DzmBEcvHddN6JXc2eAlyRJakKPTFnID++bysr1VYna6Qf04YpT96Nj65YpdKZCYYCXJElqAqvWb+TyB6dx3xsLErWOrVtw9aihfH747il0pkJjgJckSWpk/3xnGeMmVDD/o3WJ2mEDunHjWcPZrVObFDpTITLAS5IkNZLKqhpueWoWtz7zNjWZzWvlZaX84MTAVw/fm9JSl4fUjjPAS5IkNYLZi1czbkIFUxesSNT27dWe8WMOYMjuHVPoTIXOAC9JktSAMpkMf351Hlc/Op31G2sS9a8evjc/ODHQumVZCt2pGBjgJUmSGsiSVRu46N4pPD1zcaLWq2Mrbhg9nCP36ZFCZyomBnhJkqQG8OT0D7jo3iksXVOZqH12/978bNRQurQrT6EzFRsDvCRJ0i5YW1nFVY/O4C+vzkvU2pWX8ZNT9+eMA/tQUuKFqmoYBnhJkqSdNPm95YydUMHcD9ckaiP7deHms0awZ7e2KXSmYmaAlyRJqqeq6hpufeZtbnnqLaq2WB+yrLSEscftw7eOHkCLstKUOlQxM8BLkiTVw7ylaxk3sYJJ736UqO3dvR03jxnBiL6dU+hMzYUBXpIkaQdkMhnu/dcCrnhoGqs3VCXqXzxkTy47aTBty41Xalz+CZMkSdqOj9ZUcukDU3ls6qJErVu7cq47YxjHD+mVQmdqjgzwkiRJ2/D8W0u44O7JfLByQ6J27KCeXHfGMHp0aJVCZ2quDPCSJElbsX5jNdc/HvnDi3MTtdYtS7n0pCF86ZA9XR5STc4AL0mStIUZ769k7F0VxA9WJWr79+nI+DEHMLBn+xQ6kwzwkiRJ/6emJsMfXpzL9Y9HKqtrNquVlMC3jx7AecftS3kLl4dUegzwkiRJwPsr1nH+xMm89PbSRK1P5zbcPGYEB+/dNYXOpM0Z4CVJUrP3yJSF/PC+qaxcn1we8vQD+3DFKfvRsXXLFDqTkgzwkiSp2Vq5fiNXPDiN+95YkKh1atOSq0ftz8nDdk+hM6luBnhJktQsvTZ3GeMmVLBg+bpE7bAB3bjxrOHs1qlNCp1J22aAlyRJzUplVQ23PDWLW595m5rM5rXyslJ+cGLgq4fvTWmpy0MqPxngJUlSszF78WrGTahg6oIViVro1YHxZ49g8G4dU+hM2nEGeEmSVPQymQx/fnUeVz86nfUbaxL1rx2xNxd+JtC6ZVkK3Un1Y4CXJElFbcmqDVx07xSenrk4UevVsRU3jh7BEft0T6EzaecY4CVJUtF6cvoHXHTvFJauqUzUPje0Nz8bNZTObctT6EzaeQZ4SZJUdNZWVnHVozP4y6vzErV25WX85NT9OePAPpSUeKGqCo8BXpIkFZXJ7y1n7IQK5n64JlEb2a8LN581gj27tU2hM6lhGOAlSVJRqKqu4dZn3mb8U29RvcX6kC1KSxh7/D6ce9QAWpSVptSh1DAM8JIkqeDNW7qWcRMrmPTuR4la/+7tuHnMCIb37ZxCZ1LDM8BLkqSClclkuPdfC7jioWms3lCVqP/bIXty6UmDaVtu5FHx8E+zJEkqSB+tqeTSB6by2NRFiVq3duVcd8Ywjh/SK4XOpMZVtAE+hHAocA1wMLAaeBy4MMaYXARWkiQVlOffWsIFd0/mg5UbErVjB/XkujOG0aNDqxQ6kxpfUQb4EMJI4B/AU8AoYHeyYX4f4LAUW5MkSbugsrqGKx+ezh9enJuotW5ZymUnDeHfDtnT5SFV1IoywAPXA1OAU2OM1QAhhJXALSGEgTHG2al2J0mS6m3Osg1c//xi3l2+MVEb2qcT488ewYAe7VPoTGpaRRfgQwjdgKOBr20K7wAxxvuA+9LqS5Ik7Zyamgy/f2Eu1z2+gKqazWulJfDtowfyveP2obyFy0OqeSi6AA8MA0qBxSGEPwGnASXAA8B3Y4zJ9aUkSVJeen/FOs6fOJmX3l6aqO3RpQ03jxnBQXt1TaEzKT3F+KNqj9z2dmAD2QB/PvA54K8hhGL8niVJKjqPTFnIZ25+bqvh/fQD+/DYeUca3tUsFeMMfHlu+0aM8eu5x0+FEFYAdwInAo+l0pkkSdqules3csWD07jvjQWJWvvyUq49czgnD9s9hc6k/FCMAX5VbrtlSH88tz1gKzVJkpQHXpu7jHETKliwfF2iNmK3Nnz/8B58yvCuZq4YA/xbuX+1gVAAACAASURBVO2Wi7+2zG2TfyNIkqRUVVbVMP7JWdz67NtkMpvXystK+cGJgU92W0+py0NKRXkO/AzgHeDsEELt/8tPzm2fb/KOJElSnWYvXs3pt77Ir59JhvfQqwMPfudwvn5kf8O7lFN0M/AxxkwI4UJgInB3COE3QAB+BjwQY/xnqg1KkiQAMpkMf351Hlc/Op31G2sS9a8dsTcXfibQumVZCt1J+SvVAJ9bEeZlYECMsfs29usCXE72rqq7AUvIntN+ZYzx3S33jzHeE0I4Bfgx8DCwDPgNcFmDfxOSJKnelqzawA/umcw/4pJErVfHVtw4egRH7FNnNJCatbRn4K8CDgaS60Pl5ML7S8AgsheoTgH6A18FTg8hHBVjnLLl+2KMjwCPNEbTkiRp5/19+gdcfO8Ulq6pTNQ+N7Q3Pxs1lM5ty7fyTkmQ0jnwIYSSEMIVwCU7sPvtZMP7Y0CfGOMngN2BPwKdgbtCCP5uTZKkPLe2sopL7pvKN/7n9UR4b9+qBTeOHs6vvnig4V3ajpLMlleLNLIQQm/gNuDUWi8v3dopNCGEQcB0YA3QL8a4rFatDJgKDAZGxxjvaYj+Jk2alAFo27ZtQxxuh61bl10cp02bNk36uYXMMasfx6v+HLP6cbzqrzmNWVyynp+/sIQFKzcmakN6tuLCI3rSu0PLrbzzY81pvBqC41V/TTlma9euBWDkyJH1vjq7SWfgQwgnALPIhvdFbH8G/ktACfBw7fAOEGOsBu7IPR3TwK1KkqQGUF2T4S+TP+L7f12YCO9lJfDlA7pw/Wd23254l/Sxpj4HfgjQHvgTMA4Yup39D8ltX6qj/kpue+Sut7a5wYMHN/Qht2nGjBmpfG4hc8zqx/GqP8esfhyv+iv2MZu3dC3jJlYw6d2PErX+3dtx85gRDO/beYePV+zj1dAcr/pryjGbNGnSTr+3qQP8a8CBMcYKgBDC9vYfmNvOraO+aQWaXiGE9jHG1bveoiRJ2hWZTIZ7Js3nioemsaayOlH/t0P25NKTBtO2PO21NKTC1KT/58QY65pJr0uP3LauVWpqn1bTHTDAS5KUoo/WVPLD+6fy1zcXJWrd2pVz3RnDOH5IrxQ6k4pHvv/ou+kKgnV11Gu/7hUakiSl6LlZS7jg7sksXrUhUTt2UE+uO2MYPTq0SqEzqbjke4CvZtsX2tauNe1yOpIkCYD1G6u57vGZ3PHiO4la65alXHbSEP7tkD0pKan3YhuStiLfA/wasmu9t66jXvvH+Lpm6SVJUiOZvnAlYye8wawPkmexDu3TifFnj2BAj/YpdCYVr3wP8EvJBviuddS71XqcvBezJElqFDU1GX7/wlx+/rdIZXXNZrXSEvj20QM57/h9aFmWyj0jpaKW7wF+JjAA2KuOer/c9v0Y49om6UiSpGZu4fJ1nD9xMi/PSa4xsUeXNtw8ZgQH7VXX3JukXZXvPxa/ntseWkd90+uvNkEvkiQ1ew9PXsiJ45/bang//cA+PHbekYZ3qZHle4C/L7c9LYSw2d8GIYQy4Jzc0z83ZVOSJDU3K9dvZNyECr575xusXF+1Wa1Tm5b88osHcNNZI+jY2juqSo0trwN8jHEK8CjQEbgnhNANIITQGvgdMBiIwP2pNSlJUpF7dc5SPjv+ee5/Y0GidvjAbjw+9khOHrZ7Cp1JzVO+nwMPcC7wAnAMMC+EMAPoD3QBVgCjYow123i/JEnaCZVVNYx/cha3Pvs2mS0Way4vK+UHJwa+evjelJa6PKTUlPJ6Bh4gxjgfGAn8guxKM8OAKuBO4KAY44wU25MkqSjNXrya0299kV8/kwzvg3p34KHvHs7Xj+xveJdSkOoMfIzxGWC7/+fHGJcC5+W+JElSI8lkMvz5lXe5+rEZrN+Y/AX3147Ymws/E2jdsiyF7iRBYZxCI0mSmsDiVev5wT1TeCYmb63Sq2Mrbhw9giP26Z5CZ5JqM8BLkiSemLaIi++byrI1lYna54b25mejhtK5bXkKnUnakgFekqRmbG1lFT99ZDp3vvZeota+VQt+csp+nH5gH0pKPNddyhcGeEmSmqmK95YzbkIFcz9ck6h9ol8Xbh4zgr5d26bQmaRtMcBLktTMVFXX8Otn3uaWp96iumbzJWZalJYw7tP7cu5RAyhzhRkpLxngJUlqRt5duoZxEyr417zliVr/7u0Yf/YIhu3ROYXOJO0oA7wkSc1AJpPh7knz+clD01hTWZ2o/9she3LpSYNpW240kPKd/5dKklTkPlpTySX3TeXxaYsStW7tyrn+zGEcN7hXCp1J2hkGeEmSithzs5Zwwd2TWbxqQ6J23KCeXHvGMHp0aJVCZ5J2lgFekqQitH5jNdc9PpM7XnwnUWvdspQfnTyELx68p8tDSgXIAC9JUpGZvnAlYye8wawPVidqw/boxM1jRjCgR/sUOpPUEAzwkiQViZqaDL97YQ43/G0WldU1m9VKS+DbRw/kvOP3oWVZaUodSmoIBnhJkorAwuXrOH/iZF6eszRR26NLG24eM4KD9uqaQmeSGpoBXpKkAvfQ5IVcdv9UVq6vStTOOHAPrjhlCB1at0yhM0mNwQAvSVKBWrl+Iz9+4E0eqFiYqHVq05KfjRrKScN2S6EzSY3JAC9JUgF6dc5Svj9xMguWr0vUjhjYnRtGD6d3p9YpdCapsRngJUkqIJVVNdz85Cxue/ZtMpnNa+UtSrnoxEF85bC9KC11eUipWBngJUkqELMXr+K8uyqYtnBlojaodwfGnz2CQb07ptCZpKZkgJckKc9lMhn+9Mq7XP3oDDZU1STqXz9iby74TKB1y7IUupPU1AzwkiTlscWr1vODe6bwTFySqPXu2JobzxrO4QO7p9CZpLQY4CVJylNPTFvExfdNZdmaykTtpKG7cfWo/enctjyFziSlyQAvSVKeWbOhiqsenc6dr72XqLVv1YIrT92PUQf0oaTEC1Wl5sgAL0lSHnlj3keMm1DBO0vXJmoH7dWFm84aQd+ubVPoTFK+MMBLkpQHqqpr+NU/3uYXT79Fdc3m60O2KC1h3Kf35dyjBlDm8pBSs2eAlyQpZe8uXcPYCRW8MW95ota/ezvGnz2CYXt0TqEzSfnIAC9JUkoymQxPzF7F7Xc+z5rK6kT9S4fuyQ8/N5i25f5zLelj/o0gSVIKPlpTydXPfMCL85LnundvX871Zw7j2EG9UuhMUr4zwEuS1MSem7WEC+6ezOJVGxK14wf35NozhtG9fasUOpNUCAzwkiQ1kfUbq7n2rzP540vvJGqtW5byo5OH8MWD93R5SEnbZICXJKkJTFu4grF3VfDW4tWJ2rA9OnHzmBEM6NE+hc4kFRoDvCRJjaimJsPtz8/hhiciG6s3Xx6ytATGDO3MlWM+Scuy0pQ6lFRoDPCSJDWShcvX8f2JFbwyZ1mi1rdrG847pAv79WxteJdULwZ4SZIawUOTF3Lp/VNZtb4qUTtz5B5c/vkhzJ87O4XOJBU6A7wkSQ1oxbqNXP7gmzxQsTBR69SmJdecPpTPDd0thc4kFQsDvCRJDeSVOUs5f+JkFixfl6gdMbA7N4weTu9OrVPoTFIxMcBLkrSLKqtquOnvs/jNc2+T2fw6VcpblHLRiYP4ymF7UVrq8pCSdl2zCPAhhFuA7wEtY4zJkxElSdpJsxev4ry7Kpi2cGWiNqh3B8afPYJBvTum0JmkYlX0AT6EcBzw3bT7kCQVl0wmw59eeZerH53BhqqaRP0bR+7N+ScEWrcsS6E7ScWsqAN8CKEz8EdgPtA33W4kScVi8ar1XHj3FJ6dtSRR692xNTeeNZzDB3ZPoTNJzUFRB3jgV8Ac4FngRyn3IkkqAk9MW8TF901l2ZrKRO2kYbtx9Wn707lteQqdSWouijbAhxDOAk4BhgNfTrkdSVKBW7Ohip8+Mp27/vleota+VQuuPHU/Rh3Qh5ISL1SV1LiKMsCHEHYHbgUujDHOCSGk3ZIkqYC9Me8jxk2o4J2laxO1g/bqwk1njaBv17YpdCapOSrKAA/8AXg9xnhb2o1IkgpXVXUNv/rH2/zi6beortl8fcgWpSWM+/S+nHvUAMpcHlJSEyq6AB9C+DbwSWB4CGHT91ea25aFEGpijMnlAiRJquXdpWsYO6GCN+YtT9T692jHLWMOYOgenVLoTFJzV3QBHjgL6AjM3UptPfAT4IqmbEiSVDgymQx3vz6fnzw8jTWV1Yn6vx/ajx9+bjBtyl0eUlI6ijHA/yfQYYvXvgl8AzgUSF59JEkSsGxNJT+8byqPT1uUqHVvX871Zw7j2EG9UuhMkj5WdAE+xhi3fC2EcHLu4STvxCpJ2ppnZy3hwrsns3jVhkTt+ME9ufaMYXRv3yqFziRpc6kG+BBCKfAyMCDGWOcdL0IIXYDLgVHAbsAS4HHgyhjju03RqySpOK3fWM21f53JH196J1Fr07KMH508hC8c3NflISXljbRn4K8CDgaW1rVDLry/BAwCVgFTgP7AV4HTQwhHxRinbOtDYoxX4HnvkqQtTFu4grF3VfDW4tWJ2vA9OnHzmBH079E+hc4kqW6l29+l4YUQSkIIVwCX7MDut5MN748BfWKMnwB2B/4IdAbuCiF4JZEkaYfV1GT4zbNvc9qvXkyE99IS+N6xA7nnW4cZ3iXlpZJMJrP9vRpQCKE3cBtwaq2Xl27tFJoQwiBgOrAG6BdjXFarVgZMBQYDo2OM9zREf5MmTcoAtG3btDfkWLduHQBt2rRp0s8tZI5Z/The9eeY1U+hjNeSNVXc8MJipixan6j1bt+CC4/syZCerZukl0IZs3zheNWP41V/TTlma9dmbww3cuTIep+f16Qz8CGEE4BZZMP7IrY/A/8loAR4uHZ4B4gxVgN35J6OaeBWJUlF6Jm5q/nWg/O3Gt4/PbA9v/z8Hk0W3iVpZzX1OfBDgPbAn4BxwNDt7H9IbvtSHfVXctsjd721zQ0ePLihD7lNM2bMSOVzC5ljVj+OV/05ZvWTz+O1Yt1GLn/wTR6oWJyodWrTkmtOH8rnhu7W5H3l85jlI8erfhyv+mvKMZs0adJOv7epA/xrwIExxgqAEML29h+Y227tpkwAm1ag6RVCaB9jTF6FJElq1l6Zs5TzJ05mwfJ1idoRA7tzw+jh9O7krLukwtGkAT7GWNdMel165LZ1rVJT+7Sa7oABXpIEQGVVDTf9fRa/ee5ttrzcq7xFKRefOIhzDtuL0lKXh5RUWNJeRnJ7Nl1BkJw2Sb7uFRqSJABmL17F9+6sYPr7KxO1Qb07cMvZBxB6b3nTbkkqDPke4KvZ9oW2tWtNu5yOJCnvZDIZ/vTKu1z96Aw2VNUk6t/8VH/OP2FfWrVw9WFJhSvfA/wasmu913VyYu17Wtc1Sy9JagYWr1rPhXdP4dlZSxK13h1bc9NZwzlsYJ03/ZakgpHvAX4p2QDftY56t1qPk39jS5Kahb9NW8Ql901l2ZrKRO2kYbvxs9OG0qltyxQ6k6SGl+8BfiYwANirjnq/3Pb9GOPaJulIkpQ31myo4qePTOeuf76XqHVo1YIrT9uP00b0oaTEC1UlFY98D/CvAycBhwK3bqV+aG77apN1JEnKC/+a9xHjJlTw7tLk/M3Be3XlxrOG07dr095VW5KaQpPeiXUn3JfbnhZC2Ow0mhBCGXBO7umfm7IpSVJ6qqprGP/kLEbf9nIivLcoLeEHJwbu/OahhndJRSuvA3yMcQrwKNARuCeE0A0ghNAa+B0wGIjA/ak1KUlqMu8uXcPo37zM+Cfforpm88XH+vdox/3fPpxvHz2QMtd2l1TE8v0UGoBzgReAY4B5IYQZQH+gC7ACGBVjTK4VJkkqGplMhrtfn88VD09jbWV1ov7vh/bjh58bTJtyl4eUVPzyegYeIMY4HxgJ/ILsSjPDgCrgTuCgGOOMFNuTJDWyZWsqOffPk/jBvVMS4b17+3LuOOcgfnra/oZ3Sc1GqjPwMcZngO3+njPGuBQ4L/clSWomnp21hAvunsySVRsSteMH9+TaM4bRvX2rrbxTkopXIZxCI0lqZtZvrObav87kjy+9k6i1aVnGj04ewhcO7uvykJKaJQO8JCmvTFu4gvPuqmD24tWJ2vA9OnHzmBH079E+hc4kKT8Y4CVJeaG6JsPvnp/DDU9ENlZvvsJMaQl855iBfPe4fWhZlveXb0lSozLAS5JSt2D5Os6fWMErc5Ylan27tmH8mBGM7Nd1K++UpObHAC9JStWDFQu47IE3WbW+KlEbPXIPfvz5IXRo3TKFziQpPxngJUmpWLFuIz9+8E0erFiYqHVu25KfjRrK54bulkJnkpTfDPCSpCb38ttLOX9iBQtXrE/UjtynOz8/czi9O7VOoTNJyn8GeElSk6msquHGv0d++9wcMptfp0p5i1IuPnEQ5xy2F6WlLg8pSXUxwEuSmsRbH6zivLsqmP7+ykRtUO8O3HL2AYTeHVLoTJIKiwFektSoMpkM//Pyu/zssRlsqKpJ1L/5qf6cf8K+tGpRlkJ3klR4DPCSpEazeOV6LrxnCs/OWpKo9e7YmpvOGs5hA7un0JkkFS4DvCSpUTz+5iIuuW8KH63dmKidNGw3fnbaUDq1dXlISaovA7wkqUGt2VDFlQ9PZ8Lr7yVqHVq14MrT9uO0EX0oKfFCVUnaGQZ4SVKDmbFkPec+8jzvLl2bqB28V1duPGs4fbu2TaEzSSoeBnhJ0i6rqq7hfys+4i9TPqJmi+UhW5SW8P0T9uU/PzWAMpeHlKRdZoCXJO2Sdz5cw9gJFVS8tzxR69+jHb84+wD279Mphc4kqTgZ4CVJOyWTyTDx9ff4ycPTWVtZnaj/+6H9+OHnBtOm3OUhJakhGeAlSfW2bE0lF987hSemf5CodW9fzs/PHM4xg3qm0JkkFT8DvCSpXp6Ji7nwniksWbUhUTu0b1t++R+H0b19qxQ6k6TmwQAvSdoh6zdWc+1fZ/LHl95J1Nq0LOMbn+jCift0MLxLUiMzwEuStuvNBSsYO6GC2YtXJ2rD+3Zm/JgRrF8yL4XOJKn5McBLkupUXZPh9ufncOMTkY3Vm68PWVoC3zlmIN89bh9alpUyY0lKTUpSM2OAlyRt1YLl6/j+hApenbssUevbtQ3jx4xgZL+uKXQmSc2bAV6SlPBgxQIue+BNVq2vStRGj9yDy0/Zj/at/CdEktLg376SpP+zYt1GfvTAmzw0eWGi1rltS64ZNZTPDt0thc4kSZsY4CVJALz89lLOn1jBwhXrE7Uj9+nODaOH06tj6xQ6kyTVZoCXpGZuQ1U1N/19Fr99bg6Zza9TpbxFKZd8dhD/8cm9KC0tSadBSdJmDPCS1Iy99cEqzrurgunvr0zUBvXuwC++cAD79uqQQmeSpLoY4CWpGcpkMvz3S+9wzV9nsqGqZrNaSQl848j+nH/CvrRqUZZSh5KkuhjgJamZWbxyPRfcM4XnZiUXbt+tU2tuHD2cwwZ2T6EzSdKOMMBLUjPy+JuLuOS+KXy0dmOidvKw3bj6tKF0atsyhc4kSTvKAC9JzcCaDVVc+fB0Jrz+XqLWoVULfnra/pw6YndKSrxQVZLynQFekorcv+Z9xLgJFby7dG2idvDeXbnprOHs0aVtCp1JknaGAV6SilRVdQ3/7+nZ/PIfs6mu2Xx9yBalJXz/hH35z08NoMzlISWpoBjgJakIvfPhGsZOqKDiveWJ2oAe7bjl7APYv0+nFDqTJO0qA7wkFZFMJsOEf77HlY9MZ21ldaL+5U/245LPDqZNuctDSlKhKsoAH0JoAXwH+AawF7AIeBC4PMa4KsXWJKnRLFtTycX3TuGJ6R8kat3bt+LnZw7jmEE9U+hMktSQijLAAz8DxgLXAM8Bg4ArgU+GEA6PMdZs682SVGieiYu58J4pLFm1IVH79JBeXHv6ULq1b5VCZ5KkhlZ0AT6E0JZseL8hxnh57uWnQggfAncBRwNPp9SeJDWo9RurueaxGfz3y+8mam1alnH554cw5qC+Lg8pSUWk6AI80AW4Hbh7i9dn5ra7N207ktQ43lywgrETKpi9eHWiNrxvZ8aPGcHe3dul0JkkqTEVXYCPMS4A/msrpdNy2zebsB1JanDVNRl++9wcbvp7ZGP15stDlpbAd47dh+8eO5CWZaUpdShJakxFF+C3JoTwSeBi4JEYY0Xa/UjSzpr/0Vq+P3Eyr81dlqjt2bUtN48Zwch+XVLoTJLUVIo+wIcQjia7As1c4JxUm5GkXfBgxQIue+BNVq2vStTO+sQe/Pjz+9G+VdH/tS5JzV5R/00fQjgH+A0wDfhsjHFpuh1JUv2tWLeRHz3wJg9NXpiodW7bkmtPH8qJ+++WQmeSpDQUbYAPIVwJ/Aj4G3BmjDF5lZck5bmX317K+RMrWLhifaJ25D7duWH0cHp1bJ1CZ5KktBRlgA8hXEQ2vP8R+EaMMfn7ZknKYxuqqrnpiVn89vk5ZDa/TpXyFqVc8tlB/Mcn96K01OUhJam5KboAH0LYB7iK7LKRvwU+EUKovcvbMcYlafQmSTti1gerOO+uCma8vzJRG7xbR245ewT79uqQQmeSpHyQaoAPIZQCLwMDYozdt7FfF+ByYBSwG7AEeBy4Msa45d1LRpH9vgYBL23lcN8Afrfr3UtSw6qpyfDfL7/DNX+dSWXV5jeMLimBbx7Zn++fsC+tWpSl06AkKS+kPQN/FXAwUOfFpbnw/hLZQL4KmAL0B74KnB5COCrGOGXT/jHG64HrG7NpSWpoi1eu54J7pvDcrOQvCHfr1JobzxrOYQPqnOeQJDUjqdzlI4RQEkK4ArhkB3a/nWx4fwzoE2P8BNm7qf4R6AzcFUJwOkpSwXr8zUV8ZvxzWw3vnx++O4+f9ynDuyTp/5Rktrw6qpGFEHoDtwGn1np56dZOoQkhDAKmA2uAfjHGZbVqZcBUYDAwOsZ4T0P0N2nSpAxA27ZtG+JwO2zdunUAtGnTpkk/t5A5ZvXjeNVfY4/Z2o01/Oa1pTwxe1Wi1rZlCf91aHeO7V8457r7Z6z+HLP6cbzqx/Gqv6Ycs7Vr1wIwcuTIeq9G0KQz8CGEE4BZZMP7IrY/A/8loAR4uHZ4B4gxVgN35J6OaeBWJalRzVi8nv96aP5Ww/v+vVrz61P2KKjwLklqOk19DvwQoD3wJ2AcMHQ7+x+S227tYlSAV3LbI3e9tc0NHjy4oQ+5TTNmzEjlcwuZY1Y/jlf9NcaYbayu4f89PZtfPr2Qmi1+AdqyrITvfzrwzU/1p6wAl4f0z1j9OWb143jVj+NVf005ZpMmTdrp9zZ1gH8NODDGWAGwxfKOWzMwt51bR33TCjS9QgjtvVmTpHw298M1jJtQQcV7yxO1AT3accvZB7B/n04pdCZJKiRNGuBjjHXNpNelR25b1yo1tU+r6Q4Y4CXlnUwmw4R/vseVj0xnbWV1ov4fn+zHxZ8dTJtyr8eXJG1f2stIbs+mKwjW1VGv/bpXaEjKO0tXb+Di+6by9+kfJGrd27fi56OHcUzomUJnkqRCle8BvpptX2hbu9a0y+lI0nb8Iy7mwrun8OHqDYnap4f04trTh9KtfasUOpMkFbJ8D/BryK713rqOeu1/+eqapZekJrWusppr/jqD/3l5yxtFQ5uWZVz++SGMOagvJSWFd6GqJCl9+R7gl5IN8F3rqHer9Th5BxRJamJvLljB2AkVzF6cvCRneN/OjB8zgr27t0uhM0lSscj3AD8TGADsVUe9X277foxxbZN0JElbUV2T4bfPzeGmv0c2Vm9+Rl9pCXz32H34zrEDaVmWyg2wJUlFJN8D/OvAScChwK1bqR+a277aZB1J0hbmf7SW70+czGtzlyVqe3Zty81jRjCyX5cUOpMkFaN8nwq6L7c9LYSw2Wk0IYQy4Jzc0z83ZVOStMkDbyzgs+Of32p4H/OJvjx23pGGd0lSg8rrAB9jnAI8CnQE7gkhdAMIIbQGfgcMBiJwf2pNNoBMJsPTc1Zx//QVrFy/Me12JO2AFWs38r0732DshApWbajarNa5bUtu+9KBXHfmMNq3yvdfdEqSCk0h/MtyLvACcAwwL4QwA+gPdAFWAKNijDUp9rfLbn7yLX7xfPYa3BcXvMIj3z3C1SmkPPbS2x9ywcTJLFyxPlE7cp/u3DB6OL061rV4liRJuyavZ+ABYozzgZHAL8iuNDMMqALuBA6KMc5Isb0G8eysjxfQmbZwJf+/vTuPj6K+/zj+2twJJOG+5dYvIJeAeIK3YqsiVEBbq9a22motqNVqL49ar3rWttpqq9a2iFKsikfVn7eiKBKQwy+n3IRwJSEh9/7+mFnIZrO5SDI7m/fz8fAx7H5nkk/G78x+9jvfY22eFpQViUWlFZXc9epKvvPEpxHJe0pSAreeO4ynvzdeybuIiLQoT1vgrbXvAvU2NVtrdwEz3f/iTlpS+PeorXtLGNwt06NoRKQ2q3ILmflsDiu3FUSUDe2ZxcMXjuaI7rpuRUSk5fmhC03c65kd3lq3vZbH8iLijapgkCc/Ws9dr31FWUV4b71AAK6YOJDrzjiC1KREjyIUEZG2Rgl8DOheM4EvUAIvEgt2FVfw4Ed5LNoaudBzr+w07p8+muMGda7lSBERkZajBD4G9KjRX3abWuBFPPf6sm3c+NJmCkojx8ifO6oXd0weTnZGsgeRiYhIW6cEPgbU7EKTqxZ4Ec/sK63g9peX89znmyPKMlOTuGPKcCaP7u1BZCIiIg4l8DGg5owV6gMv4o1FG/Zw7ZwcNu4ujigbP6ATD0wfRZ+OGR5EJiIicpAS+BjQQ33gRTxVXlnFI2+v4Y9vr6YqGF6WlAA/O2sIP5wwkMQErc8gIiLeUwIfA7q2TyUhwIHEYXdRGaUVlZrVQqQVrN9ZxLVzcsjZtDei7LDsZG6c0I1zTxzkQWQiaSZYvQAAIABJREFUIiK1UwIfA5ISE+iYlsiu/ZUH3ttRUMphnfSoXqSlBINB5ny2idvnr6C4rDKi/NLj+jFlYIDUpJhf705ERNoYJfAxonNGUlgCvy2/RAm8SAvZta+Um+Z9yZsrciPKurRP5ffTRnKK6cbKlb5f6FlEROKQEvgY0aVdIqt2HXytfvAiLeMdu4Mbnl/Kzn2lEWVnDOvO3VNH0Ll9qgeRiYiINIwS+BjROSP8f0WuZqIRaVb7yyq567WV/GPBhoiyjJREbjl3GNPHHUYgoIGqIiIS25TAx4guNRJ4LeYk0nyWbcln5rOLWZtXFFE2+rAOPDRjNP27tPMgMhERkcZTAh8jumSEzzijxZxEDl1lVZC/vr+OB960lFeGzw+ZmBDgJ6cM5ppTB5OUqIGqIiLiH0rgY0TNLjTqAy9yaDbvKea655awcP3uiLJ+nTN4YPpoxvbr6EFkIiIih0YJfIzo0q5GAq8uNCJN9t/FW/j1f5dRWFoRUTZ9XB9+c+6RtE/V7U9ERPxJn2AxonMtXWiqqoIkaOVHkQbLLy7n1y8u46UlWyPKOmYkc9fUkUwa3sODyERERJqPEvgYkZaUQPuUBPaVVQFQURVkV1EZXTM1nZ1IQ3y8dic/e24JW2t5ejXxiK7cd8FIumWleRCZiIhI81ICH0O6ZCQeSODB6UajBF6kbqUVlTzwxir++sE6guHjVElJSuAXZw/hkuP662mWiIjEDSXwMaRzRhJf7y0/8Hp7QQkjyPYwIpHYtiq3kJnP5rByW0FE2dCeWTx84WiO6J7pQWQiIiItRwl8DImYiSZ/v0eRiMS2qqogTy/4mrte+4qyiqqwskAArpg4kOvOOILUpMTaf4CIiIiPKYGPIV3ahScbmkpSJFJuQQk3zF3K+6vyIsp6Zqdx//RRHD+oiweRiYiItA4l8DEksgW+1KNIRGLT68u2c/O8pewpLo8oO3dUL+6YPJzsjGQPIhMREWk9SuBjSJeIxZzUhUYEYF9pBbe/vJznPt8cUZaZmsQdU4YzeXRvDyITERFpfUrgY0iXGnPBazEnEVi0YQ/Xzslh4+7iiLLxAzrxwPRR9OmY4UFkIiIi3lACH0NqdqHJLVAXGmm7KiqreOTtNfzxnTVUVoXPD5mcGOC6MwxXTBxIoqaHFBGRNkYJfAzJSk0gJSnhwKwa+0orKCwpJzNNfXqlbfl6ZxGz5uSQs2lvRNmgru14+MKjGN5bU6yKiEjbpAQ+hgQCAXpkpYV1FcgtKFECL21GMBhkzmebuH3+CorLKiPKLz2uHzedPZT0FE0PKSIibZcS+BhTM4Hfnl/K4G5aiEbi3+6iMm76z1LeWJEbUdalfSq/nzaSU0w3DyITERGJLUrgY0yP7LSw19u0mJO0Ae/aHdwwdyl5hZHjPs4Y1p27p46gc/tUDyITERGJPUrgY0zNBD5XizlJHCspr+SuV1fy9IINEWXpyYnccu4wZhx9GIGABqqKiIiEKIGPMd2zwhN4rcYq8WrZlnxmzclhzY59EWWjDuvAQzNGM6BLOw8iExERiW1K4GNMzxot8JoLXuJNZVWQxz9Yx/1vWMorw6eHTAjAT049nGtOHUxyYoJHEYqIiMQ2JfAxRi3wEs+27N3PdXNy+HT97oiyvp0yeHDGaMb26+hBZCIiIv6hBD7G1OwDvz1fizlJfHgxZwu/+u8yCksqIsqmje3DLecdSftU3ZJERETqo0/LGNMtM5VAAIJuz4Kd+0opq6giJUndCcSf8veX85sXl/FiztaIsg4Zydw1ZQRnj+jpQWQiIiL+FLcJvDHmFOBOYCSwG3gSuN1aG9n8F0OSExPo0j41bDq9HYUl9OmY4WFUIk2zYO0urn8uh621jOWYcHgX7ps2KqLbmIiIiNQtLhN4Y8wxwGvAS8BtwGjgdiALmOVhaA3SIystLIHfnq8EXvyltKKSB95cxV/fX3fgaVJISlICN589hEuP609CgqaHFBERaay4TOBxkvaVwAxrbRB43RhTCvzeGHOvtTbyWX4M6ZGdxpdb8g+81kBW8ZPVuYXMfDaHFdsKIsqG9Mjk4QuPwvTQ6sIiIiJNFXcdq40xqcApwDw3eQ95DkgEJnkSWCP0qDkTjaaSFB8IBoM8/fHXnPPIhxHJeyAAV0wcyIs/OUHJu4iIyCGKxxb4gUAKYKu/aa3dYozZDwz1JKpGiJyJRgm8xLYdBSXcMHcp763KiyjrmZ3G/dNGcfzgLh5EJiIiEn/iMYHPdreRz++hEKcffEyLaIFXFxqJYf9bvp2b/rOUPcXlEWXnjOzJ784fQXZGsgeRiYiIxKd4TODr6xYUrKfcczVb4HOVwEsMKiqt4LfzV/DsZ5siyjJTk7j9/CM5f3RvAgENVBUREWlO8ZjA73W3tXW0zQTya3k/ptRM4LepC43EmC827uHaOTls2FUcUTa+fyfunz6Kwzpp5iQREZGWEI8J/FqgEhhc/U1jTG8gHWd2mphWswvNjoJSgsGgWjLFcxWVVfzxnTU88vYaKqvCH2YlJQS47swjuHLiIBI1PaSIiEiLibtZaKy1pcC7wFRjTPW/bzpQAbztRVyN0S41icxqS8qXVVaxu6jMw4hEYMOuIqb9ZQEPvbU6Inkf2LUdL1x1AledPFjJu4iISAuLxxZ4gN/iJOr/McY8jrMa6+3Ao9bajZ5G1kA9stMo3LHvwOtt+SV0bp/qYUTSVgWDQZ7/fDO3vryc4rLKiPLvHtuPX3xjKOkpiR5EJyIi0vZ4msC7LeQLgEHW2qhzzBljOgK3AFOAnkAe8Dpwu7V2Q839rbXvGWPOx0naXwBygbvc177QIzuN1dUS+NyCEob3zq7jCJHmt7uojJvnLeV/y3Mjyrq0T+H3F4zilCHdPIhMRESk7fK6Bf4OYDywK9oObvL+MTAEZxrIpThzvV+O003mJGvt0prHWWtfBl5uiaBbQ3dNJSkee29VHjc8v4QdhaURZacP7cbd3xpJFz0VEhERaXWe9IE3xgSMMbcCNzdg98dxkvdXgd7W2nFAL+ApoAPwrDEm7p7d99RiTuKRkvJKbn1pOZf+fWFE8p6enMidU0bw+CXjlLyLiIh4pNVb4I0xPYDHgMkN2HcIMBXYB3zXWlsIYK0tMcb8ADgGZ2XVKcDcFgvaAxEt8ErgpRUs35rPrGdzwrpvhYzqk82DM0YzsGt7DyITERGRkFZN4I0xZ+Ik2pnAduBhnL7p0VwMBICXrbW7qxdYayuNMU8C9wIzaOYEfuXK1p1tcv/+/WG/t7ygKKx87bZdrR5TrKt5zqRudZ2vqmCQecvzeXrxbiqqwssSAjBjRAe+PaojpTs3sXJna0QbG1THGkfnq/F0zhpH56txdL4azy/nrLVb4IcB7YFngGuBEfXsf4y7/ThK+SfudsKhhxZbumSE/6/ZWVThUSQS7/KKKrjvwx0s3R75lKdH+yRumNCNYd3SajlSREREvNDaCfxCYIy1NgfAGFPf/qHFmNZHKQ/NQNPdGNPeWhv53L+Jhg4d2lw/qkFC3/RCv7frvlKYv+VA+Z7SYKvHFOtqnjOpW23n66UlW/nl/C8pLIn8gnjB2D7ccu4wMtOSWy3GWKM61jg6X42nc9Y4Ol+No/PVeK15zhYtWtTkY1s1gbfWRmtJj6aru402S031bjVdcPrKx4VOGSmkJCZQVun0ZygsqaCotIJ2qV5PHCTxIH9/Obe8uIz/5myNKMtOT+auqSP4xoieHkQmIiIi9Yn1bDDd3e6PUl79/fQo+/hSQkKAblmpbN5z8E/cXlDCIA0glEP0ybpdXP/cErbsjbysThzchfumjaJHtrrMiIiIxKpYT+ArqXuqy+plwah7+VSPrLSwBD43Xwm8NF15ZZBncnYzd/k6gjWulpSkBG6aNITLju9PQkLAmwBFRESkQWI9gS/Cmes9WnNg9Ymoo7XS+1b3Gq2guYWaSlKaZs2OQq59dQtrd5dFlA3pkclDF45mSI8sDyITERGRxor1BH4XTgLfKUp552r/zmv5cFpX98waCXxB5IqYInUJBoM888kGfvfKSkprzg8J/HDCAK4/05CWHHdroYmIiMStWE/gvwIGAf2jlPdzt9ustcWtElEr6p4VvtJlboFa4KXhdhSWcOPcpbxrI7/b9shK4/7pozhhcBcPIhMREZFDUVf/8ljwubs9Nkp56P1PWyGWVldzNdaay9qLRPPG8u1MeuiDWpP3b47syeuzJih5FxER8alYT+DnudvzjTFh3WiMMYnAZe7Lf7ZmUK2lW40W+B1qgZd6FJVWcPO8pVzxzCJ2F4X3d09PDvCzE7vyx4uOokNGikcRioiIyKGK6QTeWrsUeAXIAuYaYzoDGGPSgCeAoYAFXvAsyBbUTX3gpREWb9zDN//wAbMXboooO7p/Rx49rw+nDcokENAsMyIiIn4W633gAX4EfAicAmw0xqwEBgIdgXxgirU2cnReHKitD3wwGFQCJmEqKqv40ztr+cPbq6msCp8fMikhwLVnHMGPThrEKvuVRxGKiIhIc4rpFngAa+1mYCzwB5yZZkYCFcBs4Ghr7UoPw2tR7VOTyEg5ODtIaUUVBfsjl7yXtmvDriKm/2UBD761KiJ5H9ilHfOuOp6rTxlMouZ2FxERiRuetsBba98F6s0srLW7gJnuf21GIBCge1Ya63cWHXgvt7CE7IxkD6OSWBAMBnl+0WZue2k5RWWVEeUXH9uXX3xjKBkpfnjIJiIiIo2hT/cY1y0zNTyBLyjhiO6ZHkYkXttTVMbN877k9eXbI8o6t0vh3gtGctrQ7h5EJiIiIq1BCXyMqzmVpAaytm3vr8rjZ88vqXVK0dOGdOPub42ka2ZqLUeKiIhIvFACH+O0mJMAlJRXcs/rX/HkR19HlKUlJ/Drc4bx7fF9NcBZRESkDVACH+NqtsDnaTGnNmfF1gJmzVnMqtx9EWUj+2Tz4IzRDOra3oPIRERExAtK4GNcze4QaoFvO6qqgjzx4Tru+98qyirDZ0pNCMBVJw9m5umHk5wY85NJiYiISDNSAh/jIvvAK4FvC7bu3c/1zy1hwbpdEWV9Oqbz4IzRHN2/Uy1HioiISLxTAh/jNIi17Xl5yVZ++cKXFJREzvn/rTF9uPW8YWSmaSpRERGRtkoJfIzrVqMLzY5CrcYarwpKyrnlxeW8sHhLRFl2ejJ3ThnBN0f29CAyERERiSVK4GNcu9QkMlOTKCx1WmPLK4PsKS6nU7sUjyOT5rRw/W6unZPDlr37I8pOGNyZ+6aNomd2ugeRiYiISKxRAu8D3bJSKcw72J0it6BECXycKKuo4qG3VvHoe2sJBsPLUhITuHGS4fITBpCQoCcuIiIi4lAC7wPds9JYmxe+GuvQnlkeRiTNYc2Ofcyas5hlWwoiykz3TB6+aDRDeuj/s4iIiIRTAu8DNQey1rYKp/hHMBjkn59u5HevrKCkvCqi/PsnDuCGswxpyYkeRCciIiKxTgm8D3SrsRrrDk0l6Vt5haXcOHcJ79i8iLLuWancP200Jx7exYPIRERExC+UwPtAt0xNJRkP3lqRy8//s5RdRWURZd8Y0YM7p4ygQ4bGNoiIiEjdlMD7QPcsrcbqZ8VlFdzxykr+/enGiLL2qUncdt6RTB3TW1ODioiISIMogfeBiMWc1AfeN5Zs2susOTms31kUUTauX0cenDGawzpleBCZiIiI+JUSeB/oXqMLjfrAx77KqiCPvbeWB99cRUVV+PyQSQkBZp1+OD86aRBJiQkeRSgiIiJ+pQTeByIGsRaWUlUV1NzgMWrznmKum7OEhV/vjigb2KUdD84YzajDOngQmYiIiMQDJfA+kJacSHZ6Mvn7ywGndXdXURldM1PrOVJa24s5W/jVf5dRWFIRUXbR+L78+pyhZKToshMREZGmUybhE92zUg8k8OAMZFUCHzsKSsr59X+X8WLO1oiyTu1SuOdbIzljWHcPIhMREZF4owTeJ7pnpbEqd9+B19vzSxjeO9vDiCRk4frdXDsnhy1790eUTTyiK/dNGxkxFaiIiIhIUymB94maM5Us3byX09Wi66nyyioefms1f353DTXGqZKSlMDNZw/h0uP6a6yCiIiINCsl8D4xtm/HsHnEP/t6j4fRyPqdRcx6djFLNudHlA3pkcnDFx6F6ZHpQWQiIiIS75TA+8TR/TuFvV68aQ/llVUkaxrCVhUMBnnu803c9vIKissqI8q/f+IAbjjLkJac6EF0IiIi0hYogfeJwzql0y0zlR3uIk4l5VUs31rAaE1H2Gr2FJVx07yl/G95bkRZt8xU7p8+igmHd/UgMhEREWlL1HzrE4FAIKIV/vNa5hmXlvHB6jzOeuj9WpP3s47szuuzJip5FxERkVahBN5HxvXvGPb6c/WDb3El5ZX8dv4Kvvu3hQeefoSkJydy99QRPHbxWDq1S/EoQhEREWlr1IXGR8b1q9ECv2E3wWCQQECznLSEVbmF/HT2Yr7aXhhRNqpPNg9deBQDurTzIDIRERFpy5TA+8jQnplkpCQeGDy5c18ZX+8qVhLZzILBIE9//DV3vvYVZRVVYWUJAbjq5MHMPP1wDSAWERERTyiB95GkxATG9O3Ih2t2Hnjvs693K4FvRjsKS7jh+aW8tyovoqx3h3QenDGa8QM61XKkiIiISOtQE6LPRPaD10DW5vLWilwmPfRBrcn7+aN78dqsCUreRURExHNqgfeZiJloNmgg66EqLqvgjldWhi2UFZKZmsQdU4YzeXRvDyITERERiaQE3mdGH9aBxIQAlVVBANblFbFrXymd26d6HJk/fbk5n5lzFrMuryiibHz/Ttw/fRSHdcrwIDIRERGR2qkLjc+0S03iyF5ZYe+pFb7xKquCPPruWqb8+aOI5D0pIcANZxlmX3GskncRERGJOWqB96Gx/TqydHP+gddfbNzDWUf28DAif9m6dz/XPZfDJ+sixw8M6NKOh2aMZpRWuBUREZEYpRZ4HxrTN3wg6+INez2KxH9e+3Ibkx56v9bk/aLxhzH/mhOVvIuIiEhMi7sWeGNMEvAT4IdAf2A78CJwi7U2ckUeHxrTLzyBX7plL+WVVZqXvA7FZRX8dv4KZi/cFFHWMSOZu6aOZNJwPcUQERGR2BePGd+dwL3AXOA84AHgUuANY0xc/L29stPolnlw0GpJeRUrtxV4GFFsW741n3Mf+bDW5H3C4V14fdZEJe8iIiLiG3HVAm+MyQBmAfdZa29x3/4/Y8xO4FngZOBtj8JrNoFAgDF9O/L68u0H3lu8cS8j+6jrR3VVVUH+/tF67n3dUlYZvqJqcmKAn08awuUnDCAhIeBRhCIiIiKNFxct0tV0BB4Hnq/x/lfutlfrhtNyxvQLT9a/2KiZaKrLKyzle099xh2vrIxI3gd2bccLV53ADyYMVPIuIiIivhNXLfDW2i3A1bUUne9ul7ViOC2q5kBWJfAHvWt38LPnl7BzX1lE2Yxxh3HLecPISImrqi8iIiJtiG+yGHdw6g/q2KXQWvuvWo47DrgJmG+tzWmp+Frb8N7ZJCUEqHAXdNq0ez95haV0zWy7CzqVVlRyz2uWv3+0PqIsKy2Ju6aO5Jsje3oQmYiIiEjz8U0CD6QBj9ZRvgEIS+CNMSfjzECzHrispQLzQlpyIkf2ymKJ5oMHYM2OQq6ZnVPrYN6j+3fkoQuPoneHdA8iExEREWlevkngrbX7gAZ3WDbGXAb8BVgOnG2t3dVCoXnmqL4dwxL4xRv3trkEPhgMMnvhRm57eTkl5eF93RMCMPO0I7j6lEEkaYpNERERiRO+SeAbwxhzO/Br4H/ABW7yH3fG9OvIUx9/feB1W+sHX1haycMLdvLRhsguM707pPPwhaMZ17+TB5GJiIiItJy4S+CNMT/HSd6fAn5ora3wNqKWc1SNFUOXbm47Czp9um4XV7+0mZ3FlRFl54zsye+mjCA7PdmDyERERERaVlwl8MaYw4E7cKaN/CswzhhTfZe11to8L2JrCX06ptM1M5W8wlLAWdDpT++s4fITB5CVFp/Ja0VlFQ//32r+9M4a3PG7B2SkJHLbeUdywdg+BAKaHlJERETiU4sk8O6KpwuAQdbaLnXs1xG4BZgC9ATygNeB2621G5rwq6fg/E1DgI9rKf8h8EQTfm5MchZ06sD/luceeO+ht1bz+PvruPrUwfz4pEFxlchu2l3MzGcX88XGvRFlI3pn8/CFoxnYtb0HkYmIiIi0npZqgb8DGA9EHTjqJu8f4yTbhcBSYCBwOTDVGHOStXZpY36ptfZe4N6mBu1Hpw7pFpbAAxSVVXLv65aUxAR+MGGgR5E1r5eWbOWX876ksDSyR9SVEwdy/ZmGlKT47zokIiIi0qwZjzEmYIy5Fbi5Abs/jpO8vwr0ttaOw1kp9SmgA/CsMSaxOeOLR1PH9OHKiQNrTV7vf2MVm3YXexBV8ykqreBnzy/hp7MXRyTvHdMT+d0ZPbj5G0OVvIuIiEibEQgGg/Xv1QDGmB7AY8Dkam/vqq0LjTFmCLACKAL6WWt3VytLBL4EhgLTrLVzmyXABlq0aFEQICMjozV/Lfv37wcgPb1pc5XvLankNVvA88v3sr/84P/Tsb3S+e3pPXzZlWbNrlLufn8HWwrKI8rG98ngx2Pak52W2ORz1tYcah1ri3TOGkfnq/F0zhpH56txdL4arzXPWXGx08g6duzYRidpzdJsaYw5E1iFk7xvp/4W+Itx5nR/uXryDmCtrQSedF/OaI742oIOaYlcNKojV4zrHPb+oq37eWedv2bRrAoG+c/yvVz76paI5D05IcCPxnfm1lO7k52mBzQiIiLS9jRXH/hhQHvgGeBaYEQ9+x/jbmsbaArwibudcOihNc3QoUNb9fetXLmyWX7vkCFBPs39hE/WHfxe9MQXe7lg4ki6Z6Ud0s9uDXmFpVz//BLeX7U7omxwt/Y8ctFRDO2ZBTTfOWsrdL4aT+escXS+Gk/nrHF0vhpH56vxWvOcLVq0qMnHNlfH4YXAGGvtJQ1c8XSwu41cgccRmoGmuzFG04o0QiAQ4K6pI8P6hO8pLufCv37C1r37PYysfu/aHZz98Pu8vypyps+Lxvfl5Z+ceCB5FxEREWmrmiWBt9Z+bK3NacQhXd1ttGS/evNr1GkopXYDurRj5mmHh723fmcR0/+yICYHtZZWVHLH/BVc9uRn7NxXFlaWlZbEYxeP4a6pI0hPUZcZEREREa+m7giNDIjWJFz9fY28aIIrJw7ktCHdwt7bvGc/0x5bwIZdRR5FFWld3j6m/vljnvgw8mHM+P6deG3WRCYN7+lBZCIiIiKxyasEvrKe8upxNc80OW1MUmICj148lrOH9wh7f3tBCd/920J2FJR4FJkjGAzy3OebOOeRD1m+tSCsLCEA155+BLOvOJbeHfT9TURERKQ6rxL4UBNwtFGVqdX+Hdsdt2NYSlICj1x0FOeP7hX2/sbdxVz65Gfk74+cnrE15BWWcuUzi7hx7lKKy8K/y/XukM5zVx7HzNMPJzHBf1NfioiIiLQ0rxL4UN/3TlHKq8+FGDmiURosKTGB+6ePZupRvcPeX7mtgB8+/Tn7y+p7GNK8Xv1yG2c99D5vrMiNKPvmiJ68OnMC4/pHqxYiIiIi4lUC/5W77R+lvJ+73Watjb1Rlz6TmBDgngtGcmqNPvELv97NxX/7lL3FZVGObD57i8v46ezFXPWvL9hdFP770pMTuedbI/jjt48iOz25xWMRERER8TOvEvjP3e2xUcpD73/aCrG0CcmJCfzp22MY269j2PuLNuzhgscWsKUFp5h8+6tcznjwfV5asjWi7Ki+HZj/0xOZcXRfX64WKyIiItLavErg57nb840xYf0ljDGJwGXuy3+2ZlDxLj0lkb9fenTEXOprduxj6p8/ImfT3mb9fdvy93P1v7/g8qc+J6+wNKwsOTHAjZMMz195HIO6aqp/ERERkYbyJIG31i4FXgGygLnGmM4Axpg04AlgKGCBF7yIL55lZyTz7BXHcsyA8H7muQWlTHvsY/7+4XqCwUOb+Ke0opK/vLeW0+5/j1eWbosoH9Yzi5evOZGrTh5MUqJX3yFFRERE/CnJw9/9I+BD4BRgozFmJTAQ6AjkA1OstVUexhe3stOTefry8Vz3XA6vfrn9wPvllUFun7+CT9bt4rbJR9Izu3FTOJZXVvH855t55O3VbMuPnKYyMSHA1acM5ienDA5bKVZEREREGs6zBN5au9kYMxb4DTAZGAnsBWYDt1hrV3sVW1uQlpzIIxeNoVf2yohFlN5Ykcu7q/K49Lh+/PjkwXRql1Lnz9qWv595X2xh9sKNbN5Te1/6Eb2z+d2U4Yzs06HZ/gYRERGRtqhFEnhr7btAvSMSrbW7gJnuf9LKEhMC/OqcYYzr35Eb5i6lsKTiQFlZRRWPf7CefyzYwPgBnTjpiK6M6J1NanIiyYkBNu/Zz7It+XyxcQ8L1u6iKkqvm6y0JG6YNIRvj++red1FREREmoGXXWgkRkwa3pNhPbO5+t9f8OWW/LCy0ooqPli9kw9W72zUz0xJSuDiY/px9SmD6Nw+tf4DRERERKRBlMALAH07ZzDvquOZu2gzD7+1mu0FkX3YGyIlMYFp4/pwzamH0yM72kK7IiIiItJUSuDlgOTEBC4a35cpR/XmmQUbeHrB11H7tNd0ZK8spo3tw+TRvelYT595EREREWk6JfASIS05kR9OHMgPJgxgbV4R76/KY8G6XewpKqOssoqyiioy05I4slc2w3tnM/qwDgzuprncRURERFqDEniJKhAIMLhbewZ3a8/lJw7wOhwRERERwbuVWEVEREREpAmUwIuIiIiI+IgSeBERERERH1ECLyIiIiLiI0rgRURERER8RAm8iIiIiIiPKIEXEREREfERJfAiIiIiIj6iBF5ERERExEdjTwyyAAAQcklEQVSUwIuIiIiI+IgSeBERERERH1ECLyIiIiLiI0rgRURERER8RAm8iIiIiIiPKIEXEREREfERJfAiIiIiIj4SCAaDXscQUxYtWqQTIiIiIiKtYuzYsYHGHqMWeBERERERH1ELvIiIiIiIj6gFXkRERETER5TAi4iIiIj4iBJ4EREREREfUQIvIiIiIuIjSuBFRERERHwkyesA2jJjTEfgFmAK0BPIA14HbrfWbvAyNq8ZY4YANwKn4pyb/cAS4Alr7TO17P8ycE4dP3KLtbZPS8QaC4wxnYGd9ez2O2vtr6odkwhcA3wfOBzYB3wK3G2t/aClYvWSMeZroF8Ddz/FWvuue1ybrF/GmARgATDIWtuljv0uAX4CjABKgRzgAWvtS3UccyTO/e8UIBPYADwL3GOtLW62P6IVNeR8GWPSgZ8C04EjcD6HNwAvAfdaayOuY2PMt4C59fz6M6y1bx1C+J5o4Dlr0vVnjDke+BVwPJACrAGeBP5gra081Ni9UNf5MsbcinNNNcTT1trLqh0bV3WssTmEe4yv7mNK4D3iJu8fA0OAQmApMBC4HJhqjDnJWrvUwxA9Y4w5F3gOSANKgK+A7sBEYKIxZhJwsbW2+hyoI9ztJ0BtN+YdLRdxTAj9/btwzldtDnwpNMYEgH8CF+Kcry+BzsA3gEnGmO9ba59qsWi98xmwuY7yAUAvnJt39f3aav26AxiPU69qZYy5G/g5EASW41y3JwEnGWN+Y639bS3HjAXeA9oB293jhgO/ASYbYyZYawub+W9pDXWeL2NMJ+AdYCTO+dqAc48bDNwAXGiMOdVau6bGoaH6tw7YFuV37z200D1Tbx2jCdefMeabwItAIs553oNz3h/Aucd901pbcQhxe6Wu87UR+KiOYzOAo9x/r61RFjd1rCk5hB/vY0rgvfM4TvL+KnChtbbQGJMGPApcBjxrjBnh11aCpjLGdAf+hXPxPA7MCn2LNcacD/wD+DZOS/Ef3PezcFpVC621x3kRdwwY6W5nW2uvacD+V+Mk7+uASdba1W5SfyXwZ+AxY8x71tr1LROuN6y106KVGWO64HyRAbgqlES1xfrl1oVbgJvr2e8cnA+93Tj16DP3/cnAHOA2Y8zb1tqPqh2ThpNYtQNuw3niWGWM6e2+Pxa4H7ii2f+wFtLQ84Vzfx+Jk1BMt9Z+6R7fF/g3cAIwxxgzrkYDRej6vtFa+59mDd4jjahjjb7+jDE9cOpfAvBDa+0T7vtDgVeAM3FaZ+9s8h/Qyhpyvqy1fwf+XsfPeAIngX+XyL89LupYE3MIX97H1AfeA+6jnak4XRa+G/qGZq0tAX4ArASG4nStaWt+gPMY6gvgR9UfQVlr/8vBm9e11Y4JtRysaJUIY1PoHCyvb0djTBJOax8453g1gLU2aK19DOemlwpc3xKBxrC/Aj2Aee4HYUibql9u8vMCDXsU/wt3e1PoQw/AWvsizodagMiE4xKgN/CxtfZWa22Ve8wW4FtAOfA9Y0zPQ/pDWklDz5cxpg8wDagCvhNK3gGstRuBC3A+E8bgtBRW1+Dr2w8aWceacv39FCexmh1K3gGstSuBi92X1xtjUhvxMz3TyPMV7WdMxukumQ9cUkvjYLzUsabkEL68jymB98bFOBXiZWvt7uoF7kX1pPtyRmsHFgNOdrfzQhdEDfPdbX+3GxLEz43nUDTmHJwM9AW2WWvfrKU89IF3gdvfMu4ZY87D+cJcgNMHsro2U7+MMWcCq4DJOI+Eo7b2GWMGA8fhfFD9u5Zd/uZuzzTGdKj2/iXu9umaB7hjf97EeTo8tbHxt7bGnC+cx/EBYJ219ouahdba7cDn7ssx1X5HBk73yjKcPty+1shzBk27/r7rbmurYx/jfBnoBJzeiJ/piSacr9p+RjrwJ/flL6y1m2qUx1MdO9ndNiiH8PN9rE18OMegY9ztx1HKP3G3E1ohlljza5wuRP+NUt6u2r9DXcBCj/7iPsGqjftodbj7siHnoL769wXOjbw7ziC7uOYO5r3bfXmHtbZm/8+2VL+GAe2BZ3Dq1Cd17BuqR0uttUU1C621O3C6aCUDx8KBcz3W3SUe7n+NOV/v4bTA/7yOfUL3t+rdW4fjfFZbn/bZrqkx5wwaef25XRhCA1oXRNktXutYNNfitBZ/CTxWS3k81bHG5hC+vY+pD7w3BrvbaP2LQ4MNuxtj2ltr97VCTDHBWvsJdd+gJrvbPA7OuhJqodlgjPkxcBrQEWcQ4jz3MVg8G8jBQTTdjDE34vRzDHJw1P3qavvXWf+stZXGmC04AzoHE31QbLz4Hk6XtS24fSJraEv1ayEwxlqbA2CMqWvf+u5j4NzLBlbbtw9O39S6jgvd/wZHKY8lDT5f1trN1DHLhzGmHzDKfVm9u8iBFmhjzKk4Y1cG4XS3+QDn+vbF4EJXY+oYNP76C9WbnXUMIIzLOlYbd+B06EvjL6K0SsdNHWtCDuHb+5gSeG90dbfRRt1X71bTBeciavPcfoA3ui//XW2QV6j1+SmclorqLjHGvIYzYCxez2Po5psNLMOZdSHkLOBaY8w11tq/uO/VV//AqYMDcOpf3HKfXoT6+j9krS2tZbc2U7/c7gUN1dB6BAfrUeiY0tpau6IcE7Maeb7qcw/OVIe5wP9Vez90fZ+Dk1hVdx5wgzHmfGtttNbmmNKEc9bY668p9TJmNUMduwLIApZZa+dH2Seu6lg0teUQxhjf3sfUhcYb6e52f5Ty6u+nR9mnTTHGtMN5JNYB51vzXe77fd33wJkW6yycm3xnnJbV3cDZHBxXEI9Cj5jTOTi7USpO95e/4Dz6e9QdaR/aD6LXv+pl8V7/Tsc5X/k4g1jDqH7VqSn1SHWvFsaYn3FwzNMv3AkNQkLXdwLOl82eOK1/x+N0y+kGzDfGHNZK4baaJl5/qmMut6vHj92X99Wxa9zXsWg5BD6+j6kF3huV1P3lqXpZMOpebYQxpj3wMk5ftUqc+Vtz3eIqnBtTJ2BmtVaYIuApY8wKnH6QFxhjjnUfr8WbL3AS9WXW2j9We3818CNjTDnOwMz7cAbwNGRq0lAdjPf6d7W7fcJaW1BLuepXdE2pR6p7NRhjrgF+7778Z40ZkMCZkm4T8JS19p1q7y9wBzguwBn0+kvgRy0dbytryvWnOnbQubgTFlD7AM2QuK5j9eQQvr2PKYH3RhHOt8C0KOXVp7aq6xte3HMfb83HWbiiCvietfZ/oXK3X+kNUQ7HWrvQGPMWzry/59K0AUAxzX0sGu3RKDjz/f4EMMaYw3HqH0Svf3CwDsZt/XNbZCa5L/9Z2z6qX3VqSj1S3avGGHMLcKv78hWcaf7CWGsfjna8tbbMGHMfTnJ2Lj5MrurSxOtPdeygC9ztc9ba8mg7xXMdqy+HwMf3MXWh8Uaor1WnKOWdq/07r4VjiVnGmIE43/zHAxU435prXQK5Hjnutl9zxeYn7qwqoZUK+1F//YODdTCe69+ZODfZVaEBYk3UVutXU+pR6Jg0d2q7hhwTd4wxicaYxzmYvL8ATLXWljXhx4XqXy9jTHJzxOczNa8/3d840H3mbPflc4f443xZxxqYQ/j2PqYE3huhWT36RykP3Yi2VV+EoC0xxozEWRJ6EFAMTLbWzo6yb6CeBTkC7rYpH46+YIxJdm/Y0VQ/B3XWP3ehp97uS7/PCVyX0JiA5+vaSfUrqvruY3DwXhaqR1s4OCg/2nE1j4krbl2ai7PgDDgrZ06rK3mvI0mAg/WvEidJiStNuP5C9bKrO795beK6jrmOx0lKNxN9Os0D4q2ONSKH8O19TAm8N0KLdRwbpTz0/qetEEvMcbt5vImzKuYe4HRr7atR9r0b58b9Uh0/crS7XdmcccYKY8wmnHMwPUp5Lw6Oml/Jwfp3TG374/R1TMZpZYjnD7jQsuzvRttB9atOoXo0yl1WPIwxphvOTEZVwGfgrPYLLHJ3aXP3P/dL9r+A89237rHWfr+WVTFD+48yxuwDit3ruDah+merzcwVF5py/Vlrd+JM4Rcg+j0ubutYNaH723t11Yt4rGONySHw8X1MCbw35rnb8905Wg9wb/CXuS9r7Zcbz9wWk5dxRr3vBE6uZ+qqHJyxHCe58yjX/HmjcOYNrgL+0/wRx4TQAieXRCkPTZP4nrU2D2de351AP2NMbSsRhloGZ0eZM9j33HoWmlA5YlXMalS/orDWfg0sxumGdHEtu4Tq0avW2j3V3g/d/yL6e7vn+HScpO1QH/vHoltxllkH+KW19qZ69v+Kgy2eEde3+3kx031Z55Mkn2rq9VdXHTseZ92HPOCN5g44hhzlbuu6v0Gc1bHG5hB+vo8pgfeAtXYpzoClLGCuMaYzgPvt7wmcm4vF6RfZ1vwSJ7GqwnmsvLSe/V/AmV4sFedcDggVGGOOxmm5SQAetdaua5mQPReaHmySMeYuY0wKHOhn+zOcVfgqcRfzcFv77nGPedJ91Ih7zJU4N6xS4MFWit8LoZUHt1trd9exn+pX3e50t/cbY04OvWmMOQ/4Dc4MDPfUOOZJnEXHTjDG3O922Qo9KfoPztOff9SyIq6vGWOGAje7L/9mrb2zrv0B3HUJHnFf3mqMCQ1KxBiTjbM653icR/rxeL029fp7CGfw4HeMMbPc9R4wxgzhYMPYw9baeB7EGloUrM4VbOOwjjU2hwCf3scCwWDMPw2JS8aYPsCHOP2kinEe/w3EWWEuHzjOWtumHsm7/RxzcRYk2oezimhdLrDWbndbYd7E6SZSAazCWcwo1MI6H/hWEweI+YIx5hfA79yX+ThdX/rhLCJRAXzfWvuPavsn47RSnIVzo/sSp+71dXf5jrW2rmnHfM0YMxlnTuCV1tph9ezbZuuX+2H2DrDLWlvrgiTGmL8Bl7svV+B8cB3uvv5lbYmqMeYMnPqXijPAejNwpPt6MTChjgVSYlZd58sY8xhwpfvyC+qeneLvoekk3Wv1BeCbbtlWnGkBh+HMMb0TOK2BiUrMqa+ONfX6M8ZcipNkBXDq106cBYsSgdeAc6N1XYplDbkm3f324Mx2d4y1dmE9PzMu6lhTcwj3WN/dx9QC7xF3eqyxOEu35+EspFABzAaObmvJu2sEzoUHzmIdJ9TzXxqAtXYJzvl7EPgaZ+niHjhfkC4HzovH5Ko69+ZyKk6LVDnO+SjDmfprXPXk3d2/HGcQ5/U4LTQGJ4H/P+DMeE7eXaEZAvLr21H1q14/wDkPC3EGdPXBGTR3UbRWZmvtm8A4nEfyAZxrfyvO06ST/Zi8N8CJ1f49hrrvbaEv0qFr9Tyc8/wRkInzBCnUIjos1hOrQ9HU689a+zQwESdZb4eTjK4GfgVM8WPy3lBut5fQZ2lD7nHxUsealEO4fHcfUwu8iIiIiIiPqAVeRERERMRHlMCLiIiIiPiIEngRERERER9RAi8iIiIi4iNK4EVEREREfEQJvIiIiIiIjyiBFxERERHxESXwIiIiIiI+ogReRERERMRHlMCLiIiIiPiIEngRERERER9RAi8iIiIi4iNK4EVEREREfEQJvIiIiIiIjyiBFxERERHxESXwIiIiIiI+ogReRERERMRHlMCLiIiIiPjI/wN8QmsrwuvL9QAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", + "w = 0.5 # on choisit w \n", + "residu = []\n", + "for i in range(200):\n", + " old_x = x\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " residu.append(np.square(A @ x - b).sum())\n", + "plt.plot(range(len(residu)), residu)\n", + "plt.title('Résidu')\n", + "plt.semilogy();" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Testons d'autres matrices avec cet algorithme\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def mk_A(seed):\n", + " np.random.seed(seed)\n", + " return np.random.randint(10, size=(4,4))\n", + "\n", + "A = mk_A(234)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_error(M, N, b, x0, w, n=200):\n", + " x = x0 \n", + " error = [np.square(x - np.ones(4)).sum()]\n", + " error2 = []\n", + " for i in range(n):\n", + " old_x = x\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error.append(np.square(x - np.ones(4)).sum())\n", + " error2.append(np.square(x - old_x).sum())\n", + " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n", + " ax1.plot(range(len(error)), error)\n", + " ax1.set_title('Erreur absolue')\n", + " ax1.semilogy();\n", + " ax2.plot(range(len(error2)), error2)\n", + " ax2.set_title('Erreur relative')\n", + " ax2.semilogy()\n", + " print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 17 40\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 822 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_error(M, N, b, x0, w=0.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On retrouve le même comportement (convergence puis divergence) mais en nettement plus cahotique.\n", + "\n", + "On peut réduire les oscillation en augmentant l'inertie c.a.d. en diminuant $w$ :" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 81 209\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 822 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "error2 = plot_error(M, N, b, x0, w=0.1, n=1000) \n", + "# w 5 fois plus petit donc je fais 5 fois plus d'itération pour \"avancer\" d'autant (grosso modo)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Les oscillations ont disparu ! Mais on a payé le prix fort puisqu'on a du faire 5 fois plus d'itérations.\n", + "\n", + "On constate que dans les 2 cas l'erreur relative (entre 2 x successifs) ne donne pas le bon minumum.\n", + "Donc arrêter un algorithme itératif en fonction de l'erreur relative n'est pas toujours le plus efficace.\n", + "\n", + "Regardons ce que donne le résidu :" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 218\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 376 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = x0 \n", + "w = 0.1\n", + "residu = []\n", + "for i in range(1000):\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " residu.append(np.square(A @ x - b).sum())\n", + "plt.plot(range(len(residu)), residu)\n", + "plt.title('Résidu')\n", + "plt.semilogy();\n", + "print(\"Itération du minimum :\", np.argmin(residu))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Exercice 20.1\n", + "\n", + "Comment se fait-il que la courbe du résidu ait la même forme que celle de l'erreur relative ?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Réponse**\n", + "\n", + "..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Nouvelle matrice" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 153 153\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 827 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "A = mk_A(123)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)\n", + "\n", + "plot_error(M, N, b, x0, w=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Voici un cas avec une convergence parfaite. Notons qu'on s'est arrêté à l'itération 150 lorsqu'on est passé\n", + "en dessous de la précision de la machine (les valeurs suivantes devant être 0 et comme log(0) = $-\\infty$,\n", + "matplolib ne les affiche pas).\n", + "\n", + "Vérifions quand même que la méthode de Jacobi de base n'aurait \n", + "pas marché :" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x_0 = [0.398 0.738 0.182 0.175]\n", + "x_1 = [4.127 1.837 1.029 2.203]\n", + "x_2 = [-0.526 -0.195 0.907 -0.906]\n", + "x_3 = [3.427 1.782 1.133 3.759]\n", + "x_4 = [-1.56 -0.204 0.913 -0.86 ]\n", + "x_5 = [3.395 2.118 1.134 3.775]\n", + "x_6 = [-1.907 -0.196 0.876 -1.616]\n", + "x_7 = [3.877 2.342 1.133 3.784]\n", + "x_8 = [-2.133 -0.357 0.851 -2.12 ]\n", + "x_9 = [4.364 2.49 1.151 4.165]\n", + "x_10 = [-2.525 -0.574 0.834 -2.467]\n", + "x_11 = [4.804 2.671 1.175 4.665]\n", + "x_12 = [-3.027 -0.792 0.814 -2.89 ]\n", + "x_13 = [5.293 2.898 1.199 5.17 ]\n", + "x_14 = [-3.581 -1.027 0.789 -3.421]\n", + "x_15 = [5.87 3.159 1.225 5.719]\n", + "x_16 = [-4.194 -1.298 0.76 -4.026]\n", + "x_17 = [6.531 3.45 1.255 6.35 ]\n", + "x_18 = [-4.891 -1.608 0.728 -4.704]\n", + "x_19 = [7.277 3.779 1.29 7.073]\n" + ] + } + ], + "source": [ + "x = x0\n", + "for i in range(20):\n", + " print(f\"x_{i} = {x}\")\n", + " x = (N @ x + b) / M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Jacobi de base diverge, donc c'est bien l'inertie qui a permis de converger." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Nouvelle matrice" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 0 0\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 827 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "A = mk_A(16)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)\n", + "\n", + "plot_error(M, N, b, x0, w=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Divergence directe mais si on baise $w$ on constate qu'on est dans le 1er cas :" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 32 38\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 817 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_error(M, N, b, x0, w=0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Mais ca reste pas terrible. Au mieux on n'est même pas à $10^{-1}$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Normaliser\n", + "\n", + "Cette dernière remarque n'a de sens que si on sait à quoi on se compare. \n", + "\n", + "* Si la solution cherchée est un milliard, avoir une erreur de 0.1 est très bien.\n", + "* Si la solution cherchée est 0.01, une erreur de 0.1 est énorme.\n", + "\n", + "On ne peut donc juger une erreur qu'en fonction d'une référence. Si on connais la solution exacte, alors \n", + "elle est la bonne référence.\n", + "\n", + "$$\n", + "\\frac{||{\\bf x}^k - {\\bf x}||}{||{\\bf x}||}\n", + "$$\n", + "\n", + "De même l'erreur entre 2 itérations successives n'a de sens que normalisée.\n", + "Si $||{\\bf x}^k|| = 1 000 000$ alors $||{\\bf x}^k - {\\bf x}^{k-1}|| = 1$ est bien mais ce n'est pas le cas\n", + "si $||{\\bf x}^k|| = 1$.\n", + "\n", + "Aussi on compare la différence entre 2 itérations avec le **x** courant ou le précédant :\n", + "\n", + "$$\n", + "\\frac{||{\\bf x}^{k+1} - {\\bf x}^k||}{||{\\bf x}^k||}\n", + "$$\n", + "\n", + "Faisons le et regardons nos résultats précédents." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_error_normalized(M, N, b, x0, w, n=200):\n", + " x = x0 \n", + " error = [np.square(x - np.ones(4)).sum()]\n", + " error2 = []\n", + " for i in range(n):\n", + " old_x = x\n", + " x = w * (N @ x + b) / M + (1-w) * x\n", + " error.append((np.square(x - np.ones(4)).sum())/4) # normalisé par rapport à la solution\n", + " error2.append((np.square(x - old_x).sum())/np.square(x).sum()) # normalisé par rapport à x\n", + " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n", + " ax1.plot(range(len(error)), error)\n", + " ax1.set_title('Erreur absolue normalisée')\n", + " ax1.semilogy();\n", + " ax2.plot(range(len(error2)), error2)\n", + " ax2.set_title('Erreur relative normalisée')\n", + " ax2.semilogy()\n", + " print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 60 70\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 821 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "A = mk_A(799)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)\n", + "plot_error(M, N, b, x0, w=0.1, n=1000) " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 60 70\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 822 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_error_normalized(M, N, b, x0, w=0.1, n=1000) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Et oui, l'erreur relative normalisée se stabilise dans ce cas alors que non normalisée elle augmentait toujours.\n", + "\n", + "Cela étant pour converger l'ecart entre 2 itérations doit tendre vers 0.\n", + "\n", + "Parfois on peut avoir une surprise :" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Itération du minimum : 500 499\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 264, + "width": 821 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "A = mk_A(308)\n", + "b = A.sum(axis=1) \n", + "\n", + "M = np.diag(A) \n", + "N = np.diag(M) - A \n", + "\n", + "x0 = np.random.random(4)\n", + "plot_error_normalized(M, N, b, x0, w=0.1, n=500) " + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.004062676542953207" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "min(error)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On converge mais à coté de la valeur cherchée. C'est rare et c'est du au très mauvais conditionnement\n", + "de la matrice A. Ce mauvais conditionnement génère des erreurs de calcul qui font qu'on ne peut pas arriver\n", + "à la solution exacte.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.1405202107473442e+17" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.linalg.cond(A)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma42 Surrelaxation pour Gauss-Seidel -- Exercice.ipynb b/PVCM/cama/fr/ma42 Surrelaxation pour Gauss-Seidel -- Exercice.ipynb new file mode 100644 index 0000000..bb2a484 --- /dev/null +++ b/PVCM/cama/fr/ma42 Surrelaxation pour Gauss-Seidel -- Exercice.ipynb @@ -0,0 +1,336 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Exercice ma21" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "\n", + "%matplotlib inline\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On va augmenter le rayon de convergence la méthode Jacobi amméliorée faite en TD à savoir la méthode de Gauss-Seidel.\n", + "\n", + "On étudiera sa convergence dans différents cas." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Gauss-Seidel\n", + "\n", + "Lorsqu'on calcul le **x** suivant avec Jacobi on ne profite pas du fait que N est triangulaire\n", + "et donc qu'on connait la nouvelle valeur de $x_n$ lorsqu'on calcule $x_{n-1}$. Avec Gauss-Seidel\n", + "on utilise toujours la dernière valeur calculée ce qui accélère la convergence.\n", + "\n", + "Pour résumer Gauss-Seidel d'un point de vu matriciel on a :\n", + "\n", + "* D = la matrice diagonale extraite de A : `D = np.diag(np.diag(A))`\n", + "* L = la matrice stritecement triangulaire inférieure de A : `L = np.tril(A, -1)`\n", + "* U = la matrice stritecement triangulaire supérieure de A : `U = np.triu(A, 1)`\n", + "\n", + "et une itération est donnée par la formule suivante :\n", + "\n", + "$$\n", + "(D + L)\\, {\\bf x}^{k+1} = -U\\; {\\bf x}^k + {\\bf b}\n", + "$$\n", + "ou\n", + "$$\n", + "{\\bf x}^{k+1} = D^{-1} \\, ( -L\\, {\\bf x}^{k+1} - U\\; {\\bf x}^k + {\\bf b})\n", + "$$\n", + "c.a.d.\n", + "$$\n", + "\\begin{bmatrix}\n", + "x_{1}^{k+1} \\\\\n", + "x_{2}^{k+1} \\\\\n", + "\\vdots \\\\\n", + "x_{n}^{k+1} \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "1/a_{11} \\quad 0 \\quad \\ldots \\quad 0 \\\\\n", + "0 \\quad 1/a_{22} \\quad \\ldots \\quad 0 \\\\\n", + " \\vdots \\\\\n", + "0 \\quad 0 \\quad \\ldots \\quad 1/a_{nn} \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\left(\n", + "\\;\n", + "-\n", + "\\begin{bmatrix}\n", + "0 \\quad 0 \\quad \\ldots \\quad 0 \\\\\n", + "a_{21} \\; 0 \\quad \\ldots \\quad 0 \\\\\n", + " \\vdots \\\\\n", + "a_{n1} \\, a_{n2} \\; \\ldots \\quad 0 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_{1}^{k+1} \\\\\n", + "x_{2}^{k+1} \\\\\n", + "\\vdots \\\\\n", + "x_{n}^{k+1} \\\\\n", + "\\end{bmatrix}\n", + "-\n", + "\\begin{bmatrix}\n", + "0 \\; a_{12} \\; \\ldots \\; a_{1n} \\\\\n", + "0 \\quad 0 \\; \\ldots \\; a_{2n} \\\\\n", + " \\vdots \\\\\n", + "0 \\quad 0 \\; \\ldots \\; 0 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_{1}^k \\\\\n", + "x_{2}^k \\\\\n", + "\\vdots \\\\\n", + "x_{n}^k \\\\\n", + "\\end{bmatrix}\n", + "+\n", + "\\begin{bmatrix}\n", + "b_{1} \\\\\n", + "b_{2} \\\\\n", + "\\vdots \\\\\n", + "b_{n} \\\\\n", + "\\end{bmatrix}\n", + "\\; \\right)\n", + "$$\n", + "\n", + "Notons que je peux mettre $L\\, {\\bf x}^{k+1}$ à droite du signe égal\n", + "si je résoud mon système ligne par ligne en commencant par le haut puisque dans\n", + "ce cas les ${\\bf x}^{k+1}$ utilisés sont connus. C'est ce qu'on a fait lors du dernier TP.\n", + "\n", + "### Surrelaxation de Gauss-Seidel\n", + "\n", + "Comme on a fait avec Jacobi, on introduit de l'inertie avec $w$ :\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = w \\, D^{-1} \\, ( -L\\, {\\bf x}^{k+1} - U\\; {\\bf x}^k + {\\bf b}) + (1-w) \\; {\\bf x}^k\n", + "$$\n", + "\n", + "Vérifiez que l'on arrive à l'écriture matricielle suivante :\n", + "\n", + "$$\n", + "\\left(\\frac{D}{w} + L\\right)\\, {\\bf x}^{k+1} = \\left(\\frac{1-w}{w} \\, D - U\\right)\\; {\\bf x}^k + {\\bf b}\n", + "$$\n", + "\n", + "Écrit ainsi on voit que cette méthode consiste à avoir les éléments de la diagonale des 2 cotés de l'égalité.\n", + "On peut interpréter cela comme un avantage lié à une meilleure répartition de l'information contenue dans la matrice (à tester pour savoir)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Programmons Gauss-Seidel surrelaxé\n", + "\n", + "On écrira deux fonctions :\n", + "\n", + "* `solve_triangular(L,b)` qui retourne la solution de L **x** = **b** lorsque L est triangulaire inférieure\n", + "* `gauss_seidel_r(A, b, x0, w, n)` qui fait `n` iteration de Gauss-Seidel en démarrant à `x0` avec `w` le coefficient de relaxation donné en argument. \n", + " Cette fonction retourne un tableau des valeurs de **x** calculées (donc tableau en 2D).\n", + " \n", + "Comme toujours, attention à limiter les `for` et à faire le plus possible d'opérations vectorielles et matricielles." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(123)\n", + "A = np.random.randint(10, size=(4,4))\n", + "b = A.sum(axis=1)\n", + "x0 = np.random.random(4)\n", + "\n", + "res = gauss_seidel_r(A, b, x0, w=0.2, n=100)\n", + "print(res[-1])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_convergences(values, result):\n", + " error = np.square(values - result).sum(axis = -1) / np.square(result).sum(axis=-1)\n", + " error2 = np.square(np.diff(values)).sum(axis = -1) / np.square(values).sum(axis=-1)\n", + " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n", + " ax1.plot(range(len(error)), error)\n", + " ax1.set_title('Erreur absolue normalisée')\n", + " ax1.semilogy();\n", + " ax2.plot(range(len(error2)), error2)\n", + " ax2.set_title('Erreur relative normalisée')\n", + " ax2.semilogy()\n", + " print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot_convergences(res, np.ones(4))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Est-ce que la méthode de Gauss-Seidel non relaxée converge dans ce cas ?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Le bon cas\n", + "\n", + "Trouver un `seed` qui permet de générer un cas qui ne converge pas avec Gauss-Seidel de base mais qui \n", + "converge avec la relaxation ($w=0.2$)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Tracer les courbes de convergence pour le cas retenu avec et sans relaxation." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Étude de $w$\n", + "\n", + "Toujours dans notre cas retenu,\n", + "indiquer quel est l'intervale de\n", + "valeurs de $w$ qui garantit la convergence pour notre système matriciel A **x** = **b** avec toujours le même `x0` \n", + "et un nombre d'itérations à déterminer.\n", + "\n", + "Trouver la valeur optimiale de $w$ pour converger le plus rapidement pour ce cas. \n", + "\n", + "La précision demandée pour l'intervale et la valeur optimale est de $10^{-2}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma50 Optimisation - M\303\251thode du gradient.ipynb" "b/PVCM/cama/fr/ma50 Optimisation - M\303\251thode du gradient.ipynb" new file mode 100644 index 0000000..a1c2a44 --- /dev/null +++ "b/PVCM/cama/fr/ma50 Optimisation - M\303\251thode du gradient.ipynb" @@ -0,0 +1,36389 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "import plotly.offline as py\n", + "import plotly.graph_objects as go\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Problème d'optimisation\n", + "\n", + "Un problème d'optimisation se présente sous la forme suivante :\n", + "\n", + "Soit une fonction $J : ℝ^n \\rightarrow ℝ$, trouver le minimum de $J$ c.a.d. trouver ${\\bf u}$ tel que\n", + "\n", + "$$J({\\bf u}) = \\inf_{{\\bf v} \\in ℝ^n} J({\\bf v})$$\n", + "\n", + "### Problème d'optimisation avec contrainte\n", + "\n", + "Il est possible de chercher **u** non pas dans $ℝ^n$ mais dans une partie de $ℝ^n$, il s'agit alors d'un \n", + "problème d'optimisation avec contrainte. \n", + "\n", + "**Exemple** On est en 2D et on cherche le minimum de $J(x,y)$ mais avec la contrainte que $y > x$. Cela revient à chercher dans la partie de $ℝ^2$ qui vérifie $y > x$.\n", + "\n", + "Nous ne regarderons pas les problèmes d'optimisation avec contraintes dans ce cours mais il s'agit de problèmes\n", + "importants que vous verrez dans votre scolarité.\n", + "\n", + "## La méthode du gradient\n", + "\n", + "Une méthode pour résoudre un problème d'optimisation en 2D est de l'imaginer comme un terrain avec du relief. La\n", + "fonction $J(x,y)$ représente l'altitude en tout point $(x,y)$.\n", + "\n", + "Pour trouver le minimum de $J$ il suffit de partir d'un point au hasard et de descendre dans la direction qui \n", + "descend le plus. Une goutte d'eau suit ce chemin.\n", + "\n", + "C'est la méthode du gradient.\n", + "\n", + "Pour bien comprendre la méthode il est nécessaire de bien comprendre les dérivées partielles ainsi que les\n", + "notations qui sont résumée dans ce [mémo sur les dérivées partielles](https://www.lrde.epita.fr/~ricou/notations.pdf).\n", + "\n", + "L'algorithme du gradient est donc :\n", + "\n", + "* prendre un point de départ au hasard ${\\bf p^0} = (x_0, y_0)$\n", + "* calculer le gradient de J en ce point \n", + "\n", + "$$\n", + "\\nabla J(x_0, y_0) = \n", + "\\begin{bmatrix} \n", + "\\frac{\\partial J}{\\partial x} \\\\\n", + "\\frac{\\partial J}{\\partial y}\n", + "\\end{bmatrix} (x_0, y_0)\n", + "$$\n", + "* avancer dans la direction opposée (le grandiant monte) : ${\\bf p}^{k+1} = {\\bf p}^k - \\mu \\, \\nabla J({\\bf p}^k)$\n", + "\n", + "et on recommence cette dernière étape jusqu'à ce qu'on arrive à un point fixe c.a.d. que \n", + "$|| {\\bf p}^{k+1} - {\\bf p}^k|| < \\varepsilon$ avec $\\varepsilon$ une toute petite valeur." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def J(x, y):\n", + " return x**2 + 0.5 * y**2 - 2 * x + 3" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "linkText": "Export to plot.ly", + "plotlyServerURL": "https://plot.ly", + "showLink": false + }, + "data": [ + { + "type": "surface", + "x": [ + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ], + [ + -3, + -2.9393939393939394, + -2.878787878787879, + -2.8181818181818183, + -2.757575757575758, + -2.696969696969697, + -2.6363636363636362, + -2.5757575757575757, + -2.515151515151515, + -2.4545454545454546, + -2.393939393939394, + -2.333333333333333, + -2.2727272727272725, + -2.212121212121212, + -2.1515151515151514, + -2.090909090909091, + -2.0303030303030303, + -1.9696969696969697, + -1.9090909090909092, + -1.8484848484848484, + -1.7878787878787878, + -1.7272727272727273, + -1.6666666666666665, + -1.606060606060606, + -1.5454545454545454, + -1.4848484848484849, + -1.4242424242424243, + -1.3636363636363635, + -1.303030303030303, + -1.2424242424242424, + -1.1818181818181817, + -1.121212121212121, + -1.0606060606060606, + -1, + -0.9393939393939394, + -0.8787878787878789, + -0.8181818181818183, + -0.7575757575757573, + -0.6969696969696968, + -0.6363636363636362, + -0.5757575757575757, + -0.5151515151515151, + -0.4545454545454546, + -0.39393939393939403, + -0.33333333333333304, + -0.2727272727272725, + -0.21212121212121193, + -0.15151515151515138, + -0.09090909090909083, + -0.030303030303030276, + 0.030303030303030276, + 0.09090909090909083, + 0.15151515151515138, + 0.21212121212121238, + 0.27272727272727293, + 0.3333333333333335, + 0.39393939393939403, + 0.4545454545454546, + 0.5151515151515151, + 0.5757575757575757, + 0.6363636363636367, + 0.6969696969696972, + 0.7575757575757578, + 0.8181818181818183, + 0.8787878787878789, + 0.9393939393939394, + 1, + 1.0606060606060606, + 1.121212121212121, + 1.1818181818181817, + 1.2424242424242422, + 1.3030303030303028, + 1.3636363636363633, + 1.4242424242424248, + 1.4848484848484853, + 1.5454545454545459, + 1.6060606060606064, + 1.666666666666667, + 1.7272727272727275, + 1.787878787878788, + 1.8484848484848486, + 1.9090909090909092, + 1.9696969696969697, + 2.0303030303030303, + 2.090909090909091, + 2.1515151515151514, + 2.212121212121212, + 2.2727272727272725, + 2.333333333333334, + 2.3939393939393945, + 2.454545454545455, + 2.5151515151515156, + 2.575757575757576, + 2.6363636363636367, + 2.6969696969696972, + 2.757575757575758, + 2.8181818181818183, + 2.878787878787879, + 2.9393939393939394, + 3 + ] + ], + "y": [ + [ + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3, + -3 + ], + [ + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394, + -2.9393939393939394 + ], + [ + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879, + -2.878787878787879 + ], + [ + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183, + -2.8181818181818183 + ], + [ + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758, + -2.757575757575758 + ], + [ + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697, + -2.696969696969697 + ], + [ + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362, + -2.6363636363636362 + ], + [ + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757, + -2.5757575757575757 + ], + [ + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515, + -2.515151515151515 + ], + [ + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546, + -2.4545454545454546 + ], + [ + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394, + -2.393939393939394 + ], + [ + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333, + -2.333333333333333 + ], + [ + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725, + -2.2727272727272725 + ], + [ + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212, + -2.212121212121212 + ], + [ + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514, + -2.1515151515151514 + ], + [ + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091, + -2.090909090909091 + ], + [ + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303, + -2.0303030303030303 + ], + [ + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697, + -1.9696969696969697 + ], + [ + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092, + -1.9090909090909092 + ], + [ + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484, + -1.8484848484848484 + ], + [ + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878, + -1.7878787878787878 + ], + [ + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273, + -1.7272727272727273 + ], + [ + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665, + -1.6666666666666665 + ], + [ + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606, + -1.606060606060606 + ], + [ + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454, + -1.5454545454545454 + ], + [ + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849, + -1.4848484848484849 + ], + [ + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243, + -1.4242424242424243 + ], + [ + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635, + -1.3636363636363635 + ], + [ + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303, + -1.303030303030303 + ], + [ + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424, + -1.2424242424242424 + ], + [ + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817, + -1.1818181818181817 + ], + [ + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121, + -1.121212121212121 + ], + [ + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606, + -1.0606060606060606 + ], + [ + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1 + ], + [ + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394, + -0.9393939393939394 + ], + [ + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789, + -0.8787878787878789 + ], + [ + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183, + -0.8181818181818183 + ], + [ + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573, + -0.7575757575757573 + ], + [ + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968, + -0.6969696969696968 + ], + [ + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362, + -0.6363636363636362 + ], + [ + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757, + -0.5757575757575757 + ], + [ + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151, + -0.5151515151515151 + ], + [ + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546, + -0.4545454545454546 + ], + [ + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403, + -0.39393939393939403 + ], + [ + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304, + -0.33333333333333304 + ], + [ + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725, + -0.2727272727272725 + ], + [ + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193, + -0.21212121212121193 + ], + [ + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138, + -0.15151515151515138 + ], + [ + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083, + -0.09090909090909083 + ], + [ + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276, + -0.030303030303030276 + ], + [ + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276, + 0.030303030303030276 + ], + [ + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083, + 0.09090909090909083 + ], + [ + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138, + 0.15151515151515138 + ], + [ + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238, + 0.21212121212121238 + ], + [ + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293, + 0.27272727272727293 + ], + [ + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335, + 0.3333333333333335 + ], + [ + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403, + 0.39393939393939403 + ], + [ + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546, + 0.4545454545454546 + ], + [ + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151, + 0.5151515151515151 + ], + [ + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757, + 0.5757575757575757 + ], + [ + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367, + 0.6363636363636367 + ], + [ + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972, + 0.6969696969696972 + ], + [ + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578, + 0.7575757575757578 + ], + [ + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183, + 0.8181818181818183 + ], + [ + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789, + 0.8787878787878789 + ], + [ + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394, + 0.9393939393939394 + ], + [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + [ + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606, + 1.0606060606060606 + ], + [ + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121, + 1.121212121212121 + ], + [ + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817, + 1.1818181818181817 + ], + [ + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422, + 1.2424242424242422 + ], + [ + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028, + 1.3030303030303028 + ], + [ + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633, + 1.3636363636363633 + ], + [ + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248, + 1.4242424242424248 + ], + [ + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853, + 1.4848484848484853 + ], + [ + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459, + 1.5454545454545459 + ], + [ + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064, + 1.6060606060606064 + ], + [ + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667, + 1.666666666666667 + ], + [ + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275, + 1.7272727272727275 + ], + [ + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788, + 1.787878787878788 + ], + [ + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486, + 1.8484848484848486 + ], + [ + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092, + 1.9090909090909092 + ], + [ + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697, + 1.9696969696969697 + ], + [ + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303, + 2.0303030303030303 + ], + [ + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091, + 2.090909090909091 + ], + [ + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514, + 2.1515151515151514 + ], + [ + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212, + 2.212121212121212 + ], + [ + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725, + 2.2727272727272725 + ], + [ + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334, + 2.333333333333334 + ], + [ + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945, + 2.3939393939393945 + ], + [ + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455, + 2.454545454545455 + ], + [ + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156, + 2.5151515151515156 + ], + [ + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576, + 2.575757575757576 + ], + [ + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367, + 2.6363636363636367 + ], + [ + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972, + 2.6969696969696972 + ], + [ + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758, + 2.757575757575758 + ], + [ + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183, + 2.8181818181818183 + ], + [ + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879, + 2.878787878787879 + ], + [ + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394, + 2.9393939393939394 + ], + [ + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ] + ], + "z": [ + [ + 22.5, + 22.0188246097337, + 21.544995408631774, + 21.078512396694215, + 20.61937557392103, + 20.167584940312214, + 19.723140495867767, + 19.286042240587694, + 18.856290174471994, + 18.433884297520663, + 18.018824609733702, + 17.611111111111107, + 17.21074380165289, + 16.817722681359044, + 16.432047750229565, + 16.053719008264462, + 15.682736455463727, + 15.319100091827364, + 14.962809917355372, + 14.61386593204775, + 14.272268135904499, + 13.93801652892562, + 13.61111111111111, + 13.291551882460972, + 12.979338842975206, + 12.67447199265381, + 12.376951331496787, + 12.086776859504132, + 11.803948576675849, + 11.528466483011938, + 11.260330578512395, + 10.999540863177227, + 10.746097337006429, + 10.5, + 10.261248852157944, + 10.029843893480258, + 9.805785123966942, + 9.589072543617998, + 9.379706152433425, + 9.177685950413224, + 8.983011937557393, + 8.795684113865931, + 8.615702479338843, + 8.443067033976124, + 8.277777777777777, + 8.1198347107438, + 7.969237832874196, + 7.825987144168962, + 7.690082644628099, + 7.561524334251607, + 7.440312213039486, + 7.3264462809917354, + 7.219926538108356, + 7.120752984389347, + 7.028925619834711, + 6.944444444444445, + 6.867309458218549, + 6.797520661157025, + 6.735078053259872, + 6.679981634527089, + 6.632231404958677, + 6.5918273645546375, + 6.558769513314967, + 6.533057851239669, + 6.514692378328742, + 6.503673094582186, + 6.5, + 6.503673094582186, + 6.514692378328742, + 6.533057851239669, + 6.558769513314967, + 6.5918273645546375, + 6.632231404958677, + 6.67998163452709, + 6.735078053259872, + 6.797520661157025, + 6.86730945821855, + 6.944444444444445, + 7.028925619834711, + 7.120752984389348, + 7.219926538108357, + 7.3264462809917354, + 7.440312213039485, + 7.561524334251606, + 7.690082644628099, + 7.825987144168961, + 7.969237832874196, + 8.1198347107438, + 8.277777777777779, + 8.443067033976126, + 8.615702479338845, + 8.795684113865933, + 8.983011937557393, + 9.177685950413224, + 9.379706152433426, + 9.589072543617998, + 9.805785123966942, + 10.029843893480258, + 10.261248852157943, + 10.5 + ], + [ + 22.32001836547291, + 21.83884297520661, + 21.365013774104685, + 20.898530762167127, + 20.43939393939394, + 19.98760330578512, + 19.54315886134068, + 19.106060606060606, + 18.676308539944905, + 18.25390266299357, + 17.838842975206614, + 17.43112947658402, + 17.0307621671258, + 16.637741046831955, + 16.252066115702476, + 15.873737373737372, + 15.502754820936639, + 15.139118457300276, + 14.782828282828284, + 14.433884297520661, + 14.09228650137741, + 13.75803489439853, + 13.431129476584022, + 13.111570247933884, + 12.799357208448118, + 12.494490358126722, + 12.196969696969697, + 11.906795224977042, + 11.62396694214876, + 11.348484848484848, + 11.080348943985307, + 10.819559228650137, + 10.566115702479339, + 10.320018365472912, + 10.081267217630854, + 9.849862258953168, + 9.625803489439853, + 9.409090909090908, + 9.199724517906336, + 8.997704315886134, + 8.803030303030303, + 8.615702479338843, + 8.435720844811755, + 8.263085399449036, + 8.097796143250687, + 7.939853076216711, + 7.789256198347107, + 7.646005509641872, + 7.5101010101010095, + 7.381542699724518, + 7.260330578512397, + 7.146464646464646, + 7.039944903581267, + 6.940771349862258, + 6.8489439853076215, + 6.764462809917355, + 6.68732782369146, + 6.617539026629935, + 6.5550964187327825, + 6.5, + 6.452249770431588, + 6.411845730027548, + 6.378787878787879, + 6.35307621671258, + 6.3347107438016526, + 6.323691460055096, + 6.320018365472911, + 6.323691460055096, + 6.3347107438016526, + 6.35307621671258, + 6.378787878787879, + 6.411845730027547, + 6.452249770431588, + 6.5, + 6.5550964187327825, + 6.617539026629936, + 6.68732782369146, + 6.764462809917355, + 6.848943985307622, + 6.940771349862259, + 7.039944903581267, + 7.146464646464647, + 7.260330578512397, + 7.381542699724518, + 7.510101010101009, + 7.646005509641872, + 7.789256198347106, + 7.939853076216712, + 8.09779614325069, + 8.263085399449036, + 8.435720844811755, + 8.615702479338843, + 8.803030303030305, + 8.997704315886136, + 9.199724517906336, + 9.40909090909091, + 9.625803489439853, + 9.84986225895317, + 10.081267217630852, + 10.320018365472912 + ], + [ + 22.143709825528006, + 21.66253443526171, + 21.188705234159784, + 20.722222222222225, + 20.26308539944904, + 19.81129476584022, + 19.366850321395777, + 18.929752066115704, + 18.5, + 18.07759412304867, + 17.66253443526171, + 17.254820936639117, + 16.8544536271809, + 16.46143250688705, + 16.075757575757578, + 15.69742883379247, + 15.326446280991737, + 14.962809917355372, + 14.60651974288338, + 14.257575757575758, + 13.915977961432507, + 13.581726354453629, + 13.254820936639117, + 12.935261707988982, + 12.623048668503214, + 12.31818181818182, + 12.020661157024794, + 11.73048668503214, + 11.447658402203857, + 11.172176308539946, + 10.904040404040405, + 10.643250688705233, + 10.389807162534435, + 10.143709825528008, + 9.90495867768595, + 9.673553719008265, + 9.449494949494952, + 9.232782369146005, + 9.023415977961433, + 8.82139577594123, + 8.6267217630854, + 8.439393939393941, + 8.259412304866851, + 8.086776859504134, + 7.921487603305785, + 7.763544536271809, + 7.612947658402204, + 7.46969696969697, + 7.333792470156107, + 7.205234159779615, + 7.084022038567494, + 6.9701561065197435, + 6.863636363636364, + 6.764462809917355, + 6.672635445362719, + 6.588154269972453, + 6.511019283746557, + 6.441230486685033, + 6.37878787878788, + 6.323691460055097, + 6.275941230486685, + 6.2355371900826455, + 6.202479338842975, + 6.176767676767677, + 6.15840220385675, + 6.147382920110194, + 6.143709825528008, + 6.147382920110194, + 6.15840220385675, + 6.176767676767677, + 6.202479338842975, + 6.2355371900826455, + 6.275941230486685, + 6.323691460055098, + 6.37878787878788, + 6.441230486685033, + 6.511019283746558, + 6.588154269972453, + 6.672635445362719, + 6.764462809917356, + 6.863636363636365, + 6.9701561065197435, + 7.084022038567493, + 7.205234159779616, + 7.333792470156107, + 7.469696969696971, + 7.612947658402204, + 7.763544536271809, + 7.921487603305788, + 8.086776859504134, + 8.259412304866853, + 8.439393939393941, + 8.626721763085401, + 8.821395775941232, + 9.023415977961434, + 9.232782369146008, + 9.449494949494952, + 9.673553719008266, + 9.90495867768595, + 10.143709825528008 + ], + [ + 21.97107438016529, + 21.48989898989899, + 21.01606978879706, + 20.549586776859506, + 20.09044995408632, + 19.6386593204775, + 19.194214876033058, + 18.757116620752985, + 18.32736455463728, + 17.90495867768595, + 17.48989898989899, + 17.082185491276398, + 16.68181818181818, + 16.288797061524335, + 15.903122130394857, + 15.524793388429751, + 15.153810835629018, + 14.790174471992653, + 14.433884297520663, + 14.084940312213039, + 13.74334251606979, + 13.40909090909091, + 13.0821854912764, + 12.762626262626263, + 12.450413223140497, + 12.145546372819101, + 11.848025711662075, + 11.557851239669422, + 11.27502295684114, + 10.999540863177227, + 10.731404958677686, + 10.470615243342516, + 10.217171717171716, + 9.97107438016529, + 9.732323232323232, + 9.500918273645548, + 9.276859504132233, + 9.060146923783286, + 8.850780532598714, + 8.648760330578511, + 8.45408631772268, + 8.266758494031222, + 8.086776859504134, + 7.914141414141415, + 7.748852157943067, + 7.590909090909091, + 7.440312213039486, + 7.297061524334252, + 7.161157024793389, + 7.032598714416896, + 6.911386593204775, + 6.797520661157026, + 6.691000918273646, + 6.5918273645546375, + 6.5, + 6.415518824609734, + 6.338383838383839, + 6.268595041322315, + 6.206152433425161, + 6.1510560146923785, + 6.103305785123967, + 6.062901744719927, + 6.029843893480257, + 6.004132231404959, + 5.985766758494032, + 5.974747474747475, + 5.971074380165289, + 5.974747474747475, + 5.985766758494032, + 6.004132231404959, + 6.029843893480257, + 6.062901744719927, + 6.103305785123967, + 6.151056014692379, + 6.206152433425162, + 6.268595041322315, + 6.338383838383839, + 6.415518824609734, + 6.500000000000001, + 6.5918273645546375, + 6.691000918273646, + 6.797520661157026, + 6.911386593204775, + 7.032598714416897, + 7.161157024793388, + 7.297061524334252, + 7.440312213039485, + 7.59090909090909, + 7.74885215794307, + 7.914141414141415, + 8.086776859504134, + 8.266758494031222, + 8.454086317722682, + 8.648760330578513, + 8.850780532598716, + 9.06014692378329, + 9.276859504132233, + 9.500918273645548, + 9.732323232323232, + 9.97107438016529 + ], + [ + 21.80211202938476, + 21.320936639118457, + 20.84710743801653, + 20.380624426078974, + 19.92148760330579, + 19.46969696969697, + 19.025252525252526, + 18.588154269972453, + 18.15840220385675, + 17.73599632690542, + 17.320936639118457, + 16.913223140495866, + 16.512855831037648, + 16.119834710743802, + 15.734159779614325, + 15.355831037649219, + 14.984848484848486, + 14.621212121212121, + 14.264921946740131, + 13.915977961432507, + 13.574380165289258, + 13.240128558310378, + 12.913223140495868, + 12.59366391184573, + 12.281450872359965, + 11.976584022038569, + 11.679063360881543, + 11.38888888888889, + 11.106060606060607, + 10.830578512396695, + 10.562442607897154, + 10.301652892561984, + 10.048209366391184, + 9.802112029384757, + 9.5633608815427, + 9.331955922865015, + 9.1078971533517, + 8.891184573002754, + 8.681818181818182, + 8.47979797979798, + 8.285123966942148, + 8.09779614325069, + 7.917814508723601, + 7.745179063360883, + 7.579889807162534, + 7.421946740128559, + 7.271349862258953, + 7.12809917355372, + 6.992194674012857, + 6.863636363636364, + 6.742424242424243, + 6.628558310376493, + 6.522038567493114, + 6.422865013774105, + 6.331037649219468, + 6.246556473829202, + 6.169421487603307, + 6.099632690541783, + 6.037190082644629, + 5.982093663911846, + 5.934343434343435, + 5.8939393939393945, + 5.860881542699725, + 5.835169880624427, + 5.8168044077135, + 5.805785123966943, + 5.802112029384757, + 5.805785123966943, + 5.8168044077135, + 5.835169880624427, + 5.860881542699725, + 5.8939393939393945, + 5.934343434343435, + 5.982093663911847, + 6.03719008264463, + 6.099632690541783, + 6.169421487603307, + 6.246556473829202, + 6.331037649219469, + 6.422865013774105, + 6.522038567493114, + 6.628558310376493, + 6.742424242424243, + 6.863636363636365, + 6.992194674012856, + 7.12809917355372, + 7.271349862258953, + 7.421946740128558, + 7.579889807162537, + 7.745179063360883, + 7.917814508723602, + 8.09779614325069, + 8.28512396694215, + 8.479797979797981, + 8.681818181818183, + 8.891184573002757, + 9.1078971533517, + 9.331955922865015, + 9.5633608815427, + 9.802112029384757 + ], + [ + 21.63682277318641, + 21.155647382920108, + 20.681818181818183, + 20.215335169880625, + 19.75619834710744, + 19.30440771349862, + 18.859963269054177, + 18.422865013774103, + 17.993112947658403, + 17.57070707070707, + 17.15564738292011, + 16.747933884297517, + 16.3475665748393, + 15.954545454545453, + 15.568870523415976, + 15.190541781450872, + 14.819559228650137, + 14.455922865013774, + 14.099632690541782, + 13.75068870523416, + 13.409090909090908, + 13.074839302112029, + 12.74793388429752, + 12.428374655647382, + 12.116161616161616, + 11.81129476584022, + 11.513774104683197, + 11.22359963269054, + 10.940771349862258, + 10.665289256198347, + 10.397153351698805, + 10.136363636363637, + 9.882920110192837, + 9.63682277318641, + 9.398071625344352, + 9.166666666666668, + 8.942607897153351, + 8.725895316804406, + 8.516528925619834, + 8.314508723599632, + 8.1198347107438, + 7.932506887052341, + 7.752525252525253, + 7.579889807162534, + 7.414600550964186, + 7.25665748393021, + 7.1060606060606055, + 6.962809917355371, + 6.826905417814508, + 6.698347107438016, + 6.577134986225895, + 6.463269054178145, + 6.356749311294766, + 6.257575757575757, + 6.165748393021119, + 6.081267217630853, + 6.004132231404958, + 5.934343434343434, + 5.87190082644628, + 5.816804407713498, + 5.769054178145087, + 5.728650137741046, + 5.695592286501377, + 5.669880624426078, + 5.651515151515151, + 5.640495867768594, + 5.63682277318641, + 5.640495867768594, + 5.651515151515151, + 5.669880624426078, + 5.695592286501377, + 5.728650137741046, + 5.769054178145087, + 5.816804407713499, + 5.87190082644628, + 5.934343434343434, + 6.0041322314049586, + 6.081267217630854, + 6.16574839302112, + 6.257575757575758, + 6.356749311294766, + 6.463269054178145, + 6.577134986225895, + 6.698347107438016, + 6.826905417814508, + 6.96280991735537, + 7.1060606060606055, + 7.25665748393021, + 7.414600550964188, + 7.579889807162536, + 7.752525252525254, + 7.932506887052343, + 8.119834710743802, + 8.314508723599634, + 8.516528925619836, + 8.725895316804408, + 8.942607897153351, + 9.166666666666668, + 9.398071625344352, + 9.63682277318641 + ], + [ + 21.475206611570247, + 20.99403122130395, + 20.52020202020202, + 20.053719008264466, + 19.594582185491277, + 19.14279155188246, + 18.698347107438018, + 18.261248852157944, + 17.83149678604224, + 17.40909090909091, + 16.99403122130395, + 16.586317722681358, + 16.18595041322314, + 15.792929292929292, + 15.407254361799815, + 15.028925619834709, + 14.657943067033976, + 14.294306703397613, + 13.93801652892562, + 13.589072543617998, + 13.247474747474747, + 12.913223140495868, + 12.586317722681358, + 12.26675849403122, + 11.954545454545453, + 11.649678604224057, + 11.352157943067034, + 11.06198347107438, + 10.779155188246097, + 10.503673094582185, + 10.235537190082644, + 9.974747474747474, + 9.721303948576676, + 9.475206611570247, + 9.236455463728191, + 9.005050505050505, + 8.78099173553719, + 8.564279155188245, + 8.354912764003672, + 8.152892561983471, + 7.95821854912764, + 7.77089072543618, + 7.590909090909091, + 7.418273645546373, + 7.252984389348025, + 7.095041322314049, + 6.944444444444444, + 6.8011937557392095, + 6.6652892561983474, + 6.536730945821855, + 6.415518824609734, + 6.301652892561984, + 6.195133149678604, + 6.095959595959595, + 6.004132231404958, + 5.9196510560146915, + 5.842516069788797, + 5.7727272727272725, + 5.7102846648301195, + 5.655188246097337, + 5.607438016528925, + 5.567033976124884, + 5.533976124885216, + 5.508264462809917, + 5.48989898989899, + 5.4788797061524335, + 5.475206611570248, + 5.4788797061524335, + 5.48989898989899, + 5.508264462809917, + 5.533976124885216, + 5.567033976124884, + 5.607438016528925, + 5.655188246097337, + 5.7102846648301195, + 5.772727272727273, + 5.842516069788797, + 5.919651056014692, + 6.004132231404959, + 6.095959595959596, + 6.195133149678604, + 6.301652892561984, + 6.415518824609734, + 6.536730945821855, + 6.665289256198347, + 6.8011937557392095, + 6.944444444444445, + 7.095041322314048, + 7.252984389348027, + 7.418273645546375, + 7.5909090909090935, + 7.770890725436182, + 7.95821854912764, + 8.152892561983471, + 8.354912764003675, + 8.564279155188247, + 8.78099173553719, + 9.005050505050505, + 9.236455463728191, + 9.475206611570247 + ], + [ + 21.31726354453627, + 20.836088154269973, + 20.362258953168045, + 19.89577594123049, + 19.4366391184573, + 18.984848484848484, + 18.54040404040404, + 18.10330578512397, + 17.673553719008265, + 17.251147842056934, + 16.836088154269973, + 16.42837465564738, + 16.028007346189163, + 15.634986225895316, + 15.249311294765839, + 14.870982552800733, + 14.5, + 14.136363636363637, + 13.780073461891645, + 13.431129476584022, + 13.089531680440771, + 12.755280073461892, + 12.428374655647382, + 12.108815426997245, + 11.796602387511477, + 11.491735537190081, + 11.194214876033058, + 10.904040404040403, + 10.621212121212121, + 10.345730027548209, + 10.077594123048668, + 9.816804407713498, + 9.5633608815427, + 9.31726354453627, + 9.078512396694215, + 8.847107438016529, + 8.623048668503214, + 8.40633608815427, + 8.196969696969695, + 7.994949494949495, + 7.800275482093664, + 7.612947658402204, + 7.432966023875115, + 7.260330578512397, + 7.0950413223140485, + 6.937098255280073, + 6.786501377410468, + 6.643250688705233, + 6.507346189164371, + 6.378787878787879, + 6.257575757575758, + 6.143709825528008, + 6.037190082644628, + 5.938016528925619, + 5.846189164370982, + 5.7617079889807155, + 5.684573002754821, + 5.614784205693296, + 5.5523415977961434, + 5.497245179063361, + 5.449494949494949, + 5.409090909090908, + 5.37603305785124, + 5.350321395775941, + 5.3319559228650135, + 5.320936639118457, + 5.317263544536272, + 5.320936639118457, + 5.3319559228650135, + 5.350321395775941, + 5.37603305785124, + 5.409090909090908, + 5.449494949494949, + 5.497245179063361, + 5.5523415977961434, + 5.614784205693297, + 5.684573002754821, + 5.761707988980716, + 5.846189164370983, + 5.93801652892562, + 6.037190082644628, + 6.143709825528008, + 6.257575757575758, + 6.378787878787879, + 6.5073461891643705, + 6.643250688705233, + 6.7865013774104685, + 6.9370982552800715, + 7.095041322314051, + 7.260330578512399, + 7.432966023875117, + 7.612947658402206, + 7.800275482093664, + 7.994949494949495, + 8.196969696969699, + 8.406336088154271, + 8.623048668503214, + 8.847107438016529, + 9.078512396694215, + 9.31726354453627 + ], + [ + 21.16299357208448, + 20.68181818181818, + 20.207988980716255, + 19.741505968778696, + 19.28236914600551, + 18.830578512396695, + 18.38613406795225, + 17.949035812672175, + 17.519283746556475, + 17.096877869605144, + 16.681818181818183, + 16.27410468319559, + 15.873737373737372, + 15.480716253443525, + 15.09504132231405, + 14.716712580348943, + 14.34573002754821, + 13.982093663911845, + 13.625803489439853, + 13.276859504132231, + 12.93526170798898, + 12.601010101010102, + 12.274104683195592, + 11.954545454545453, + 11.642332415059688, + 11.337465564738292, + 11.039944903581269, + 10.749770431588614, + 10.46694214876033, + 10.19146005509642, + 9.923324150596876, + 9.662534435261708, + 9.40909090909091, + 9.162993572084481, + 8.924242424242426, + 8.69283746556474, + 8.468778696051423, + 8.25206611570248, + 8.042699724517906, + 7.8406795224977035, + 7.646005509641873, + 7.458677685950413, + 7.278696051423324, + 7.106060606060606, + 6.940771349862258, + 6.782828282828282, + 6.632231404958677, + 6.488980716253444, + 6.35307621671258, + 6.224517906336088, + 6.1033057851239665, + 5.989439853076217, + 5.882920110192838, + 5.7837465564738295, + 5.691919191919192, + 5.607438016528926, + 5.53030303030303, + 5.460514233241506, + 5.398071625344352, + 5.3429752066115705, + 5.2952249770431585, + 5.254820936639119, + 5.221763085399449, + 5.196051423324151, + 5.177685950413223, + 5.166666666666667, + 5.162993572084481, + 5.166666666666667, + 5.177685950413223, + 5.196051423324151, + 5.221763085399449, + 5.254820936639119, + 5.2952249770431585, + 5.342975206611571, + 5.398071625344353, + 5.460514233241506, + 5.530303030303031, + 5.607438016528926, + 5.691919191919192, + 5.7837465564738295, + 5.882920110192838, + 5.989439853076217, + 6.1033057851239665, + 6.2245179063360885, + 6.35307621671258, + 6.488980716253443, + 6.632231404958677, + 6.782828282828282, + 6.94077134986226, + 7.106060606060607, + 7.278696051423326, + 7.4586776859504145, + 7.646005509641874, + 7.840679522497705, + 8.042699724517908, + 8.25206611570248, + 8.468778696051423, + 8.69283746556474, + 8.924242424242424, + 9.162993572084481 + ], + [ + 21.01239669421488, + 20.531221303948577, + 20.05739210284665, + 19.590909090909093, + 19.131772268135904, + 18.67998163452709, + 18.235537190082646, + 17.798438934802572, + 17.36868686868687, + 16.946280991735538, + 16.531221303948577, + 16.123507805325985, + 15.723140495867767, + 15.33011937557392, + 14.944444444444443, + 14.566115702479339, + 14.195133149678604, + 13.83149678604224, + 13.475206611570249, + 13.126262626262626, + 12.784664830119375, + 12.450413223140496, + 12.123507805325985, + 11.80394857667585, + 11.491735537190081, + 11.186868686868687, + 10.889348025711662, + 10.599173553719007, + 10.316345270890725, + 10.040863177226814, + 9.772727272727272, + 9.511937557392102, + 9.258494031221304, + 9.012396694214877, + 8.77364554637282, + 8.542240587695133, + 8.318181818181818, + 8.101469237832873, + 7.892102846648301, + 7.690082644628099, + 7.495408631772268, + 7.308080808080808, + 7.12809917355372, + 6.955463728191001, + 6.790174471992653, + 6.632231404958677, + 6.4816345270890725, + 6.338383838383838, + 6.202479338842975, + 6.073921028466483, + 5.952708907254362, + 5.838842975206612, + 5.732323232323233, + 5.633149678604224, + 5.541322314049586, + 5.45684113865932, + 5.379706152433425, + 5.309917355371901, + 5.247474747474747, + 5.192378328741965, + 5.144628099173554, + 5.104224058769513, + 5.071166207529844, + 5.045454545454545, + 5.0270890725436175, + 5.016069788797061, + 5.0123966942148765, + 5.016069788797061, + 5.027089072543618, + 5.045454545454545, + 5.071166207529844, + 5.104224058769513, + 5.144628099173554, + 5.192378328741966, + 5.247474747474747, + 5.309917355371901, + 5.3797061524334255, + 5.456841138659321, + 5.541322314049587, + 5.633149678604225, + 5.732323232323233, + 5.838842975206612, + 5.952708907254362, + 6.073921028466483, + 6.202479338842975, + 6.338383838383837, + 6.4816345270890725, + 6.632231404958677, + 6.790174471992655, + 6.955463728191003, + 7.128099173553721, + 7.30808080808081, + 7.4954086317722695, + 7.6900826446281005, + 7.892102846648303, + 8.101469237832875, + 8.318181818181818, + 8.542240587695135, + 8.77364554637282, + 9.012396694214877 + ], + [ + 20.86547291092746, + 20.384297520661157, + 19.91046831955923, + 19.443985307621674, + 18.984848484848488, + 18.53305785123967, + 18.088613406795226, + 17.651515151515152, + 17.22176308539945, + 16.799357208448118, + 16.384297520661157, + 15.976584022038566, + 15.576216712580347, + 15.1831955922865, + 14.797520661157023, + 14.419191919191919, + 14.048209366391184, + 13.68457300275482, + 13.328282828282829, + 12.979338842975206, + 12.637741046831955, + 12.303489439853077, + 11.976584022038566, + 11.65702479338843, + 11.344811753902663, + 11.039944903581269, + 10.742424242424242, + 10.452249770431589, + 10.169421487603305, + 9.893939393939394, + 9.625803489439853, + 9.365013774104682, + 9.111570247933884, + 8.865472910927457, + 8.6267217630854, + 8.395316804407713, + 8.1712580348944, + 7.954545454545454, + 7.745179063360881, + 7.543158861340679, + 7.348484848484849, + 7.161157024793388, + 6.9811753902663, + 6.808539944903582, + 6.643250688705233, + 6.485307621671257, + 6.3347107438016526, + 6.191460055096419, + 6.055555555555555, + 5.926997245179063, + 5.805785123966942, + 5.691919191919192, + 5.585399449035814, + 5.486225895316805, + 5.394398530762167, + 5.309917355371901, + 5.232782369146006, + 5.162993572084481, + 5.1005509641873275, + 5.045454545454546, + 4.997704315886134, + 4.957300275482094, + 4.924242424242424, + 4.898530762167126, + 4.880165289256198, + 4.869146005509642, + 4.865472910927457, + 4.869146005509642, + 4.880165289256198, + 4.898530762167126, + 4.924242424242424, + 4.957300275482094, + 4.997704315886134, + 5.045454545454547, + 5.100550964187328, + 5.162993572084481, + 5.2327823691460065, + 5.309917355371901, + 5.394398530762167, + 5.486225895316805, + 5.585399449035814, + 5.691919191919192, + 5.805785123966942, + 5.926997245179064, + 6.055555555555555, + 6.191460055096418, + 6.3347107438016526, + 6.485307621671257, + 6.643250688705237, + 6.808539944903583, + 6.981175390266301, + 7.16115702479339, + 7.3484848484848495, + 7.543158861340681, + 7.745179063360883, + 7.954545454545457, + 8.1712580348944, + 8.395316804407715, + 8.6267217630854, + 8.865472910927457 + ], + [ + 20.72222222222222, + 20.24104683195592, + 19.767217630853995, + 19.300734618916437, + 18.84159779614325, + 18.389807162534435, + 17.94536271808999, + 17.508264462809915, + 17.078512396694215, + 16.656106519742885, + 16.241046831955924, + 15.83333333333333, + 15.432966023875112, + 15.039944903581265, + 14.65426997245179, + 14.275941230486684, + 13.90495867768595, + 13.541322314049586, + 13.185032139577594, + 12.836088154269971, + 12.49449035812672, + 12.160238751147842, + 11.833333333333332, + 11.513774104683193, + 11.201561065197428, + 10.896694214876032, + 10.599173553719009, + 10.308999081726354, + 10.02617079889807, + 9.75068870523416, + 9.482552800734616, + 9.221763085399449, + 8.96831955922865, + 8.722222222222221, + 8.483471074380166, + 8.25206611570248, + 8.028007346189163, + 7.811294765840219, + 7.601928374655646, + 7.399908172635444, + 7.2052341597796135, + 7.017906336088153, + 6.8379247015610645, + 6.665289256198347, + 6.499999999999998, + 6.342056932966022, + 6.191460055096417, + 6.048209366391184, + 5.91230486685032, + 5.783746556473828, + 5.662534435261707, + 5.548668503213957, + 5.4421487603305785, + 5.34297520661157, + 5.251147842056932, + 5.166666666666666, + 5.08953168044077, + 5.019742883379246, + 4.957300275482092, + 4.902203856749311, + 4.854453627180899, + 4.814049586776859, + 4.780991735537189, + 4.755280073461891, + 4.736914600550963, + 4.725895316804407, + 4.722222222222221, + 4.725895316804407, + 4.736914600550963, + 4.755280073461891, + 4.780991735537189, + 4.814049586776859, + 4.854453627180899, + 4.902203856749312, + 4.957300275482093, + 5.019742883379246, + 5.089531680440771, + 5.166666666666666, + 5.251147842056932, + 5.34297520661157, + 5.4421487603305785, + 5.548668503213957, + 5.662534435261707, + 5.783746556473829, + 5.91230486685032, + 6.048209366391183, + 6.191460055096417, + 6.342056932966022, + 6.5, + 6.6652892561983474, + 6.837924701561066, + 7.017906336088155, + 7.205234159779614, + 7.399908172635445, + 7.601928374655648, + 7.81129476584022, + 8.028007346189163, + 8.25206611570248, + 8.483471074380164, + 8.722222222222221 + ], + [ + 20.582644628099175, + 20.101469237832873, + 19.627640036730945, + 19.16115702479339, + 18.702020202020204, + 18.250229568411385, + 17.805785123966942, + 17.36868686868687, + 16.938934802571165, + 16.516528925619834, + 16.101469237832873, + 15.693755739210282, + 15.293388429752063, + 14.900367309458217, + 14.51469237832874, + 14.136363636363635, + 13.7653810835629, + 13.401744719926537, + 13.045454545454545, + 12.696510560146923, + 12.354912764003672, + 12.020661157024794, + 11.693755739210282, + 11.374196510560147, + 11.06198347107438, + 10.757116620752985, + 10.459595959595958, + 10.169421487603305, + 9.886593204775021, + 9.61111111111111, + 9.34297520661157, + 9.082185491276398, + 8.8287419651056, + 8.582644628099173, + 8.343893480257115, + 8.11248852157943, + 7.8884297520661155, + 7.67171717171717, + 7.4623507805325975, + 7.260330578512395, + 7.065656565656565, + 6.878328741965104, + 6.698347107438016, + 6.525711662075298, + 6.36042240587695, + 6.2024793388429735, + 6.051882460973369, + 5.908631772268135, + 5.772727272727272, + 5.644168962350779, + 5.522956841138658, + 5.409090909090908, + 5.30257116620753, + 5.203397612488521, + 5.111570247933884, + 5.0270890725436175, + 4.949954086317722, + 4.8801652892561975, + 4.817722681359044, + 4.762626262626262, + 4.71487603305785, + 4.67447199265381, + 4.64141414141414, + 4.615702479338842, + 4.597337006427915, + 4.5863177226813585, + 4.582644628099173, + 4.5863177226813585, + 4.597337006427915, + 4.615702479338842, + 4.64141414141414, + 4.67447199265381, + 4.71487603305785, + 4.762626262626263, + 4.817722681359045, + 4.8801652892561975, + 4.949954086317723, + 5.0270890725436175, + 5.111570247933884, + 5.203397612488521, + 5.30257116620753, + 5.409090909090908, + 5.522956841138658, + 5.64416896235078, + 5.772727272727272, + 5.9086317722681345, + 6.051882460973369, + 6.2024793388429735, + 6.360422405876953, + 6.525711662075299, + 6.698347107438018, + 6.878328741965106, + 7.065656565656566, + 7.260330578512397, + 7.462350780532599, + 7.671717171717173, + 7.888429752066116, + 8.112488521579431, + 8.343893480257115, + 8.582644628099173 + ], + [ + 20.44674012855831, + 19.96556473829201, + 19.491735537190085, + 19.025252525252526, + 18.56611570247934, + 18.11432506887052, + 17.669880624426078, + 17.232782369146005, + 16.803030303030305, + 16.38062442607897, + 15.965564738292013, + 15.557851239669418, + 15.1574839302112, + 14.764462809917354, + 14.378787878787877, + 14.000459136822773, + 13.629476584022038, + 13.265840220385675, + 12.909550045913683, + 12.56060606060606, + 12.21900826446281, + 11.88475665748393, + 11.557851239669422, + 11.238292011019283, + 10.926078971533517, + 10.621212121212121, + 10.323691460055096, + 10.033516988062441, + 9.75068870523416, + 9.475206611570247, + 9.207070707070706, + 8.946280991735536, + 8.692837465564738, + 8.44674012855831, + 8.207988980716253, + 7.976584022038567, + 7.752525252525253, + 7.5358126721763075, + 7.326446280991735, + 7.124426078971533, + 6.929752066115702, + 6.742424242424242, + 6.562442607897153, + 6.389807162534435, + 6.224517906336087, + 6.0665748393021115, + 5.915977961432506, + 5.772727272727272, + 5.63682277318641, + 5.508264462809917, + 5.387052341597796, + 5.273186409550046, + 5.166666666666666, + 5.067493112947657, + 4.97566574839302, + 4.891184573002754, + 4.814049586776859, + 4.744260789715335, + 4.681818181818182, + 4.626721763085399, + 4.578971533516987, + 4.5385674931129465, + 4.505509641873278, + 4.479797979797979, + 4.461432506887052, + 4.450413223140496, + 4.44674012855831, + 4.450413223140496, + 4.461432506887052, + 4.479797979797979, + 4.505509641873278, + 4.5385674931129465, + 4.578971533516987, + 4.626721763085399, + 4.681818181818182, + 4.7442607897153355, + 4.814049586776859, + 4.8911845730027546, + 4.975665748393022, + 5.067493112947658, + 5.166666666666666, + 5.273186409550046, + 5.387052341597796, + 5.508264462809917, + 5.636822773186409, + 5.772727272727272, + 5.915977961432506, + 6.066574839302111, + 6.224517906336089, + 6.389807162534435, + 6.562442607897154, + 6.742424242424242, + 6.929752066115704, + 7.124426078971535, + 7.3264462809917354, + 7.535812672176309, + 7.752525252525253, + 7.976584022038569, + 8.207988980716252, + 8.44674012855831 + ], + [ + 20.31450872359963, + 19.833333333333332, + 19.359504132231407, + 18.89302112029385, + 18.433884297520663, + 17.982093663911844, + 17.5376492194674, + 17.100550964187327, + 16.670798898071624, + 16.248393021120293, + 15.833333333333332, + 15.42561983471074, + 15.025252525252522, + 14.632231404958675, + 14.2465564738292, + 13.868227731864094, + 13.497245179063361, + 13.133608815426996, + 12.777318640955006, + 12.428374655647382, + 12.086776859504132, + 11.752525252525253, + 11.425619834710742, + 11.106060606060606, + 10.79384756657484, + 10.488980716253444, + 10.191460055096417, + 9.901285583103764, + 9.618457300275482, + 9.34297520661157, + 9.074839302112029, + 8.814049586776859, + 8.560606060606059, + 8.314508723599632, + 8.075757575757574, + 7.84435261707989, + 7.620293847566575, + 7.403581267217629, + 7.194214876033056, + 6.992194674012855, + 6.797520661157025, + 6.610192837465564, + 6.430211202938475, + 6.257575757575758, + 6.092286501377409, + 5.934343434343433, + 5.783746556473828, + 5.640495867768594, + 5.504591368227731, + 5.376033057851239, + 5.254820936639118, + 5.140955004591368, + 5.034435261707989, + 4.93526170798898, + 4.8434343434343425, + 4.758953168044076, + 4.681818181818182, + 4.6120293847566565, + 4.5495867768595035, + 4.494490358126722, + 4.44674012855831, + 4.406336088154269, + 4.3732782369146, + 4.347566574839302, + 4.3292011019283745, + 4.3181818181818175, + 4.314508723599632, + 4.3181818181818175, + 4.3292011019283745, + 4.347566574839302, + 4.3732782369146, + 4.406336088154269, + 4.44674012855831, + 4.494490358126722, + 4.549586776859504, + 4.612029384756657, + 4.681818181818182, + 4.758953168044076, + 4.843434343434343, + 4.93526170798898, + 5.034435261707989, + 5.140955004591368, + 5.254820936639118, + 5.37603305785124, + 5.5045913682277305, + 5.640495867768594, + 5.783746556473828, + 5.9343434343434325, + 6.092286501377412, + 6.257575757575758, + 6.430211202938477, + 6.610192837465565, + 6.797520661157025, + 6.992194674012856, + 7.194214876033058, + 7.403581267217632, + 7.620293847566575, + 7.84435261707989, + 8.075757575757574, + 8.314508723599632 + ], + [ + 20.18595041322314, + 19.70477502295684, + 19.230945821854913, + 18.764462809917354, + 18.305325987144172, + 17.853535353535353, + 17.40909090909091, + 16.971992653810837, + 16.542240587695133, + 16.119834710743802, + 15.704775022956841, + 15.29706152433425, + 14.896694214876032, + 14.503673094582183, + 14.117998163452707, + 13.739669421487601, + 13.368686868686869, + 13.005050505050505, + 12.648760330578513, + 12.29981634527089, + 11.95821854912764, + 11.62396694214876, + 11.29706152433425, + 10.977502295684113, + 10.665289256198346, + 10.36042240587695, + 10.062901744719927, + 9.772727272727272, + 9.48989898989899, + 9.214416896235077, + 8.946280991735536, + 8.685491276400366, + 8.432047750229568, + 8.18595041322314, + 7.947199265381084, + 7.715794306703398, + 7.491735537190083, + 7.275022956841138, + 7.065656565656565, + 6.863636363636363, + 6.668962350780532, + 6.4816345270890725, + 6.301652892561983, + 6.129017447199265, + 5.963728191000917, + 5.805785123966942, + 5.655188246097336, + 5.511937557392102, + 5.37603305785124, + 5.247474747474747, + 5.126262626262626, + 5.0123966942148765, + 4.905876951331496, + 4.8067033976124875, + 4.71487603305785, + 4.630394857667584, + 4.553259871441689, + 4.483471074380165, + 4.421028466483012, + 4.3659320477502295, + 4.3181818181818175, + 4.277777777777777, + 4.244719926538108, + 4.2190082644628095, + 4.200642791551882, + 4.189623507805326, + 4.18595041322314, + 4.189623507805326, + 4.200642791551882, + 4.2190082644628095, + 4.244719926538108, + 4.277777777777777, + 4.3181818181818175, + 4.3659320477502295, + 4.421028466483012, + 4.483471074380166, + 4.553259871441689, + 4.630394857667585, + 4.714876033057852, + 4.806703397612488, + 4.905876951331496, + 5.0123966942148765, + 5.126262626262626, + 5.247474747474747, + 5.376033057851239, + 5.511937557392102, + 5.655188246097336, + 5.805785123966941, + 5.96372819100092, + 6.129017447199266, + 6.301652892561986, + 6.481634527089074, + 6.668962350780532, + 6.863636363636363, + 7.0656565656565675, + 7.2750229568411395, + 7.491735537190083, + 7.715794306703398, + 7.947199265381084, + 8.18595041322314 + ], + [ + 20.06106519742883, + 19.579889807162534, + 19.10606060606061, + 18.63957759412305, + 18.180440771349865, + 17.728650137741045, + 17.284205693296602, + 16.84710743801653, + 16.417355371900825, + 15.994949494949495, + 15.579889807162534, + 15.172176308539942, + 14.771808999081724, + 14.378787878787877, + 13.993112947658402, + 13.614784205693296, + 13.243801652892563, + 12.880165289256198, + 12.523875114784207, + 12.174931129476583, + 11.833333333333334, + 11.499081726354454, + 11.172176308539944, + 10.852617079889807, + 10.540404040404042, + 10.235537190082646, + 9.938016528925619, + 9.647842056932966, + 9.365013774104684, + 9.089531680440771, + 8.82139577594123, + 8.56060606060606, + 8.30716253443526, + 8.061065197428833, + 7.822314049586777, + 7.590909090909092, + 7.366850321395777, + 7.150137741046831, + 6.940771349862258, + 6.7387511478420565, + 6.544077134986226, + 6.356749311294766, + 6.1767676767676765, + 6.004132231404959, + 5.83884297520661, + 5.680899908172635, + 5.530303030303029, + 5.387052341597796, + 5.251147842056933, + 5.122589531680441, + 5.0013774104683195, + 4.88751147842057, + 4.7809917355371905, + 4.681818181818182, + 4.589990817263544, + 4.505509641873278, + 4.428374655647383, + 4.358585858585858, + 4.296143250688705, + 4.241046831955924, + 4.193296602387512, + 4.152892561983471, + 4.119834710743802, + 4.094123048668504, + 4.075757575757576, + 4.064738292011019, + 4.061065197428833, + 4.064738292011019, + 4.075757575757576, + 4.094123048668504, + 4.119834710743802, + 4.152892561983471, + 4.193296602387512, + 4.241046831955924, + 4.296143250688706, + 4.358585858585859, + 4.428374655647383, + 4.505509641873278, + 4.589990817263545, + 4.681818181818182, + 4.7809917355371905, + 4.88751147842057, + 5.0013774104683195, + 5.1225895316804415, + 5.251147842056932, + 5.387052341597796, + 5.530303030303029, + 5.680899908172634, + 5.838842975206614, + 6.004132231404959, + 6.176767676767678, + 6.356749311294767, + 6.544077134986226, + 6.738751147842057, + 6.94077134986226, + 7.150137741046834, + 7.366850321395777, + 7.590909090909092, + 7.822314049586776, + 8.061065197428833 + ], + [ + 19.939853076216714, + 19.458677685950413, + 18.984848484848484, + 18.51836547291093, + 18.059228650137744, + 17.607438016528924, + 17.16299357208448, + 16.725895316804408, + 16.296143250688704, + 15.873737373737374, + 15.458677685950413, + 15.050964187327821, + 14.650596877869603, + 14.257575757575756, + 13.871900826446279, + 13.493572084481174, + 13.12258953168044, + 12.758953168044076, + 12.402662993572086, + 12.053719008264462, + 11.712121212121211, + 11.377869605142333, + 11.050964187327823, + 10.731404958677686, + 10.419191919191919, + 10.114325068870524, + 9.816804407713498, + 9.526629935720845, + 9.24380165289256, + 8.96831955922865, + 8.70018365472911, + 8.43939393939394, + 8.18595041322314, + 7.939853076216712, + 7.701101928374656, + 7.469696969696971, + 7.245638200183655, + 7.02892561983471, + 6.819559228650137, + 6.617539026629935, + 6.422865013774104, + 6.235537190082645, + 6.055555555555555, + 5.882920110192838, + 5.717630853994489, + 5.559687786960513, + 5.409090909090908, + 5.265840220385675, + 5.129935720844811, + 5.0013774104683195, + 4.880165289256198, + 4.766299357208448, + 4.659779614325069, + 4.5606060606060606, + 4.468778696051423, + 4.384297520661157, + 4.307162534435262, + 4.237373737373737, + 4.174931129476584, + 4.119834710743802, + 4.07208448117539, + 4.03168044077135, + 3.9986225895316805, + 3.9729109274563816, + 3.9545454545454546, + 3.943526170798898, + 3.9398530762167123, + 3.943526170798898, + 3.9545454545454546, + 3.9729109274563816, + 3.9986225895316805, + 4.03168044077135, + 4.07208448117539, + 4.1198347107438025, + 4.174931129476584, + 4.237373737373738, + 4.307162534435262, + 4.384297520661157, + 4.468778696051424, + 4.5606060606060606, + 4.659779614325069, + 4.766299357208449, + 4.880165289256198, + 5.0013774104683195, + 5.129935720844811, + 5.265840220385674, + 5.409090909090908, + 5.559687786960513, + 5.717630853994492, + 5.882920110192838, + 6.055555555555557, + 6.2355371900826455, + 6.422865013774105, + 6.617539026629936, + 6.819559228650139, + 7.0289256198347125, + 7.245638200183656, + 7.469696969696971, + 7.701101928374655, + 7.939853076216712 + ], + [ + 19.82231404958678, + 19.341138659320478, + 18.86730945821855, + 18.400826446280995, + 17.941689623507806, + 17.48989898989899, + 17.045454545454547, + 16.608356290174473, + 16.17860422405877, + 15.75619834710744, + 15.341138659320478, + 14.933425160697887, + 14.533057851239668, + 14.14003673094582, + 13.754361799816344, + 13.376033057851238, + 13.005050505050505, + 12.641414141414142, + 12.28512396694215, + 11.936179981634528, + 11.594582185491277, + 11.260330578512397, + 10.933425160697887, + 10.61386593204775, + 10.301652892561982, + 9.996786042240588, + 9.699265381083563, + 9.409090909090908, + 9.126262626262626, + 8.850780532598716, + 8.582644628099173, + 8.321854912764003, + 8.068411386593205, + 7.822314049586777, + 7.58356290174472, + 7.352157943067034, + 7.12809917355372, + 6.911386593204774, + 6.7020202020202015, + 6.5, + 6.305325987144169, + 6.117998163452709, + 5.938016528925621, + 5.765381083562902, + 5.600091827364555, + 5.4421487603305785, + 5.291551882460973, + 5.1483011937557395, + 5.0123966942148765, + 4.883838383838384, + 4.762626262626263, + 4.648760330578513, + 4.542240587695134, + 4.443067033976124, + 4.351239669421488, + 4.2667584940312215, + 4.189623507805326, + 4.1198347107438025, + 4.057392102846649, + 4.002295684113866, + 3.9545454545454546, + 3.9141414141414144, + 3.881083562901745, + 3.855371900826446, + 3.837006427915519, + 3.8259871441689626, + 3.822314049586777, + 3.8259871441689626, + 3.837006427915519, + 3.855371900826446, + 3.881083562901745, + 3.9141414141414144, + 3.9545454545454546, + 4.002295684113867, + 4.057392102846649, + 4.1198347107438025, + 4.189623507805327, + 4.2667584940312215, + 4.3512396694214885, + 4.443067033976125, + 4.542240587695134, + 4.648760330578513, + 4.762626262626263, + 4.883838383838384, + 5.012396694214876, + 5.148301193755739, + 5.291551882460973, + 5.442148760330578, + 5.600091827364556, + 5.765381083562903, + 5.938016528925622, + 6.117998163452711, + 6.305325987144171, + 6.500000000000002, + 6.702020202020204, + 6.911386593204776, + 7.12809917355372, + 7.352157943067036, + 7.58356290174472, + 7.822314049586778 + ], + [ + 19.708448117539028, + 19.227272727272727, + 18.7534435261708, + 18.286960514233243, + 17.827823691460058, + 17.376033057851238, + 16.931588613406795, + 16.494490358126722, + 16.064738292011018, + 15.642332415059688, + 15.227272727272727, + 14.819559228650135, + 14.419191919191917, + 14.02617079889807, + 13.640495867768593, + 13.262167125803488, + 12.891184573002754, + 12.52754820936639, + 12.1712580348944, + 11.822314049586776, + 11.480716253443525, + 11.146464646464647, + 10.819559228650137, + 10.5, + 10.187786960514233, + 9.882920110192838, + 9.585399449035812, + 9.295224977043159, + 9.012396694214875, + 8.736914600550964, + 8.468778696051423, + 8.207988980716253, + 7.954545454545454, + 7.708448117539026, + 7.46969696969697, + 7.2382920110192845, + 7.014233241505969, + 6.797520661157024, + 6.588154269972451, + 6.386134067952249, + 6.191460055096418, + 6.0041322314049586, + 5.824150596877869, + 5.651515151515151, + 5.486225895316803, + 5.328282828282827, + 5.177685950413222, + 5.034435261707989, + 4.898530762167125, + 4.7699724517906334, + 4.648760330578512, + 4.534894398530762, + 4.428374655647383, + 4.3292011019283745, + 4.237373737373737, + 4.152892561983471, + 4.075757575757575, + 4.005968778696051, + 3.943526170798898, + 3.8884297520661155, + 3.840679522497704, + 3.8002754820936637, + 3.7672176308539944, + 3.7415059687786956, + 3.7231404958677685, + 3.712121212121212, + 3.7084481175390263, + 3.712121212121212, + 3.7231404958677685, + 3.7415059687786956, + 3.7672176308539944, + 3.8002754820936637, + 3.840679522497704, + 3.8884297520661164, + 3.943526170798898, + 4.005968778696052, + 4.075757575757576, + 4.152892561983471, + 4.237373737373738, + 4.3292011019283745, + 4.428374655647383, + 4.534894398530763, + 4.648760330578512, + 4.7699724517906334, + 4.898530762167125, + 5.034435261707988, + 5.177685950413222, + 5.328282828282827, + 5.486225895316806, + 5.651515151515152, + 5.824150596877871, + 6.004132231404959, + 6.191460055096419, + 6.38613406795225, + 6.588154269972453, + 6.7975206611570265, + 7.01423324150597, + 7.2382920110192845, + 7.469696969696969, + 7.708448117539026 + ], + [ + 19.59825528007346, + 19.11707988980716, + 18.643250688705237, + 18.17676767676768, + 17.717630853994493, + 17.265840220385673, + 16.82139577594123, + 16.384297520661157, + 15.954545454545453, + 15.532139577594123, + 15.117079889807162, + 14.70936639118457, + 14.308999081726352, + 13.915977961432505, + 13.53030303030303, + 13.151974288337923, + 12.78099173553719, + 12.417355371900825, + 12.061065197428835, + 11.712121212121211, + 11.370523415977962, + 11.036271808999082, + 10.709366391184572, + 10.389807162534435, + 10.077594123048668, + 9.772727272727273, + 9.475206611570249, + 9.185032139577594, + 8.902203856749312, + 8.6267217630854, + 8.358585858585858, + 8.097796143250688, + 7.844352617079889, + 7.598255280073461, + 7.359504132231405, + 7.12809917355372, + 6.904040404040405, + 6.687327823691459, + 6.477961432506886, + 6.275941230486684, + 6.081267217630854, + 5.893939393939394, + 5.713957759412304, + 5.541322314049587, + 5.376033057851239, + 5.218089990817263, + 5.067493112947657, + 4.924242424242424, + 4.788337924701561, + 4.6597796143250685, + 4.538567493112947, + 4.424701561065198, + 4.318181818181818, + 4.2190082644628095, + 4.127180899908172, + 4.042699724517906, + 3.9655647382920107, + 3.8957759412304864, + 3.833333333333333, + 3.778236914600551, + 3.7304866850321394, + 3.6900826446280988, + 3.6570247933884295, + 3.631313131313131, + 3.6129476584022036, + 3.601928374655647, + 3.5982552800734617, + 3.601928374655647, + 3.612947658402204, + 3.631313131313131, + 3.6570247933884295, + 3.6900826446280988, + 3.7304866850321394, + 3.7782369146005514, + 3.8333333333333335, + 3.895775941230487, + 3.965564738292011, + 4.042699724517906, + 4.127180899908173, + 4.2190082644628095, + 4.318181818181818, + 4.424701561065198, + 4.538567493112947, + 4.659779614325069, + 4.78833792470156, + 4.924242424242424, + 5.067493112947657, + 5.218089990817262, + 5.376033057851242, + 5.541322314049587, + 5.713957759412306, + 5.8939393939393945, + 6.081267217630854, + 6.275941230486685, + 6.477961432506888, + 6.6873278236914615, + 6.904040404040405, + 7.12809917355372, + 7.359504132231404, + 7.598255280073461 + ], + [ + 19.49173553719008, + 19.010560146923783, + 18.53673094582186, + 18.070247933884296, + 17.611111111111114, + 17.159320477502295, + 16.714876033057852, + 16.27777777777778, + 15.848025711662075, + 15.425619834710744, + 15.010560146923783, + 14.602846648301192, + 14.202479338842974, + 13.809458218549127, + 13.42378328741965, + 13.045454545454545, + 12.67447199265381, + 12.310835629017447, + 11.954545454545455, + 11.605601469237833, + 11.264003673094582, + 10.929752066115702, + 10.602846648301192, + 10.283287419651057, + 9.97107438016529, + 9.666207529843893, + 9.368686868686869, + 9.078512396694215, + 8.795684113865931, + 8.52020202020202, + 8.25206611570248, + 7.991276400367309, + 7.73783287419651, + 7.491735537190083, + 7.2529843893480255, + 7.02157943067034, + 6.797520661157026, + 6.5808080808080796, + 6.3714416896235075, + 6.169421487603305, + 5.974747474747474, + 5.787419651056014, + 5.607438016528926, + 5.434802571166208, + 5.26951331496786, + 5.111570247933884, + 4.960973370064279, + 4.817722681359045, + 4.681818181818182, + 4.553259871441689, + 4.432047750229568, + 4.318181818181818, + 4.211662075298439, + 4.11248852157943, + 4.020661157024794, + 3.9361799816345266, + 3.859044995408632, + 3.7892561983471076, + 3.726813590449954, + 3.6717171717171717, + 3.62396694214876, + 3.58356290174472, + 3.55050505050505, + 3.524793388429752, + 3.5064279155188247, + 3.495408631772268, + 3.491735537190083, + 3.495408631772268, + 3.5064279155188247, + 3.524793388429752, + 3.55050505050505, + 3.5835629017447195, + 3.62396694214876, + 3.671717171717172, + 3.7268135904499546, + 3.7892561983471076, + 3.859044995408632, + 3.9361799816345275, + 4.020661157024794, + 4.112488521579431, + 4.211662075298439, + 4.318181818181818, + 4.432047750229568, + 4.55325987144169, + 4.681818181818182, + 4.817722681359045, + 4.960973370064279, + 5.111570247933884, + 5.269513314967862, + 5.434802571166209, + 5.607438016528928, + 5.787419651056016, + 5.974747474747476, + 6.169421487603307, + 6.371441689623509, + 6.580808080808081, + 6.797520661157025, + 7.021579430670341, + 7.2529843893480255, + 7.491735537190083 + ], + [ + 19.38888888888889, + 18.90771349862259, + 18.433884297520663, + 17.967401285583104, + 17.50826446280992, + 17.0564738292011, + 16.612029384756656, + 16.174931129476583, + 15.745179063360881, + 15.322773186409549, + 14.90771349862259, + 14.499999999999996, + 14.099632690541778, + 13.706611570247933, + 13.320936639118456, + 12.942607897153351, + 12.571625344352617, + 12.207988980716253, + 11.851698806244261, + 11.502754820936639, + 11.161157024793388, + 10.826905417814508, + 10.5, + 10.180440771349861, + 9.868227731864096, + 9.5633608815427, + 9.265840220385675, + 8.97566574839302, + 8.692837465564738, + 8.417355371900825, + 8.149219467401284, + 7.888429752066115, + 7.634986225895316, + 7.388888888888888, + 7.150137741046832, + 6.918732782369146, + 6.694674012855831, + 6.477961432506886, + 6.268595041322313, + 6.0665748393021115, + 5.87190082644628, + 5.684573002754821, + 5.504591368227731, + 5.3319559228650135, + 5.166666666666666, + 5.00872359963269, + 4.858126721763084, + 4.714876033057851, + 4.578971533516988, + 4.450413223140496, + 4.3292011019283745, + 4.215335169880625, + 4.1088154269972454, + 4.009641873278236, + 3.917814508723599, + 3.833333333333333, + 3.7561983471074374, + 3.686409550045913, + 3.62396694214876, + 3.5688705234159777, + 3.521120293847566, + 3.480716253443526, + 3.4476584022038566, + 3.4219467401285577, + 3.4035812672176307, + 3.392561983471074, + 3.3888888888888884, + 3.392561983471074, + 3.4035812672176307, + 3.4219467401285577, + 3.4476584022038566, + 3.480716253443526, + 3.521120293847566, + 3.5688705234159785, + 3.62396694214876, + 3.686409550045914, + 3.7561983471074383, + 3.833333333333333, + 3.9178145087236, + 4.009641873278237, + 4.1088154269972454, + 4.215335169880625, + 4.3292011019283745, + 4.450413223140496, + 4.578971533516987, + 4.71487603305785, + 4.858126721763084, + 5.008723599632689, + 5.166666666666668, + 5.331955922865014, + 5.504591368227733, + 5.684573002754822, + 5.871900826446282, + 6.066574839302113, + 6.268595041322316, + 6.477961432506888, + 6.694674012855831, + 6.918732782369148, + 7.150137741046832, + 7.388888888888889 + ], + [ + 19.28971533516988, + 18.80853994490358, + 18.334710743801654, + 17.868227731864096, + 17.40909090909091, + 16.957300275482094, + 16.512855831037648, + 16.075757575757574, + 15.646005509641874, + 15.223599632690542, + 14.808539944903583, + 14.40082644628099, + 14.000459136822771, + 13.607438016528924, + 13.221763085399449, + 12.843434343434343, + 12.47245179063361, + 12.108815426997245, + 11.752525252525253, + 11.40358126721763, + 11.06198347107438, + 10.727731864095501, + 10.400826446280991, + 10.081267217630852, + 9.769054178145087, + 9.46418732782369, + 9.166666666666668, + 8.876492194674013, + 8.593663911845729, + 8.318181818181818, + 8.050045913682276, + 7.789256198347107, + 7.535812672176308, + 7.2897153351698805, + 7.050964187327824, + 6.819559228650138, + 6.595500459136823, + 6.378787878787878, + 6.169421487603305, + 5.967401285583103, + 5.7727272727272725, + 5.585399449035813, + 5.4054178145087235, + 5.232782369146006, + 5.067493112947657, + 4.909550045913681, + 4.758953168044076, + 4.615702479338843, + 4.479797979797979, + 4.351239669421488, + 4.2300275482093666, + 4.116161616161616, + 4.0096418732782375, + 3.910468319559228, + 3.818640955004591, + 3.7341597796143247, + 3.6570247933884295, + 3.587235996326905, + 3.524793388429752, + 3.4696969696969697, + 3.4219467401285577, + 3.3815426997245175, + 3.348484848484848, + 3.3227731864095498, + 3.3044077134986223, + 3.293388429752066, + 3.2897153351698805, + 3.293388429752066, + 3.3044077134986223, + 3.3227731864095498, + 3.348484848484848, + 3.3815426997245175, + 3.4219467401285577, + 3.46969696969697, + 3.524793388429752, + 3.5872359963269056, + 3.65702479338843, + 3.734159779614325, + 3.818640955004591, + 3.9104683195592287, + 4.0096418732782375, + 4.116161616161616, + 4.230027548209366, + 4.351239669421488, + 4.479797979797979, + 4.615702479338842, + 4.758953168044076, + 4.909550045913681, + 5.06749311294766, + 5.2327823691460065, + 5.405417814508725, + 5.585399449035814, + 5.772727272727273, + 5.9674012855831045, + 6.169421487603307, + 6.378787878787879, + 6.595500459136822, + 6.819559228650139, + 7.050964187327823, + 7.2897153351698805 + ], + [ + 19.194214876033058, + 18.713039485766757, + 18.239210284664832, + 17.772727272727273, + 17.313590449954088, + 16.86179981634527, + 16.417355371900825, + 15.980257116620752, + 15.550505050505052, + 15.128099173553718, + 14.71303948576676, + 14.305325987144167, + 13.904958677685949, + 13.511937557392102, + 13.126262626262625, + 12.74793388429752, + 12.376951331496786, + 12.013314967860422, + 11.65702479338843, + 11.308080808080808, + 10.966483011937557, + 10.632231404958677, + 10.305325987144169, + 9.98576675849403, + 9.673553719008265, + 9.368686868686869, + 9.071166207529844, + 8.780991735537189, + 8.498163452708907, + 8.222681359044996, + 7.954545454545453, + 7.693755739210284, + 7.440312213039485, + 7.194214876033058, + 6.955463728191001, + 6.724058769513315, + 6.5, + 6.283287419651055, + 6.073921028466483, + 5.87190082644628, + 5.677226813590449, + 5.48989898989899, + 5.309917355371901, + 5.137281910009182, + 4.971992653810835, + 4.814049586776859, + 4.663452708907254, + 4.52020202020202, + 4.384297520661157, + 4.2557392102846645, + 4.134527089072543, + 4.020661157024794, + 3.9141414141414144, + 3.8149678604224055, + 3.723140495867768, + 3.638659320477502, + 3.5615243342516067, + 3.4917355371900825, + 3.429292929292929, + 3.374196510560147, + 3.3264462809917354, + 3.286042240587695, + 3.2529843893480255, + 3.227272727272727, + 3.2089072543617996, + 3.197887970615243, + 3.1942148760330578, + 3.197887970615243, + 3.2089072543618, + 3.227272727272727, + 3.2529843893480255, + 3.286042240587695, + 3.3264462809917354, + 3.3741965105601475, + 3.4292929292929295, + 3.491735537190083, + 3.561524334251607, + 3.6386593204775024, + 3.723140495867769, + 3.8149678604224064, + 3.9141414141414144, + 4.020661157024794, + 4.134527089072543, + 4.2557392102846645, + 4.384297520661157, + 4.520202020202019, + 4.663452708907254, + 4.814049586776859, + 4.971992653810837, + 5.137281910009184, + 5.309917355371903, + 5.489898989898991, + 5.677226813590451, + 5.871900826446282, + 6.073921028466485, + 6.283287419651057, + 6.5, + 6.7240587695133165, + 6.955463728191001, + 7.194214876033058 + ], + [ + 19.10238751147842, + 18.62121212121212, + 18.147382920110196, + 17.680899908172634, + 17.221763085399452, + 16.769972451790633, + 16.32552800734619, + 15.888429752066116, + 15.458677685950413, + 15.036271808999082, + 14.621212121212121, + 14.21349862258953, + 13.813131313131311, + 13.420110192837464, + 13.034435261707987, + 12.656106519742883, + 12.285123966942148, + 11.921487603305785, + 11.565197428833793, + 11.21625344352617, + 10.87465564738292, + 10.54040404040404, + 10.21349862258953, + 9.893939393939394, + 9.581726354453627, + 9.276859504132231, + 8.979338842975206, + 8.689164370982553, + 8.40633608815427, + 8.130853994490359, + 7.862718089990817, + 7.601928374655647, + 7.348484848484848, + 7.102387511478421, + 6.863636363636363, + 6.632231404958678, + 6.408172635445363, + 6.191460055096417, + 5.982093663911845, + 5.780073461891643, + 5.585399449035812, + 5.398071625344352, + 5.218089990817264, + 5.045454545454546, + 4.8801652892561975, + 4.722222222222221, + 4.571625344352617, + 4.428374655647382, + 4.2924701561065195, + 4.163911845730027, + 4.042699724517906, + 3.928833792470156, + 3.822314049586777, + 3.723140495867768, + 3.631313131313131, + 3.5468319559228645, + 3.4696969696969697, + 3.3999081726354454, + 3.337465564738292, + 3.2823691460055096, + 3.234618916437098, + 3.1942148760330578, + 3.161157024793388, + 3.13544536271809, + 3.1170798898071626, + 3.106060606060606, + 3.1023875114784207, + 3.106060606060606, + 3.1170798898071626, + 3.13544536271809, + 3.161157024793388, + 3.1942148760330573, + 3.234618916437098, + 3.28236914600551, + 3.3374655647382925, + 3.3999081726354454, + 3.4696969696969697, + 3.5468319559228654, + 3.6313131313131315, + 3.723140495867769, + 3.822314049586777, + 3.928833792470156, + 4.042699724517906, + 4.163911845730028, + 4.2924701561065195, + 4.428374655647382, + 4.571625344352617, + 4.722222222222221, + 4.8801652892562, + 5.045454545454547, + 5.2180899908172655, + 5.398071625344354, + 5.585399449035814, + 5.780073461891645, + 5.982093663911847, + 6.191460055096419, + 6.4081726354453625, + 6.632231404958679, + 6.863636363636363, + 7.102387511478421 + ], + [ + 19.01423324150597, + 18.53305785123967, + 18.059228650137744, + 17.592745638200185, + 17.133608815427, + 16.68181818181818, + 16.237373737373737, + 15.800275482093664, + 15.370523415977962, + 14.94811753902663, + 14.53305785123967, + 14.125344352617077, + 13.724977043158859, + 13.331955922865014, + 12.946280991735536, + 12.567952249770432, + 12.196969696969697, + 11.833333333333334, + 11.477043158861342, + 11.12809917355372, + 10.786501377410469, + 10.452249770431589, + 10.125344352617079, + 9.805785123966942, + 9.493572084481176, + 9.18870523415978, + 8.891184573002755, + 8.6010101010101, + 8.318181818181818, + 8.042699724517906, + 7.774563820018365, + 7.513774104683195, + 7.260330578512397, + 7.014233241505969, + 6.775482093663912, + 6.544077134986226, + 6.320018365472912, + 6.1033057851239665, + 5.893939393939394, + 5.691919191919192, + 5.497245179063361, + 5.309917355371901, + 5.129935720844812, + 4.957300275482094, + 4.792011019283746, + 4.6340679522497705, + 4.483471074380165, + 4.340220385674931, + 4.204315886134068, + 4.075757575757576, + 3.954545454545455, + 3.8406795224977044, + 3.7341597796143255, + 3.6349862258953163, + 3.5431588613406797, + 3.458677685950413, + 3.381542699724518, + 3.3117539026629936, + 3.2493112947658407, + 3.194214876033058, + 3.146464646464646, + 3.106060606060606, + 3.0730027548209367, + 3.0472910927456383, + 3.0289256198347108, + 3.0179063360881546, + 3.014233241505969, + 3.0179063360881546, + 3.0289256198347108, + 3.0472910927456383, + 3.0730027548209367, + 3.106060606060606, + 3.146464646464646, + 3.1942148760330586, + 3.2493112947658407, + 3.311753902662994, + 3.3815426997245184, + 3.4586776859504136, + 3.54315886134068, + 3.634986225895317, + 3.734159779614325, + 3.8406795224977053, + 3.954545454545455, + 4.075757575757576, + 4.204315886134068, + 4.340220385674931, + 4.483471074380165, + 4.63406795224977, + 4.792011019283748, + 4.957300275482095, + 5.129935720844814, + 5.309917355371902, + 5.497245179063362, + 5.691919191919193, + 5.8939393939393945, + 6.103305785123968, + 6.320018365472912, + 6.544077134986228, + 6.775482093663911, + 7.01423324150597 + ], + [ + 18.929752066115704, + 18.448576675849402, + 17.974747474747474, + 17.50826446280992, + 17.049127640036733, + 16.597337006427914, + 16.15289256198347, + 15.715794306703398, + 15.286042240587694, + 14.863636363636363, + 14.448576675849402, + 14.04086317722681, + 13.640495867768593, + 13.247474747474746, + 12.86179981634527, + 12.483471074380164, + 12.112488521579431, + 11.748852157943066, + 11.392561983471076, + 11.043617998163452, + 10.702020202020202, + 10.367768595041323, + 10.040863177226813, + 9.721303948576676, + 9.409090909090908, + 9.104224058769514, + 8.80670339761249, + 8.516528925619834, + 8.233700642791552, + 7.95821854912764, + 7.690082644628099, + 7.429292929292929, + 7.17584940312213, + 6.929752066115702, + 6.691000918273645, + 6.45959595959596, + 6.2355371900826455, + 6.0188246097336995, + 5.809458218549127, + 5.607438016528925, + 5.412764003673095, + 5.225436179981634, + 5.045454545454545, + 4.872819100091828, + 4.70752984389348, + 4.5495867768595035, + 4.398989898989898, + 4.2557392102846645, + 4.119834710743802, + 3.991276400367309, + 3.870064279155188, + 3.7561983471074383, + 3.649678604224059, + 3.55050505050505, + 3.4586776859504127, + 3.3741965105601466, + 3.2970615243342514, + 3.227272727272727, + 3.1648301193755737, + 3.1097337006427916, + 3.06198347107438, + 3.0215794306703394, + 2.98852157943067, + 2.9628099173553717, + 2.944444444444444, + 2.9334251606978876, + 2.9297520661157024, + 2.9334251606978876, + 2.9444444444444446, + 2.9628099173553717, + 2.98852157943067, + 3.0215794306703394, + 3.06198347107438, + 3.109733700642792, + 3.164830119375574, + 3.2272727272727275, + 3.297061524334252, + 3.374196510560147, + 3.4586776859504136, + 3.55050505050505, + 3.649678604224059, + 3.7561983471074383, + 3.870064279155188, + 3.99127640036731, + 4.119834710743801, + 4.2557392102846645, + 4.398989898989898, + 4.549586776859503, + 4.707529843893482, + 4.872819100091828, + 5.045454545454547, + 5.225436179981635, + 5.412764003673095, + 5.607438016528926, + 5.809458218549128, + 6.018824609733702, + 6.2355371900826455, + 6.45959595959596, + 6.6910009182736445, + 6.929752066115702 + ], + [ + 18.84894398530762, + 18.367768595041323, + 17.893939393939398, + 17.427456382001836, + 16.968319559228654, + 16.516528925619834, + 16.072084481175388, + 15.634986225895316, + 15.205234159779614, + 14.782828282828284, + 14.367768595041323, + 13.960055096418731, + 13.559687786960513, + 13.166666666666664, + 12.780991735537189, + 12.402662993572083, + 12.03168044077135, + 11.668044077134986, + 11.311753902662995, + 10.962809917355372, + 10.621212121212121, + 10.286960514233241, + 9.960055096418731, + 9.640495867768594, + 9.328282828282827, + 9.023415977961433, + 8.725895316804408, + 8.435720844811753, + 8.152892561983471, + 7.877410468319559, + 7.609274563820017, + 7.348484848484848, + 7.095041322314049, + 6.8489439853076215, + 6.610192837465565, + 6.378787878787879, + 6.154729109274564, + 5.938016528925619, + 5.728650137741046, + 5.526629935720845, + 5.3319559228650135, + 5.144628099173554, + 4.9646464646464645, + 4.792011019283747, + 4.626721763085399, + 4.468778696051423, + 4.3181818181818175, + 4.174931129476583, + 4.039026629935721, + 3.9104683195592287, + 3.7892561983471076, + 3.6753902662993574, + 3.568870523415978, + 3.4696969696969693, + 3.3778696051423323, + 3.293388429752066, + 3.2162534435261705, + 3.146464646464646, + 3.0840220385674932, + 3.0289256198347108, + 2.981175390266299, + 2.940771349862259, + 2.907713498622589, + 2.882001836547291, + 2.8636363636363633, + 2.852617079889807, + 2.8489439853076215, + 2.852617079889807, + 2.8636363636363638, + 2.882001836547291, + 2.907713498622589, + 2.9407713498622585, + 2.981175390266299, + 3.028925619834711, + 3.0840220385674932, + 3.1464646464646466, + 3.216253443526171, + 3.293388429752066, + 3.3778696051423327, + 3.4696969696969697, + 3.5688705234159785, + 3.675390266299358, + 3.7892561983471076, + 3.9104683195592287, + 4.03902662993572, + 4.174931129476583, + 4.3181818181818175, + 4.468778696051422, + 4.626721763085401, + 4.7920110192837475, + 4.964646464646466, + 5.144628099173555, + 5.331955922865014, + 5.5266299357208455, + 5.728650137741049, + 5.938016528925621, + 6.154729109274564, + 6.378787878787881, + 6.610192837465565, + 6.848943985307622 + ], + [ + 18.771808999081728, + 18.290633608815426, + 17.816804407713498, + 17.350321395775943, + 16.891184573002757, + 16.439393939393938, + 15.994949494949495, + 15.557851239669422, + 15.12809917355372, + 14.705693296602387, + 14.290633608815428, + 13.882920110192835, + 13.482552800734616, + 13.089531680440771, + 12.703856749311294, + 12.32552800734619, + 11.954545454545455, + 11.59090909090909, + 11.2346189164371, + 10.885674931129476, + 10.544077134986225, + 10.209825528007347, + 9.882920110192837, + 9.5633608815427, + 9.251147842056932, + 8.946280991735538, + 8.648760330578513, + 8.358585858585858, + 8.075757575757576, + 7.800275482093664, + 7.532139577594123, + 7.271349862258953, + 7.017906336088155, + 6.771808999081726, + 6.53305785123967, + 6.301652892561984, + 6.077594123048669, + 5.860881542699724, + 5.6515151515151505, + 5.449494949494949, + 5.254820936639119, + 5.067493112947658, + 4.88751147842057, + 4.714876033057852, + 4.5495867768595035, + 4.391643709825527, + 4.241046831955923, + 4.097796143250688, + 3.9618916437098255, + 3.8333333333333335, + 3.7121212121212124, + 3.598255280073462, + 3.491735537190083, + 3.392561983471074, + 3.3007346189164366, + 3.2162534435261705, + 3.1391184573002753, + 3.0693296602387514, + 3.0068870523415976, + 2.9517906336088156, + 2.904040404040404, + 2.8636363636363633, + 2.830578512396694, + 2.8048668503213956, + 2.7865013774104685, + 2.775482093663912, + 2.7718089990817263, + 2.775482093663912, + 2.7865013774104685, + 2.8048668503213956, + 2.830578512396694, + 2.8636363636363633, + 2.904040404040404, + 2.951790633608816, + 3.006887052341598, + 3.0693296602387514, + 3.1391184573002757, + 3.216253443526171, + 3.3007346189164375, + 3.3925619834710745, + 3.491735537190083, + 3.598255280073462, + 3.712121212121212, + 3.833333333333334, + 3.9618916437098255, + 4.097796143250688, + 4.241046831955923, + 4.391643709825527, + 4.549586776859506, + 4.714876033057853, + 4.8875114784205715, + 5.06749311294766, + 5.25482093663912, + 5.449494949494951, + 5.651515151515152, + 5.860881542699726, + 6.077594123048669, + 6.301652892561984, + 6.533057851239668, + 6.771808999081726 + ], + [ + 18.698347107438018, + 18.217171717171716, + 17.743342516069788, + 17.276859504132233, + 16.817722681359047, + 16.365932047750228, + 15.921487603305785, + 15.484389348025712, + 15.054637281910008, + 14.632231404958677, + 14.217171717171716, + 13.809458218549125, + 13.409090909090907, + 13.01606978879706, + 12.630394857667584, + 12.252066115702478, + 11.881083562901745, + 11.51744719926538, + 11.16115702479339, + 10.812213039485766, + 10.470615243342515, + 10.136363636363637, + 9.809458218549127, + 9.48989898989899, + 9.177685950413222, + 8.872819100091828, + 8.575298438934803, + 8.285123966942148, + 8.002295684113866, + 7.726813590449954, + 7.458677685950413, + 7.197887970615243, + 6.944444444444444, + 6.698347107438016, + 6.459595959595959, + 6.228191000918274, + 6.004132231404959, + 5.787419651056013, + 5.5780532598714405, + 5.376033057851239, + 5.181359044995409, + 4.994031221303948, + 4.814049586776859, + 4.641414141414142, + 4.4761248852157935, + 4.3181818181818175, + 4.167584940312212, + 4.024334251606978, + 3.8884297520661155, + 3.759871441689623, + 3.638659320477502, + 3.524793388429752, + 3.418273645546373, + 3.319100091827364, + 3.2272727272727266, + 3.1427915518824605, + 3.0656565656565653, + 2.995867768595041, + 2.9334251606978876, + 2.8783287419651056, + 2.830578512396694, + 2.7901744719926533, + 2.757116620752984, + 2.7314049586776856, + 2.713039485766758, + 2.7020202020202015, + 2.6983471074380163, + 2.7020202020202015, + 2.7130394857667586, + 2.7314049586776856, + 2.757116620752984, + 2.7901744719926533, + 2.830578512396694, + 2.878328741965106, + 2.933425160697888, + 2.9958677685950414, + 3.0656565656565657, + 3.142791551882461, + 3.2272727272727275, + 3.3191000918273645, + 3.418273645546373, + 3.524793388429752, + 3.638659320477502, + 3.759871441689624, + 3.8884297520661146, + 4.024334251606978, + 4.167584940312212, + 4.318181818181817, + 4.476124885215796, + 4.641414141414142, + 4.814049586776861, + 4.994031221303949, + 5.181359044995409, + 5.37603305785124, + 5.578053259871442, + 5.787419651056016, + 6.004132231404959, + 6.228191000918274, + 6.4595959595959584, + 6.698347107438016 + ], + [ + 18.62855831037649, + 18.147382920110193, + 17.673553719008268, + 17.207070707070706, + 16.747933884297524, + 16.296143250688704, + 15.851698806244261, + 15.414600550964188, + 14.984848484848484, + 14.562442607897154, + 14.147382920110193, + 13.739669421487601, + 13.339302112029383, + 12.946280991735536, + 12.560606060606059, + 12.182277318640955, + 11.81129476584022, + 11.447658402203857, + 11.091368227731865, + 10.742424242424242, + 10.400826446280991, + 10.066574839302111, + 9.739669421487601, + 9.420110192837464, + 9.107897153351699, + 8.803030303030303, + 8.505509641873278, + 8.215335169880625, + 7.932506887052341, + 7.65702479338843, + 7.3888888888888875, + 7.128099173553719, + 6.8746556473829195, + 6.6285583103764925, + 6.389807162534435, + 6.15840220385675, + 5.934343434343434, + 5.717630853994489, + 5.508264462809917, + 5.306244260789715, + 5.111570247933884, + 4.924242424242424, + 4.7442607897153355, + 4.571625344352617, + 4.406336088154269, + 4.248393021120293, + 4.097796143250688, + 3.954545454545454, + 3.818640955004591, + 3.690082644628099, + 3.568870523415978, + 3.455004591368228, + 3.3484848484848486, + 3.24931129476584, + 3.1574839302112023, + 3.073002754820936, + 2.995867768595041, + 2.926078971533517, + 2.8636363636363633, + 2.8085399449035813, + 2.7607897153351697, + 2.720385674931129, + 2.6873278236914597, + 2.6616161616161613, + 2.6432506887052343, + 2.6322314049586777, + 2.628558310376492, + 2.6322314049586777, + 2.6432506887052343, + 2.6616161616161613, + 2.6873278236914597, + 2.720385674931129, + 2.7607897153351697, + 2.8085399449035817, + 2.8636363636363638, + 2.926078971533517, + 2.9958677685950414, + 3.0730027548209367, + 3.157483930211203, + 3.2493112947658402, + 3.3484848484848486, + 3.455004591368228, + 3.5688705234159777, + 3.6900826446280997, + 3.818640955004591, + 3.954545454545454, + 4.097796143250688, + 4.248393021120293, + 4.406336088154272, + 4.5716253443526185, + 4.744260789715337, + 4.924242424242426, + 5.111570247933885, + 5.3062442607897164, + 5.508264462809919, + 5.717630853994491, + 5.934343434343434, + 6.158402203856751, + 6.389807162534435, + 6.6285583103764925 + ], + [ + 18.562442607897154, + 18.081267217630852, + 17.607438016528928, + 17.14095500459137, + 16.681818181818183, + 16.230027548209364, + 15.785583103764921, + 15.348484848484848, + 14.918732782369146, + 14.496326905417813, + 14.081267217630854, + 13.673553719008261, + 13.273186409550043, + 12.880165289256198, + 12.49449035812672, + 12.116161616161616, + 11.745179063360881, + 11.381542699724518, + 11.025252525252526, + 10.676308539944904, + 10.334710743801653, + 10.000459136822773, + 9.673553719008265, + 9.353994490358126, + 9.04178145087236, + 8.736914600550964, + 8.43939393939394, + 8.149219467401284, + 7.866391184573002, + 7.590909090909091, + 7.322773186409549, + 7.061983471074379, + 6.808539944903581, + 6.562442607897154, + 6.323691460055096, + 6.09228650137741, + 5.868227731864096, + 5.6515151515151505, + 5.442148760330578, + 5.240128558310376, + 5.045454545454545, + 4.858126721763085, + 4.678145087235997, + 4.505509641873278, + 4.340220385674931, + 4.1822773186409545, + 4.03168044077135, + 3.8884297520661155, + 3.752525252525252, + 3.62396694214876, + 3.502754820936639, + 3.388888888888889, + 3.28236914600551, + 3.183195592286501, + 3.0913682277318637, + 3.0068870523415976, + 2.9297520661157024, + 2.859963269054178, + 2.7975206611570247, + 2.742424242424242, + 2.6946740128558306, + 2.6542699724517904, + 2.621212121212121, + 2.5955004591368227, + 2.577134986225895, + 2.5661157024793386, + 2.5624426078971534, + 2.5661157024793386, + 2.577134986225895, + 2.5955004591368227, + 2.621212121212121, + 2.6542699724517904, + 2.6946740128558306, + 2.742424242424243, + 2.797520661157025, + 2.8599632690541785, + 2.929752066115703, + 3.006887052341598, + 3.0913682277318646, + 3.1831955922865016, + 3.28236914600551, + 3.3888888888888893, + 3.502754820936639, + 3.62396694214876, + 3.7525252525252517, + 3.8884297520661146, + 4.031680440771349, + 4.182277318640954, + 4.340220385674932, + 4.505509641873279, + 4.678145087235998, + 4.858126721763086, + 5.045454545454546, + 5.240128558310377, + 5.442148760330579, + 5.651515151515152, + 5.868227731864096, + 6.092286501377412, + 6.323691460055096, + 6.562442607897154 + ], + [ + 18.5, + 18.0188246097337, + 17.544995408631774, + 17.078512396694215, + 16.61937557392103, + 16.16758494031221, + 15.723140495867767, + 15.286042240587694, + 14.856290174471994, + 14.433884297520661, + 14.018824609733702, + 13.611111111111109, + 13.21074380165289, + 12.817722681359044, + 12.432047750229568, + 12.053719008264462, + 11.68273645546373, + 11.319100091827364, + 10.962809917355372, + 10.61386593204775, + 10.272268135904499, + 9.938016528925619, + 9.61111111111111, + 9.291551882460972, + 8.979338842975206, + 8.67447199265381, + 8.376951331496787, + 8.086776859504132, + 7.8039485766758485, + 7.528466483011938, + 7.260330578512396, + 6.999540863177226, + 6.746097337006428, + 6.5, + 6.2612488521579435, + 6.029843893480257, + 5.805785123966943, + 5.5890725436179975, + 5.379706152433425, + 5.177685950413222, + 4.983011937557392, + 4.795684113865932, + 4.615702479338843, + 4.443067033976125, + 4.277777777777777, + 4.119834710743801, + 3.969237832874196, + 3.825987144168962, + 3.6900826446280988, + 3.561524334251607, + 3.440312213039486, + 3.3264462809917354, + 3.2199265381083566, + 3.120752984389348, + 3.0289256198347103, + 2.944444444444444, + 2.867309458218549, + 2.7975206611570247, + 2.7350780532598717, + 2.6799816345270893, + 2.6322314049586772, + 2.591827364554637, + 2.5587695133149677, + 2.5330578512396693, + 2.514692378328742, + 2.5036730945821857, + 2.5, + 2.5036730945821857, + 2.514692378328742, + 2.5330578512396693, + 2.5587695133149677, + 2.591827364554637, + 2.6322314049586772, + 2.6799816345270897, + 2.7350780532598717, + 2.797520661157025, + 2.8673094582185494, + 2.9444444444444446, + 3.028925619834711, + 3.1207529843893482, + 3.2199265381083566, + 3.3264462809917354, + 3.440312213039485, + 3.561524334251607, + 3.6900826446280988, + 3.8259871441689617, + 3.969237832874196, + 4.119834710743801, + 4.2777777777777795, + 4.443067033976126, + 4.615702479338845, + 4.795684113865933, + 4.983011937557393, + 5.177685950413224, + 5.379706152433426, + 5.589072543617998, + 5.805785123966942, + 6.029843893480258, + 6.261248852157943, + 6.5 + ], + [ + 18.441230486685033, + 17.960055096418735, + 17.486225895316807, + 17.019742883379248, + 16.560606060606062, + 16.108815426997243, + 15.6643709825528, + 15.227272727272727, + 14.797520661157025, + 14.375114784205692, + 13.960055096418733, + 13.55234159779614, + 13.151974288337922, + 12.758953168044076, + 12.373278236914599, + 11.994949494949495, + 11.62396694214876, + 11.260330578512397, + 10.904040404040405, + 10.555096418732782, + 10.213498622589531, + 9.879247015610652, + 9.552341597796143, + 9.232782369146005, + 8.920569329660239, + 8.615702479338843, + 8.318181818181818, + 8.028007346189163, + 7.745179063360881, + 7.46969696969697, + 7.201561065197428, + 6.940771349862258, + 6.68732782369146, + 6.441230486685033, + 6.202479338842975, + 5.971074380165289, + 5.7470156106519745, + 5.530303030303029, + 5.3209366391184565, + 5.118916437098255, + 4.924242424242424, + 4.736914600550964, + 4.556932966023876, + 4.384297520661157, + 4.2190082644628095, + 4.061065197428833, + 3.9104683195592282, + 3.7672176308539944, + 3.631313131313131, + 3.502754820936639, + 3.381542699724518, + 3.2676767676767677, + 3.161157024793389, + 3.0619834710743796, + 2.9701561065197426, + 2.8856749311294765, + 2.8085399449035813, + 2.738751147842057, + 2.6763085399449036, + 2.621212121212121, + 2.5734618916437095, + 2.5330578512396693, + 2.5, + 2.4742883379247016, + 2.455922865013774, + 2.4449035812672175, + 2.4412304866850323, + 2.4449035812672175, + 2.455922865013774, + 2.4742883379247016, + 2.5, + 2.5330578512396693, + 2.5734618916437095, + 2.621212121212122, + 2.676308539944904, + 2.7387511478420574, + 2.8085399449035817, + 2.885674931129477, + 2.9701561065197435, + 3.0619834710743805, + 3.161157024793389, + 3.267676767676768, + 3.381542699724518, + 3.502754820936639, + 3.6313131313131306, + 3.7672176308539935, + 3.910468319559228, + 4.0610651974288325, + 4.219008264462811, + 4.384297520661158, + 4.556932966023877, + 4.736914600550965, + 4.924242424242425, + 5.118916437098256, + 5.320936639118458, + 5.530303030303031, + 5.7470156106519745, + 5.971074380165291, + 6.202479338842975, + 6.441230486685033 + ], + [ + 18.38613406795225, + 17.90495867768595, + 17.431129476584026, + 16.964646464646464, + 16.50550964187328, + 16.053719008264462, + 15.60927456382002, + 15.172176308539946, + 14.742424242424242, + 14.320018365472912, + 13.90495867768595, + 13.49724517906336, + 13.09687786960514, + 12.703856749311294, + 12.318181818181817, + 11.939853076216712, + 11.568870523415978, + 11.205234159779614, + 10.848943985307622, + 10.5, + 10.158402203856749, + 9.82415059687787, + 9.49724517906336, + 9.177685950413222, + 8.865472910927457, + 8.56060606060606, + 8.263085399449036, + 7.972910927456382, + 7.690082644628099, + 7.414600550964187, + 7.146464646464645, + 6.8856749311294765, + 6.632231404958677, + 6.38613406795225, + 6.147382920110193, + 5.915977961432508, + 5.691919191919192, + 5.475206611570247, + 5.265840220385675, + 5.0638200183654725, + 4.869146005509641, + 4.681818181818182, + 4.501836547291093, + 4.3292011019283745, + 4.163911845730027, + 4.005968778696051, + 3.855371900826446, + 3.712121212121212, + 3.576216712580349, + 3.4476584022038566, + 3.3264462809917354, + 3.2125803489439857, + 3.1060606060606064, + 3.0068870523415976, + 2.91505968778696, + 2.830578512396694, + 2.753443526170799, + 2.6836547291092745, + 2.621212121212121, + 2.566115702479339, + 2.5183654729109275, + 2.477961432506887, + 2.4449035812672175, + 2.419191919191919, + 2.400826446280992, + 2.389807162534435, + 2.38613406795225, + 2.389807162534435, + 2.400826446280992, + 2.419191919191919, + 2.4449035812672175, + 2.477961432506887, + 2.5183654729109275, + 2.5661157024793395, + 2.6212121212121215, + 2.683654729109275, + 2.7534435261707992, + 2.8305785123966944, + 2.915059687786961, + 3.006887052341598, + 3.1060606060606064, + 3.2125803489439857, + 3.3264462809917354, + 3.4476584022038574, + 3.576216712580349, + 3.712121212121212, + 3.855371900826446, + 4.005968778696051, + 4.16391184573003, + 4.329201101928376, + 4.501836547291095, + 4.681818181818183, + 4.869146005509643, + 5.063820018365474, + 5.265840220385677, + 5.47520661157025, + 5.691919191919192, + 5.9159779614325085, + 6.147382920110193, + 6.38613406795225 + ], + [ + 18.33471074380165, + 17.853535353535353, + 17.379706152433428, + 16.91322314049587, + 16.454086317722684, + 16.002295684113864, + 15.557851239669422, + 15.120752984389348, + 14.691000918273645, + 14.268595041322314, + 13.853535353535353, + 13.445821854912761, + 13.045454545454543, + 12.652433425160696, + 12.26675849403122, + 11.888429752066115, + 11.517447199265382, + 11.153810835629017, + 10.797520661157026, + 10.448576675849402, + 10.106978879706151, + 9.772727272727273, + 9.445821854912763, + 9.126262626262626, + 8.814049586776859, + 8.509182736455465, + 8.21166207529844, + 7.921487603305785, + 7.638659320477503, + 7.36317722681359, + 7.095041322314049, + 6.83425160697888, + 6.58080808080808, + 6.3347107438016526, + 6.095959595959596, + 5.864554637281911, + 5.640495867768596, + 5.42378328741965, + 5.214416896235077, + 5.012396694214876, + 4.8177226813590455, + 4.630394857667585, + 4.450413223140496, + 4.277777777777779, + 4.11248852157943, + 3.954545454545454, + 3.803948576675849, + 3.660697887970615, + 3.524793388429752, + 3.3962350780532597, + 3.2750229568411386, + 3.161157024793389, + 3.0546372819100096, + 2.955463728191001, + 2.8636363636363633, + 2.779155188246097, + 2.702020202020202, + 2.6322314049586777, + 2.5697887970615243, + 2.5146923783287423, + 2.4669421487603307, + 2.42653810835629, + 2.3934802571166207, + 2.3677685950413223, + 2.349403122130395, + 2.3383838383838382, + 2.334710743801653, + 2.3383838383838382, + 2.3494031221303953, + 2.3677685950413223, + 2.3934802571166207, + 2.42653810835629, + 2.4669421487603307, + 2.5146923783287427, + 2.5697887970615247, + 2.632231404958678, + 2.7020202020202024, + 2.7791551882460976, + 2.863636363636364, + 2.9554637281910012, + 3.0546372819100096, + 3.161157024793389, + 3.2750229568411386, + 3.3962350780532606, + 3.5247933884297513, + 3.660697887970615, + 3.8039485766758485, + 3.9545454545454533, + 4.112488521579433, + 4.277777777777779, + 4.450413223140497, + 4.630394857667586, + 4.8177226813590455, + 5.0123966942148765, + 5.214416896235079, + 5.423783287419653, + 5.640495867768596, + 5.864554637281911, + 6.095959595959595, + 6.3347107438016526 + ], + [ + 18.286960514233243, + 17.805785123966942, + 17.331955922865014, + 16.86547291092746, + 16.406336088154273, + 15.954545454545453, + 15.51010101010101, + 15.073002754820937, + 14.643250688705233, + 14.220844811753903, + 13.805785123966942, + 13.39807162534435, + 12.997704315886132, + 12.604683195592285, + 12.219008264462808, + 11.840679522497704, + 11.469696969696969, + 11.106060606060606, + 10.749770431588614, + 10.400826446280991, + 10.05922865013774, + 9.724977043158862, + 9.398071625344352, + 9.078512396694215, + 8.766299357208448, + 8.461432506887052, + 8.163911845730027, + 7.873737373737374, + 7.59090909090909, + 7.315426997245179, + 7.047291092745637, + 6.786501377410468, + 6.533057851239668, + 6.286960514233241, + 6.048209366391184, + 5.816804407713499, + 5.592745638200184, + 5.376033057851238, + 5.166666666666666, + 4.964646464646464, + 4.7699724517906334, + 4.582644628099173, + 4.4026629935720845, + 4.2300275482093666, + 4.064738292011018, + 3.906795224977042, + 3.7561983471074374, + 3.612947658402203, + 3.47704315886134, + 3.348484848484848, + 3.227272727272727, + 3.113406795224977, + 3.0068870523415976, + 2.9077134986225888, + 2.8158861340679517, + 2.7314049586776856, + 2.6542699724517904, + 2.584481175390266, + 2.5220385674931127, + 2.4669421487603307, + 2.4191919191919187, + 2.3787878787878785, + 2.345730027548209, + 2.3200183654729107, + 2.3016528925619832, + 2.2906336088154267, + 2.2869605142332414, + 2.2906336088154267, + 2.3016528925619832, + 2.3200183654729107, + 2.345730027548209, + 2.3787878787878785, + 2.4191919191919187, + 2.466942148760331, + 2.522038567493113, + 2.5844811753902666, + 2.654269972451791, + 2.731404958677686, + 2.8158861340679526, + 2.9077134986225897, + 3.006887052341598, + 3.1134067952249773, + 3.2272727272727266, + 3.3484848484848486, + 3.47704315886134, + 3.612947658402203, + 3.7561983471074374, + 3.906795224977042, + 4.064738292011021, + 4.230027548209367, + 4.402662993572086, + 4.582644628099175, + 4.769972451790634, + 4.964646464646465, + 5.166666666666668, + 5.376033057851241, + 5.592745638200183, + 5.8168044077135, + 6.048209366391184, + 6.286960514233241 + ], + [ + 18.242883379247015, + 17.761707988980717, + 17.28787878787879, + 16.821395775941234, + 16.362258953168045, + 15.910468319559227, + 15.466023875114782, + 15.028925619834709, + 14.599173553719009, + 14.176767676767676, + 13.761707988980717, + 13.353994490358124, + 12.953627180899906, + 12.560606060606059, + 12.174931129476583, + 11.796602387511477, + 11.425619834710744, + 11.061983471074381, + 10.705693296602387, + 10.356749311294765, + 10.015151515151516, + 9.680899908172636, + 9.353994490358126, + 9.034435261707989, + 8.722222222222221, + 8.417355371900825, + 8.119834710743802, + 7.829660238751147, + 7.5468319559228645, + 7.271349862258953, + 7.003213957759412, + 6.742424242424242, + 6.488980716253443, + 6.242883379247015, + 6.0041322314049586, + 5.772727272727273, + 5.548668503213959, + 5.331955922865013, + 5.12258953168044, + 4.920569329660238, + 4.725895316804408, + 4.538567493112947, + 4.358585858585858, + 4.185950413223141, + 4.020661157024793, + 3.8627180899908167, + 3.7121212121212115, + 3.5688705234159777, + 3.4329660238751147, + 3.3044077134986223, + 3.183195592286501, + 3.0693296602387514, + 2.962809917355372, + 2.8636363636363633, + 2.771808999081726, + 2.6873278236914597, + 2.6101928374655645, + 2.54040404040404, + 2.477961432506887, + 2.422865013774105, + 2.375114784205693, + 2.3347107438016526, + 2.3016528925619832, + 2.275941230486685, + 2.2575757575757573, + 2.2465564738292008, + 2.2428833792470155, + 2.2465564738292008, + 2.257575757575758, + 2.275941230486685, + 2.3016528925619832, + 2.3347107438016526, + 2.3751147842056928, + 2.4228650137741052, + 2.4779614325068873, + 2.5404040404040407, + 2.610192837465565, + 2.68732782369146, + 2.7718089990817267, + 2.8636363636363638, + 2.962809917355372, + 3.0693296602387514, + 3.183195592286501, + 3.3044077134986223, + 3.432966023875114, + 3.5688705234159768, + 3.712121212121211, + 3.862718089990816, + 4.0206611570247945, + 4.185950413223141, + 4.35858585858586, + 4.538567493112948, + 4.725895316804408, + 4.920569329660239, + 5.1225895316804415, + 5.331955922865014, + 5.548668503213959, + 5.772727272727273, + 6.004132231404958, + 6.242883379247015 + ], + [ + 18.202479338842977, + 17.721303948576676, + 17.247474747474747, + 16.780991735537192, + 16.321854912764007, + 15.870064279155187, + 15.425619834710744, + 14.988521579430671, + 14.558769513314967, + 14.136363636363637, + 13.721303948576676, + 13.313590449954084, + 12.913223140495866, + 12.520202020202019, + 12.134527089072542, + 11.756198347107437, + 11.385215794306703, + 11.02157943067034, + 10.665289256198347, + 10.316345270890725, + 9.974747474747474, + 9.640495867768596, + 9.313590449954086, + 8.994031221303949, + 8.681818181818182, + 8.376951331496786, + 8.079430670339761, + 7.789256198347108, + 7.506427915518824, + 7.230945821854913, + 6.962809917355371, + 6.7020202020202015, + 6.448576675849402, + 6.202479338842975, + 5.963728191000918, + 5.732323232323233, + 5.508264462809918, + 5.291551882460972, + 5.0821854912764, + 4.8801652892561975, + 4.685491276400367, + 4.498163452708907, + 4.318181818181818, + 4.1455463728191, + 3.980257116620752, + 3.822314049586776, + 3.6717171717171713, + 3.528466483011937, + 3.392561983471074, + 3.264003673094582, + 3.142791551882461, + 3.0289256198347108, + 2.9224058769513315, + 2.8232323232323226, + 2.7314049586776856, + 2.6469237832874195, + 2.5697887970615243, + 2.5, + 2.4375573921028466, + 2.3824609733700646, + 2.3347107438016526, + 2.2943067033976123, + 2.2612488521579426, + 2.2355371900826446, + 2.217171717171717, + 2.2061524334251605, + 2.2024793388429753, + 2.2061524334251605, + 2.217171717171717, + 2.2355371900826446, + 2.2612488521579426, + 2.294306703397612, + 2.3347107438016526, + 2.382460973370065, + 2.437557392102847, + 2.5000000000000004, + 2.5697887970615247, + 2.64692378328742, + 2.7314049586776865, + 2.8232323232323235, + 2.922405876951332, + 3.028925619834711, + 3.1427915518824605, + 3.2640036730945825, + 3.392561983471074, + 3.528466483011937, + 3.6717171717171713, + 3.822314049586776, + 3.9802571166207548, + 4.145546372819101, + 4.31818181818182, + 4.4981634527089085, + 4.685491276400368, + 4.880165289256199, + 5.082185491276402, + 5.291551882460975, + 5.508264462809917, + 5.732323232323234, + 5.963728191000918, + 6.202479338842975 + ], + [ + 18.16574839302112, + 17.68457300275482, + 17.210743801652896, + 16.744260789715334, + 16.28512396694215, + 15.833333333333332, + 15.38888888888889, + 14.951790633608816, + 14.522038567493112, + 14.099632690541782, + 13.68457300275482, + 13.27685950413223, + 12.876492194674011, + 12.483471074380164, + 12.097796143250687, + 11.719467401285582, + 11.348484848484848, + 10.984848484848484, + 10.628558310376492, + 10.27961432506887, + 9.938016528925619, + 9.603764921946741, + 9.276859504132231, + 8.957300275482094, + 8.645087235996327, + 8.34022038567493, + 8.042699724517906, + 7.752525252525253, + 7.46969696969697, + 7.194214876033058, + 6.926078971533516, + 6.665289256198347, + 6.411845730027548, + 6.16574839302112, + 5.926997245179064, + 5.695592286501378, + 5.471533516988063, + 5.254820936639118, + 5.045454545454545, + 4.8434343434343425, + 4.648760330578512, + 4.461432506887052, + 4.281450872359963, + 4.1088154269972454, + 3.943526170798897, + 3.785583103764921, + 3.6349862258953163, + 3.4917355371900825, + 3.355831037649219, + 3.227272727272727, + 3.106060606060606, + 2.9921946740128558, + 2.885674931129477, + 2.7865013774104677, + 2.6946740128558306, + 2.6101928374655645, + 2.5330578512396693, + 2.463269054178145, + 2.4008264462809916, + 2.3457300275482096, + 2.2979797979797976, + 2.2575757575757573, + 2.224517906336088, + 2.1988062442607896, + 2.180440771349862, + 2.169421487603306, + 2.1657483930211203, + 2.169421487603306, + 2.180440771349862, + 2.1988062442607896, + 2.224517906336088, + 2.2575757575757573, + 2.2979797979797976, + 2.34573002754821, + 2.400826446280992, + 2.4632690541781455, + 2.5330578512396698, + 2.610192837465565, + 2.6946740128558315, + 2.7865013774104685, + 2.885674931129477, + 2.992194674012856, + 3.1060606060606055, + 3.2272727272727275, + 3.355831037649219, + 3.491735537190082, + 3.6349862258953163, + 3.785583103764921, + 3.9435261707988998, + 4.108815426997246, + 4.281450872359965, + 4.4614325068870535, + 4.648760330578513, + 4.843434343434344, + 5.045454545454547, + 5.25482093663912, + 5.471533516988062, + 5.695592286501379, + 5.926997245179063, + 6.16574839302112 + ], + [ + 18.13269054178145, + 17.65151515151515, + 17.177685950413224, + 16.711202938475665, + 16.252066115702483, + 15.800275482093664, + 15.355831037649219, + 14.918732782369146, + 14.488980716253444, + 14.066574839302113, + 13.651515151515152, + 13.24380165289256, + 12.843434343434343, + 12.450413223140494, + 12.064738292011018, + 11.686409550045912, + 11.31542699724518, + 10.951790633608816, + 10.595500459136824, + 10.246556473829202, + 9.90495867768595, + 9.570707070707071, + 9.24380165289256, + 8.924242424242424, + 8.612029384756656, + 8.307162534435262, + 8.009641873278238, + 7.719467401285582, + 7.4366391184573, + 7.161157024793388, + 6.893021120293847, + 6.632231404958677, + 6.378787878787879, + 6.132690541781451, + 5.8939393939393945, + 5.662534435261708, + 5.438475665748394, + 5.221763085399449, + 5.012396694214876, + 4.810376492194674, + 4.615702479338843, + 4.428374655647383, + 4.248393021120294, + 4.075757575757576, + 3.910468319559228, + 3.7525252525252517, + 3.601928374655647, + 3.4586776859504127, + 3.3227731864095498, + 3.1942148760330578, + 3.0730027548209367, + 2.9591368227731865, + 2.852617079889807, + 2.7534435261707983, + 2.6616161616161613, + 2.577134986225895, + 2.5, + 2.4302112029384757, + 2.3677685950413223, + 2.3126721763085403, + 2.2649219467401283, + 2.224517906336088, + 2.1914600550964187, + 2.1657483930211203, + 2.147382920110193, + 2.1363636363636362, + 2.132690541781451, + 2.1363636363636362, + 2.147382920110193, + 2.1657483930211203, + 2.1914600550964183, + 2.2245179063360876, + 2.2649219467401283, + 2.3126721763085407, + 2.3677685950413228, + 2.430211202938476, + 2.5000000000000004, + 2.5771349862258957, + 2.661616161616162, + 2.7534435261707992, + 2.8526170798898076, + 2.959136822773187, + 3.073002754820936, + 3.194214876033058, + 3.3227731864095498, + 3.4586776859504127, + 3.601928374655647, + 3.7525252525252517, + 3.9104683195592305, + 4.075757575757577, + 4.248393021120296, + 4.428374655647384, + 4.615702479338844, + 4.810376492194675, + 5.012396694214877, + 5.22176308539945, + 5.438475665748394, + 5.662534435261708, + 5.893939393939393, + 6.13269054178145 + ], + [ + 18.103305785123965, + 17.622130394857667, + 17.148301193755742, + 16.681818181818183, + 16.222681359044998, + 15.770890725436178, + 15.326446280991735, + 14.889348025711662, + 14.45959595959596, + 14.037190082644628, + 13.622130394857669, + 13.214416896235075, + 12.814049586776857, + 12.421028466483012, + 12.035353535353535, + 11.65702479338843, + 11.286042240587696, + 10.92240587695133, + 10.56611570247934, + 10.217171717171716, + 9.875573921028465, + 9.541322314049587, + 9.214416896235077, + 8.89485766758494, + 8.582644628099173, + 8.277777777777779, + 7.980257116620754, + 7.690082644628099, + 7.407254361799816, + 7.131772268135904, + 6.863636363636363, + 6.602846648301194, + 6.349403122130394, + 6.1033057851239665, + 5.86455463728191, + 5.633149678604225, + 5.40909090909091, + 5.192378328741964, + 4.983011937557391, + 4.78099173553719, + 4.586317722681359, + 4.398989898989899, + 4.2190082644628095, + 4.0463728191000925, + 3.881083562901744, + 3.723140495867768, + 3.572543617998163, + 3.429292929292929, + 3.293388429752066, + 3.1648301193755737, + 3.0436179981634526, + 2.929752066115703, + 2.8232323232323235, + 2.7240587695133147, + 2.6322314049586772, + 2.547750229568411, + 2.470615243342516, + 2.4008264462809916, + 2.3383838383838382, + 2.283287419651056, + 2.2355371900826446, + 2.195133149678604, + 2.1620752984389346, + 2.1363636363636362, + 2.1179981634527087, + 2.106978879706152, + 2.103305785123967, + 2.106978879706152, + 2.117998163452709, + 2.1363636363636362, + 2.1620752984389346, + 2.195133149678604, + 2.2355371900826446, + 2.2832874196510566, + 2.3383838383838387, + 2.400826446280992, + 2.4706152433425164, + 2.5477502295684116, + 2.632231404958678, + 2.724058769513315, + 2.8232323232323235, + 2.929752066115703, + 3.0436179981634526, + 3.1648301193755746, + 3.293388429752066, + 3.429292929292929, + 3.5725436179981633, + 3.723140495867768, + 3.881083562901747, + 4.046372819100093, + 4.219008264462812, + 4.398989898989901, + 4.58631772268136, + 4.780991735537191, + 4.983011937557394, + 5.192378328741967, + 5.40909090909091, + 5.633149678604225, + 5.864554637281909, + 6.1033057851239665 + ], + [ + 18.07759412304867, + 17.596418732782368, + 17.122589531680443, + 16.656106519742885, + 16.1969696969697, + 15.74517906336088, + 15.300734618916437, + 14.863636363636363, + 14.433884297520661, + 14.011478420569329, + 13.59641873278237, + 13.188705234159777, + 12.788337924701558, + 12.395316804407713, + 12.009641873278236, + 11.631313131313131, + 11.260330578512397, + 10.896694214876034, + 10.540404040404042, + 10.191460055096417, + 9.849862258953168, + 9.515610651974288, + 9.188705234159778, + 8.869146005509641, + 8.556932966023876, + 8.25206611570248, + 7.954545454545455, + 7.6643709825528, + 7.381542699724518, + 7.106060606060606, + 6.8379247015610645, + 6.577134986225895, + 6.323691460055096, + 6.0775941230486685, + 5.838842975206612, + 5.607438016528926, + 5.383379247015611, + 5.166666666666666, + 4.957300275482093, + 4.755280073461892, + 4.5606060606060606, + 4.373278236914601, + 4.193296602387512, + 4.020661157024794, + 3.8553719008264453, + 3.6974288337924697, + 3.5468319559228645, + 3.4035812672176307, + 3.2676767676767673, + 3.1391184573002753, + 3.017906336088154, + 2.9040404040404044, + 2.797520661157025, + 2.6983471074380163, + 2.606519742883379, + 2.5220385674931127, + 2.4449035812672175, + 2.375114784205693, + 2.3126721763085403, + 2.257575757575758, + 2.2098255280073458, + 2.1694214876033056, + 2.1363636363636362, + 2.110651974288338, + 2.0922865013774103, + 2.081267217630854, + 2.0775941230486685, + 2.081267217630854, + 2.0922865013774103, + 2.110651974288338, + 2.1363636363636362, + 2.1694214876033056, + 2.2098255280073458, + 2.2575757575757582, + 2.3126721763085403, + 2.3751147842056937, + 2.444903581267218, + 2.522038567493113, + 2.6065197428833797, + 2.6983471074380168, + 2.797520661157025, + 2.9040404040404044, + 3.017906336088154, + 3.1391184573002757, + 3.2676767676767673, + 3.40358126721763, + 3.5468319559228645, + 3.6974288337924692, + 3.855371900826448, + 4.0206611570247945, + 4.193296602387513, + 4.373278236914602, + 4.560606060606061, + 4.7552800734618925, + 4.957300275482095, + 5.166666666666668, + 5.383379247015611, + 5.607438016528928, + 5.838842975206612, + 6.077594123048669 + ], + [ + 18.055555555555557, + 17.574380165289256, + 17.100550964187327, + 16.634067952249772, + 16.174931129476587, + 15.723140495867767, + 15.278696051423324, + 14.841597796143251, + 14.411845730027547, + 13.989439853076217, + 13.574380165289256, + 13.166666666666664, + 12.766299357208446, + 12.373278236914599, + 11.987603305785122, + 11.609274563820017, + 11.238292011019283, + 10.87465564738292, + 10.518365472910927, + 10.169421487603305, + 9.827823691460054, + 9.493572084481176, + 9.166666666666666, + 8.847107438016529, + 8.534894398530762, + 8.230027548209366, + 7.932506887052342, + 7.642332415059688, + 7.359504132231405, + 7.084022038567493, + 6.815886134067951, + 6.555096418732782, + 6.301652892561983, + 6.055555555555555, + 5.816804407713499, + 5.585399449035813, + 5.361340679522498, + 5.144628099173553, + 4.93526170798898, + 4.7332415059687785, + 4.538567493112947, + 4.351239669421488, + 4.171258034894398, + 3.9986225895316805, + 3.833333333333332, + 3.6753902662993565, + 3.5247933884297513, + 3.3815426997245175, + 3.2456382001836546, + 3.1170798898071626, + 2.9958677685950414, + 2.8820018365472913, + 2.775482093663912, + 2.676308539944903, + 2.584481175390266, + 2.5, + 2.4228650137741043, + 2.35307621671258, + 2.290633608815427, + 2.2355371900826446, + 2.187786960514233, + 2.147382920110193, + 2.114325068870523, + 2.0886134067952247, + 2.070247933884297, + 2.059228650137741, + 2.0555555555555554, + 2.059228650137741, + 2.070247933884297, + 2.0886134067952247, + 2.114325068870523, + 2.1473829201101924, + 2.1877869605142326, + 2.235537190082645, + 2.290633608815427, + 2.3530762167125805, + 2.422865013774105, + 2.5, + 2.5844811753902666, + 2.6763085399449036, + 2.775482093663912, + 2.8820018365472913, + 2.995867768595041, + 3.1170798898071626, + 3.245638200183654, + 3.381542699724517, + 3.5247933884297513, + 3.675390266299356, + 3.833333333333335, + 3.9986225895316814, + 4.1712580348944, + 4.3512396694214885, + 4.538567493112948, + 4.733241505968779, + 4.935261707988982, + 5.144628099173555, + 5.361340679522498, + 5.585399449035814, + 5.816804407713498, + 6.055555555555555 + ], + [ + 18.037190082644628, + 17.556014692378326, + 17.0821854912764, + 16.615702479338843, + 16.156565656565657, + 15.70477502295684, + 15.260330578512395, + 14.823232323232322, + 14.393480257116622, + 13.97107438016529, + 13.55601469237833, + 13.148301193755737, + 12.747933884297519, + 12.354912764003672, + 11.969237832874196, + 11.59090909090909, + 11.219926538108357, + 10.856290174471992, + 10.5, + 10.151056014692378, + 9.809458218549127, + 9.475206611570247, + 9.148301193755739, + 8.8287419651056, + 8.516528925619834, + 8.211662075298438, + 7.914141414141414, + 7.62396694214876, + 7.341138659320477, + 7.065656565656566, + 6.797520661157024, + 6.536730945821855, + 6.283287419651056, + 6.037190082644628, + 5.798438934802571, + 5.567033976124885, + 5.3429752066115705, + 5.126262626262625, + 4.9168962350780525, + 4.714876033057851, + 4.52020202020202, + 4.33287419651056, + 4.152892561983471, + 3.980257116620753, + 3.814967860422405, + 3.657024793388429, + 3.506427915518824, + 3.36317722681359, + 3.227272727272727, + 3.098714416896235, + 2.977502295684114, + 2.8636363636363638, + 2.7571166207529845, + 2.6579430670339756, + 2.5661157024793386, + 2.4816345270890725, + 2.404499540863177, + 2.3347107438016526, + 2.2722681359044996, + 2.217171717171717, + 2.1694214876033056, + 2.1290174471992653, + 2.095959595959596, + 2.070247933884297, + 2.0518824609733697, + 2.0408631772268135, + 2.037190082644628, + 2.0408631772268135, + 2.05188246097337, + 2.070247933884297, + 2.095959595959596, + 2.1290174471992653, + 2.1694214876033056, + 2.2171717171717176, + 2.2722681359044996, + 2.334710743801653, + 2.4044995408631773, + 2.4816345270890725, + 2.566115702479339, + 2.657943067033976, + 2.7571166207529845, + 2.8636363636363638, + 2.9775022956841135, + 3.098714416896235, + 3.2272727272727266, + 3.3631772268135895, + 3.506427915518824, + 3.6570247933884286, + 3.8149678604224073, + 3.980257116620754, + 4.152892561983473, + 4.332874196510561, + 4.520202020202021, + 4.714876033057852, + 4.916896235078054, + 5.126262626262627, + 5.3429752066115705, + 5.567033976124886, + 5.79843893480257, + 6.037190082644628 + ], + [ + 18.02249770431589, + 17.541322314049587, + 17.06749311294766, + 16.601010101010104, + 16.141873278236915, + 15.690082644628099, + 15.245638200183654, + 14.80853994490358, + 14.378787878787879, + 13.956382001836548, + 13.541322314049587, + 13.133608815426996, + 12.733241505968778, + 12.340220385674929, + 11.954545454545453, + 11.576216712580347, + 11.205234159779614, + 10.841597796143251, + 10.485307621671259, + 10.136363636363637, + 9.794765840220386, + 9.460514233241506, + 9.133608815426996, + 8.814049586776859, + 8.501836547291092, + 8.196969696969697, + 7.8994490358126725, + 7.609274563820017, + 7.3264462809917354, + 7.050964187327824, + 6.782828282828282, + 6.522038567493112, + 6.268595041322314, + 6.022497704315886, + 5.7837465564738295, + 5.5523415977961434, + 5.328282828282829, + 5.111570247933884, + 4.902203856749311, + 4.700183654729109, + 4.505509641873278, + 4.318181818181818, + 4.138200183654729, + 3.965564738292011, + 3.800275482093663, + 3.642332415059687, + 3.491735537190082, + 3.348484848484848, + 3.2125803489439853, + 3.0840220385674932, + 2.962809917355372, + 2.848943985307622, + 2.7424242424242427, + 2.643250688705234, + 2.551423324150597, + 2.4669421487603302, + 2.389807162534435, + 2.3200183654729107, + 2.257575757575758, + 2.2024793388429753, + 2.1547291092745633, + 2.114325068870523, + 2.0812672176308538, + 2.0555555555555554, + 2.037190082644628, + 2.0261707988980717, + 2.022497704315886, + 2.0261707988980717, + 2.037190082644628, + 2.0555555555555554, + 2.0812672176308538, + 2.114325068870523, + 2.1547291092745633, + 2.2024793388429758, + 2.257575757575758, + 2.320018365472911, + 2.3898071625344355, + 2.4669421487603307, + 2.5514233241505972, + 2.6432506887052343, + 2.7424242424242427, + 2.848943985307622, + 2.9628099173553717, + 3.0840220385674932, + 3.212580348943985, + 3.3484848484848477, + 3.491735537190082, + 3.6423324150596867, + 3.8002754820936655, + 3.965564738292012, + 4.138200183654731, + 4.318181818181819, + 4.505509641873279, + 4.70018365472911, + 4.9022038567493125, + 5.111570247933885, + 5.328282828282829, + 5.552341597796145, + 5.7837465564738295, + 6.022497704315887 + ], + [ + 18.01147842056933, + 17.53030303030303, + 17.056473829201103, + 16.589990817263548, + 16.13085399449036, + 15.679063360881543, + 15.234618916437098, + 14.797520661157025, + 14.367768595041323, + 13.945362718089992, + 13.530303030303031, + 13.12258953168044, + 12.722222222222221, + 12.329201101928373, + 11.943526170798897, + 11.565197428833791, + 11.194214876033058, + 10.830578512396695, + 10.474288337924701, + 10.125344352617079, + 9.78374655647383, + 9.44949494949495, + 9.12258953168044, + 8.803030303030303, + 8.490817263544535, + 8.18595041322314, + 7.888429752066116, + 7.598255280073461, + 7.315426997245179, + 7.039944903581267, + 6.771808999081726, + 6.511019283746556, + 6.257575757575758, + 6.01147842056933, + 5.772727272727273, + 5.541322314049587, + 5.317263544536273, + 5.1005509641873275, + 4.891184573002754, + 4.689164370982552, + 4.494490358126722, + 4.307162534435262, + 4.127180899908173, + 3.954545454545455, + 3.7892561983471067, + 3.6313131313131306, + 3.480716253443526, + 3.3374655647382916, + 3.2015610651974287, + 3.0730027548209367, + 2.9517906336088156, + 2.8379247015610654, + 2.731404958677686, + 2.6322314049586772, + 2.54040404040404, + 2.4559228650137737, + 2.378787878787879, + 2.3089990817263546, + 2.246556473829201, + 2.1914600550964187, + 2.143709825528007, + 2.1033057851239665, + 2.070247933884297, + 2.044536271808999, + 2.0261707988980717, + 2.015151515151515, + 2.01147842056933, + 2.015151515151515, + 2.0261707988980717, + 2.044536271808999, + 2.070247933884297, + 2.1033057851239665, + 2.143709825528007, + 2.191460055096419, + 2.246556473829201, + 2.3089990817263546, + 2.378787878787879, + 2.455922865013774, + 2.5404040404040407, + 2.6322314049586777, + 2.731404958677686, + 2.8379247015610654, + 2.951790633608815, + 3.073002754820937, + 3.2015610651974287, + 3.3374655647382916, + 3.480716253443526, + 3.6313131313131306, + 3.7892561983471094, + 3.954545454545456, + 4.127180899908175, + 4.307162534435263, + 4.494490358126723, + 4.689164370982554, + 4.891184573002756, + 5.100550964187329, + 5.317263544536273, + 5.541322314049587, + 5.772727272727272, + 6.011478420569329 + ], + [ + 18.00413223140496, + 17.522956841138658, + 17.049127640036733, + 16.582644628099175, + 16.12350780532599, + 15.67171717171717, + 15.227272727272727, + 14.790174471992653, + 14.360422405876951, + 13.938016528925619, + 13.52295684113866, + 13.115243342516067, + 12.714876033057848, + 12.321854912764003, + 11.936179981634526, + 11.557851239669422, + 11.186868686868687, + 10.823232323232324, + 10.466942148760332, + 10.117998163452707, + 9.776400367309458, + 9.442148760330578, + 9.115243342516068, + 8.795684113865931, + 8.483471074380166, + 8.17860422405877, + 7.881083562901745, + 7.590909090909091, + 7.308080808080808, + 7.032598714416896, + 6.7644628099173545, + 6.503673094582185, + 6.250229568411386, + 6.0041322314049586, + 5.765381083562902, + 5.533976124885216, + 5.309917355371901, + 5.093204775022956, + 4.883838383838383, + 4.681818181818182, + 4.487144168962351, + 4.299816345270891, + 4.119834710743802, + 3.9471992653810837, + 3.781910009182736, + 3.6239669421487597, + 3.4733700642791545, + 3.3301193755739207, + 3.1942148760330578, + 3.0656565656565657, + 2.9444444444444446, + 2.8305785123966944, + 2.724058769513315, + 2.6248852157943063, + 2.5330578512396693, + 2.448576675849403, + 2.3714416896235075, + 2.3016528925619832, + 2.2392102846648303, + 2.184113865932048, + 2.1363636363636362, + 2.095959595959596, + 2.0629017447199263, + 2.037190082644628, + 2.0188246097337004, + 2.0078053259871442, + 2.0041322314049586, + 2.0078053259871442, + 2.018824609733701, + 2.037190082644628, + 2.0629017447199267, + 2.095959595959596, + 2.1363636363636362, + 2.1841138659320483, + 2.2392102846648303, + 2.3016528925619837, + 2.371441689623508, + 2.448576675849403, + 2.5330578512396698, + 2.624885215794307, + 2.724058769513315, + 2.8305785123966944, + 2.944444444444444, + 3.0656565656565657, + 3.1942148760330573, + 3.3301193755739202, + 3.4733700642791545, + 3.6239669421487593, + 3.781910009182738, + 3.9471992653810846, + 4.119834710743803, + 4.299816345270892, + 4.4871441689623515, + 4.6818181818181825, + 4.883838383838385, + 5.093204775022958, + 5.309917355371901, + 5.533976124885218, + 5.765381083562902, + 6.004132231404959 + ], + [ + 18.000459136822773, + 17.519283746556475, + 17.045454545454547, + 16.578971533516988, + 16.119834710743802, + 15.668044077134985, + 15.22359963269054, + 14.786501377410467, + 14.356749311294767, + 13.934343434343434, + 13.519283746556475, + 13.111570247933882, + 12.711202938475664, + 12.318181818181817, + 11.932506887052341, + 11.554178145087235, + 11.183195592286502, + 10.819559228650139, + 10.463269054178145, + 10.114325068870523, + 9.772727272727273, + 9.438475665748394, + 9.111570247933884, + 8.792011019283747, + 8.47979797979798, + 8.174931129476583, + 7.87741046831956, + 7.587235996326905, + 7.304407713498622, + 7.028925619834711, + 6.760789715335169, + 6.5, + 6.246556473829201, + 6.000459136822773, + 5.761707988980716, + 5.530303030303031, + 5.3062442607897164, + 5.08953168044077, + 4.8801652892561975, + 4.678145087235996, + 4.483471074380165, + 4.296143250688705, + 4.116161616161616, + 3.9435261707988984, + 3.77823691460055, + 3.6202938475665745, + 3.4696969696969693, + 3.3264462809917354, + 3.190541781450872, + 3.06198347107438, + 2.940771349862259, + 2.8269054178145088, + 2.72038567493113, + 2.6212121212121207, + 2.5293847566574836, + 2.4449035812672175, + 2.3677685950413223, + 2.297979797979798, + 2.2355371900826446, + 2.180440771349862, + 2.1326905417814506, + 2.0922865013774103, + 2.059228650137741, + 2.0335169880624426, + 2.015151515151515, + 2.0041322314049586, + 2.000459136822773, + 2.0041322314049586, + 2.015151515151515, + 2.033516988062442, + 2.059228650137741, + 2.0922865013774103, + 2.1326905417814506, + 2.180440771349863, + 2.235537190082645, + 2.2979797979797985, + 2.3677685950413228, + 2.444903581267218, + 2.5293847566574845, + 2.6212121212121215, + 2.72038567493113, + 2.826905417814509, + 2.940771349862259, + 3.06198347107438, + 3.1905417814508716, + 3.3264462809917346, + 3.469696969696969, + 3.6202938475665736, + 3.7782369146005523, + 3.943526170798899, + 4.116161616161618, + 4.296143250688706, + 4.483471074380166, + 4.678145087235997, + 4.880165289256199, + 5.089531680440772, + 5.306244260789716, + 5.530303030303031, + 5.7617079889807155, + 6.000459136822773 + ], + [ + 18.000459136822773, + 17.519283746556475, + 17.045454545454547, + 16.578971533516988, + 16.119834710743802, + 15.668044077134985, + 15.22359963269054, + 14.786501377410467, + 14.356749311294767, + 13.934343434343434, + 13.519283746556475, + 13.111570247933882, + 12.711202938475664, + 12.318181818181817, + 11.932506887052341, + 11.554178145087235, + 11.183195592286502, + 10.819559228650139, + 10.463269054178145, + 10.114325068870523, + 9.772727272727273, + 9.438475665748394, + 9.111570247933884, + 8.792011019283747, + 8.47979797979798, + 8.174931129476583, + 7.87741046831956, + 7.587235996326905, + 7.304407713498622, + 7.028925619834711, + 6.760789715335169, + 6.5, + 6.246556473829201, + 6.000459136822773, + 5.761707988980716, + 5.530303030303031, + 5.3062442607897164, + 5.08953168044077, + 4.8801652892561975, + 4.678145087235996, + 4.483471074380165, + 4.296143250688705, + 4.116161616161616, + 3.9435261707988984, + 3.77823691460055, + 3.6202938475665745, + 3.4696969696969693, + 3.3264462809917354, + 3.190541781450872, + 3.06198347107438, + 2.940771349862259, + 2.8269054178145088, + 2.72038567493113, + 2.6212121212121207, + 2.5293847566574836, + 2.4449035812672175, + 2.3677685950413223, + 2.297979797979798, + 2.2355371900826446, + 2.180440771349862, + 2.1326905417814506, + 2.0922865013774103, + 2.059228650137741, + 2.0335169880624426, + 2.015151515151515, + 2.0041322314049586, + 2.000459136822773, + 2.0041322314049586, + 2.015151515151515, + 2.033516988062442, + 2.059228650137741, + 2.0922865013774103, + 2.1326905417814506, + 2.180440771349863, + 2.235537190082645, + 2.2979797979797985, + 2.3677685950413228, + 2.444903581267218, + 2.5293847566574845, + 2.6212121212121215, + 2.72038567493113, + 2.826905417814509, + 2.940771349862259, + 3.06198347107438, + 3.1905417814508716, + 3.3264462809917346, + 3.469696969696969, + 3.6202938475665736, + 3.7782369146005523, + 3.943526170798899, + 4.116161616161618, + 4.296143250688706, + 4.483471074380166, + 4.678145087235997, + 4.880165289256199, + 5.089531680440772, + 5.306244260789716, + 5.530303030303031, + 5.7617079889807155, + 6.000459136822773 + ], + [ + 18.00413223140496, + 17.522956841138658, + 17.049127640036733, + 16.582644628099175, + 16.12350780532599, + 15.67171717171717, + 15.227272727272727, + 14.790174471992653, + 14.360422405876951, + 13.938016528925619, + 13.52295684113866, + 13.115243342516067, + 12.714876033057848, + 12.321854912764003, + 11.936179981634526, + 11.557851239669422, + 11.186868686868687, + 10.823232323232324, + 10.466942148760332, + 10.117998163452707, + 9.776400367309458, + 9.442148760330578, + 9.115243342516068, + 8.795684113865931, + 8.483471074380166, + 8.17860422405877, + 7.881083562901745, + 7.590909090909091, + 7.308080808080808, + 7.032598714416896, + 6.7644628099173545, + 6.503673094582185, + 6.250229568411386, + 6.0041322314049586, + 5.765381083562902, + 5.533976124885216, + 5.309917355371901, + 5.093204775022956, + 4.883838383838383, + 4.681818181818182, + 4.487144168962351, + 4.299816345270891, + 4.119834710743802, + 3.9471992653810837, + 3.781910009182736, + 3.6239669421487597, + 3.4733700642791545, + 3.3301193755739207, + 3.1942148760330578, + 3.0656565656565657, + 2.9444444444444446, + 2.8305785123966944, + 2.724058769513315, + 2.6248852157943063, + 2.5330578512396693, + 2.448576675849403, + 2.3714416896235075, + 2.3016528925619832, + 2.2392102846648303, + 2.184113865932048, + 2.1363636363636362, + 2.095959595959596, + 2.0629017447199263, + 2.037190082644628, + 2.0188246097337004, + 2.0078053259871442, + 2.0041322314049586, + 2.0078053259871442, + 2.018824609733701, + 2.037190082644628, + 2.0629017447199267, + 2.095959595959596, + 2.1363636363636362, + 2.1841138659320483, + 2.2392102846648303, + 2.3016528925619837, + 2.371441689623508, + 2.448576675849403, + 2.5330578512396698, + 2.624885215794307, + 2.724058769513315, + 2.8305785123966944, + 2.944444444444444, + 3.0656565656565657, + 3.1942148760330573, + 3.3301193755739202, + 3.4733700642791545, + 3.6239669421487593, + 3.781910009182738, + 3.9471992653810846, + 4.119834710743803, + 4.299816345270892, + 4.4871441689623515, + 4.6818181818181825, + 4.883838383838385, + 5.093204775022958, + 5.309917355371901, + 5.533976124885218, + 5.765381083562902, + 6.004132231404959 + ], + [ + 18.01147842056933, + 17.53030303030303, + 17.056473829201103, + 16.589990817263548, + 16.13085399449036, + 15.679063360881543, + 15.234618916437098, + 14.797520661157025, + 14.367768595041323, + 13.945362718089992, + 13.530303030303031, + 13.12258953168044, + 12.722222222222221, + 12.329201101928373, + 11.943526170798897, + 11.565197428833791, + 11.194214876033058, + 10.830578512396695, + 10.474288337924701, + 10.125344352617079, + 9.78374655647383, + 9.44949494949495, + 9.12258953168044, + 8.803030303030303, + 8.490817263544535, + 8.18595041322314, + 7.888429752066116, + 7.598255280073461, + 7.315426997245179, + 7.039944903581267, + 6.771808999081726, + 6.511019283746556, + 6.257575757575758, + 6.01147842056933, + 5.772727272727273, + 5.541322314049587, + 5.317263544536273, + 5.1005509641873275, + 4.891184573002754, + 4.689164370982552, + 4.494490358126722, + 4.307162534435262, + 4.127180899908173, + 3.954545454545455, + 3.7892561983471067, + 3.6313131313131306, + 3.480716253443526, + 3.3374655647382916, + 3.2015610651974287, + 3.0730027548209367, + 2.9517906336088156, + 2.8379247015610654, + 2.731404958677686, + 2.6322314049586772, + 2.54040404040404, + 2.4559228650137737, + 2.378787878787879, + 2.3089990817263546, + 2.246556473829201, + 2.1914600550964187, + 2.143709825528007, + 2.1033057851239665, + 2.070247933884297, + 2.044536271808999, + 2.0261707988980717, + 2.015151515151515, + 2.01147842056933, + 2.015151515151515, + 2.0261707988980717, + 2.044536271808999, + 2.070247933884297, + 2.1033057851239665, + 2.143709825528007, + 2.191460055096419, + 2.246556473829201, + 2.3089990817263546, + 2.378787878787879, + 2.455922865013774, + 2.5404040404040407, + 2.6322314049586777, + 2.731404958677686, + 2.8379247015610654, + 2.951790633608815, + 3.073002754820937, + 3.2015610651974287, + 3.3374655647382916, + 3.480716253443526, + 3.6313131313131306, + 3.7892561983471094, + 3.954545454545456, + 4.127180899908175, + 4.307162534435263, + 4.494490358126723, + 4.689164370982554, + 4.891184573002756, + 5.100550964187329, + 5.317263544536273, + 5.541322314049587, + 5.772727272727272, + 6.011478420569329 + ], + [ + 18.02249770431589, + 17.541322314049587, + 17.06749311294766, + 16.601010101010104, + 16.141873278236915, + 15.690082644628099, + 15.245638200183654, + 14.80853994490358, + 14.378787878787879, + 13.956382001836548, + 13.541322314049587, + 13.133608815426996, + 12.733241505968778, + 12.340220385674929, + 11.954545454545453, + 11.576216712580347, + 11.205234159779614, + 10.841597796143251, + 10.485307621671259, + 10.136363636363637, + 9.794765840220386, + 9.460514233241506, + 9.133608815426996, + 8.814049586776859, + 8.501836547291092, + 8.196969696969697, + 7.8994490358126725, + 7.609274563820018, + 7.3264462809917354, + 7.050964187327824, + 6.782828282828282, + 6.522038567493112, + 6.268595041322314, + 6.022497704315886, + 5.7837465564738295, + 5.5523415977961434, + 5.328282828282829, + 5.111570247933884, + 4.902203856749311, + 4.700183654729109, + 4.505509641873278, + 4.318181818181818, + 4.138200183654729, + 3.965564738292011, + 3.8002754820936633, + 3.642332415059687, + 3.491735537190082, + 3.348484848484848, + 3.2125803489439853, + 3.0840220385674932, + 2.962809917355372, + 2.848943985307622, + 2.7424242424242427, + 2.643250688705234, + 2.551423324150597, + 2.4669421487603307, + 2.389807162534435, + 2.3200183654729107, + 2.257575757575758, + 2.2024793388429753, + 2.1547291092745637, + 2.1143250688705235, + 2.0812672176308538, + 2.0555555555555554, + 2.037190082644628, + 2.0261707988980717, + 2.022497704315886, + 2.0261707988980717, + 2.0371900826446283, + 2.0555555555555554, + 2.081267217630854, + 2.1143250688705235, + 2.1547291092745637, + 2.2024793388429758, + 2.257575757575758, + 2.320018365472911, + 2.3898071625344355, + 2.4669421487603307, + 2.5514233241505972, + 2.6432506887052343, + 2.7424242424242427, + 2.848943985307622, + 2.9628099173553717, + 3.0840220385674932, + 3.212580348943985, + 3.3484848484848477, + 3.491735537190082, + 3.6423324150596867, + 3.8002754820936655, + 3.965564738292012, + 4.138200183654731, + 4.318181818181819, + 4.505509641873279, + 4.70018365472911, + 4.9022038567493125, + 5.111570247933885, + 5.328282828282829, + 5.552341597796145, + 5.7837465564738295, + 6.022497704315887 + ], + [ + 18.037190082644628, + 17.556014692378326, + 17.0821854912764, + 16.615702479338843, + 16.156565656565657, + 15.70477502295684, + 15.260330578512395, + 14.823232323232322, + 14.393480257116622, + 13.97107438016529, + 13.55601469237833, + 13.148301193755737, + 12.747933884297519, + 12.354912764003672, + 11.969237832874196, + 11.59090909090909, + 11.219926538108357, + 10.856290174471994, + 10.5, + 10.151056014692378, + 9.809458218549128, + 9.475206611570249, + 9.148301193755739, + 8.828741965105602, + 8.516528925619834, + 8.211662075298438, + 7.914141414141415, + 7.62396694214876, + 7.341138659320477, + 7.065656565656566, + 6.797520661157024, + 6.536730945821855, + 6.283287419651056, + 6.037190082644628, + 5.798438934802571, + 5.567033976124886, + 5.342975206611571, + 5.126262626262625, + 4.9168962350780525, + 4.714876033057851, + 4.52020202020202, + 4.33287419651056, + 4.152892561983471, + 3.9802571166207534, + 3.814967860422405, + 3.6570247933884295, + 3.5064279155188243, + 3.3631772268135904, + 3.227272727272727, + 3.098714416896235, + 2.977502295684114, + 2.8636363636363638, + 2.757116620752985, + 2.6579430670339756, + 2.5661157024793386, + 2.4816345270890725, + 2.4044995408631773, + 2.334710743801653, + 2.2722681359044996, + 2.217171717171717, + 2.1694214876033056, + 2.1290174471992653, + 2.095959595959596, + 2.0702479338842976, + 2.05188246097337, + 2.0408631772268135, + 2.037190082644628, + 2.0408631772268135, + 2.05188246097337, + 2.070247933884297, + 2.095959595959596, + 2.1290174471992653, + 2.1694214876033056, + 2.217171717171718, + 2.2722681359045, + 2.3347107438016534, + 2.4044995408631777, + 2.481634527089073, + 2.5661157024793395, + 2.6579430670339765, + 2.757116620752985, + 2.863636363636364, + 2.977502295684114, + 3.098714416896235, + 3.2272727272727266, + 3.3631772268135895, + 3.506427915518824, + 3.6570247933884286, + 3.8149678604224073, + 3.980257116620754, + 4.152892561983473, + 4.332874196510561, + 4.520202020202021, + 4.714876033057852, + 4.916896235078054, + 5.126262626262627, + 5.3429752066115705, + 5.567033976124886, + 5.79843893480257, + 6.037190082644628 + ], + [ + 18.055555555555557, + 17.574380165289256, + 17.100550964187327, + 16.634067952249772, + 16.174931129476587, + 15.723140495867767, + 15.278696051423324, + 14.841597796143251, + 14.411845730027547, + 13.989439853076217, + 13.574380165289256, + 13.166666666666664, + 12.766299357208446, + 12.373278236914599, + 11.987603305785122, + 11.609274563820017, + 11.238292011019283, + 10.87465564738292, + 10.51836547291093, + 10.169421487603305, + 9.827823691460054, + 9.493572084481176, + 9.166666666666666, + 8.847107438016529, + 8.534894398530762, + 8.230027548209367, + 7.932506887052343, + 7.642332415059688, + 7.359504132231405, + 7.084022038567493, + 6.815886134067951, + 6.5550964187327825, + 6.301652892561983, + 6.055555555555555, + 5.816804407713499, + 5.585399449035814, + 5.361340679522498, + 5.144628099173553, + 4.93526170798898, + 4.7332415059687785, + 4.538567493112947, + 4.351239669421488, + 4.171258034894398, + 3.9986225895316805, + 3.8333333333333326, + 3.6753902662993565, + 3.5247933884297518, + 3.3815426997245175, + 3.2456382001836546, + 3.1170798898071626, + 2.9958677685950414, + 2.8820018365472913, + 2.775482093663912, + 2.676308539944903, + 2.584481175390266, + 2.5, + 2.4228650137741043, + 2.3530762167125805, + 2.290633608815427, + 2.2355371900826446, + 2.187786960514233, + 2.147382920110193, + 2.1143250688705235, + 2.0886134067952247, + 2.0702479338842976, + 2.059228650137741, + 2.0555555555555554, + 2.059228650137741, + 2.0702479338842976, + 2.0886134067952247, + 2.1143250688705235, + 2.147382920110193, + 2.187786960514233, + 2.2355371900826455, + 2.2906336088154275, + 2.353076216712581, + 2.4228650137741052, + 2.5000000000000004, + 2.584481175390267, + 2.676308539944904, + 2.7754820936639124, + 2.8820018365472917, + 2.9958677685950414, + 3.1170798898071626, + 3.245638200183654, + 3.381542699724517, + 3.5247933884297513, + 3.675390266299356, + 3.833333333333335, + 3.9986225895316814, + 4.1712580348944, + 4.3512396694214885, + 4.538567493112948, + 4.733241505968779, + 4.935261707988982, + 5.144628099173555, + 5.361340679522498, + 5.585399449035814, + 5.816804407713498, + 6.055555555555555 + ], + [ + 18.07759412304867, + 17.596418732782368, + 17.122589531680443, + 16.656106519742885, + 16.1969696969697, + 15.74517906336088, + 15.300734618916437, + 14.863636363636363, + 14.433884297520661, + 14.011478420569329, + 13.59641873278237, + 13.188705234159777, + 12.788337924701558, + 12.395316804407713, + 12.009641873278236, + 11.631313131313131, + 11.260330578512397, + 10.896694214876034, + 10.540404040404042, + 10.191460055096417, + 9.849862258953168, + 9.515610651974288, + 9.188705234159778, + 8.869146005509641, + 8.556932966023876, + 8.25206611570248, + 7.954545454545455, + 7.6643709825528, + 7.381542699724518, + 7.106060606060606, + 6.8379247015610645, + 6.577134986225895, + 6.323691460055096, + 6.0775941230486685, + 5.838842975206612, + 5.607438016528926, + 5.383379247015611, + 5.166666666666666, + 4.957300275482093, + 4.755280073461892, + 4.5606060606060606, + 4.373278236914601, + 4.193296602387512, + 4.020661157024794, + 3.8553719008264453, + 3.6974288337924697, + 3.5468319559228645, + 3.4035812672176307, + 3.2676767676767673, + 3.1391184573002753, + 3.017906336088154, + 2.9040404040404044, + 2.797520661157025, + 2.6983471074380163, + 2.606519742883379, + 2.5220385674931127, + 2.4449035812672175, + 2.375114784205693, + 2.3126721763085403, + 2.257575757575758, + 2.2098255280073458, + 2.1694214876033056, + 2.1363636363636362, + 2.110651974288338, + 2.0922865013774103, + 2.081267217630854, + 2.0775941230486685, + 2.081267217630854, + 2.0922865013774103, + 2.110651974288338, + 2.1363636363636362, + 2.1694214876033056, + 2.2098255280073458, + 2.2575757575757582, + 2.3126721763085403, + 2.3751147842056937, + 2.444903581267218, + 2.522038567493113, + 2.6065197428833797, + 2.6983471074380168, + 2.797520661157025, + 2.9040404040404044, + 3.017906336088154, + 3.1391184573002757, + 3.2676767676767673, + 3.40358126721763, + 3.5468319559228645, + 3.6974288337924692, + 3.855371900826448, + 4.0206611570247945, + 4.193296602387513, + 4.373278236914602, + 4.560606060606061, + 4.7552800734618925, + 4.957300275482095, + 5.166666666666668, + 5.383379247015611, + 5.607438016528928, + 5.838842975206612, + 6.077594123048669 + ], + [ + 18.103305785123965, + 17.622130394857667, + 17.148301193755742, + 16.681818181818183, + 16.222681359044998, + 15.770890725436178, + 15.326446280991735, + 14.889348025711662, + 14.45959595959596, + 14.037190082644628, + 13.622130394857669, + 13.214416896235075, + 12.814049586776857, + 12.421028466483012, + 12.035353535353535, + 11.65702479338843, + 11.286042240587696, + 10.92240587695133, + 10.56611570247934, + 10.217171717171716, + 9.875573921028465, + 9.541322314049587, + 9.214416896235077, + 8.89485766758494, + 8.582644628099173, + 8.277777777777779, + 7.980257116620754, + 7.690082644628099, + 7.407254361799816, + 7.131772268135904, + 6.863636363636363, + 6.602846648301194, + 6.349403122130394, + 6.1033057851239665, + 5.86455463728191, + 5.633149678604225, + 5.40909090909091, + 5.192378328741964, + 4.983011937557391, + 4.78099173553719, + 4.586317722681359, + 4.398989898989899, + 4.2190082644628095, + 4.0463728191000925, + 3.881083562901744, + 3.723140495867768, + 3.572543617998163, + 3.429292929292929, + 3.293388429752066, + 3.1648301193755737, + 3.0436179981634526, + 2.929752066115703, + 2.8232323232323235, + 2.7240587695133147, + 2.6322314049586772, + 2.547750229568411, + 2.470615243342516, + 2.4008264462809916, + 2.3383838383838382, + 2.283287419651056, + 2.2355371900826446, + 2.195133149678604, + 2.1620752984389346, + 2.1363636363636362, + 2.1179981634527087, + 2.106978879706152, + 2.103305785123967, + 2.106978879706152, + 2.117998163452709, + 2.1363636363636362, + 2.1620752984389346, + 2.195133149678604, + 2.2355371900826446, + 2.2832874196510566, + 2.3383838383838387, + 2.400826446280992, + 2.4706152433425164, + 2.5477502295684116, + 2.632231404958678, + 2.724058769513315, + 2.8232323232323235, + 2.929752066115703, + 3.0436179981634526, + 3.1648301193755746, + 3.293388429752066, + 3.429292929292929, + 3.5725436179981633, + 3.723140495867768, + 3.881083562901747, + 4.046372819100093, + 4.219008264462812, + 4.398989898989901, + 4.58631772268136, + 4.780991735537191, + 4.983011937557394, + 5.192378328741967, + 5.40909090909091, + 5.633149678604225, + 5.864554637281909, + 6.1033057851239665 + ], + [ + 18.13269054178145, + 17.65151515151515, + 17.177685950413224, + 16.711202938475665, + 16.252066115702483, + 15.800275482093664, + 15.355831037649219, + 14.918732782369146, + 14.488980716253444, + 14.066574839302113, + 13.651515151515152, + 13.24380165289256, + 12.843434343434343, + 12.450413223140494, + 12.064738292011018, + 11.686409550045912, + 11.31542699724518, + 10.951790633608816, + 10.595500459136824, + 10.246556473829202, + 9.90495867768595, + 9.570707070707071, + 9.24380165289256, + 8.924242424242424, + 8.612029384756656, + 8.307162534435262, + 8.009641873278238, + 7.719467401285582, + 7.4366391184573, + 7.161157024793388, + 6.893021120293847, + 6.632231404958677, + 6.378787878787879, + 6.132690541781451, + 5.8939393939393945, + 5.662534435261708, + 5.438475665748394, + 5.221763085399449, + 5.012396694214876, + 4.810376492194674, + 4.615702479338843, + 4.428374655647383, + 4.248393021120294, + 4.075757575757576, + 3.910468319559228, + 3.7525252525252517, + 3.601928374655647, + 3.4586776859504127, + 3.3227731864095498, + 3.1942148760330578, + 3.0730027548209367, + 2.9591368227731865, + 2.852617079889807, + 2.7534435261707983, + 2.6616161616161613, + 2.577134986225895, + 2.5, + 2.4302112029384757, + 2.3677685950413223, + 2.3126721763085403, + 2.2649219467401283, + 2.224517906336088, + 2.1914600550964187, + 2.1657483930211203, + 2.147382920110193, + 2.1363636363636362, + 2.132690541781451, + 2.1363636363636362, + 2.147382920110193, + 2.1657483930211203, + 2.1914600550964183, + 2.2245179063360876, + 2.2649219467401283, + 2.3126721763085407, + 2.3677685950413228, + 2.430211202938476, + 2.5000000000000004, + 2.5771349862258957, + 2.661616161616162, + 2.7534435261707992, + 2.8526170798898076, + 2.959136822773187, + 3.073002754820936, + 3.194214876033058, + 3.3227731864095498, + 3.4586776859504127, + 3.601928374655647, + 3.7525252525252517, + 3.9104683195592305, + 4.075757575757577, + 4.248393021120296, + 4.428374655647384, + 4.615702479338844, + 4.810376492194675, + 5.012396694214877, + 5.22176308539945, + 5.438475665748394, + 5.662534435261708, + 5.893939393939393, + 6.13269054178145 + ], + [ + 18.16574839302112, + 17.68457300275482, + 17.210743801652896, + 16.744260789715334, + 16.28512396694215, + 15.833333333333332, + 15.38888888888889, + 14.951790633608816, + 14.522038567493112, + 14.099632690541782, + 13.68457300275482, + 13.27685950413223, + 12.876492194674011, + 12.483471074380164, + 12.097796143250687, + 11.719467401285582, + 11.348484848484848, + 10.984848484848484, + 10.628558310376492, + 10.27961432506887, + 9.938016528925619, + 9.603764921946741, + 9.276859504132231, + 8.957300275482094, + 8.645087235996327, + 8.34022038567493, + 8.042699724517906, + 7.752525252525253, + 7.46969696969697, + 7.194214876033058, + 6.926078971533516, + 6.665289256198347, + 6.411845730027548, + 6.16574839302112, + 5.926997245179064, + 5.695592286501378, + 5.471533516988063, + 5.254820936639118, + 5.045454545454545, + 4.8434343434343425, + 4.648760330578512, + 4.461432506887052, + 4.281450872359963, + 4.1088154269972454, + 3.943526170798897, + 3.785583103764921, + 3.6349862258953163, + 3.4917355371900825, + 3.355831037649219, + 3.227272727272727, + 3.106060606060606, + 2.9921946740128558, + 2.885674931129477, + 2.7865013774104677, + 2.6946740128558306, + 2.6101928374655645, + 2.5330578512396693, + 2.463269054178145, + 2.4008264462809916, + 2.3457300275482096, + 2.2979797979797976, + 2.2575757575757573, + 2.224517906336088, + 2.1988062442607896, + 2.180440771349862, + 2.169421487603306, + 2.1657483930211203, + 2.169421487603306, + 2.180440771349862, + 2.1988062442607896, + 2.224517906336088, + 2.2575757575757573, + 2.2979797979797976, + 2.34573002754821, + 2.400826446280992, + 2.4632690541781455, + 2.5330578512396698, + 2.610192837465565, + 2.6946740128558315, + 2.7865013774104685, + 2.885674931129477, + 2.992194674012856, + 3.1060606060606055, + 3.2272727272727275, + 3.355831037649219, + 3.491735537190082, + 3.6349862258953163, + 3.785583103764921, + 3.9435261707988998, + 4.108815426997246, + 4.281450872359965, + 4.4614325068870535, + 4.648760330578513, + 4.843434343434344, + 5.045454545454547, + 5.25482093663912, + 5.471533516988062, + 5.695592286501379, + 5.926997245179063, + 6.16574839302112 + ], + [ + 18.202479338842977, + 17.721303948576676, + 17.247474747474747, + 16.780991735537192, + 16.321854912764007, + 15.870064279155187, + 15.425619834710744, + 14.988521579430671, + 14.558769513314967, + 14.136363636363637, + 13.721303948576676, + 13.313590449954084, + 12.913223140495866, + 12.520202020202019, + 12.134527089072542, + 11.756198347107437, + 11.385215794306703, + 11.02157943067034, + 10.665289256198347, + 10.316345270890725, + 9.974747474747474, + 9.640495867768596, + 9.313590449954086, + 8.994031221303949, + 8.681818181818182, + 8.376951331496786, + 8.079430670339761, + 7.789256198347108, + 7.506427915518825, + 7.230945821854913, + 6.962809917355371, + 6.702020202020202, + 6.448576675849403, + 6.202479338842975, + 5.963728191000919, + 5.732323232323233, + 5.508264462809918, + 5.291551882460973, + 5.0821854912764, + 4.880165289256198, + 4.685491276400367, + 4.498163452708908, + 4.318181818181818, + 4.1455463728191, + 3.9802571166207525, + 3.8223140495867765, + 3.6717171717171713, + 3.5284664830119374, + 3.3925619834710745, + 3.2640036730945825, + 3.1427915518824614, + 3.028925619834711, + 2.922405876951332, + 2.823232323232323, + 2.731404958677686, + 2.6469237832874195, + 2.5697887970615243, + 2.5, + 2.437557392102847, + 2.3824609733700646, + 2.334710743801653, + 2.294306703397613, + 2.261248852157943, + 2.2355371900826446, + 2.217171717171717, + 2.206152433425161, + 2.2024793388429753, + 2.206152433425161, + 2.2171717171717176, + 2.2355371900826446, + 2.261248852157943, + 2.2943067033976123, + 2.334710743801653, + 2.382460973370065, + 2.437557392102847, + 2.5000000000000004, + 2.5697887970615247, + 2.64692378328742, + 2.7314049586776865, + 2.8232323232323235, + 2.922405876951332, + 3.028925619834711, + 3.1427915518824614, + 3.2640036730945825, + 3.392561983471074, + 3.528466483011937, + 3.6717171717171713, + 3.822314049586776, + 3.9802571166207548, + 4.145546372819101, + 4.31818181818182, + 4.4981634527089085, + 4.685491276400368, + 4.880165289256199, + 5.082185491276402, + 5.291551882460975, + 5.508264462809919, + 5.732323232323234, + 5.963728191000918, + 6.202479338842975 + ], + [ + 18.242883379247015, + 17.761707988980717, + 17.28787878787879, + 16.821395775941234, + 16.362258953168045, + 15.910468319559229, + 15.466023875114784, + 15.02892561983471, + 14.599173553719009, + 14.176767676767678, + 13.761707988980717, + 13.353994490358126, + 12.953627180899908, + 12.560606060606059, + 12.174931129476583, + 11.796602387511477, + 11.425619834710744, + 11.061983471074381, + 10.705693296602389, + 10.356749311294767, + 10.015151515151516, + 9.680899908172636, + 9.353994490358126, + 9.034435261707989, + 8.722222222222221, + 8.417355371900827, + 8.119834710743802, + 7.829660238751147, + 7.546831955922865, + 7.271349862258953, + 7.003213957759412, + 6.742424242424242, + 6.488980716253444, + 6.242883379247016, + 6.004132231404959, + 5.772727272727273, + 5.548668503213959, + 5.3319559228650135, + 5.122589531680441, + 4.920569329660239, + 4.725895316804408, + 4.538567493112948, + 4.358585858585859, + 4.185950413223141, + 4.020661157024793, + 3.8627180899908167, + 3.712121212121212, + 3.5688705234159777, + 3.4329660238751147, + 3.3044077134986227, + 3.1831955922865016, + 3.0693296602387514, + 2.962809917355372, + 2.8636363636363633, + 2.7718089990817263, + 2.68732782369146, + 2.610192837465565, + 2.5404040404040407, + 2.4779614325068873, + 2.4228650137741052, + 2.375114784205693, + 2.334710743801653, + 2.3016528925619832, + 2.2759412304866853, + 2.257575757575758, + 2.246556473829201, + 2.242883379247016, + 2.246556473829201, + 2.257575757575758, + 2.2759412304866853, + 2.3016528925619832, + 2.3347107438016526, + 2.375114784205693, + 2.4228650137741057, + 2.4779614325068877, + 2.540404040404041, + 2.6101928374655654, + 2.6873278236914606, + 2.771808999081727, + 2.863636363636364, + 2.9628099173553726, + 3.069329660238752, + 3.183195592286501, + 3.304407713498623, + 3.4329660238751147, + 3.5688705234159777, + 3.712121212121212, + 3.8627180899908167, + 4.020661157024795, + 4.185950413223142, + 4.358585858585861, + 4.538567493112949, + 4.725895316804409, + 4.92056932966024, + 5.122589531680442, + 5.331955922865015, + 5.548668503213959, + 5.772727272727273, + 6.004132231404958, + 6.242883379247015 + ], + [ + 18.286960514233243, + 17.805785123966942, + 17.331955922865014, + 16.86547291092746, + 16.406336088154273, + 15.954545454545453, + 15.51010101010101, + 15.073002754820937, + 14.643250688705233, + 14.220844811753903, + 13.805785123966942, + 13.39807162534435, + 12.997704315886132, + 12.604683195592285, + 12.219008264462808, + 11.840679522497704, + 11.469696969696969, + 11.106060606060606, + 10.749770431588615, + 10.400826446280991, + 10.05922865013774, + 9.724977043158862, + 9.398071625344352, + 9.078512396694215, + 8.766299357208448, + 8.461432506887054, + 8.163911845730027, + 7.873737373737374, + 7.590909090909091, + 7.315426997245179, + 7.047291092745637, + 6.7865013774104685, + 6.533057851239669, + 6.286960514233241, + 6.048209366391185, + 5.8168044077135, + 5.592745638200184, + 5.376033057851239, + 5.166666666666666, + 4.9646464646464645, + 4.7699724517906334, + 4.582644628099174, + 4.4026629935720845, + 4.2300275482093666, + 4.064738292011018, + 3.9067952249770426, + 3.756198347107438, + 3.6129476584022036, + 3.4770431588613406, + 3.3484848484848486, + 3.2272727272727275, + 3.1134067952249773, + 3.006887052341598, + 2.907713498622589, + 2.815886134067952, + 2.731404958677686, + 2.6542699724517904, + 2.5844811753902666, + 2.522038567493113, + 2.4669421487603307, + 2.419191919191919, + 2.378787878787879, + 2.3457300275482096, + 2.3200183654729107, + 2.3016528925619837, + 2.290633608815427, + 2.2869605142332414, + 2.290633608815427, + 2.3016528925619837, + 2.3200183654729107, + 2.3457300275482096, + 2.378787878787879, + 2.419191919191919, + 2.4669421487603316, + 2.522038567493113, + 2.584481175390267, + 2.6542699724517913, + 2.731404958677686, + 2.815886134067953, + 2.9077134986225897, + 3.0068870523415985, + 3.1134067952249778, + 3.2272727272727275, + 3.3484848484848486, + 3.47704315886134, + 3.612947658402203, + 3.7561983471074374, + 3.906795224977042, + 4.064738292011021, + 4.230027548209367, + 4.402662993572086, + 4.582644628099175, + 4.769972451790634, + 4.964646464646465, + 5.166666666666668, + 5.376033057851241, + 5.592745638200185, + 5.8168044077135, + 6.048209366391184, + 6.286960514233241 + ], + [ + 18.33471074380165, + 17.853535353535353, + 17.379706152433428, + 16.91322314049587, + 16.454086317722684, + 16.002295684113864, + 15.557851239669422, + 15.120752984389348, + 14.691000918273645, + 14.268595041322314, + 13.853535353535353, + 13.445821854912761, + 13.045454545454543, + 12.652433425160696, + 12.26675849403122, + 11.888429752066115, + 11.517447199265382, + 11.153810835629017, + 10.797520661157026, + 10.448576675849402, + 10.106978879706151, + 9.772727272727273, + 9.445821854912763, + 9.126262626262626, + 8.814049586776859, + 8.509182736455465, + 8.21166207529844, + 7.921487603305785, + 7.638659320477503, + 7.36317722681359, + 7.095041322314049, + 6.83425160697888, + 6.58080808080808, + 6.3347107438016526, + 6.095959595959596, + 5.864554637281911, + 5.640495867768596, + 5.42378328741965, + 5.214416896235077, + 5.012396694214876, + 4.8177226813590455, + 4.630394857667585, + 4.450413223140496, + 4.277777777777779, + 4.11248852157943, + 3.954545454545454, + 3.803948576675849, + 3.660697887970615, + 3.524793388429752, + 3.3962350780532597, + 3.2750229568411386, + 3.161157024793389, + 3.0546372819100096, + 2.955463728191001, + 2.8636363636363633, + 2.779155188246097, + 2.702020202020202, + 2.6322314049586777, + 2.5697887970615243, + 2.5146923783287423, + 2.4669421487603307, + 2.42653810835629, + 2.3934802571166207, + 2.3677685950413223, + 2.349403122130395, + 2.3383838383838382, + 2.334710743801653, + 2.3383838383838382, + 2.3494031221303953, + 2.3677685950413223, + 2.3934802571166207, + 2.42653810835629, + 2.4669421487603307, + 2.5146923783287427, + 2.5697887970615247, + 2.632231404958678, + 2.7020202020202024, + 2.7791551882460976, + 2.863636363636364, + 2.9554637281910012, + 3.0546372819100096, + 3.161157024793389, + 3.2750229568411386, + 3.3962350780532606, + 3.5247933884297513, + 3.660697887970615, + 3.8039485766758485, + 3.9545454545454533, + 4.112488521579433, + 4.277777777777779, + 4.450413223140497, + 4.630394857667586, + 4.8177226813590455, + 5.0123966942148765, + 5.214416896235079, + 5.423783287419653, + 5.640495867768596, + 5.864554637281911, + 6.095959595959595, + 6.3347107438016526 + ], + [ + 18.38613406795225, + 17.90495867768595, + 17.431129476584026, + 16.964646464646464, + 16.50550964187328, + 16.053719008264462, + 15.60927456382002, + 15.172176308539946, + 14.742424242424242, + 14.320018365472912, + 13.90495867768595, + 13.49724517906336, + 13.09687786960514, + 12.703856749311294, + 12.318181818181817, + 11.939853076216712, + 11.568870523415978, + 11.205234159779614, + 10.848943985307622, + 10.5, + 10.158402203856749, + 9.82415059687787, + 9.49724517906336, + 9.177685950413222, + 8.865472910927457, + 8.56060606060606, + 8.263085399449036, + 7.972910927456382, + 7.690082644628099, + 7.414600550964187, + 7.146464646464645, + 6.8856749311294765, + 6.632231404958677, + 6.38613406795225, + 6.147382920110193, + 5.915977961432508, + 5.691919191919192, + 5.475206611570247, + 5.265840220385675, + 5.0638200183654725, + 4.869146005509641, + 4.681818181818182, + 4.501836547291093, + 4.3292011019283745, + 4.163911845730027, + 4.005968778696051, + 3.855371900826446, + 3.712121212121212, + 3.576216712580349, + 3.4476584022038566, + 3.3264462809917354, + 3.2125803489439857, + 3.1060606060606064, + 3.0068870523415976, + 2.91505968778696, + 2.830578512396694, + 2.753443526170799, + 2.6836547291092745, + 2.621212121212121, + 2.566115702479339, + 2.5183654729109275, + 2.477961432506887, + 2.4449035812672175, + 2.419191919191919, + 2.400826446280992, + 2.389807162534435, + 2.38613406795225, + 2.389807162534435, + 2.400826446280992, + 2.419191919191919, + 2.4449035812672175, + 2.477961432506887, + 2.5183654729109275, + 2.5661157024793395, + 2.6212121212121215, + 2.683654729109275, + 2.7534435261707992, + 2.8305785123966944, + 2.915059687786961, + 3.006887052341598, + 3.1060606060606064, + 3.2125803489439857, + 3.3264462809917354, + 3.4476584022038574, + 3.576216712580349, + 3.712121212121212, + 3.855371900826446, + 4.005968778696051, + 4.16391184573003, + 4.329201101928376, + 4.501836547291095, + 4.681818181818183, + 4.869146005509643, + 5.063820018365474, + 5.265840220385677, + 5.47520661157025, + 5.691919191919192, + 5.9159779614325085, + 6.147382920110193, + 6.38613406795225 + ], + [ + 18.441230486685033, + 17.960055096418735, + 17.486225895316807, + 17.019742883379248, + 16.560606060606062, + 16.108815426997243, + 15.6643709825528, + 15.227272727272727, + 14.797520661157025, + 14.375114784205692, + 13.960055096418733, + 13.55234159779614, + 13.151974288337922, + 12.758953168044076, + 12.373278236914599, + 11.994949494949495, + 11.62396694214876, + 11.260330578512397, + 10.904040404040405, + 10.555096418732782, + 10.213498622589531, + 9.879247015610652, + 9.552341597796143, + 9.232782369146005, + 8.920569329660239, + 8.615702479338843, + 8.318181818181818, + 8.028007346189163, + 7.745179063360881, + 7.46969696969697, + 7.201561065197428, + 6.940771349862258, + 6.68732782369146, + 6.441230486685033, + 6.202479338842975, + 5.971074380165289, + 5.7470156106519745, + 5.530303030303029, + 5.3209366391184565, + 5.118916437098255, + 4.924242424242424, + 4.736914600550964, + 4.556932966023876, + 4.384297520661157, + 4.2190082644628095, + 4.061065197428833, + 3.9104683195592282, + 3.7672176308539944, + 3.631313131313131, + 3.502754820936639, + 3.381542699724518, + 3.2676767676767677, + 3.161157024793389, + 3.0619834710743796, + 2.9701561065197426, + 2.8856749311294765, + 2.8085399449035813, + 2.738751147842057, + 2.6763085399449036, + 2.621212121212121, + 2.5734618916437095, + 2.5330578512396693, + 2.5, + 2.4742883379247016, + 2.455922865013774, + 2.4449035812672175, + 2.4412304866850323, + 2.4449035812672175, + 2.455922865013774, + 2.4742883379247016, + 2.5, + 2.5330578512396693, + 2.5734618916437095, + 2.621212121212122, + 2.676308539944904, + 2.7387511478420574, + 2.8085399449035817, + 2.885674931129477, + 2.9701561065197435, + 3.0619834710743805, + 3.161157024793389, + 3.267676767676768, + 3.381542699724518, + 3.502754820936639, + 3.6313131313131306, + 3.7672176308539935, + 3.910468319559228, + 4.0610651974288325, + 4.219008264462811, + 4.384297520661158, + 4.556932966023877, + 4.736914600550965, + 4.924242424242425, + 5.118916437098256, + 5.320936639118458, + 5.530303030303031, + 5.7470156106519745, + 5.971074380165291, + 6.202479338842975, + 6.441230486685033 + ], + [ + 18.5, + 18.0188246097337, + 17.544995408631774, + 17.078512396694215, + 16.61937557392103, + 16.16758494031221, + 15.723140495867767, + 15.286042240587694, + 14.856290174471994, + 14.433884297520661, + 14.018824609733702, + 13.611111111111109, + 13.21074380165289, + 12.817722681359044, + 12.432047750229568, + 12.053719008264462, + 11.68273645546373, + 11.319100091827364, + 10.962809917355372, + 10.61386593204775, + 10.272268135904499, + 9.938016528925619, + 9.61111111111111, + 9.291551882460972, + 8.979338842975206, + 8.67447199265381, + 8.376951331496787, + 8.086776859504132, + 7.8039485766758485, + 7.528466483011938, + 7.260330578512396, + 6.999540863177226, + 6.746097337006428, + 6.5, + 6.2612488521579435, + 6.029843893480257, + 5.805785123966943, + 5.5890725436179975, + 5.379706152433425, + 5.177685950413222, + 4.983011937557392, + 4.795684113865932, + 4.615702479338843, + 4.443067033976125, + 4.277777777777777, + 4.119834710743801, + 3.969237832874196, + 3.825987144168962, + 3.6900826446280988, + 3.561524334251607, + 3.440312213039486, + 3.3264462809917354, + 3.2199265381083566, + 3.120752984389348, + 3.0289256198347103, + 2.944444444444444, + 2.867309458218549, + 2.7975206611570247, + 2.7350780532598717, + 2.6799816345270893, + 2.6322314049586772, + 2.591827364554637, + 2.5587695133149677, + 2.5330578512396693, + 2.514692378328742, + 2.5036730945821857, + 2.5, + 2.5036730945821857, + 2.514692378328742, + 2.5330578512396693, + 2.5587695133149677, + 2.591827364554637, + 2.6322314049586772, + 2.6799816345270897, + 2.7350780532598717, + 2.797520661157025, + 2.8673094582185494, + 2.9444444444444446, + 3.028925619834711, + 3.1207529843893482, + 3.2199265381083566, + 3.3264462809917354, + 3.440312213039485, + 3.561524334251607, + 3.6900826446280988, + 3.8259871441689617, + 3.969237832874196, + 4.119834710743801, + 4.2777777777777795, + 4.443067033976126, + 4.615702479338845, + 4.795684113865933, + 4.983011937557393, + 5.177685950413224, + 5.379706152433426, + 5.589072543617998, + 5.805785123966942, + 6.029843893480258, + 6.261248852157943, + 6.5 + ], + [ + 18.562442607897154, + 18.081267217630852, + 17.607438016528928, + 17.14095500459137, + 16.681818181818183, + 16.230027548209364, + 15.785583103764921, + 15.348484848484848, + 14.918732782369146, + 14.496326905417813, + 14.081267217630854, + 13.673553719008261, + 13.273186409550043, + 12.880165289256198, + 12.49449035812672, + 12.116161616161616, + 11.745179063360881, + 11.381542699724518, + 11.025252525252526, + 10.676308539944904, + 10.334710743801653, + 10.000459136822773, + 9.673553719008265, + 9.353994490358126, + 9.04178145087236, + 8.736914600550964, + 8.43939393939394, + 8.149219467401284, + 7.866391184573002, + 7.590909090909091, + 7.322773186409549, + 7.061983471074379, + 6.808539944903581, + 6.562442607897154, + 6.323691460055096, + 6.09228650137741, + 5.868227731864096, + 5.6515151515151505, + 5.442148760330578, + 5.240128558310376, + 5.045454545454545, + 4.858126721763085, + 4.678145087235997, + 4.505509641873278, + 4.340220385674931, + 4.1822773186409545, + 4.03168044077135, + 3.8884297520661155, + 3.752525252525252, + 3.62396694214876, + 3.502754820936639, + 3.388888888888889, + 3.28236914600551, + 3.183195592286501, + 3.0913682277318637, + 3.0068870523415976, + 2.9297520661157024, + 2.859963269054178, + 2.7975206611570247, + 2.742424242424242, + 2.6946740128558306, + 2.6542699724517904, + 2.621212121212121, + 2.5955004591368227, + 2.577134986225895, + 2.5661157024793386, + 2.5624426078971534, + 2.5661157024793386, + 2.577134986225895, + 2.5955004591368227, + 2.621212121212121, + 2.6542699724517904, + 2.6946740128558306, + 2.742424242424243, + 2.797520661157025, + 2.8599632690541785, + 2.929752066115703, + 3.006887052341598, + 3.0913682277318646, + 3.1831955922865016, + 3.28236914600551, + 3.3888888888888893, + 3.502754820936639, + 3.62396694214876, + 3.7525252525252517, + 3.8884297520661146, + 4.031680440771349, + 4.182277318640954, + 4.340220385674932, + 4.505509641873279, + 4.678145087235998, + 4.858126721763086, + 5.045454545454546, + 5.240128558310377, + 5.442148760330579, + 5.651515151515152, + 5.868227731864096, + 6.092286501377412, + 6.323691460055096, + 6.562442607897154 + ], + [ + 18.62855831037649, + 18.147382920110193, + 17.673553719008268, + 17.207070707070706, + 16.747933884297524, + 16.296143250688704, + 15.851698806244261, + 15.414600550964188, + 14.984848484848484, + 14.562442607897154, + 14.147382920110193, + 13.739669421487601, + 13.339302112029383, + 12.946280991735536, + 12.560606060606059, + 12.182277318640955, + 11.81129476584022, + 11.447658402203857, + 11.091368227731865, + 10.742424242424242, + 10.400826446280991, + 10.066574839302111, + 9.739669421487601, + 9.420110192837464, + 9.107897153351699, + 8.803030303030303, + 8.505509641873278, + 8.215335169880625, + 7.932506887052341, + 7.65702479338843, + 7.3888888888888875, + 7.128099173553719, + 6.8746556473829195, + 6.6285583103764925, + 6.389807162534435, + 6.15840220385675, + 5.934343434343434, + 5.717630853994489, + 5.508264462809917, + 5.306244260789715, + 5.111570247933884, + 4.924242424242424, + 4.7442607897153355, + 4.571625344352617, + 4.406336088154269, + 4.248393021120293, + 4.097796143250688, + 3.954545454545454, + 3.818640955004591, + 3.690082644628099, + 3.568870523415978, + 3.455004591368228, + 3.3484848484848486, + 3.24931129476584, + 3.1574839302112023, + 3.073002754820936, + 2.995867768595041, + 2.926078971533517, + 2.8636363636363633, + 2.8085399449035813, + 2.7607897153351697, + 2.720385674931129, + 2.6873278236914597, + 2.6616161616161613, + 2.6432506887052343, + 2.6322314049586777, + 2.628558310376492, + 2.6322314049586777, + 2.6432506887052343, + 2.6616161616161613, + 2.6873278236914597, + 2.720385674931129, + 2.7607897153351697, + 2.8085399449035817, + 2.8636363636363638, + 2.926078971533517, + 2.9958677685950414, + 3.0730027548209367, + 3.157483930211203, + 3.2493112947658402, + 3.3484848484848486, + 3.455004591368228, + 3.5688705234159777, + 3.6900826446280997, + 3.818640955004591, + 3.954545454545454, + 4.097796143250688, + 4.248393021120293, + 4.406336088154272, + 4.5716253443526185, + 4.744260789715337, + 4.924242424242426, + 5.111570247933885, + 5.3062442607897164, + 5.508264462809919, + 5.717630853994491, + 5.934343434343434, + 6.158402203856751, + 6.389807162534435, + 6.6285583103764925 + ], + [ + 18.698347107438018, + 18.217171717171716, + 17.743342516069788, + 17.276859504132233, + 16.817722681359047, + 16.365932047750228, + 15.921487603305785, + 15.484389348025712, + 15.054637281910008, + 14.632231404958677, + 14.217171717171716, + 13.809458218549125, + 13.409090909090907, + 13.01606978879706, + 12.630394857667584, + 12.252066115702478, + 11.881083562901745, + 11.51744719926538, + 11.16115702479339, + 10.812213039485766, + 10.470615243342515, + 10.136363636363637, + 9.809458218549127, + 9.48989898989899, + 9.177685950413222, + 8.872819100091828, + 8.575298438934803, + 8.285123966942148, + 8.002295684113866, + 7.726813590449954, + 7.458677685950413, + 7.197887970615243, + 6.944444444444444, + 6.698347107438016, + 6.459595959595959, + 6.228191000918274, + 6.004132231404959, + 5.787419651056013, + 5.5780532598714405, + 5.376033057851239, + 5.181359044995409, + 4.994031221303948, + 4.814049586776859, + 4.641414141414142, + 4.4761248852157935, + 4.3181818181818175, + 4.167584940312212, + 4.024334251606978, + 3.8884297520661155, + 3.759871441689623, + 3.638659320477502, + 3.524793388429752, + 3.418273645546373, + 3.319100091827364, + 3.2272727272727266, + 3.1427915518824605, + 3.0656565656565653, + 2.995867768595041, + 2.9334251606978876, + 2.8783287419651056, + 2.830578512396694, + 2.7901744719926533, + 2.757116620752984, + 2.7314049586776856, + 2.713039485766758, + 2.7020202020202015, + 2.6983471074380163, + 2.7020202020202015, + 2.7130394857667586, + 2.7314049586776856, + 2.757116620752984, + 2.7901744719926533, + 2.830578512396694, + 2.878328741965106, + 2.933425160697888, + 2.9958677685950414, + 3.0656565656565657, + 3.142791551882461, + 3.2272727272727275, + 3.3191000918273645, + 3.418273645546373, + 3.524793388429752, + 3.638659320477502, + 3.759871441689624, + 3.8884297520661146, + 4.024334251606978, + 4.167584940312212, + 4.318181818181817, + 4.476124885215796, + 4.641414141414142, + 4.814049586776861, + 4.994031221303949, + 5.181359044995409, + 5.37603305785124, + 5.578053259871442, + 5.787419651056016, + 6.004132231404959, + 6.228191000918274, + 6.4595959595959584, + 6.698347107438016 + ], + [ + 18.771808999081728, + 18.290633608815426, + 17.816804407713498, + 17.350321395775943, + 16.891184573002757, + 16.439393939393938, + 15.994949494949495, + 15.557851239669422, + 15.128099173553718, + 14.705693296602387, + 14.290633608815426, + 13.882920110192835, + 13.482552800734616, + 13.08953168044077, + 12.703856749311292, + 12.325528007346188, + 11.954545454545453, + 11.59090909090909, + 11.2346189164371, + 10.885674931129476, + 10.544077134986225, + 10.209825528007347, + 9.882920110192837, + 9.5633608815427, + 9.251147842056932, + 8.946280991735538, + 8.648760330578511, + 8.358585858585858, + 8.075757575757574, + 7.800275482093664, + 7.532139577594122, + 7.271349862258953, + 7.017906336088154, + 6.771808999081726, + 6.533057851239669, + 6.301652892561984, + 6.0775941230486685, + 5.860881542699723, + 5.6515151515151505, + 5.449494949494949, + 5.254820936639118, + 5.067493112947658, + 4.887511478420569, + 4.714876033057851, + 4.549586776859503, + 4.3916437098255265, + 4.241046831955922, + 4.097796143250688, + 3.961891643709825, + 3.833333333333333, + 3.712121212121212, + 3.5982552800734617, + 3.4917355371900825, + 3.3925619834710736, + 3.3007346189164366, + 3.2162534435261705, + 3.139118457300275, + 3.0693296602387505, + 3.0068870523415976, + 2.951790633608815, + 2.9040404040404035, + 2.8636363636363633, + 2.830578512396694, + 2.804866850321395, + 2.786501377410468, + 2.7754820936639115, + 2.771808999081726, + 2.7754820936639115, + 2.786501377410468, + 2.804866850321395, + 2.830578512396694, + 2.8636363636363633, + 2.9040404040404035, + 2.951790633608816, + 3.0068870523415976, + 3.0693296602387514, + 3.1391184573002757, + 3.2162534435261705, + 3.3007346189164375, + 3.392561983471074, + 3.491735537190083, + 3.598255280073462, + 3.712121212121212, + 3.833333333333333, + 3.9618916437098246, + 4.0977961432506875, + 4.241046831955922, + 4.3916437098255265, + 4.549586776859505, + 4.714876033057852, + 4.887511478420571, + 5.067493112947659, + 5.254820936639119, + 5.44949494949495, + 5.651515151515152, + 5.860881542699726, + 6.077594123048669, + 6.301652892561984, + 6.533057851239668, + 6.771808999081726 + ], + [ + 18.84894398530762, + 18.36776859504132, + 17.893939393939394, + 17.427456382001836, + 16.968319559228654, + 16.516528925619834, + 16.072084481175388, + 15.634986225895316, + 15.205234159779614, + 14.782828282828284, + 14.367768595041323, + 13.960055096418731, + 13.559687786960513, + 13.166666666666664, + 12.780991735537189, + 12.402662993572083, + 12.03168044077135, + 11.668044077134986, + 11.311753902662993, + 10.96280991735537, + 10.621212121212121, + 10.286960514233241, + 9.960055096418731, + 9.640495867768594, + 9.328282828282827, + 9.023415977961431, + 8.725895316804408, + 8.435720844811753, + 8.152892561983471, + 7.8774104683195585, + 7.609274563820017, + 7.348484848484848, + 7.095041322314049, + 6.8489439853076215, + 6.610192837465565, + 6.378787878787879, + 6.154729109274564, + 5.938016528925619, + 5.728650137741046, + 5.526629935720845, + 5.3319559228650135, + 5.144628099173554, + 4.9646464646464645, + 4.792011019283747, + 4.626721763085398, + 4.468778696051422, + 4.3181818181818175, + 4.174931129476583, + 4.03902662993572, + 3.9104683195592282, + 3.789256198347107, + 3.675390266299357, + 3.5688705234159777, + 3.469696969696969, + 3.377869605142332, + 3.2933884297520652, + 3.2162534435261705, + 3.146464646464646, + 3.084022038567493, + 3.0289256198347103, + 2.9811753902662987, + 2.9407713498622585, + 2.9077134986225888, + 2.882001836547291, + 2.8636363636363633, + 2.8526170798898067, + 2.8489439853076215, + 2.8526170798898067, + 2.8636363636363633, + 2.882001836547291, + 2.9077134986225888, + 2.940771349862258, + 2.9811753902662987, + 3.0289256198347108, + 3.0840220385674932, + 3.146464646464646, + 3.2162534435261705, + 3.293388429752066, + 3.3778696051423323, + 3.4696969696969697, + 3.5688705234159777, + 3.675390266299357, + 3.7892561983471067, + 3.9104683195592287, + 4.03902662993572, + 4.174931129476583, + 4.3181818181818175, + 4.468778696051422, + 4.626721763085401, + 4.7920110192837475, + 4.964646464646466, + 5.144628099173555, + 5.331955922865014, + 5.5266299357208455, + 5.728650137741047, + 5.938016528925621, + 6.154729109274564, + 6.378787878787879, + 6.610192837465563, + 6.848943985307621 + ], + [ + 18.929752066115704, + 18.448576675849402, + 17.974747474747474, + 17.50826446280992, + 17.049127640036733, + 16.597337006427914, + 16.15289256198347, + 15.715794306703398, + 15.286042240587694, + 14.863636363636363, + 14.448576675849402, + 14.04086317722681, + 13.640495867768593, + 13.247474747474746, + 12.861799816345268, + 12.483471074380164, + 12.11248852157943, + 11.748852157943066, + 11.392561983471076, + 11.043617998163452, + 10.7020202020202, + 10.367768595041323, + 10.040863177226813, + 9.721303948576676, + 9.409090909090908, + 9.104224058769512, + 8.806703397612488, + 8.516528925619834, + 8.23370064279155, + 7.95821854912764, + 7.690082644628098, + 7.429292929292929, + 7.17584940312213, + 6.929752066115702, + 6.691000918273645, + 6.459595959595959, + 6.235537190082645, + 6.0188246097336995, + 5.809458218549127, + 5.607438016528925, + 5.412764003673094, + 5.225436179981634, + 5.045454545454545, + 4.872819100091827, + 4.707529843893479, + 4.549586776859503, + 4.398989898989898, + 4.2557392102846645, + 4.119834710743801, + 3.991276400367309, + 3.870064279155188, + 3.756198347107438, + 3.6496786042240585, + 3.5505050505050497, + 3.4586776859504127, + 3.3741965105601466, + 3.297061524334251, + 3.2272727272727266, + 3.1648301193755737, + 3.109733700642791, + 3.0619834710743796, + 3.0215794306703394, + 2.9885215794306697, + 2.9628099173553712, + 2.9444444444444438, + 2.9334251606978876, + 2.929752066115702, + 2.9334251606978876, + 2.944444444444444, + 2.9628099173553712, + 2.9885215794306697, + 3.021579430670339, + 3.0619834710743796, + 3.1097337006427916, + 3.1648301193755737, + 3.227272727272727, + 3.2970615243342514, + 3.3741965105601466, + 3.458677685950413, + 3.55050505050505, + 3.649678604224059, + 3.7561983471074383, + 3.870064279155188, + 3.991276400367309, + 4.119834710743801, + 4.255739210284664, + 4.398989898989898, + 4.549586776859503, + 4.707529843893481, + 4.872819100091828, + 5.045454545454547, + 5.225436179981635, + 5.412764003673095, + 5.607438016528926, + 5.809458218549128, + 6.018824609733702, + 6.2355371900826455, + 6.45959595959596, + 6.6910009182736445, + 6.929752066115702 + ], + [ + 19.01423324150597, + 18.53305785123967, + 18.059228650137744, + 17.592745638200185, + 17.133608815427, + 16.68181818181818, + 16.237373737373737, + 15.800275482093664, + 15.370523415977964, + 14.948117539026631, + 14.533057851239672, + 14.125344352617079, + 13.72497704315886, + 13.331955922865014, + 12.946280991735538, + 12.567952249770432, + 12.196969696969699, + 11.833333333333334, + 11.477043158861342, + 11.12809917355372, + 10.786501377410469, + 10.452249770431589, + 10.12534435261708, + 9.805785123966942, + 9.493572084481176, + 9.18870523415978, + 8.891184573002757, + 8.601010101010102, + 8.318181818181818, + 8.042699724517908, + 7.774563820018366, + 7.513774104683196, + 7.260330578512397, + 7.01423324150597, + 6.775482093663912, + 6.544077134986227, + 6.3200183654729125, + 6.1033057851239665, + 5.8939393939393945, + 5.691919191919192, + 5.497245179063361, + 5.309917355371901, + 5.129935720844813, + 4.957300275482095, + 4.792011019283747, + 4.6340679522497705, + 4.483471074380166, + 4.3402203856749315, + 4.204315886134069, + 4.075757575757576, + 3.9545454545454555, + 3.8406795224977053, + 3.734159779614326, + 3.634986225895317, + 3.54315886134068, + 3.4586776859504136, + 3.381542699724519, + 3.3117539026629945, + 3.249311294765841, + 3.1942148760330586, + 3.146464646464647, + 3.106060606060607, + 3.073002754820937, + 3.047291092745639, + 3.0289256198347116, + 3.017906336088155, + 3.01423324150597, + 3.017906336088155, + 3.0289256198347116, + 3.047291092745639, + 3.073002754820937, + 3.1060606060606064, + 3.146464646464647, + 3.194214876033059, + 3.2493112947658416, + 3.3117539026629945, + 3.381542699724519, + 3.4586776859504145, + 3.5431588613406806, + 3.634986225895318, + 3.734159779614326, + 3.8406795224977053, + 3.954545454545455, + 4.075757575757577, + 4.204315886134069, + 4.3402203856749315, + 4.483471074380166, + 4.6340679522497705, + 4.792011019283749, + 4.957300275482096, + 5.129935720844815, + 5.309917355371903, + 5.497245179063363, + 5.691919191919194, + 5.893939393939396, + 6.103305785123968, + 6.320018365472912, + 6.544077134986228, + 6.775482093663912, + 7.01423324150597 + ], + [ + 19.10238751147842, + 18.62121212121212, + 18.147382920110196, + 17.680899908172638, + 17.221763085399452, + 16.769972451790633, + 16.32552800734619, + 15.888429752066116, + 15.458677685950413, + 15.036271808999082, + 14.621212121212121, + 14.21349862258953, + 13.813131313131311, + 13.420110192837464, + 13.034435261707989, + 12.656106519742883, + 12.28512396694215, + 11.921487603305785, + 11.565197428833795, + 11.21625344352617, + 10.874655647382921, + 10.540404040404042, + 10.213498622589531, + 9.893939393939394, + 9.581726354453627, + 9.276859504132233, + 8.979338842975208, + 8.689164370982553, + 8.406336088154271, + 8.130853994490359, + 7.862718089990818, + 7.601928374655648, + 7.348484848484849, + 7.102387511478421, + 6.863636363636364, + 6.632231404958679, + 6.408172635445364, + 6.191460055096418, + 5.982093663911845, + 5.780073461891644, + 5.585399449035814, + 5.398071625344353, + 5.218089990817264, + 5.045454545454547, + 4.880165289256198, + 4.722222222222222, + 4.571625344352617, + 4.428374655647383, + 4.29247015610652, + 4.163911845730028, + 4.042699724517907, + 3.928833792470157, + 3.822314049586778, + 3.723140495867769, + 3.6313131313131315, + 3.5468319559228654, + 3.46969696969697, + 3.399908172635446, + 3.3374655647382925, + 3.2823691460055104, + 3.234618916437099, + 3.194214876033058, + 3.161157024793389, + 3.1354453627180905, + 3.117079889807163, + 3.1060606060606064, + 3.102387511478421, + 3.1060606060606064, + 3.1170798898071634, + 3.1354453627180905, + 3.161157024793389, + 3.194214876033058, + 3.234618916437099, + 3.282369146005511, + 3.337465564738293, + 3.3999081726354463, + 3.4696969696969706, + 3.546831955922866, + 3.6313131313131324, + 3.723140495867769, + 3.822314049586778, + 3.928833792470157, + 4.042699724517907, + 4.163911845730029, + 4.2924701561065195, + 4.428374655647383, + 4.571625344352617, + 4.722222222222221, + 4.880165289256201, + 5.045454545454547, + 5.2180899908172655, + 5.398071625344354, + 5.585399449035814, + 5.780073461891645, + 5.982093663911847, + 6.191460055096421, + 6.408172635445364, + 6.632231404958679, + 6.863636363636363, + 7.102387511478421 + ], + [ + 19.194214876033058, + 18.713039485766757, + 18.239210284664832, + 17.772727272727273, + 17.31359044995409, + 16.861799816345272, + 16.417355371900825, + 15.980257116620752, + 15.550505050505052, + 15.12809917355372, + 14.71303948576676, + 14.305325987144167, + 13.904958677685949, + 13.511937557392102, + 13.126262626262626, + 12.74793388429752, + 12.376951331496787, + 12.013314967860424, + 11.65702479338843, + 11.308080808080808, + 10.966483011937557, + 10.632231404958679, + 10.305325987144169, + 9.98576675849403, + 9.673553719008265, + 9.368686868686869, + 9.071166207529846, + 8.78099173553719, + 8.498163452708908, + 8.222681359044996, + 7.954545454545454, + 7.693755739210285, + 7.440312213039486, + 7.194214876033058, + 6.955463728191002, + 6.7240587695133165, + 6.500000000000001, + 6.283287419651056, + 6.073921028466483, + 5.871900826446281, + 5.67722681359045, + 5.4898989898989905, + 5.309917355371901, + 5.137281910009183, + 4.971992653810835, + 4.814049586776859, + 4.663452708907254, + 4.520202020202021, + 4.384297520661157, + 4.255739210284665, + 4.134527089072544, + 4.020661157024794, + 3.9141414141414153, + 3.814967860422406, + 3.723140495867769, + 3.638659320477503, + 3.561524334251607, + 3.491735537190083, + 3.42929292929293, + 3.3741965105601475, + 3.326446280991736, + 3.2860422405876957, + 3.2529843893480264, + 3.2272727272727275, + 3.2089072543618005, + 3.197887970615244, + 3.194214876033058, + 3.197887970615244, + 3.2089072543618005, + 3.2272727272727275, + 3.2529843893480264, + 3.2860422405876957, + 3.326446280991736, + 3.3741965105601484, + 3.42929292929293, + 3.491735537190084, + 3.561524334251608, + 3.638659320477503, + 3.72314049586777, + 3.8149678604224064, + 3.9141414141414153, + 4.0206611570247945, + 4.134527089072544, + 4.255739210284665, + 4.384297520661157, + 4.52020202020202, + 4.663452708907254, + 4.814049586776859, + 4.971992653810838, + 5.137281910009184, + 5.309917355371903, + 5.489898989898991, + 5.677226813590451, + 5.871900826446282, + 6.073921028466485, + 6.283287419651058, + 6.500000000000002, + 6.7240587695133165, + 6.955463728191001, + 7.194214876033058 + ], + [ + 19.28971533516988, + 18.80853994490358, + 18.334710743801654, + 17.868227731864096, + 17.409090909090914, + 16.957300275482094, + 16.512855831037648, + 16.075757575757578, + 15.646005509641874, + 15.223599632690544, + 14.808539944903583, + 14.400826446280991, + 14.000459136822773, + 13.607438016528924, + 13.221763085399449, + 12.843434343434343, + 12.47245179063361, + 12.108815426997246, + 11.752525252525253, + 11.40358126721763, + 11.061983471074381, + 10.727731864095501, + 10.400826446280991, + 10.081267217630854, + 9.769054178145087, + 9.46418732782369, + 9.166666666666668, + 8.876492194674013, + 8.59366391184573, + 8.318181818181818, + 8.050045913682277, + 7.789256198347108, + 7.535812672176309, + 7.289715335169881, + 7.050964187327825, + 6.819559228650139, + 6.595500459136824, + 6.378787878787879, + 6.169421487603306, + 5.9674012855831045, + 5.772727272727273, + 5.585399449035814, + 5.405417814508724, + 5.2327823691460065, + 5.067493112947658, + 4.909550045913682, + 4.758953168044077, + 4.615702479338843, + 4.47979797979798, + 4.3512396694214885, + 4.230027548209367, + 4.116161616161617, + 4.0096418732782375, + 3.9104683195592287, + 3.8186409550045917, + 3.734159779614325, + 3.6570247933884303, + 3.587235996326906, + 3.5247933884297526, + 3.46969696969697, + 3.4219467401285586, + 3.3815426997245184, + 3.3484848484848486, + 3.3227731864095507, + 3.304407713498623, + 3.2933884297520666, + 3.2897153351698813, + 3.2933884297520666, + 3.304407713498623, + 3.3227731864095507, + 3.3484848484848486, + 3.381542699724518, + 3.4219467401285586, + 3.4696969696969706, + 3.524793388429753, + 3.587235996326906, + 3.6570247933884303, + 3.734159779614326, + 3.818640955004592, + 3.9104683195592296, + 4.0096418732782375, + 4.116161616161617, + 4.2300275482093666, + 4.3512396694214885, + 4.47979797979798, + 4.615702479338843, + 4.758953168044077, + 4.909550045913682, + 5.067493112947661, + 5.232782369146007, + 5.405417814508726, + 5.5853994490358145, + 5.772727272727274, + 5.9674012855831045, + 6.169421487603307, + 6.378787878787881, + 6.595500459136824, + 6.819559228650139, + 7.050964187327823, + 7.2897153351698805 + ], + [ + 19.38888888888889, + 18.90771349862259, + 18.433884297520663, + 17.967401285583104, + 17.50826446280992, + 17.056473829201103, + 16.612029384756656, + 16.174931129476583, + 15.745179063360883, + 15.32277318640955, + 14.907713498622591, + 14.499999999999998, + 14.09963269054178, + 13.706611570247933, + 13.320936639118457, + 12.942607897153351, + 12.571625344352618, + 12.207988980716253, + 11.851698806244261, + 11.502754820936639, + 11.161157024793388, + 10.82690541781451, + 10.5, + 10.180440771349861, + 9.868227731864096, + 9.5633608815427, + 9.265840220385677, + 8.975665748393022, + 8.692837465564738, + 8.417355371900827, + 8.149219467401284, + 7.8884297520661155, + 7.634986225895317, + 7.388888888888889, + 7.150137741046833, + 6.918732782369147, + 6.694674012855832, + 6.477961432506887, + 6.268595041322314, + 6.0665748393021115, + 5.871900826446281, + 5.684573002754822, + 5.504591368227732, + 5.331955922865014, + 5.166666666666666, + 5.00872359963269, + 4.858126721763085, + 4.714876033057852, + 4.578971533516988, + 4.4504132231404965, + 4.329201101928375, + 4.215335169880625, + 4.108815426997246, + 4.009641873278237, + 3.9178145087236, + 3.8333333333333335, + 3.7561983471074383, + 3.686409550045914, + 3.623966942148761, + 3.5688705234159785, + 3.5211202938475665, + 3.4807162534435263, + 3.447658402203857, + 3.4219467401285586, + 3.403581267217631, + 3.392561983471075, + 3.3888888888888893, + 3.392561983471075, + 3.403581267217631, + 3.4219467401285586, + 3.447658402203857, + 3.4807162534435263, + 3.5211202938475665, + 3.568870523415979, + 3.623966942148761, + 3.6864095500459144, + 3.7561983471074387, + 3.833333333333334, + 3.9178145087236, + 4.0096418732782375, + 4.108815426997246, + 4.215335169880625, + 4.3292011019283745, + 4.4504132231404965, + 4.578971533516988, + 4.714876033057851, + 4.858126721763085, + 5.00872359963269, + 5.166666666666669, + 5.331955922865015, + 5.504591368227734, + 5.6845730027548225, + 5.871900826446282, + 6.066574839302113, + 6.268595041322316, + 6.477961432506888, + 6.694674012855831, + 6.918732782369148, + 7.150137741046832, + 7.388888888888889 + ], + [ + 19.49173553719008, + 19.010560146923783, + 18.53673094582186, + 18.0702479338843, + 17.611111111111114, + 17.159320477502295, + 16.714876033057852, + 16.27777777777778, + 15.848025711662075, + 15.425619834710744, + 15.010560146923783, + 14.602846648301192, + 14.202479338842974, + 13.809458218549127, + 13.42378328741965, + 13.045454545454545, + 12.67447199265381, + 12.310835629017447, + 11.954545454545457, + 11.605601469237833, + 11.264003673094582, + 10.929752066115704, + 10.602846648301194, + 10.283287419651057, + 9.97107438016529, + 9.666207529843895, + 9.368686868686869, + 9.078512396694215, + 8.795684113865931, + 8.52020202020202, + 8.25206611570248, + 7.99127640036731, + 7.737832874196511, + 7.491735537190083, + 7.252984389348026, + 7.021579430670341, + 6.797520661157026, + 6.58080808080808, + 6.3714416896235075, + 6.169421487603306, + 5.974747474747475, + 5.787419651056015, + 5.607438016528926, + 5.434802571166208, + 5.26951331496786, + 5.111570247933884, + 4.960973370064279, + 4.8177226813590455, + 4.681818181818182, + 4.55325987144169, + 4.432047750229569, + 4.318181818181818, + 4.21166207529844, + 4.112488521579431, + 4.020661157024794, + 3.9361799816345275, + 3.859044995408632, + 3.7892561983471076, + 3.7268135904499546, + 3.671717171717172, + 3.6239669421487606, + 3.5835629017447204, + 3.550505050505051, + 3.524793388429752, + 3.506427915518825, + 3.4954086317722686, + 3.491735537190083, + 3.4954086317722686, + 3.506427915518825, + 3.524793388429752, + 3.550505050505051, + 3.5835629017447204, + 3.6239669421487606, + 3.671717171717173, + 3.7268135904499546, + 3.7892561983471085, + 3.8590449954086328, + 3.9361799816345275, + 4.0206611570247945, + 4.112488521579431, + 4.21166207529844, + 4.318181818181819, + 4.432047750229569, + 4.55325987144169, + 4.681818181818182, + 4.817722681359045, + 4.960973370064279, + 5.111570247933884, + 5.269513314967862, + 5.434802571166209, + 5.607438016528928, + 5.787419651056016, + 5.974747474747476, + 6.169421487603307, + 6.371441689623509, + 6.580808080808083, + 6.7975206611570265, + 7.021579430670341, + 7.2529843893480255, + 7.491735537190083 + ], + [ + 19.598255280073463, + 19.11707988980716, + 18.643250688705237, + 18.17676767676768, + 17.717630853994493, + 17.265840220385673, + 16.82139577594123, + 16.384297520661157, + 15.954545454545455, + 15.532139577594123, + 15.117079889807163, + 14.70936639118457, + 14.308999081726352, + 13.915977961432507, + 13.53030303030303, + 13.151974288337925, + 12.78099173553719, + 12.417355371900827, + 12.061065197428835, + 11.712121212121213, + 11.370523415977962, + 11.036271808999082, + 10.709366391184574, + 10.389807162534435, + 10.07759412304867, + 9.772727272727273, + 9.475206611570249, + 9.185032139577594, + 8.902203856749312, + 8.6267217630854, + 8.358585858585858, + 8.097796143250688, + 7.84435261707989, + 7.598255280073462, + 7.359504132231406, + 7.12809917355372, + 6.904040404040405, + 6.68732782369146, + 6.477961432506887, + 6.275941230486685, + 6.081267217630854, + 5.8939393939393945, + 5.713957759412305, + 5.541322314049587, + 5.376033057851239, + 5.218089990817264, + 5.067493112947658, + 4.924242424242424, + 4.788337924701561, + 4.659779614325069, + 4.538567493112948, + 4.424701561065198, + 4.318181818181818, + 4.2190082644628095, + 4.127180899908173, + 4.042699724517906, + 3.965564738292011, + 3.895775941230487, + 3.833333333333334, + 3.7782369146005514, + 3.7304866850321394, + 3.690082644628099, + 3.65702479338843, + 3.6313131313131315, + 3.612947658402204, + 3.601928374655648, + 3.598255280073462, + 3.601928374655648, + 3.612947658402204, + 3.6313131313131315, + 3.65702479338843, + 3.690082644628099, + 3.7304866850321394, + 3.778236914600552, + 3.833333333333334, + 3.8957759412304873, + 3.965564738292011, + 4.042699724517907, + 4.127180899908174, + 4.21900826446281, + 4.318181818181818, + 4.4247015610651985, + 4.538567493112948, + 4.659779614325069, + 4.788337924701561, + 4.924242424242424, + 5.067493112947658, + 5.218089990817263, + 5.376033057851242, + 5.541322314049588, + 5.713957759412307, + 5.893939393939395, + 6.081267217630856, + 6.275941230486687, + 6.477961432506888, + 6.6873278236914615, + 6.904040404040405, + 7.128099173553721, + 7.359504132231404, + 7.598255280073463 + ], + [ + 19.708448117539028, + 19.227272727272727, + 18.7534435261708, + 18.286960514233243, + 17.827823691460058, + 17.376033057851238, + 16.931588613406795, + 16.494490358126722, + 16.064738292011018, + 15.642332415059688, + 15.227272727272728, + 14.819559228650135, + 14.419191919191917, + 14.026170798898072, + 13.640495867768594, + 13.26216712580349, + 12.891184573002755, + 12.52754820936639, + 12.1712580348944, + 11.822314049586776, + 11.480716253443527, + 11.146464646464647, + 10.819559228650137, + 10.5, + 10.187786960514234, + 9.882920110192838, + 9.585399449035814, + 9.295224977043159, + 9.012396694214877, + 8.736914600550964, + 8.468778696051423, + 8.207988980716253, + 7.954545454545455, + 7.708448117539027, + 7.469696969696971, + 7.2382920110192845, + 7.01423324150597, + 6.797520661157025, + 6.588154269972451, + 6.38613406795225, + 6.191460055096419, + 6.004132231404959, + 5.82415059687787, + 5.651515151515152, + 5.486225895316804, + 5.328282828282828, + 5.177685950413223, + 5.034435261707989, + 4.898530762167126, + 4.769972451790634, + 4.648760330578513, + 4.534894398530763, + 4.428374655647383, + 4.3292011019283745, + 4.237373737373737, + 4.152892561983471, + 4.075757575757576, + 4.005968778696052, + 3.9435261707988984, + 3.888429752066116, + 3.8406795224977044, + 3.800275482093664, + 3.7672176308539944, + 3.7415059687786965, + 3.723140495867769, + 3.7121212121212124, + 3.708448117539027, + 3.7121212121212124, + 3.723140495867769, + 3.7415059687786965, + 3.7672176308539944, + 3.8002754820936637, + 3.8406795224977044, + 3.8884297520661164, + 3.943526170798899, + 4.005968778696052, + 4.075757575757576, + 4.152892561983472, + 4.237373737373738, + 4.329201101928375, + 4.428374655647383, + 4.534894398530763, + 4.648760330578512, + 4.769972451790634, + 4.898530762167126, + 5.034435261707989, + 5.177685950413223, + 5.328282828282828, + 5.486225895316807, + 5.651515151515153, + 5.824150596877872, + 6.004132231404959, + 6.191460055096419, + 6.38613406795225, + 6.588154269972453, + 6.7975206611570265, + 7.01423324150597, + 7.2382920110192845, + 7.469696969696969, + 7.708448117539026 + ], + [ + 19.82231404958678, + 19.341138659320478, + 18.86730945821855, + 18.400826446280995, + 17.941689623507806, + 17.48989898989899, + 17.045454545454547, + 16.608356290174473, + 16.17860422405877, + 15.75619834710744, + 15.341138659320478, + 14.933425160697887, + 14.533057851239668, + 14.14003673094582, + 13.754361799816344, + 13.376033057851238, + 13.005050505050505, + 12.641414141414142, + 12.28512396694215, + 11.936179981634528, + 11.594582185491277, + 11.260330578512397, + 10.933425160697887, + 10.61386593204775, + 10.301652892561982, + 9.996786042240588, + 9.699265381083563, + 9.409090909090908, + 9.126262626262626, + 8.850780532598716, + 8.582644628099173, + 8.321854912764003, + 8.068411386593205, + 7.822314049586777, + 7.58356290174472, + 7.352157943067034, + 7.12809917355372, + 6.911386593204774, + 6.7020202020202015, + 6.5, + 6.305325987144169, + 6.117998163452709, + 5.938016528925621, + 5.765381083562902, + 5.600091827364555, + 5.4421487603305785, + 5.291551882460973, + 5.1483011937557395, + 5.0123966942148765, + 4.883838383838384, + 4.762626262626263, + 4.648760330578513, + 4.542240587695134, + 4.443067033976124, + 4.351239669421488, + 4.2667584940312215, + 4.189623507805326, + 4.1198347107438025, + 4.057392102846649, + 4.002295684113866, + 3.9545454545454546, + 3.9141414141414144, + 3.881083562901745, + 3.855371900826446, + 3.837006427915519, + 3.8259871441689626, + 3.822314049586777, + 3.8259871441689626, + 3.837006427915519, + 3.855371900826446, + 3.881083562901745, + 3.9141414141414144, + 3.9545454545454546, + 4.002295684113867, + 4.057392102846649, + 4.1198347107438025, + 4.189623507805327, + 4.2667584940312215, + 4.3512396694214885, + 4.443067033976125, + 4.542240587695134, + 4.648760330578513, + 4.762626262626263, + 4.883838383838384, + 5.012396694214876, + 5.148301193755739, + 5.291551882460973, + 5.442148760330578, + 5.600091827364556, + 5.765381083562903, + 5.938016528925622, + 6.117998163452711, + 6.305325987144171, + 6.500000000000002, + 6.702020202020204, + 6.911386593204776, + 7.12809917355372, + 7.352157943067036, + 7.58356290174472, + 7.822314049586778 + ], + [ + 19.939853076216714, + 19.458677685950413, + 18.984848484848484, + 18.51836547291093, + 18.059228650137744, + 17.607438016528924, + 17.16299357208448, + 16.725895316804408, + 16.296143250688704, + 15.873737373737374, + 15.458677685950413, + 15.050964187327821, + 14.650596877869603, + 14.257575757575756, + 13.871900826446279, + 13.493572084481174, + 13.12258953168044, + 12.758953168044076, + 12.402662993572086, + 12.053719008264462, + 11.712121212121211, + 11.377869605142333, + 11.050964187327823, + 10.731404958677686, + 10.419191919191919, + 10.114325068870524, + 9.816804407713498, + 9.526629935720845, + 9.24380165289256, + 8.96831955922865, + 8.70018365472911, + 8.43939393939394, + 8.18595041322314, + 7.939853076216712, + 7.701101928374656, + 7.469696969696971, + 7.245638200183655, + 7.02892561983471, + 6.819559228650137, + 6.617539026629935, + 6.422865013774104, + 6.235537190082645, + 6.055555555555555, + 5.882920110192838, + 5.717630853994489, + 5.559687786960513, + 5.409090909090908, + 5.265840220385675, + 5.129935720844811, + 5.0013774104683195, + 4.880165289256198, + 4.766299357208448, + 4.659779614325069, + 4.5606060606060606, + 4.468778696051423, + 4.384297520661157, + 4.307162534435262, + 4.237373737373737, + 4.174931129476584, + 4.119834710743802, + 4.07208448117539, + 4.03168044077135, + 3.9986225895316805, + 3.9729109274563816, + 3.9545454545454546, + 3.943526170798898, + 3.9398530762167123, + 3.943526170798898, + 3.9545454545454546, + 3.9729109274563816, + 3.9986225895316805, + 4.03168044077135, + 4.07208448117539, + 4.1198347107438025, + 4.174931129476584, + 4.237373737373738, + 4.307162534435262, + 4.384297520661157, + 4.468778696051424, + 4.5606060606060606, + 4.659779614325069, + 4.766299357208449, + 4.880165289256198, + 5.0013774104683195, + 5.129935720844811, + 5.265840220385674, + 5.409090909090908, + 5.559687786960513, + 5.717630853994492, + 5.882920110192838, + 6.055555555555557, + 6.2355371900826455, + 6.422865013774105, + 6.617539026629936, + 6.819559228650139, + 7.0289256198347125, + 7.245638200183656, + 7.469696969696971, + 7.701101928374655, + 7.939853076216712 + ], + [ + 20.06106519742883, + 19.579889807162534, + 19.10606060606061, + 18.63957759412305, + 18.180440771349865, + 17.728650137741045, + 17.284205693296602, + 16.84710743801653, + 16.417355371900825, + 15.994949494949495, + 15.579889807162534, + 15.172176308539942, + 14.771808999081724, + 14.378787878787877, + 13.993112947658402, + 13.614784205693296, + 13.243801652892563, + 12.880165289256198, + 12.523875114784207, + 12.174931129476583, + 11.833333333333334, + 11.499081726354454, + 11.172176308539944, + 10.852617079889807, + 10.540404040404042, + 10.235537190082646, + 9.938016528925619, + 9.647842056932966, + 9.365013774104684, + 9.089531680440771, + 8.82139577594123, + 8.56060606060606, + 8.30716253443526, + 8.061065197428833, + 7.822314049586777, + 7.590909090909092, + 7.366850321395777, + 7.150137741046831, + 6.940771349862258, + 6.7387511478420565, + 6.544077134986226, + 6.356749311294766, + 6.1767676767676765, + 6.004132231404959, + 5.83884297520661, + 5.680899908172635, + 5.530303030303029, + 5.387052341597796, + 5.251147842056933, + 5.122589531680441, + 5.0013774104683195, + 4.88751147842057, + 4.7809917355371905, + 4.681818181818182, + 4.589990817263544, + 4.505509641873278, + 4.428374655647383, + 4.358585858585858, + 4.296143250688705, + 4.241046831955924, + 4.193296602387512, + 4.152892561983471, + 4.119834710743802, + 4.094123048668504, + 4.075757575757576, + 4.064738292011019, + 4.061065197428833, + 4.064738292011019, + 4.075757575757576, + 4.094123048668504, + 4.119834710743802, + 4.152892561983471, + 4.193296602387512, + 4.241046831955924, + 4.296143250688706, + 4.358585858585859, + 4.428374655647383, + 4.505509641873278, + 4.589990817263545, + 4.681818181818182, + 4.7809917355371905, + 4.88751147842057, + 5.0013774104683195, + 5.1225895316804415, + 5.251147842056932, + 5.387052341597796, + 5.530303030303029, + 5.680899908172634, + 5.838842975206614, + 6.004132231404959, + 6.176767676767678, + 6.356749311294767, + 6.544077134986226, + 6.738751147842057, + 6.94077134986226, + 7.150137741046834, + 7.366850321395777, + 7.590909090909092, + 7.822314049586776, + 8.061065197428833 + ], + [ + 20.18595041322314, + 19.70477502295684, + 19.230945821854913, + 18.764462809917354, + 18.305325987144172, + 17.853535353535353, + 17.40909090909091, + 16.971992653810837, + 16.542240587695133, + 16.119834710743802, + 15.704775022956841, + 15.29706152433425, + 14.896694214876032, + 14.503673094582183, + 14.117998163452707, + 13.739669421487601, + 13.368686868686869, + 13.005050505050505, + 12.648760330578513, + 12.29981634527089, + 11.95821854912764, + 11.62396694214876, + 11.29706152433425, + 10.977502295684113, + 10.665289256198346, + 10.36042240587695, + 10.062901744719927, + 9.772727272727272, + 9.48989898989899, + 9.214416896235077, + 8.946280991735536, + 8.685491276400366, + 8.432047750229568, + 8.18595041322314, + 7.947199265381084, + 7.715794306703398, + 7.491735537190083, + 7.275022956841138, + 7.065656565656565, + 6.863636363636363, + 6.668962350780532, + 6.4816345270890725, + 6.301652892561983, + 6.129017447199265, + 5.963728191000917, + 5.805785123966942, + 5.655188246097336, + 5.511937557392102, + 5.37603305785124, + 5.247474747474747, + 5.126262626262626, + 5.0123966942148765, + 4.905876951331496, + 4.8067033976124875, + 4.71487603305785, + 4.630394857667584, + 4.553259871441689, + 4.483471074380165, + 4.421028466483012, + 4.3659320477502295, + 4.3181818181818175, + 4.277777777777777, + 4.244719926538108, + 4.2190082644628095, + 4.200642791551882, + 4.189623507805326, + 4.18595041322314, + 4.189623507805326, + 4.200642791551882, + 4.2190082644628095, + 4.244719926538108, + 4.277777777777777, + 4.3181818181818175, + 4.3659320477502295, + 4.421028466483012, + 4.483471074380166, + 4.553259871441689, + 4.630394857667585, + 4.714876033057852, + 4.806703397612488, + 4.905876951331496, + 5.0123966942148765, + 5.126262626262626, + 5.247474747474747, + 5.376033057851239, + 5.511937557392102, + 5.655188246097336, + 5.805785123966941, + 5.96372819100092, + 6.129017447199266, + 6.301652892561986, + 6.481634527089074, + 6.668962350780532, + 6.863636363636363, + 7.0656565656565675, + 7.2750229568411395, + 7.491735537190083, + 7.715794306703398, + 7.947199265381084, + 8.18595041322314 + ], + [ + 20.31450872359963, + 19.833333333333332, + 19.359504132231407, + 18.89302112029385, + 18.433884297520663, + 17.982093663911844, + 17.5376492194674, + 17.100550964187327, + 16.670798898071624, + 16.248393021120293, + 15.833333333333332, + 15.42561983471074, + 15.025252525252522, + 14.632231404958675, + 14.2465564738292, + 13.868227731864094, + 13.497245179063361, + 13.133608815426996, + 12.777318640955006, + 12.428374655647382, + 12.086776859504132, + 11.752525252525253, + 11.425619834710742, + 11.106060606060606, + 10.79384756657484, + 10.488980716253444, + 10.191460055096417, + 9.901285583103764, + 9.618457300275482, + 9.34297520661157, + 9.074839302112029, + 8.814049586776859, + 8.560606060606059, + 8.314508723599632, + 8.075757575757574, + 7.84435261707989, + 7.620293847566575, + 7.403581267217629, + 7.194214876033056, + 6.992194674012855, + 6.797520661157025, + 6.610192837465564, + 6.430211202938475, + 6.257575757575758, + 6.092286501377409, + 5.934343434343433, + 5.783746556473828, + 5.640495867768594, + 5.504591368227731, + 5.376033057851239, + 5.254820936639118, + 5.140955004591368, + 5.034435261707989, + 4.93526170798898, + 4.8434343434343425, + 4.758953168044076, + 4.681818181818182, + 4.6120293847566565, + 4.5495867768595035, + 4.494490358126722, + 4.44674012855831, + 4.406336088154269, + 4.3732782369146, + 4.347566574839302, + 4.3292011019283745, + 4.3181818181818175, + 4.314508723599632, + 4.3181818181818175, + 4.3292011019283745, + 4.347566574839302, + 4.3732782369146, + 4.406336088154269, + 4.44674012855831, + 4.494490358126722, + 4.549586776859504, + 4.612029384756657, + 4.681818181818182, + 4.758953168044076, + 4.843434343434343, + 4.93526170798898, + 5.034435261707989, + 5.140955004591368, + 5.254820936639118, + 5.37603305785124, + 5.5045913682277305, + 5.640495867768594, + 5.783746556473828, + 5.9343434343434325, + 6.092286501377412, + 6.257575757575758, + 6.430211202938477, + 6.610192837465565, + 6.797520661157025, + 6.992194674012856, + 7.194214876033058, + 7.403581267217632, + 7.620293847566575, + 7.84435261707989, + 8.075757575757574, + 8.314508723599632 + ], + [ + 20.44674012855831, + 19.96556473829201, + 19.491735537190085, + 19.025252525252526, + 18.56611570247934, + 18.11432506887052, + 17.669880624426078, + 17.232782369146005, + 16.803030303030305, + 16.38062442607897, + 15.965564738292013, + 15.557851239669418, + 15.1574839302112, + 14.764462809917354, + 14.378787878787877, + 14.000459136822773, + 13.629476584022038, + 13.265840220385675, + 12.909550045913683, + 12.56060606060606, + 12.21900826446281, + 11.88475665748393, + 11.557851239669422, + 11.238292011019283, + 10.926078971533517, + 10.621212121212121, + 10.323691460055096, + 10.033516988062441, + 9.75068870523416, + 9.475206611570247, + 9.207070707070706, + 8.946280991735536, + 8.692837465564738, + 8.44674012855831, + 8.207988980716253, + 7.976584022038567, + 7.752525252525253, + 7.5358126721763075, + 7.326446280991735, + 7.124426078971533, + 6.929752066115702, + 6.742424242424242, + 6.562442607897153, + 6.389807162534435, + 6.224517906336087, + 6.0665748393021115, + 5.915977961432506, + 5.772727272727272, + 5.63682277318641, + 5.508264462809917, + 5.387052341597796, + 5.273186409550046, + 5.166666666666666, + 5.067493112947657, + 4.97566574839302, + 4.891184573002754, + 4.814049586776859, + 4.744260789715335, + 4.681818181818182, + 4.626721763085399, + 4.578971533516987, + 4.5385674931129465, + 4.505509641873278, + 4.479797979797979, + 4.461432506887052, + 4.450413223140496, + 4.44674012855831, + 4.450413223140496, + 4.461432506887052, + 4.479797979797979, + 4.505509641873278, + 4.5385674931129465, + 4.578971533516987, + 4.626721763085399, + 4.681818181818182, + 4.7442607897153355, + 4.814049586776859, + 4.8911845730027546, + 4.975665748393022, + 5.067493112947658, + 5.166666666666666, + 5.273186409550046, + 5.387052341597796, + 5.508264462809917, + 5.636822773186409, + 5.772727272727272, + 5.915977961432506, + 6.066574839302111, + 6.224517906336089, + 6.389807162534435, + 6.562442607897154, + 6.742424242424242, + 6.929752066115704, + 7.124426078971535, + 7.3264462809917354, + 7.535812672176309, + 7.752525252525253, + 7.976584022038569, + 8.207988980716252, + 8.44674012855831 + ], + [ + 20.582644628099175, + 20.101469237832873, + 19.627640036730945, + 19.16115702479339, + 18.702020202020204, + 18.250229568411385, + 17.805785123966942, + 17.36868686868687, + 16.938934802571165, + 16.516528925619834, + 16.101469237832873, + 15.693755739210282, + 15.293388429752063, + 14.900367309458217, + 14.51469237832874, + 14.136363636363635, + 13.7653810835629, + 13.401744719926537, + 13.045454545454545, + 12.696510560146923, + 12.354912764003672, + 12.020661157024794, + 11.693755739210282, + 11.374196510560147, + 11.06198347107438, + 10.757116620752985, + 10.459595959595958, + 10.169421487603305, + 9.886593204775021, + 9.61111111111111, + 9.34297520661157, + 9.082185491276398, + 8.8287419651056, + 8.582644628099173, + 8.343893480257115, + 8.11248852157943, + 7.8884297520661155, + 7.67171717171717, + 7.4623507805325975, + 7.260330578512395, + 7.065656565656565, + 6.878328741965104, + 6.698347107438016, + 6.525711662075298, + 6.36042240587695, + 6.2024793388429735, + 6.051882460973369, + 5.908631772268135, + 5.772727272727272, + 5.644168962350779, + 5.522956841138658, + 5.409090909090908, + 5.30257116620753, + 5.203397612488521, + 5.111570247933884, + 5.0270890725436175, + 4.949954086317722, + 4.8801652892561975, + 4.817722681359044, + 4.762626262626262, + 4.71487603305785, + 4.67447199265381, + 4.64141414141414, + 4.615702479338842, + 4.597337006427915, + 4.5863177226813585, + 4.582644628099173, + 4.5863177226813585, + 4.597337006427915, + 4.615702479338842, + 4.64141414141414, + 4.67447199265381, + 4.71487603305785, + 4.762626262626263, + 4.817722681359045, + 4.8801652892561975, + 4.949954086317723, + 5.0270890725436175, + 5.111570247933884, + 5.203397612488521, + 5.30257116620753, + 5.409090909090908, + 5.522956841138658, + 5.64416896235078, + 5.772727272727272, + 5.9086317722681345, + 6.051882460973369, + 6.2024793388429735, + 6.360422405876953, + 6.525711662075299, + 6.698347107438018, + 6.878328741965106, + 7.065656565656566, + 7.260330578512397, + 7.462350780532599, + 7.671717171717173, + 7.888429752066116, + 8.112488521579431, + 8.343893480257115, + 8.582644628099173 + ], + [ + 20.72222222222222, + 20.241046831955924, + 19.767217630854, + 19.30073461891644, + 18.841597796143255, + 18.389807162534435, + 17.945362718089992, + 17.50826446280992, + 17.078512396694215, + 16.656106519742885, + 16.241046831955924, + 15.833333333333332, + 15.432966023875114, + 15.039944903581267, + 14.654269972451791, + 14.275941230486685, + 13.904958677685952, + 13.541322314049587, + 13.185032139577597, + 12.836088154269973, + 12.494490358126724, + 12.160238751147844, + 11.833333333333334, + 11.513774104683197, + 11.201561065197431, + 10.896694214876035, + 10.599173553719009, + 10.308999081726355, + 10.026170798898073, + 9.750688705234161, + 9.48255280073462, + 9.22176308539945, + 8.96831955922865, + 8.722222222222223, + 8.483471074380166, + 8.252066115702481, + 8.028007346189167, + 7.811294765840221, + 7.601928374655648, + 7.399908172635446, + 7.205234159779616, + 7.0179063360881555, + 6.837924701561066, + 6.665289256198349, + 6.5, + 6.342056932966025, + 6.191460055096419, + 6.048209366391186, + 5.912304866850323, + 5.78374655647383, + 5.662534435261709, + 5.5486685032139595, + 5.44214876033058, + 5.342975206611571, + 5.251147842056934, + 5.166666666666668, + 5.089531680440773, + 5.019742883379248, + 4.957300275482095, + 4.902203856749313, + 4.854453627180901, + 4.814049586776861, + 4.780991735537191, + 4.755280073461893, + 4.736914600550966, + 4.725895316804409, + 4.722222222222223, + 4.725895316804409, + 4.736914600550966, + 4.755280073461893, + 4.780991735537191, + 4.814049586776861, + 4.854453627180901, + 4.902203856749313, + 4.957300275482096, + 5.019742883379249, + 5.089531680440773, + 5.166666666666668, + 5.251147842056935, + 5.342975206611571, + 5.44214876033058, + 5.5486685032139595, + 5.662534435261709, + 5.783746556473831, + 5.912304866850322, + 6.048209366391186, + 6.191460055096419, + 6.342056932966024, + 6.5000000000000036, + 6.665289256198349, + 6.837924701561068, + 7.017906336088156, + 7.205234159779616, + 7.399908172635447, + 7.60192837465565, + 7.811294765840223, + 8.028007346189167, + 8.252066115702481, + 8.483471074380166, + 8.722222222222223 + ], + [ + 20.86547291092746, + 20.384297520661157, + 19.910468319559232, + 19.443985307621674, + 18.984848484848488, + 18.53305785123967, + 18.088613406795226, + 17.651515151515152, + 17.221763085399452, + 16.799357208448118, + 16.38429752066116, + 15.976584022038567, + 15.576216712580349, + 15.183195592286502, + 14.797520661157025, + 14.41919191919192, + 14.048209366391186, + 13.684573002754822, + 13.32828282828283, + 12.979338842975208, + 12.637741046831957, + 12.303489439853077, + 11.976584022038569, + 11.65702479338843, + 11.344811753902665, + 11.039944903581269, + 10.742424242424244, + 10.452249770431589, + 10.169421487603307, + 9.893939393939394, + 9.625803489439853, + 9.365013774104684, + 9.111570247933885, + 8.865472910927458, + 8.626721763085401, + 8.395316804407715, + 8.1712580348944, + 7.954545454545455, + 7.745179063360882, + 7.543158861340681, + 7.3484848484848495, + 7.16115702479339, + 6.9811753902663005, + 6.808539944903583, + 6.643250688705234, + 6.485307621671259, + 6.334710743801653, + 6.191460055096419, + 6.055555555555557, + 5.926997245179065, + 5.805785123966944, + 5.691919191919194, + 5.585399449035814, + 5.486225895316805, + 5.394398530762167, + 5.309917355371901, + 5.2327823691460065, + 5.162993572084482, + 5.100550964187329, + 5.045454545454547, + 4.997704315886135, + 4.957300275482094, + 4.924242424242426, + 4.898530762167127, + 4.880165289256199, + 4.869146005509643, + 4.8654729109274575, + 4.869146005509643, + 4.880165289256199, + 4.898530762167127, + 4.924242424242426, + 4.957300275482094, + 4.997704315886135, + 5.045454545454547, + 5.100550964187329, + 5.162993572084483, + 5.2327823691460065, + 5.309917355371902, + 5.394398530762169, + 5.486225895316806, + 5.585399449035814, + 5.691919191919194, + 5.805785123966944, + 5.926997245179065, + 6.055555555555556, + 6.191460055096419, + 6.334710743801653, + 6.485307621671259, + 6.643250688705237, + 6.808539944903583, + 6.981175390266301, + 7.16115702479339, + 7.348484848484851, + 7.543158861340682, + 7.745179063360883, + 7.954545454545457, + 8.1712580348944, + 8.395316804407717, + 8.6267217630854, + 8.865472910927458 + ], + [ + 21.01239669421488, + 20.531221303948577, + 20.057392102846652, + 19.590909090909093, + 19.131772268135908, + 18.67998163452709, + 18.235537190082646, + 17.798438934802572, + 17.368686868686872, + 16.946280991735538, + 16.53122130394858, + 16.123507805325985, + 15.723140495867769, + 15.330119375573922, + 14.944444444444445, + 14.56611570247934, + 14.195133149678606, + 13.831496786042242, + 13.47520661157025, + 13.126262626262628, + 12.784664830119377, + 12.450413223140497, + 12.123507805325989, + 11.80394857667585, + 11.491735537190085, + 11.186868686868689, + 10.889348025711664, + 10.599173553719009, + 10.316345270890727, + 10.040863177226814, + 9.772727272727273, + 9.511937557392104, + 9.258494031221305, + 9.012396694214878, + 8.773645546372821, + 8.542240587695135, + 8.31818181818182, + 8.101469237832875, + 7.892102846648302, + 7.6900826446281005, + 7.4954086317722695, + 7.30808080808081, + 7.1280991735537205, + 6.955463728191003, + 6.790174471992654, + 6.632231404958679, + 6.481634527089073, + 6.338383838383839, + 6.202479338842977, + 6.073921028466485, + 5.9527089072543635, + 5.838842975206614, + 5.732323232323234, + 5.633149678604225, + 5.541322314049587, + 5.456841138659321, + 5.379706152433426, + 5.309917355371902, + 5.247474747474749, + 5.192378328741967, + 5.144628099173555, + 5.104224058769514, + 5.071166207529846, + 5.045454545454547, + 5.027089072543619, + 5.016069788797063, + 5.012396694214877, + 5.016069788797063, + 5.027089072543619, + 5.045454545454547, + 5.071166207529846, + 5.104224058769514, + 5.144628099173555, + 5.192378328741967, + 5.247474747474749, + 5.309917355371903, + 5.379706152433426, + 5.456841138659322, + 5.541322314049589, + 5.633149678604226, + 5.732323232323234, + 5.838842975206614, + 5.9527089072543635, + 6.073921028466485, + 6.202479338842976, + 6.338383838383839, + 6.481634527089073, + 6.632231404958679, + 6.790174471992657, + 6.955463728191003, + 7.128099173553721, + 7.30808080808081, + 7.495408631772271, + 7.690082644628102, + 7.892102846648303, + 8.101469237832877, + 8.31818181818182, + 8.542240587695137, + 8.77364554637282, + 9.012396694214878 + ], + [ + 21.16299357208448, + 20.681818181818183, + 20.207988980716255, + 19.741505968778696, + 19.282369146005514, + 18.830578512396695, + 18.386134067952252, + 17.94903581267218, + 17.519283746556475, + 17.096877869605144, + 16.681818181818183, + 16.27410468319559, + 15.873737373737372, + 15.480716253443527, + 15.09504132231405, + 14.716712580348943, + 14.34573002754821, + 13.982093663911847, + 13.625803489439855, + 13.276859504132233, + 12.935261707988982, + 12.601010101010102, + 12.274104683195592, + 11.954545454545455, + 11.642332415059688, + 11.337465564738292, + 11.039944903581269, + 10.749770431588614, + 10.466942148760332, + 10.19146005509642, + 9.923324150596878, + 9.662534435261708, + 9.40909090909091, + 9.162993572084481, + 8.924242424242426, + 8.69283746556474, + 8.468778696051425, + 8.25206611570248, + 8.042699724517906, + 7.840679522497705, + 7.646005509641874, + 7.4586776859504145, + 7.278696051423325, + 7.106060606060607, + 6.940771349862259, + 6.782828282828284, + 6.632231404958678, + 6.488980716253444, + 6.353076216712582, + 6.224517906336089, + 6.103305785123968, + 5.9894398530762185, + 5.882920110192838, + 5.7837465564738295, + 5.691919191919192, + 5.607438016528926, + 5.530303030303031, + 5.460514233241507, + 5.398071625344354, + 5.342975206611571, + 5.295224977043159, + 5.254820936639119, + 5.22176308539945, + 5.1960514233241515, + 5.177685950413224, + 5.166666666666668, + 5.162993572084482, + 5.166666666666668, + 5.177685950413224, + 5.1960514233241515, + 5.22176308539945, + 5.254820936639119, + 5.295224977043159, + 5.342975206611571, + 5.398071625344354, + 5.460514233241508, + 5.530303030303031, + 5.607438016528927, + 5.691919191919194, + 5.78374655647383, + 5.882920110192838, + 5.9894398530762185, + 6.103305785123968, + 6.224517906336089, + 6.353076216712581, + 6.488980716253444, + 6.632231404958679, + 6.782828282828282, + 6.940771349862262, + 7.106060606060609, + 7.278696051423328, + 7.458677685950416, + 7.646005509641874, + 7.840679522497705, + 8.04269972451791, + 8.252066115702481, + 8.468778696051425, + 8.69283746556474, + 8.924242424242426, + 9.162993572084481 + ], + [ + 21.317263544536274, + 20.836088154269973, + 20.362258953168045, + 19.89577594123049, + 19.436639118457304, + 18.984848484848484, + 18.54040404040404, + 18.10330578512397, + 17.673553719008265, + 17.251147842056934, + 16.836088154269973, + 16.42837465564738, + 16.028007346189163, + 15.634986225895316, + 15.249311294765839, + 14.870982552800735, + 14.5, + 14.136363636363637, + 13.780073461891645, + 13.431129476584022, + 13.089531680440771, + 12.755280073461893, + 12.428374655647382, + 12.108815426997246, + 11.796602387511479, + 11.491735537190085, + 11.194214876033058, + 10.904040404040405, + 10.621212121212121, + 10.34573002754821, + 10.07759412304867, + 9.816804407713498, + 9.5633608815427, + 9.317263544536273, + 9.078512396694215, + 8.847107438016529, + 8.623048668503216, + 8.40633608815427, + 8.196969696969697, + 7.994949494949495, + 7.800275482093665, + 7.612947658402204, + 7.432966023875116, + 7.260330578512398, + 7.095041322314049, + 6.937098255280073, + 6.7865013774104685, + 6.643250688705235, + 6.507346189164371, + 6.378787878787879, + 6.257575757575758, + 6.143709825528008, + 6.03719008264463, + 5.938016528925621, + 5.846189164370983, + 5.761707988980717, + 5.684573002754822, + 5.614784205693297, + 5.5523415977961434, + 5.497245179063362, + 5.44949494949495, + 5.40909090909091, + 5.37603305785124, + 5.350321395775942, + 5.331955922865014, + 5.320936639118458, + 5.317263544536273, + 5.320936639118458, + 5.331955922865014, + 5.350321395775942, + 5.37603305785124, + 5.40909090909091, + 5.44949494949495, + 5.497245179063363, + 5.552341597796144, + 5.614784205693297, + 5.6845730027548225, + 5.761707988980717, + 5.846189164370983, + 5.938016528925621, + 6.03719008264463, + 6.143709825528008, + 6.257575757575758, + 6.37878787878788, + 6.507346189164371, + 6.643250688705234, + 6.7865013774104685, + 6.937098255280073, + 7.095041322314053, + 7.260330578512399, + 7.432966023875117, + 7.612947658402206, + 7.8002754820936655, + 7.994949494949497, + 8.196969696969699, + 8.406336088154273, + 8.623048668503216, + 8.84710743801653, + 9.078512396694215, + 9.317263544536273 + ], + [ + 21.47520661157025, + 20.99403122130395, + 20.52020202020202, + 20.053719008264466, + 19.59458218549128, + 19.14279155188246, + 18.698347107438018, + 18.261248852157944, + 17.83149678604224, + 17.40909090909091, + 16.99403122130395, + 16.586317722681358, + 16.18595041322314, + 15.792929292929292, + 15.407254361799817, + 15.02892561983471, + 14.657943067033976, + 14.294306703397613, + 13.93801652892562, + 13.589072543617998, + 13.247474747474747, + 12.91322314049587, + 12.586317722681358, + 12.266758494031222, + 11.954545454545455, + 11.64967860422406, + 11.352157943067034, + 11.061983471074381, + 10.779155188246097, + 10.503673094582187, + 10.235537190082646, + 9.974747474747474, + 9.721303948576676, + 9.475206611570249, + 9.236455463728191, + 9.005050505050505, + 8.780991735537192, + 8.564279155188245, + 8.354912764003673, + 8.152892561983471, + 7.958218549127641, + 7.77089072543618, + 7.590909090909092, + 7.418273645546374, + 7.2529843893480255, + 7.095041322314049, + 6.944444444444445, + 6.801193755739211, + 6.6652892561983474, + 6.536730945821855, + 6.415518824609734, + 6.301652892561984, + 6.195133149678606, + 6.095959595959597, + 6.004132231404959, + 5.919651056014693, + 5.842516069788798, + 5.772727272727273, + 5.7102846648301195, + 5.655188246097338, + 5.607438016528926, + 5.567033976124886, + 5.533976124885216, + 5.508264462809918, + 5.4898989898989905, + 5.478879706152434, + 5.475206611570249, + 5.478879706152434, + 5.4898989898989905, + 5.508264462809918, + 5.533976124885216, + 5.567033976124886, + 5.607438016528926, + 5.655188246097339, + 5.71028466483012, + 5.772727272727273, + 5.842516069788799, + 5.919651056014693, + 6.004132231404959, + 6.095959595959597, + 6.195133149678606, + 6.301652892561984, + 6.415518824609734, + 6.536730945821856, + 6.6652892561983474, + 6.801193755739211, + 6.944444444444445, + 7.095041322314049, + 7.252984389348029, + 7.418273645546375, + 7.5909090909090935, + 7.770890725436182, + 7.958218549127642, + 8.152892561983473, + 8.354912764003675, + 8.564279155188249, + 8.780991735537192, + 9.005050505050507, + 9.236455463728191, + 9.475206611570249 + ], + [ + 21.63682277318641, + 21.15564738292011, + 20.681818181818183, + 20.215335169880625, + 19.756198347107443, + 19.304407713498623, + 18.85996326905418, + 18.422865013774107, + 17.993112947658403, + 17.570707070707073, + 17.15564738292011, + 16.747933884297517, + 16.3475665748393, + 15.954545454545455, + 15.568870523415978, + 15.190541781450873, + 14.819559228650139, + 14.455922865013775, + 14.099632690541783, + 13.750688705234161, + 13.40909090909091, + 13.07483930211203, + 12.74793388429752, + 12.428374655647383, + 12.116161616161616, + 11.81129476584022, + 11.513774104683197, + 11.223599632690542, + 10.94077134986226, + 10.665289256198347, + 10.397153351698806, + 10.136363636363637, + 9.882920110192838, + 9.63682277318641, + 9.398071625344354, + 9.166666666666668, + 8.942607897153353, + 8.725895316804408, + 8.516528925619834, + 8.314508723599634, + 8.119834710743802, + 7.932506887052343, + 7.7525252525252535, + 7.579889807162536, + 7.414600550964187, + 7.256657483930212, + 7.106060606060606, + 6.962809917355372, + 6.82690541781451, + 6.698347107438018, + 6.5771349862258965, + 6.463269054178147, + 6.356749311294767, + 6.257575757575758, + 6.16574839302112, + 6.081267217630854, + 6.004132231404959, + 5.934343434343435, + 5.871900826446282, + 5.8168044077135, + 5.769054178145088, + 5.728650137741048, + 5.695592286501379, + 5.66988062442608, + 5.651515151515152, + 5.640495867768596, + 5.6368227731864105, + 5.640495867768596, + 5.651515151515152, + 5.66988062442608, + 5.695592286501379, + 5.728650137741047, + 5.769054178145088, + 5.8168044077135, + 5.871900826446282, + 5.934343434343436, + 6.004132231404959, + 6.081267217630855, + 6.165748393021122, + 6.257575757575759, + 6.356749311294767, + 6.463269054178147, + 6.5771349862258965, + 6.698347107438018, + 6.82690541781451, + 6.962809917355372, + 7.106060606060607, + 7.25665748393021, + 7.41460055096419, + 7.579889807162537, + 7.752525252525256, + 7.9325068870523445, + 8.119834710743802, + 8.314508723599634, + 8.516528925619838, + 8.72589531680441, + 8.942607897153353, + 9.166666666666668, + 9.398071625344354, + 9.63682277318641 + ], + [ + 21.80211202938476, + 21.320936639118457, + 20.84710743801653, + 20.380624426078974, + 19.92148760330579, + 19.46969696969697, + 19.025252525252526, + 18.588154269972453, + 18.15840220385675, + 17.73599632690542, + 17.320936639118457, + 16.913223140495866, + 16.512855831037648, + 16.119834710743802, + 15.734159779614325, + 15.355831037649219, + 14.984848484848486, + 14.621212121212121, + 14.264921946740131, + 13.915977961432507, + 13.574380165289258, + 13.240128558310378, + 12.913223140495868, + 12.59366391184573, + 12.281450872359965, + 11.976584022038569, + 11.679063360881543, + 11.38888888888889, + 11.106060606060607, + 10.830578512396695, + 10.562442607897154, + 10.301652892561984, + 10.048209366391184, + 9.802112029384757, + 9.5633608815427, + 9.331955922865015, + 9.1078971533517, + 8.891184573002754, + 8.681818181818182, + 8.47979797979798, + 8.285123966942148, + 8.09779614325069, + 7.917814508723601, + 7.745179063360883, + 7.579889807162534, + 7.421946740128559, + 7.271349862258953, + 7.12809917355372, + 6.992194674012857, + 6.863636363636364, + 6.742424242424243, + 6.628558310376493, + 6.522038567493114, + 6.422865013774105, + 6.331037649219468, + 6.246556473829202, + 6.169421487603307, + 6.099632690541783, + 6.037190082644629, + 5.982093663911846, + 5.934343434343435, + 5.8939393939393945, + 5.860881542699725, + 5.835169880624427, + 5.8168044077135, + 5.805785123966943, + 5.802112029384757, + 5.805785123966943, + 5.8168044077135, + 5.835169880624427, + 5.860881542699725, + 5.8939393939393945, + 5.934343434343435, + 5.982093663911847, + 6.03719008264463, + 6.099632690541783, + 6.169421487603307, + 6.246556473829202, + 6.331037649219469, + 6.422865013774105, + 6.522038567493114, + 6.628558310376493, + 6.742424242424243, + 6.863636363636365, + 6.992194674012856, + 7.12809917355372, + 7.271349862258953, + 7.421946740128558, + 7.579889807162537, + 7.745179063360883, + 7.917814508723602, + 8.09779614325069, + 8.28512396694215, + 8.479797979797981, + 8.681818181818183, + 8.891184573002757, + 9.1078971533517, + 9.331955922865015, + 9.5633608815427, + 9.802112029384757 + ], + [ + 21.97107438016529, + 21.48989898989899, + 21.01606978879706, + 20.549586776859506, + 20.09044995408632, + 19.6386593204775, + 19.194214876033058, + 18.757116620752985, + 18.32736455463728, + 17.90495867768595, + 17.48989898989899, + 17.082185491276398, + 16.68181818181818, + 16.288797061524335, + 15.903122130394857, + 15.524793388429751, + 15.153810835629018, + 14.790174471992653, + 14.433884297520663, + 14.084940312213039, + 13.74334251606979, + 13.40909090909091, + 13.0821854912764, + 12.762626262626263, + 12.450413223140497, + 12.145546372819101, + 11.848025711662075, + 11.557851239669422, + 11.27502295684114, + 10.999540863177227, + 10.731404958677686, + 10.470615243342516, + 10.217171717171716, + 9.97107438016529, + 9.732323232323232, + 9.500918273645548, + 9.276859504132233, + 9.060146923783286, + 8.850780532598714, + 8.648760330578511, + 8.45408631772268, + 8.266758494031222, + 8.086776859504134, + 7.914141414141415, + 7.748852157943067, + 7.590909090909091, + 7.440312213039486, + 7.297061524334252, + 7.161157024793389, + 7.032598714416896, + 6.911386593204775, + 6.797520661157026, + 6.691000918273646, + 6.5918273645546375, + 6.5, + 6.415518824609734, + 6.338383838383839, + 6.268595041322315, + 6.206152433425161, + 6.1510560146923785, + 6.103305785123967, + 6.062901744719927, + 6.029843893480257, + 6.004132231404959, + 5.985766758494032, + 5.974747474747475, + 5.971074380165289, + 5.974747474747475, + 5.985766758494032, + 6.004132231404959, + 6.029843893480257, + 6.062901744719927, + 6.103305785123967, + 6.151056014692379, + 6.206152433425162, + 6.268595041322315, + 6.338383838383839, + 6.415518824609734, + 6.500000000000001, + 6.5918273645546375, + 6.691000918273646, + 6.797520661157026, + 6.911386593204775, + 7.032598714416897, + 7.161157024793388, + 7.297061524334252, + 7.440312213039485, + 7.59090909090909, + 7.74885215794307, + 7.914141414141415, + 8.086776859504134, + 8.266758494031222, + 8.454086317722682, + 8.648760330578513, + 8.850780532598716, + 9.06014692378329, + 9.276859504132233, + 9.500918273645548, + 9.732323232323232, + 9.97107438016529 + ], + [ + 22.143709825528006, + 21.66253443526171, + 21.188705234159784, + 20.722222222222225, + 20.26308539944904, + 19.81129476584022, + 19.366850321395777, + 18.929752066115704, + 18.5, + 18.07759412304867, + 17.66253443526171, + 17.254820936639117, + 16.8544536271809, + 16.46143250688705, + 16.075757575757578, + 15.69742883379247, + 15.326446280991737, + 14.962809917355372, + 14.60651974288338, + 14.257575757575758, + 13.915977961432507, + 13.581726354453629, + 13.254820936639117, + 12.935261707988982, + 12.623048668503214, + 12.31818181818182, + 12.020661157024794, + 11.73048668503214, + 11.447658402203857, + 11.172176308539946, + 10.904040404040405, + 10.643250688705233, + 10.389807162534435, + 10.143709825528008, + 9.90495867768595, + 9.673553719008265, + 9.449494949494952, + 9.232782369146005, + 9.023415977961433, + 8.82139577594123, + 8.6267217630854, + 8.439393939393941, + 8.259412304866851, + 8.086776859504134, + 7.921487603305785, + 7.763544536271809, + 7.612947658402204, + 7.46969696969697, + 7.333792470156107, + 7.205234159779615, + 7.084022038567494, + 6.9701561065197435, + 6.863636363636364, + 6.764462809917355, + 6.672635445362719, + 6.588154269972453, + 6.511019283746557, + 6.441230486685033, + 6.37878787878788, + 6.323691460055097, + 6.275941230486685, + 6.2355371900826455, + 6.202479338842975, + 6.176767676767677, + 6.15840220385675, + 6.147382920110194, + 6.143709825528008, + 6.147382920110194, + 6.15840220385675, + 6.176767676767677, + 6.202479338842975, + 6.2355371900826455, + 6.275941230486685, + 6.323691460055098, + 6.37878787878788, + 6.441230486685033, + 6.511019283746558, + 6.588154269972453, + 6.672635445362719, + 6.764462809917356, + 6.863636363636365, + 6.9701561065197435, + 7.084022038567493, + 7.205234159779616, + 7.333792470156107, + 7.469696969696971, + 7.612947658402204, + 7.763544536271809, + 7.921487603305788, + 8.086776859504134, + 8.259412304866853, + 8.439393939393941, + 8.626721763085401, + 8.821395775941232, + 9.023415977961434, + 9.232782369146008, + 9.449494949494952, + 9.673553719008266, + 9.90495867768595, + 10.143709825528008 + ], + [ + 22.32001836547291, + 21.83884297520661, + 21.365013774104685, + 20.898530762167127, + 20.43939393939394, + 19.98760330578512, + 19.54315886134068, + 19.106060606060606, + 18.676308539944905, + 18.25390266299357, + 17.838842975206614, + 17.43112947658402, + 17.0307621671258, + 16.637741046831955, + 16.252066115702476, + 15.873737373737372, + 15.502754820936639, + 15.139118457300276, + 14.782828282828284, + 14.433884297520661, + 14.09228650137741, + 13.75803489439853, + 13.431129476584022, + 13.111570247933884, + 12.799357208448118, + 12.494490358126722, + 12.196969696969697, + 11.906795224977042, + 11.62396694214876, + 11.348484848484848, + 11.080348943985307, + 10.819559228650137, + 10.566115702479339, + 10.320018365472912, + 10.081267217630854, + 9.849862258953168, + 9.625803489439853, + 9.409090909090908, + 9.199724517906336, + 8.997704315886134, + 8.803030303030303, + 8.615702479338843, + 8.435720844811755, + 8.263085399449036, + 8.097796143250687, + 7.939853076216711, + 7.789256198347107, + 7.646005509641872, + 7.5101010101010095, + 7.381542699724518, + 7.260330578512397, + 7.146464646464646, + 7.039944903581267, + 6.940771349862258, + 6.8489439853076215, + 6.764462809917355, + 6.68732782369146, + 6.617539026629935, + 6.5550964187327825, + 6.5, + 6.452249770431588, + 6.411845730027548, + 6.378787878787879, + 6.35307621671258, + 6.3347107438016526, + 6.323691460055096, + 6.320018365472911, + 6.323691460055096, + 6.3347107438016526, + 6.35307621671258, + 6.378787878787879, + 6.411845730027547, + 6.452249770431588, + 6.5, + 6.5550964187327825, + 6.617539026629936, + 6.68732782369146, + 6.764462809917355, + 6.848943985307622, + 6.940771349862259, + 7.039944903581267, + 7.146464646464647, + 7.260330578512397, + 7.381542699724518, + 7.510101010101009, + 7.646005509641872, + 7.789256198347106, + 7.939853076216712, + 8.09779614325069, + 8.263085399449036, + 8.435720844811755, + 8.615702479338843, + 8.803030303030305, + 8.997704315886136, + 9.199724517906336, + 9.40909090909091, + 9.625803489439853, + 9.84986225895317, + 10.081267217630852, + 10.320018365472912 + ], + [ + 22.5, + 22.0188246097337, + 21.544995408631774, + 21.078512396694215, + 20.61937557392103, + 20.167584940312214, + 19.723140495867767, + 19.286042240587694, + 18.856290174471994, + 18.433884297520663, + 18.018824609733702, + 17.611111111111107, + 17.21074380165289, + 16.817722681359044, + 16.432047750229565, + 16.053719008264462, + 15.682736455463727, + 15.319100091827364, + 14.962809917355372, + 14.61386593204775, + 14.272268135904499, + 13.93801652892562, + 13.61111111111111, + 13.291551882460972, + 12.979338842975206, + 12.67447199265381, + 12.376951331496787, + 12.086776859504132, + 11.803948576675849, + 11.528466483011938, + 11.260330578512395, + 10.999540863177227, + 10.746097337006429, + 10.5, + 10.261248852157944, + 10.029843893480258, + 9.805785123966942, + 9.589072543617998, + 9.379706152433425, + 9.177685950413224, + 8.983011937557393, + 8.795684113865931, + 8.615702479338843, + 8.443067033976124, + 8.277777777777777, + 8.1198347107438, + 7.969237832874196, + 7.825987144168962, + 7.690082644628099, + 7.561524334251607, + 7.440312213039486, + 7.3264462809917354, + 7.219926538108356, + 7.120752984389347, + 7.028925619834711, + 6.944444444444445, + 6.867309458218549, + 6.797520661157025, + 6.735078053259872, + 6.679981634527089, + 6.632231404958677, + 6.5918273645546375, + 6.558769513314967, + 6.533057851239669, + 6.514692378328742, + 6.503673094582186, + 6.5, + 6.503673094582186, + 6.514692378328742, + 6.533057851239669, + 6.558769513314967, + 6.5918273645546375, + 6.632231404958677, + 6.67998163452709, + 6.735078053259872, + 6.797520661157025, + 6.86730945821855, + 6.944444444444445, + 7.028925619834711, + 7.120752984389348, + 7.219926538108357, + 7.3264462809917354, + 7.440312213039485, + 7.561524334251606, + 7.690082644628099, + 7.825987144168961, + 7.969237832874196, + 8.1198347107438, + 8.277777777777779, + 8.443067033976126, + 8.615702479338845, + 8.795684113865933, + 8.983011937557393, + 9.177685950413224, + 9.379706152433426, + 9.589072543617998, + 9.805785123966942, + 10.029843893480258, + 10.261248852157943, + 10.5 + ] + ] + } + ], + "layout": { + "scene": { + "aspectmode": "data" + }, + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-3,3,100)\n", + "y = np.linspace(-3,3,100)\n", + "\n", + "mx, my = np.meshgrid(x,y)\n", + "mz = J(mx, my)\n", + "\n", + "trace = go.Surface(x=mx, y=my, z=mz)\n", + "layout = go.Layout(scene = {'aspectmode':'data'})\n", + "fig = go.Figure(data=[trace], layout=layout)\n", + "py.iplot(fig, show_link=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def grad_J(x,y):\n", + " return np.array([2*x-2, y]) # calculé à la main à partir de J (on aimerait que cela soit automatique)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Si vous ne comprennez pas le calcul du gradiant de $J$, n'allez pas plus loin. Retrouvez votre cours sur ce\n", + "sujet, regardez le mémo, posez des questions." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Le minimum est au point [1. 0.] La valeur de J en ce point est 2.0000001053122918\n" + ] + } + ], + "source": [ + "# Algo du gradient pour trouver le minimum\n", + "\n", + "x = np.array([0,0]) # un point au hasard, changez pour voir\n", + "µ = 0.1 # plus il est petit et moins on avance vite, cf formule ci-dessus\n", + "e = 0.0001 # mon epsilon pour la condition d'arrêt\n", + "\n", + "while True:\n", + " x_old = x\n", + " x = x - µ * grad_J(*x) # *x donne en arguments toutes les valeurs de x donc x[0] en 1er arg et x[1] en 2e\n", + " if np.square(x_old - x).sum() < e**2:\n", + " break\n", + "print(\"Le minimum est au point \", x, \"La valeur de J en ce point est \", J(*x))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Je vous invite à bouger la figure pour être au dessus, zoomer pour voir ce qui va se passer et maintenant \n", + "déplacer la souris sur la figure. Vous devez voir une ellipse qui montre la ligne de niveau (tous les points ayant la même valeur de z). Le minimum est lorsque cette ellipse n'est qu'un point. C'est justement en [1, 0, 2]." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Étude de la convergence du gradient\n", + "\n", + "On stocke toutes les valeurs des points entre notre point initial et la solution pour pouvoir tracer des courbes\n", + "de convergence.\n", + "\n", + "Donc le résultat de notre méthode de gradient doit être un ensemble de points." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def minimum_J(start_value, µ=0.1, e = 0.001):\n", + " x = [np.array(start_value)]\n", + " while True:\n", + " x.append(x[-1] - µ * grad_J(*x[-1]))\n", + " if np.square(x[-1] - x[-2]).sum() < e**2:\n", + " break\n", + " # la suite n'est que des tests pour se protéger\n", + " if np.square(x[-1] - x[-2]).sum() > 1E6: # au cas où on diverge\n", + " print(\"DIVERGE\")\n", + " break\n", + " if len(x) > 200: # c'est trop long, je crains la boucle infinie\n", + " print('Trop long, boucle infinie ?')\n", + " break\n", + " return np.array(x)\n", + "\n", + "\n", + "x = minimum_J(start_value = (0,1)) # je prends une valeur initiale qui n'est pas alignée avec la solution" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 369 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x[:,0], x[:,1], 'x:')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "type": "scatter3d", + "x": [ + 0, + 0.2, + 0.36000000000000004, + 0.488, + 0.5904, + 0.67232, + 0.7378560000000001, + 0.7902848, + 0.83222784, + 0.865782272, + 0.8926258176, + 0.9141006540800001, + 0.931280523264, + 0.9450244186112, + 0.95601953488896, + 0.9648156279111679, + 0.9718525023289344, + 0.9774820018631475, + 0.981985601490518, + 0.9855884811924144, + 0.9884707849539315, + 0.9907766279631451, + 0.9926213023705162, + 0.9940970418964129, + 0.9952776335171303, + 0.9962221068137043, + 0.9969776854509634, + 0.9975821483607707, + 0.9980657186886166, + 0.9984525749508932, + 0.9987620599607145, + 0.9990096479685716, + 0.9992077183748573, + 0.9993661746998859, + 0.9994929397599087, + 0.999594351807927, + 0.9996754814463416, + 0.9997403851570732, + 0.9997923081256586, + 0.9998338465005269, + 0.9998670772004215, + 0.9998936617603371, + 0.9999149294082696, + 0.9999319435266157, + 0.9999455548212925, + 0.9999564438570341 + ], + "y": [ + 1, + 0.9, + 0.81, + 0.7290000000000001, + 0.6561000000000001, + 0.5904900000000001, + 0.531441, + 0.4782969, + 0.43046721, + 0.387420489, + 0.3486784401, + 0.31381059609, + 0.282429536481, + 0.2541865828329, + 0.22876792454961, + 0.20589113209464902, + 0.1853020188851841, + 0.16677181699666568, + 0.15009463529699912, + 0.1350851717672992, + 0.12157665459056928, + 0.10941898913151235, + 0.09847709021836111, + 0.088629381196525, + 0.0797664430768725, + 0.07178979876918525, + 0.06461081889226672, + 0.05814973700304005, + 0.052334763302736044, + 0.047101286972462436, + 0.042391158275216195, + 0.03815204244769457, + 0.034336838202925116, + 0.030903154382632605, + 0.027812838944369346, + 0.02503155504993241, + 0.022528399544939168, + 0.02027555959044525, + 0.018248003631400726, + 0.016423203268260654, + 0.014780882941434589, + 0.01330279464729113, + 0.011972515182562017, + 0.010775263664305815, + 0.009697737297875235, + 0.00872796356808771 + ], + "z": [ + 3.5, + 3.045, + 2.73765, + 2.5278645, + 2.383005765, + 2.28171340245, + 2.2099342449765, + 2.158364427385845, + 2.1207985071136575, + 2.0930617161579814, + 2.072317542341353, + 2.0566172427386644, + 2.044605588021306, + 2.03532772399517, + 2.0281016629627513, + 2.0224335191768934, + 2.017960700726605, + 2.014413479712276, + 2.011588718326128, + 2.009331693690042, + 2.0075233642702957, + 2.0060713281830114, + 2.004903313827645, + 2.003962428520012, + 2.0032036434657665, + 2.0025911600805872, + 2.002096413344198, + 2.0016965419633106, + 2.0013732051691684, + 2.0011116601415138, + 2.000900037645498, + 2.0007287699686116, + 2.0005901369390604, + 2.0004779042099097, + 2.00038703411516, + 2.000313453924565, + 2.00025386970532, + 2.0002056165582194, + 2.0001665379541804, + 2.0001348884097805, + 2.000109254918735, + 2.0000884934805354, + 2.000071677796904, + 2.000058057785201, + 2.0000470260186267, + 2.0000380905711603 + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "C'est joli, n'est-ce pas ?\n", + "\n", + "#### Impact de µ\n", + "\n", + "Regardons comment µ influence sur la convergence c.a.d. une fois qu'on a la direction de la plus grande pente\n", + "en un point de combien doit-on avancer. Avec un µ grand on fait des grands pas, avec un µ petit on fait des petits pas.\n", + "\n", + "Avec µ = 0.1 on a fait des petits pas." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DIVERGE\n" + ] + }, + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 383 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# µ = 2\n", + "\n", + "x = minimum_J(start_value = (0,1), µ = 2)\n", + "plt.plot(x[:,0], x[:,1], 'x:')" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "type": "scatter3d", + "x": [ + 0, + 4, + -8, + 28, + -80, + 244, + -728, + 2188 + ], + "y": [ + 1, + -1, + 1, + -1, + 1, + -1, + 1, + -1 + ], + "z": [ + 3.5, + 11.5, + 83.5, + 731.5, + 6563.5, + 59051.5, + 531443.5, + 4782971.5 + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Pas bon, on a divergé. Les pas sont trop grands. On va dans la bonne direction mais tellement loin qu'on remonte \n", + "de l'autre coté de la cuvette. \n", + "\n", + "On voit bien qu'en y on passe de 1 a -1 puis à 1, -1 etc sans jamais s'arrêter\n", + "à 0 qui est la solution pour y.\n", + "\n", + "**Question** Pourquoi la valeur de x explose au lieu de faire comme y ?" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 369 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# µ = 0.8\n", + "\n", + "x = minimum_J(start_value = (0,1), µ = 0.8)\n", + "plt.plot(x[:,0], x[:,1], 'x:')" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "type": "scatter3d", + "x": [ + 0, + 1.6, + 0.6399999999999999, + 1.2160000000000002, + 0.8703999999999998, + 1.07776, + 0.953344, + 1.0279936, + 0.9832038399999999, + 1.010077696, + 0.9939533824, + 1.00362797056, + 0.9978232176640001, + 1.0013060694016, + 0.99921635835904, + 1.000470184984576, + 0.9997178890092544 + ], + "y": [ + 1, + 0.19999999999999996, + 0.03999999999999998, + 0.007999999999999993, + 0.0015999999999999981, + 0.00031999999999999954, + 6.399999999999988e-05, + 1.2799999999999972e-05, + 2.559999999999994e-06, + 5.119999999999987e-07, + 1.023999999999997e-07, + 2.047999999999993e-08, + 4.095999999999986e-09, + 8.191999999999969e-10, + 1.638399999999993e-10, + 3.276799999999986e-11, + 6.553599999999971e-12 + ], + "z": [ + 3.5, + 2.3800000000000003, + 2.1304, + 2.046688, + 2.01679744, + 2.0060466688, + 2.002176784384, + 2.00078364172288, + 2.0002821109940223, + 2.0001015599567995, + 2.000036561584406, + 2.0000131621703847, + 2.0000047383813384, + 2.000001705817282, + 2.0000006140942217, + 2.0000002210739196, + 2.000000079586611 + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On a convergé mais c'est moins joli que la première fois. Par contre " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "17" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "on a convergé en 17 itérations. Regardons combien il a fallu d'itération pour µ = 0.1 :" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "46" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = minimum_J(start_value = (0,1), µ = 0.1)\n", + "len(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "µ = 0.8 donne une courbe moins jolie mais on converge presque 3 fois plus vite qu'avec µ = 0.1. Donc c'est mieux." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Trop long, boucle infinie ?\n" + ] + }, + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 246, + "width": 369 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# µ = 1\n", + "\n", + "x = minimum_J(start_value = (0,1), µ = 1)\n", + "plt.plot(x[:,0], x[:,1], 'x:')" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "type": "scatter3d", + "x": [ + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0, + 2, + 0 + ], + "y": [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "z": [ + 3.5, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
\n", + " \n", + " \n", + "
\n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On est parti de [0,1] pour aller en [2,0] puis en [0,0] puis en [2.0].\n", + "\n", + "Comme on a vu que depuis [2,0] on va en [0,0] cela veut dire qu'on oscille infiniment entre [0,0] et [2,0].\n", + "\n", + "Sachant que la solution recherchée est [1,0] cela veut dire qu'on va bien dans la bonne direction mais on fait\n", + "un pas 2 fois trop grand à chaque fois.\n", + "\n", + "**Moralité** La valeur de µ est importante. Si elle est trop petite on perd du temps, si elle est trop grande on ne trouve pas la solution." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma51 x.T A x sur un maillage en Numpy .ipynb b/PVCM/cama/fr/ma51 x.T A x sur un maillage en Numpy .ipynb new file mode 100644 index 0000000..9933335 --- /dev/null +++ b/PVCM/cama/fr/ma51 x.T A x sur un maillage en Numpy .ipynb @@ -0,0 +1,32043 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "import plotly.offline as py\n", + "import plotly.graph_objects as go\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Calculons ${\\bf x}^T \\, A \\, {\\bf x} $ avec Numpy\n", + "\n", + "Le but est de tracer la courbe $J_A({\\bf x})$ avec ${\\bf x} \\in ℝ^2$ pour que les pauvres petits humains que nous\n", + "sommes puissent voir quelque chose.\n", + "\n", + "$$\n", + "J_A({\\bf x}) = {\\bf x}^T \\, A \\, {\\bf x}\n", + "$$\n", + "\n", + "Plus tard on prendra ${\\bf x} \\in ℝ^n$.\n", + "\n", + "Pour une valeur **x** ce calcule est simple : `x.T @ A @ x` mais on veut faire ce calcul pour un ensemble de\n", + "**x**." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On commence par construire un maillage c.a.d. un ensemble de points ${\\bf x}$ pour lesquels on calculera \n", + "$J_A({\\bf x})$. Pour cela on utilise `np.meshgrid`. Regardons ce que cela donne." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "shape of M: (2, 4, 3)\n", + "[[[-1. 0. 1.]\n", + " [-1. 0. 1.]\n", + " [-1. 0. 1.]\n", + " [-1. 0. 1.]]\n", + "\n", + " [[-1. -1. -1.]\n", + " [ 0. 0. 0.]\n", + " [ 1. 1. 1.]\n", + " [ 2. 2. 2.]]]\n", + "\n", + "shape of M: (4, 3, 2)\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[[-1., -1.],\n", + " [ 0., -1.],\n", + " [ 1., -1.]],\n", + "\n", + " [[-1., 0.],\n", + " [ 0., 0.],\n", + " [ 1., 0.]],\n", + "\n", + " [[-1., 1.],\n", + " [ 0., 1.],\n", + " [ 1., 1.]],\n", + "\n", + " [[-1., 2.],\n", + " [ 0., 2.],\n", + " [ 1., 2.]]])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.linspace(-1,1,3)\n", + "y = np.linspace(-1,2,4)\n", + "\n", + "mesh = np.meshgrid(x,y) # donne les x puis les y du maillage\n", + "M = np.array(mesh)\n", + "print(\"shape of M:\", M.shape)\n", + "print(M)\n", + "M = M.transpose([1,2,0]) # je préfère avoir un tableau 4x3 de points\n", + "print(\"\\nshape of M:\", M.shape)\n", + "M" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Je veux appliquer ${\\bf x}^T \\, A \\, {\\bf x}$ à chaque point de mon maillage. Je commence avec la matrice identité\n", + "pour que je puisse facilement vérifier les calculs.\n", + "\n", + "En premier je calcule ${\\bf x}^T \\, A$ pour tous les points du maillage.\n", + "\n", + "### Cas test avec A = 2 Id\n", + "\n", + "Je regarde sur un tout petit maillage comment écrire les calculs. Je prends pour A deux fois\n", + "la matrice identité pour pouvoir vérifier les calculs de tête." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[[-2., -2.],\n", + " [ 0., -2.],\n", + " [ 2., -2.]],\n", + "\n", + " [[-2., 0.],\n", + " [ 0., 0.],\n", + " [ 2., 0.]],\n", + "\n", + " [[-2., 2.],\n", + " [ 0., 2.],\n", + " [ 2., 2.]],\n", + "\n", + " [[-2., 4.],\n", + " [ 0., 4.],\n", + " [ 2., 4.]]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = 2 * np.diag([1, 1])\n", + "MA = np.einsum(\"ijk, ka -> ija\", M, A) # voici un cas où la notation d'Einstein simplifie bien la vie\n", + "MA # k est en double et pas dans le résultat, donc on somme sur lui" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Je retrouve `2 M` ce qui est cohérent.\n", + "\n", + "Dans un autre cas on pourrait vérifier certains points :" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0., -2.])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# vérification sur un point particulier\n", + "M[0,1] @ A" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Notez que j'ai écrit ${\\bf x} \\, A$ et non ${\\bf x}^T \\, A$ mais lorsqu'on a un vecteur Numpy s'adapte et privilégie le produit matrice vecteur qui donne un vecteur. Ainsi `m[0,1] @ A == m[0,1].T @ A` car, comme\n", + "dit la doc, \"Transposing a 1-D array returns an unchanged view of the original array\". \n", + "\n", + "Si on veux avoir une différence entre un vecteur vertical et un vecteur horizontal il faut utiliser\n", + "des `array` 2D de taille 1xn ou nx1." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 4., 2., 4.],\n", + " [ 2., 0., 2.],\n", + " [ 4., 2., 4.],\n", + " [10., 8., 10.]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.einsum(\"ijk, ijk -> ij\", MA, M) # comme k n'est pas dans le résultat, c'est sur lui qu'on fait la somme" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Comme A est 2 fois l'identité on doit trouver pour tout point 2 fois sa norme au carré. C'est bon.\n", + "\n", + "### Un vrai cas\n", + "\n", + "On prend un maillage de 100x100 et une matrice A aléatoire :" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-0.02 0.05]\n", + " [ 0.03 -0.02]]\n" + ] + } + ], + "source": [ + "np.random.seed(2)\n", + "A = np.random.randint(-10,10, size=(2,2)) / 100\n", + "print(A)\n", + "\n", + "x = np.linspace(-20,20,100)\n", + "y = np.linspace(-20,20,100)\n", + "\n", + "mx, my = np.meshgrid(x,y) \n", + "M = np.array(np.meshgrid(x,y)).transpose([1,2,0])\n", + "\n", + "MA = np.einsum(\"ijk, ka -> ija\", M, A)\n", + "mz = np.einsum(\"ijk, ijk -> ij\", MA, M)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "linkText": "Export to plot.ly", + "plotlyServerURL": "https://plot.ly", + "showLink": false + }, + "data": [ + { + "type": "surface", + "x": [ + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ] + ], + "y": [ + [ + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20 + ], + [ + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595 + ], + [ + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919 + ], + [ + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879 + ], + [ + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384 + ], + [ + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798 + ], + [ + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574 + ], + [ + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173 + ], + [ + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768 + ], + [ + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363 + ], + [ + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958 + ], + [ + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555 + ], + [ + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152 + ], + [ + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747 + ], + [ + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343 + ], + [ + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394 + ], + [ + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536 + ], + [ + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131 + ], + [ + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727 + ], + [ + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324 + ], + [ + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919 + ], + [ + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516 + ], + [ + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111 + ], + [ + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708 + ], + [ + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303 + ], + [ + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899 + ], + [ + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495 + ], + [ + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092 + ], + [ + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687 + ], + [ + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284 + ], + [ + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879 + ], + [ + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476 + ], + [ + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071 + ], + [ + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666 + ], + [ + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263 + ], + [ + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858 + ], + [ + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455 + ], + [ + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505 + ], + [ + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647 + ], + [ + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242 + ], + [ + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373 + ], + [ + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436 + ], + [ + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031 + ], + [ + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263 + ], + [ + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214 + ], + [ + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201 + ], + [ + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153 + ], + [ + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104 + ], + [ + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055 + ], + [ + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066 + ], + [ + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066 + ], + [ + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055 + ], + [ + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104 + ], + [ + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153 + ], + [ + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166 + ], + [ + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214 + ], + [ + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263 + ], + [ + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031 + ], + [ + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325 + ], + [ + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373 + ], + [ + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242 + ], + [ + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647 + ], + [ + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048 + ], + [ + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453 + ], + [ + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858 + ], + [ + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263 + ], + [ + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668 + ], + [ + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069 + ], + [ + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474 + ], + [ + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879 + ], + [ + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284 + ], + [ + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685 + ], + [ + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909 + ], + [ + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495 + ], + [ + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899 + ], + [ + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301 + ], + [ + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706 + ], + [ + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111 + ], + [ + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516 + ], + [ + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917 + ], + [ + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325 + ], + [ + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727 + ], + [ + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128 + ], + [ + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536 + ], + [ + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938 + ], + [ + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346 + ], + [ + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747 + ], + [ + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149 + ], + [ + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557 + ], + [ + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958 + ], + [ + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636 + ], + [ + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768 + ], + [ + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717 + ], + [ + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578 + ], + [ + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798 + ], + [ + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838 + ], + [ + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879 + ], + [ + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919 + ], + [ + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596 + ], + [ + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20 + ] + ], + "z": [ + [ + 16, + 15.673502703805733, + 15.340475461687582, + 15.000918273645546, + 14.654831139679624, + 14.302214059789817, + 13.943067033976124, + 13.577390062238548, + 13.205183144577084, + 12.826446280991735, + 12.441179471482503, + 12.049382716049383, + 11.65105601469238, + 11.246199367411489, + 10.83481277420671, + 10.416896235078053, + 9.99244975002551, + 9.561473319049076, + 9.123966942148758, + 8.679930619324558, + 8.229364350576471, + 7.7722681359045, + 7.3086419753086425, + 6.838485868788898, + 6.36179981634527, + 5.878583817977757, + 5.388837873686358, + 4.892561983471074, + 4.389756147331905, + 3.8804203652688507, + 3.36455463728191, + 2.842158963371086, + 2.3132333435363743, + 1.7777777777777766, + 1.235792266095296, + 0.6872768084889289, + 0.13223140495867813, + -0.4293439444954603, + -0.9974492398734816, + -1.5720844811753905, + -2.153249668401185, + -2.7409448015508597, + -3.335169880624425, + -3.9359249056218752, + -4.543209876543212, + -5.157024793388428, + -5.777369656157533, + -6.404244464850526, + -7.0376492194674025, + -7.677583920008165, + -8.324048566472806, + -8.97704315886134, + -9.636567697173758, + -10.302622181410062, + -10.975206611570245, + -11.65432098765432, + -12.339965309662281, + -13.032139577594126, + -13.73084379144985, + -14.436077951229466, + -15.147842056932967, + -15.866136108560353, + -16.59096010611162, + -17.322314049586772, + -18.060197938985816, + -18.804611774308746, + -19.555555555555557, + -20.313029282726248, + -21.077032955820833, + -21.847566574839302, + -22.624630139781658, + -23.40822365064789, + -24.198347107438014, + -24.995000510152025, + -25.79818385878992, + -26.607897153351693, + -27.424140393837362, + -28.24691358024691, + -29.07621671258035, + -29.912049790837663, + -30.75441281501888, + -31.603305785123965, + -32.458728701152936, + -33.32068156310581, + -34.189164370982546, + -35.06417712478319, + -35.945719824507705, + -36.8337924701561, + -37.728395061728406, + -38.629527599224566, + -39.53719008264462, + -40.45138251198858, + -41.3721048872564, + -42.29935720844812, + -43.23313947556372, + -44.173451688603194, + -45.12029384756658, + -46.07366595245383, + -47.033568003264975, + -48 + ], + [ + 15.673502703805731, + 15.360065299459237, + 15.040097949188857, + 14.713600652994591, + 14.38057341087644, + 14.041016222834404, + 13.69492908886848, + 13.342312008978677, + 12.983164983164983, + 12.617488011427405, + 12.245281093765941, + 11.866544230180594, + 11.481277420671361, + 11.089480665238241, + 10.691153963881234, + 10.286297316600347, + 9.874910723395573, + 9.456994184266911, + 9.032547699214366, + 8.601571268237937, + 8.164064891337617, + 7.720028568513417, + 7.26946229976533, + 6.812366085093357, + 6.348739924497499, + 5.878583817977758, + 5.4018977655341285, + 4.918681767166616, + 4.428935822875217, + 3.932659932659934, + 3.4298540965207636, + 2.92051831445771, + 2.4046525864707693, + 1.8822569125599422, + 1.3533312927252323, + 0.8178757269666361, + 0.27589021528415536, + -0.2726252423222113, + -0.8276706458524625, + -1.389245995306601, + -1.9573512906846247, + -2.5319865319865285, + -3.1131517192123237, + -3.7008468523620035, + -4.295071931435569, + -4.895826956433014, + -5.503111927354349, + -6.116926844199571, + -6.737271706968676, + -7.364146515661668, + -7.9975512702785405, + -8.637485970819302, + -9.28395061728395, + -9.936945209672484, + -10.596469747984896, + -11.262524232221198, + -11.93510866238139, + -12.614223038465465, + -13.299867360473415, + -13.992041628405264, + -14.690745842260993, + -15.39598000204061, + -16.107744107744104, + -16.826038159371485, + -17.55086215692276, + -18.282216100397918, + -19.02009998979696, + -19.76451382511988, + -20.515457606366695, + -21.272931333537393, + -22.03693500663198, + -22.807468625650436, + -23.584532190592792, + -24.368125701459032, + -25.15824915824916, + -25.954902560963163, + -26.758085909601057, + -27.56779920416284, + -28.384042444648504, + -29.20681563105805, + -30.036118763391492, + -30.87195184164881, + -31.71431486583001, + -32.56320783593511, + -33.41863075196407, + -34.28058361391695, + -35.14906642179369, + -36.024079175594316, + -36.90562187531885, + -37.79369452096724, + -38.68829711253953, + -39.58942965003571, + -40.49709213345576, + -41.41128456279971, + -42.33200693806754, + -43.259259259259245, + -44.193041526374856, + -45.133353739414346, + -46.080195898377724, + -47.03356800326497 + ], + [ + 15.34047546168758, + 15.040097949188858, + 14.733190490766244, + 14.419753086419751, + 14.099785736149373, + 13.773288439955104, + 13.440261197836953, + 13.100704009794919, + 12.754616875828997, + 12.40199979593919, + 12.042852770125496, + 11.677175798387918, + 11.304968880726456, + 10.926232017141107, + 10.54096520763187, + 10.149168452198754, + 9.750841750841753, + 9.34598510356086, + 8.934598510356086, + 8.516681971227428, + 8.092235486174879, + 7.66125905519845, + 7.223752678298133, + 6.77971635547393, + 6.329150086725844, + 5.872053872053873, + 5.408427711458014, + 4.938271604938272, + 4.461585552494643, + 3.978369554127131, + 3.4886236098357317, + 2.9923477196204487, + 2.4895418834812784, + 1.9802061014182222, + 1.4643403734312832, + 0.9419446995204572, + 0.41301907968574714, + -0.12243648607284907, + -0.6644219977553298, + -1.212937455361697, + -1.7679828588919504, + -2.329558208346083, + -2.897663503724108, + -3.4722987450260163, + -4.053463932251811, + -4.641159065401486, + -5.23538414447505, + -5.836139169472501, + -6.443424140393837, + -7.057239057239058, + -7.67758392000816, + -8.304458728701151, + -8.93786348331803, + -9.577798183858791, + -10.224262830323433, + -10.877257422711967, + -11.536781961024385, + -12.202836445260687, + -12.875420875420872, + -13.554535251504944, + -14.240179573512904, + -14.93235384144475, + -15.631058055300475, + -16.33629221508009, + -17.04805632078359, + -17.766350372410976, + -18.49117436996225, + -19.2225283134374, + -19.960412202836444, + -20.70482603815937, + -21.455769819406182, + -22.213243546576876, + -22.977247219671458, + -23.747780838689927, + -24.524844403632283, + -25.308437914498512, + -26.09856137128864, + -26.895214774002653, + -27.698398122640548, + -28.50811141720232, + -29.324354657687994, + -30.14712784409754, + -30.976430976430965, + -31.8122640546883, + -32.654627078869495, + -33.5035200489746, + -34.35894296500357, + -35.22089582695642, + -36.08937863483318, + -36.964391388633814, + -37.84593408835832, + -38.73400673400673, + -39.62860932557902, + -40.5297418630752, + -41.437404346495256, + -42.35159677583919, + -43.27231915110703, + -44.19957147229874, + -45.133353739414346, + -46.07366595245383 + ], + [ + 15.000918273645546, + 14.71360065299459, + 14.419753086419753, + 14.11937557392103, + 13.812468115498417, + 13.499030711151924, + 13.17906336088154, + 12.852566064687277, + 12.519538822569126, + 12.179981634527088, + 11.833894500561167, + 11.48127742067136, + 11.122130394857669, + 10.75645342312009, + 10.384246505458623, + 10.005509641873278, + 9.620242832364045, + 9.228446076930924, + 8.83011937557392, + 8.425262728293031, + 8.013876135088253, + 7.595959595959595, + 7.17151311090705, + 6.740536679930618, + 6.303030303030302, + 5.858993980206102, + 5.408427711458014, + 4.951331496786042, + 4.487705336190184, + 4.0175492296704425, + 3.5408631772268135, + 3.057647178859301, + 2.5679012345679015, + 2.071625344352616, + 1.568819508213447, + 1.0594837261503918, + 0.5436179981634524, + 0.02122232425262638, + -0.507703295582083, + -1.0431588613406806, + -1.5851443730231631, + -2.133659830629526, + -2.6887052341597792, + -3.250280583613918, + -3.8183858789919407, + -4.393021120293846, + -4.97418630751964, + -5.561881440669319, + -6.156106519742885, + -6.756861544740335, + -7.364146515661666, + -7.977961432506888, + -8.598306295275995, + -9.225181103968985, + -9.858585858585856, + -10.49852055912662, + -11.144985205591269, + -11.7979797979798, + -12.457504336292214, + -13.123558820528517, + -13.796143250688706, + -14.475257626772784, + -15.160901948780735, + -15.85307621671258, + -16.55178043056831, + -17.257014590347925, + -17.968778696051427, + -18.68707274767881, + -19.411896745230077, + -20.143250688705237, + -20.88113457810428, + -21.6255484134272, + -22.376492194674015, + -23.133965921844712, + -23.897969594939294, + -24.668503213957756, + -25.445566778900115, + -26.229160289766348, + -27.01928374655648, + -27.815937149270482, + -28.619120497908384, + -29.428833792470158, + -30.24507703295582, + -31.067850219365376, + -31.897153351698805, + -32.732986429956135, + -33.57534945413734, + -34.42424242424242, + -35.27966534027141, + -36.141618202224265, + -37.01010101010101, + -37.88511376390164, + -38.766656463626155, + -39.65472910927457, + -40.54933170084685, + -41.45046423834302, + -42.358126721763085, + -43.27231915110703, + -44.19304152637487, + -45.12029384756657 + ], + [ + 14.654831139679622, + 14.38057341087644, + 14.099785736149371, + 13.812468115498419, + 13.518620548923579, + 13.218243036424855, + 12.911335578002245, + 12.59789817365575, + 12.27793082338537, + 11.951433527191103, + 11.61840628507295, + 11.278849097030914, + 10.932761963064994, + 10.580144883175187, + 10.220997857361493, + 9.855320885623916, + 9.483113967962455, + 9.104377104377104, + 8.71911029486787, + 8.327313539434751, + 7.928986838077746, + 7.524130190796857, + 7.1127435975920825, + 6.694827058463421, + 6.2703805734108755, + 5.8394041424344465, + 5.4018977655341285, + 4.957861442709928, + 4.50729517396184, + 4.050198959289869, + 3.586572798694011, + 3.1164166921742686, + 2.63973063973064, + 2.156514641363125, + 1.6667686970717268, + 1.1704928068564422, + 0.6676869707172737, + 0.1583511886542186, + -0.3575145393327208, + -0.8799102132435475, + -1.408835833078259, + -1.9442913988368515, + -2.486276910519334, + -3.034792368125702, + -3.5898377716559553, + -4.151413121110089, + -4.719518416488112, + -5.294153657790022, + -5.8753188450158165, + -6.463013978165495, + -7.057239057239056, + -7.657994082236506, + -8.265279053157842, + -8.879093970003064, + -9.499438832772165, + -10.126313641465156, + -10.759718396082034, + -11.399653096622796, + -12.046117743087438, + -12.699112335475972, + -13.35863687378839, + -14.024691358024695, + -14.697275788184877, + -15.37639016426895, + -16.06203448627691, + -16.754208754208754, + -17.452912968064485, + -18.158147127844096, + -18.869911233547597, + -19.588205285174983, + -20.313029282726255, + -21.044383226201404, + -21.782267115600447, + -22.526680950923378, + -23.27762473217019, + -24.03509845934088, + -24.799102132435465, + -25.569635751453934, + -26.34669931639629, + -27.130292827262522, + -27.920416284052656, + -28.717069686766656, + -29.520253035404544, + -30.329966329966332, + -31.146209570451994, + -31.96898275686155, + -32.798285889194986, + -33.634118967452295, + -34.476481991633506, + -35.3253749617386, + -36.18079787776757, + -37.04275073972043, + -37.911233547597185, + -38.786246301397824, + -39.66778900112233, + -40.55586164677074, + -41.45046423834303, + -42.3515967758392, + -43.25925925925927, + -44.17345168860321 + ], + [ + 14.302214059789815, + 14.041016222834402, + 13.773288439955104, + 13.499030711151923, + 13.218243036424852, + 12.930925415773899, + 12.63707784919906, + 12.336700336700336, + 12.029792878277728, + 11.71635547393123, + 11.396388123660849, + 11.069890827466583, + 10.736863585348434, + 10.397306397306398, + 10.051219263340473, + 9.698602183450667, + 9.339455157636978, + 8.973778185899398, + 8.601571268237935, + 8.222834404652588, + 7.837567595143351, + 7.445770839710233, + 7.047444138353229, + 6.642587491072339, + 6.231200897867564, + 5.813284358738905, + 5.388837873686358, + 4.957861442709928, + 4.5203550658096106, + 4.076318742985411, + 3.625752474237323, + 3.168656259565352, + 2.7050300989694938, + 2.2348739924497494, + 1.7581879400061218, + 1.274971941638608, + 0.7852259973472102, + 0.28895010713192537, + -0.21385572900724314, + -0.7231915110702989, + -1.23905723905724, + -1.7614529129680618, + -2.290378532802774, + -2.825834098561371, + -3.367819610243853, + -3.9163350678502162, + -4.471380471380469, + -5.032955820834609, + -5.601061116212632, + -6.17569635751454, + -6.756861544740331, + -7.34455667789001, + -7.938781756963574, + -8.539536781961026, + -9.146821752882355, + -9.760636669727576, + -10.380981532496683, + -11.007856341189676, + -11.641261095806547, + -12.28119579634731, + -12.927660442811957, + -13.58065503520049, + -14.240179573512904, + -14.906234057749206, + -15.578818487909396, + -16.257932863993467, + -16.94357718600143, + -17.63575145393327, + -18.334455667788998, + -19.039689827568615, + -19.751453933272117, + -20.469747984899495, + -21.194571982450768, + -21.925925925925924, + -22.663809815324967, + -23.408223650647887, + -24.1591674318947, + -24.9166411590654, + -25.680644832159985, + -26.451178451178443, + -27.22824201612081, + -28.011835526987042, + -28.801958983777155, + -29.598612386491176, + -30.401795735129063, + -31.211509029690852, + -32.027752270176514, + -32.850525456586055, + -33.6798285889195, + -34.51566166717682, + -35.35802469135801, + -36.20691766146311, + -37.062340577492094, + -37.92429343944496, + -38.7927762473217, + -39.66778900112233, + -40.54933170084686, + -41.43740434649525, + -42.33200693806755, + -43.23313947556372 + ], + [ + 13.94306703397612, + 13.69492908886848, + 13.440261197836953, + 13.17906336088154, + 12.911335578002245, + 12.63707784919906, + 12.356290174471992, + 12.06897255382104, + 11.7751249872462, + 11.474747474747474, + 11.167840016324865, + 10.854402611978369, + 10.53443526170799, + 10.207937965513723, + 9.874910723395569, + 9.535353535353535, + 9.189266401387615, + 8.836649321497806, + 8.477502295684113, + 8.111825323946537, + 7.7396184062850715, + 7.360881542699724, + 6.975614733190491, + 6.583817977757371, + 6.1854912764003664, + 5.7806346291194775, + 5.369248035914702, + 4.951331496786042, + 4.526885011733496, + 4.095908580757067, + 3.6584022038567494, + 3.214365881032549, + 2.7637996122844615, + 2.306703397612488, + 1.8430772370166313, + 1.3729211304968878, + 0.8962350780532609, + 0.4130190796857469, + -0.07672686460565137, + -0.5730027548209364, + -1.075808590960107, + -1.585144373023158, + -2.1010101010100994, + -2.6234057749209256, + -3.1523313947556377, + -3.687786960514231, + -4.2297724721967125, + -4.77828792980308, + -5.333333333333333, + -5.894908682787472, + -6.463013978165491, + -7.0376492194674, + -7.618814406693194, + -8.206509539842875, + -8.800734618916433, + -9.401489643913886, + -10.008774614835222, + -10.62258953168044, + -11.242934394449541, + -11.869809203142534, + -12.50321395775941, + -13.143148658300172, + -13.789613304764815, + -14.442607897153348, + -15.102132435465766, + -15.768186919702071, + -16.44077134986226, + -17.119885725946325, + -17.80553004795429, + -18.497704315886132, + -19.196408529741863, + -19.901642689521474, + -20.613406795224975, + -21.33170084685236, + -22.056524844403633, + -22.787878787878782, + -23.525762677277825, + -24.270176512600756, + -25.021120293847567, + -25.778594021018257, + -26.54259769411285, + -27.313131313131308, + -28.090194878073653, + -28.873788388939907, + -29.66391184573002, + -30.46056524844404, + -31.26374859708193, + -32.0734618916437, + -32.88970513212938, + -33.71247831853892, + -34.54178145087235, + -35.37761452912968, + -36.21997755331088, + -37.06887052341598, + -37.92429343944495, + -38.78624630139781, + -39.65472910927457, + -40.52974186307519, + -41.41128456279972, + -42.299357208448114 + ], + [ + 13.577390062238548, + 13.342312008978675, + 13.10070400979492, + 12.852566064687279, + 12.597898173655746, + 12.336700336700337, + 12.068972553821038, + 11.794714825017856, + 11.513927150290787, + 11.226609529639832, + 10.932761963064992, + 10.632384450566269, + 10.32547699214366, + 10.012039587797165, + 9.69207223752678, + 9.365574941332516, + 9.032547699214367, + 8.69299051117233, + 8.346903377206406, + 7.9942862973166005, + 7.635139271502906, + 7.26946229976533, + 6.897255382103866, + 6.518518518518517, + 6.133251709009284, + 5.7414549535761665, + 5.343128252219161, + 4.938271604938271, + 4.526885011733496, + 4.108968472604836, + 3.6845219875522903, + 3.2535455565758604, + 2.8160391796755433, + 2.3720028568513407, + 1.921436588103254, + 1.4643403734312819, + 1.0007142128354245, + 0.530558106315681, + 0.05387205387205385, + -0.42934394449546054, + -0.9190898887868608, + -1.4153657790021412, + -1.918171615141312, + -2.4275073972043675, + -2.943373125191309, + -3.4657687991021313, + -3.9946944189368425, + -4.53014998469544, + -5.072135496377923, + -5.62065095398429, + -6.175696357514539, + -6.737271706968677, + -7.3053770023467015, + -7.88001224364861, + -8.4611774308744, + -9.04887256402408, + -9.643097643097645, + -10.243852668095094, + -10.851137639016425, + -11.464952555861647, + -12.085297418630752, + -12.712172227323748, + -13.345576981940617, + -13.98551168248138, + -14.631976328946028, + -15.284970921334558, + -15.944495459646978, + -16.610549943883278, + -17.283134374043463, + -17.96224875012754, + -18.6478930721355, + -19.34006734006734, + -20.03877155392307, + -20.744005713702684, + -21.455769819406186, + -22.174063871033567, + -22.89888786858484, + -23.630241812059992, + -24.36812570145904, + -25.11253953678196, + -25.863483318028777, + -26.62095704519947, + -27.38496071829405, + -28.155494337312522, + -28.93255790225487, + -29.716151413121118, + -30.506274869911238, + -31.302928272625238, + -32.10611162126314, + -32.91582491582491, + -33.732068156310575, + -34.55484134272014, + -35.38414447505357, + -36.2199775533109, + -37.062340577492094, + -37.91123354759718, + -38.76665646362616, + -39.62860932557902, + -40.49709213345578, + -41.372104887256405 + ], + [ + 13.205183144577084, + 12.983164983164983, + 12.754616875828999, + 12.519538822569128, + 12.277930823385368, + 12.029792878277728, + 11.7751249872462, + 11.513927150290787, + 11.246199367411492, + 10.971941638608307, + 10.691153963881238, + 10.403836343230283, + 10.109988776655445, + 9.80961126415672, + 9.502703805734107, + 9.189266401387615, + 8.869299051117235, + 8.542801754922968, + 8.209774512804817, + 7.8702173247627805, + 7.524130190796857, + 7.171513110907052, + 6.812366085093359, + 6.44668911335578, + 6.074482195694317, + 5.69574533210897, + 5.310478522599736, + 4.918681767166616, + 4.520355065809612, + 4.115498418528723, + 3.704111825323947, + 3.286195286195288, + 2.861748801142742, + 2.4307723701663098, + 1.9932659932659935, + 1.5492296704417918, + 1.0986634016937054, + 0.6415671870217328, + 0.17794102642587606, + -0.2922150800938679, + -0.7689011325374973, + -1.2521171309050074, + -1.7418630751964068, + -2.238138965411692, + -2.740944801550863, + -3.2502805836139146, + -3.7661463116008553, + -4.2885419855116815, + -4.817467605346394, + -5.352923171104991, + -5.89490868278747, + -6.443424140393836, + -6.99846954392409, + -7.560044893378229, + -8.128150188756248, + -8.702785430058157, + -9.283950617283951, + -9.871645750433629, + -10.465870829507192, + -11.06662585450464, + -11.673910825425978, + -12.2877257422712, + -12.908070605040301, + -13.53494541373329, + -14.16835016835017, + -14.80828486889093, + -15.45474951535558, + -16.107744107744107, + -16.76726864605652, + -17.433323130292827, + -18.105907560453016, + -18.785021936537085, + -19.470666258545045, + -20.16284052647689, + -20.86154474033262, + -21.566778900112233, + -22.278543005815735, + -22.996837057443116, + -23.721661054994392, + -24.45301499846954, + -25.19089888786859, + -25.93531272319151, + -26.68625650443832, + -27.443730231609024, + -28.2077339047036, + -28.978267523722074, + -29.755331088664423, + -30.53892459953066, + -31.329048056320786, + -32.125701459034794, + -32.92888480767268, + -33.73859810223446, + -34.554841342720124, + -35.37761452912969, + -36.206917661463116, + -37.04275073972043, + -37.88511376390164, + -38.734006734006726, + -39.589429650035726, + -40.45138251198857 + ], + [ + 12.826446280991735, + 12.617488011427405, + 12.401999795939188, + 12.17998163452709, + 11.951433527191103, + 11.716355473931232, + 11.474747474747474, + 11.226609529639834, + 10.971941638608307, + 10.710743801652892, + 10.443016018773594, + 10.16875828997041, + 9.887970615243344, + 9.60065299459239, + 9.306805428017547, + 9.006427915518824, + 8.699520457096217, + 8.386083052749719, + 8.066115702479339, + 7.739618406285074, + 7.4065911641669215, + 7.067033976124886, + 6.720946842158964, + 6.368329762269157, + 6.009182736455463, + 5.643505764717887, + 5.271298847056423, + 4.892561983471075, + 4.507295173961841, + 4.115498418528723, + 3.717171717171718, + 3.312315069890829, + 2.9009284766860537, + 2.4830119375573916, + 2.058565452504847, + 1.6275890215284154, + 1.1900826446281, + 0.7460463218038977, + 0.29548005305581193, + -0.16161616161616155, + -0.6252423222120203, + -1.0953984287317597, + -1.5720844811753887, + -2.055300479542903, + -2.545046423834304, + -3.0413223140495846, + -3.5441281501887545, + -4.053463932251811, + -4.569329660238752, + -5.091725334149578, + -5.620650953984286, + -6.156106519742882, + -6.6980920314253645, + -7.2466074890317325, + -7.801652892561981, + -8.36322824201612, + -8.931333537394144, + -9.505968778696053, + -10.087133965921842, + -10.674829099071522, + -11.269054178145087, + -11.869809203142538, + -12.477094174063868, + -13.090909090909088, + -13.711253953678195, + -14.338128762371186, + -14.971533516988064, + -15.611468217528822, + -16.25793286399347, + -16.910927456382, + -17.570451994694423, + -18.236506478930718, + -18.909090909090907, + -19.588205285174983, + -20.273849607182942, + -20.96602387511478, + -21.664728088970513, + -22.369962248750127, + -23.08172635445363, + -23.80002040608101, + -24.524844403632287, + -25.256198347107436, + -25.994082236506472, + -26.73849607182941, + -27.489439853076213, + -28.24691358024692, + -29.010917253341496, + -29.781450872359958, + -30.55851443730232, + -31.342107948168554, + -32.13223140495867, + -32.92888480767269, + -33.732068156310575, + -34.541781450872364, + -35.358024691358025, + -36.18079787776757, + -37.01010101010101, + -37.845934088358334, + -38.688297112539544, + -39.53719008264463 + ], + [ + 12.4411794714825, + 12.245281093765943, + 12.042852770125494, + 11.833894500561165, + 11.61840628507295, + 11.396388123660849, + 11.167840016324865, + 10.932761963064994, + 10.691153963881236, + 10.443016018773594, + 10.188348127742067, + 9.927150290786654, + 9.659422507907356, + 9.385164779104173, + 9.104377104377102, + 8.817059483726151, + 8.523211917151311, + 8.222834404652586, + 7.915926946229976, + 7.602489541883482, + 7.2825221916131, + 6.956024895418835, + 6.622997653300684, + 6.283440465258646, + 5.937353331292725, + 5.584736251402919, + 5.225589225589225, + 4.859912253851648, + 4.487705336190185, + 4.108968472604837, + 3.7237016630956026, + 3.3319049076624845, + 2.9335782063054796, + 2.528721559024589, + 2.1173349658198144, + 1.699418426691154, + 1.2749719416386087, + 0.8439955106621775, + 0.4064891337618619, + -0.03754718906234045, + -0.4881134578104287, + -0.9452096724823975, + -1.408835833078256, + -1.878991939598, + -2.3556779920416293, + -2.8388939904091393, + -3.328639934700539, + -3.824915824915824, + -4.327721661054994, + -4.83705744311805, + -5.352923171104988, + -5.875318845015814, + -6.4042444648505255, + -6.9397000306091225, + -7.481685542291601, + -8.030200999897968, + -8.585246403428222, + -9.146821752882358, + -9.71492704826038, + -10.289562289562287, + -10.870727476788083, + -11.458422609937761, + -12.052647689011323, + -12.653402714008772, + -13.260687684930106, + -13.87450260177533, + -14.494847464544435, + -15.12172227323742, + -15.7551270278543, + -16.395061728395063, + -17.041526374859707, + -17.694520967248238, + -18.354045505560656, + -19.020099989796957, + -19.69268441995715, + -20.371798796041215, + -21.05744311804918, + -21.749617385981022, + -22.448321599836753, + -23.15355575961636, + -23.86531986531987, + -24.583613916947247, + -25.308437914498512, + -26.039791857973675, + -26.77767574737271, + -27.52208958269565, + -28.273033363942453, + -29.030507091113144, + -29.794510764207736, + -30.5650443832262, + -31.342107948168547, + -32.125701459034794, + -32.91582491582491, + -33.71247831853893, + -34.515661667176815, + -35.32537496173859, + -36.141618202224265, + -36.964391388633814, + -37.79369452096725, + -38.629527599224566 + ], + [ + 12.049382716049381, + 11.866544230180594, + 11.677175798387918, + 11.48127742067136, + 11.278849097030914, + 11.069890827466585, + 10.854402611978369, + 10.632384450566269, + 10.403836343230282, + 10.16875828997041, + 9.927150290786654, + 9.679012345679013, + 9.424344454647485, + 9.163146617692073, + 8.895418834812773, + 8.621161106009591, + 8.340373431282524, + 8.053055810631568, + 7.759208244056728, + 7.458830731558004, + 7.151923273135393, + 6.838485868788899, + 6.518518518518519, + 6.192021222324252, + 5.858993980206101, + 5.519436792164066, + 5.173349658198143, + 4.820732578308336, + 4.461585552494643, + 4.095908580757066, + 3.7237016630956026, + 3.3449647995102554, + 2.959697990001021, + 2.5679012345679, + 2.169574533210897, + 1.7647178859300068, + 1.3533312927252326, + 0.9354147535965716, + 0.5109682685440269, + 0.07999183756759498, + -0.35751453933272237, + -0.801550862156921, + -1.2521171309050083, + -1.7092133455769818, + -2.1728395061728403, + -2.64299561269258, + -3.119681665136209, + -3.602897663503724, + -4.092643607795123, + -4.588919498010408, + -5.091725334149575, + -5.60106111621263, + -6.116926844199571, + -6.639322518110398, + -7.168248137945105, + -7.703703703703702, + -8.245689215386186, + -8.794204672992553, + -9.3492500765228, + -9.910825425976938, + -10.478930721354963, + -11.053565962656872, + -11.63473114988266, + -12.222426283032343, + -12.816651362105906, + -13.417406387103357, + -14.024691358024693, + -14.63850627486991, + -15.258851137639015, + -15.885725946332009, + -16.51913070094888, + -17.15906540148964, + -17.80553004795429, + -18.458524640342823, + -19.11804917865524, + -19.78410366289154, + -20.456688093051728, + -21.1358024691358, + -21.821446791143764, + -22.5136210590756, + -23.212325272931338, + -23.917559432710945, + -24.62932353841444, + -25.347617590041835, + -26.0724415875931, + -26.80379553106826, + -27.5416794204673, + -28.28609325579022, + -29.037037037037038, + -29.794510764207732, + -30.55851443730231, + -31.329048056320786, + -32.10611162126313, + -32.88970513212938, + -33.6798285889195, + -34.4764819916335, + -35.2796653402714, + -36.08937863483318, + -36.90562187531885, + -37.72839506172839 + ], + [ + 11.65105601469238, + 11.48127742067136, + 11.304968880726458, + 11.122130394857669, + 10.932761963064992, + 10.736863585348434, + 10.534435261707989, + 10.32547699214366, + 10.109988776655445, + 9.887970615243342, + 9.659422507907358, + 9.424344454647485, + 9.18273645546373, + 8.934598510356087, + 8.679930619324558, + 8.418732782369146, + 8.15100499948985, + 7.876747270686664, + 7.595959595959595, + 7.308641975308643, + 7.0147944087338026, + 6.714416896235078, + 6.407509437812468, + 6.094072033465973, + 5.774104683195592, + 5.4476073870013275, + 5.114580144883175, + 4.7750229568411395, + 4.428935822875217, + 4.076318742985411, + 3.7171717171717176, + 3.351494745434141, + 2.9792878277726773, + 2.600550964187327, + 2.2152841546780944, + 1.8234873992449747, + 1.4251606978879712, + 1.020304050607081, + 0.6089174574023068, + 0.19100091827364518, + -0.23344556677890127, + -0.6644219977553292, + -1.1019283746556465, + -1.545964697479849, + -1.996530966227937, + -2.4536271808999066, + -2.9172533414957647, + -3.387409448015508, + -3.8640955004591375, + -4.347311498826652, + -4.837057443118049, + -5.333333333333333, + -5.836139169472504, + -6.34547495153556, + -6.861340679522495, + -7.383736353433323, + -7.912661973268035, + -8.448117539026631, + -8.99010305070911, + -9.538618508315478, + -10.093663911845729, + -10.65523926129987, + -11.223344556677887, + -11.797979797979798, + -12.379144985205592, + -12.96684011835527, + -13.561065197428837, + -14.161820222426282, + -14.769105193347617, + -15.382920110192838, + -16.003264972961944, + -16.63013978165493, + -17.26354453627181, + -17.903479236812572, + -18.54994388327722, + -19.202938475665746, + -19.862463013978164, + -20.528517498214466, + -21.20110192837466, + -21.880216304458727, + -22.565860626466694, + -23.258034894398527, + -23.956739108254254, + -24.661973268033876, + -25.37373737373737, + -26.092031425364766, + -26.816855422916028, + -27.548209366391184, + -28.28609325579023, + -29.03050709111315, + -29.78145087235996, + -30.53892459953066, + -31.302928272625238, + -32.07346189164372, + -32.85052545658606, + -33.634118967452295, + -34.42424242424243, + -35.22089582695643, + -36.02407917559434, + -36.833792470156105 + ], + [ + 11.246199367411487, + 11.08948066523824, + 10.926232017141107, + 10.756453423120089, + 10.580144883175185, + 10.397306397306398, + 10.207937965513722, + 10.012039587797164, + 9.809611264156718, + 9.600652994592389, + 9.385164779104173, + 9.163146617692071, + 8.934598510356087, + 8.699520457096215, + 8.457912457912457, + 8.209774512804815, + 7.9551066217732895, + 7.693908784817875, + 7.426181001938577, + 7.151923273135395, + 6.871135598408324, + 6.583817977757372, + 6.289970411182532, + 5.989592898683807, + 5.6826854402611975, + 5.369248035914703, + 5.049280685644321, + 4.722783389450056, + 4.389756147331905, + 4.050198959289869, + 3.7041118253239462, + 3.35149474543414, + 2.9923477196204473, + 2.6266707478828684, + 2.2544638302214057, + 1.875726966636057, + 1.490460157126824, + 1.0986634016937047, + 0.7003367003367007, + 0.2954800530558104, + -0.11590654014896562, + -0.5338230792776231, + -0.9582695643301697, + -1.3892459953066014, + -1.826752372206919, + -2.2707886950311176, + -2.7213549637792047, + -3.178451178451178, + -3.6420773390470367, + -4.112233445566781, + -4.588919498010406, + -5.07213549637792, + -5.561881440669319, + -6.058157330884605, + -6.560963167023772, + -7.070298949086826, + -7.586164677073768, + -8.108560350984595, + -8.637485970819302, + -9.172941536577898, + -9.714927048260382, + -10.263442505866749, + -10.818487909397, + -11.380063258851136, + -11.94816855422916, + -12.522803795531068, + -13.103968982756863, + -13.691664115906537, + -14.285889194980104, + -14.886644219977555, + -15.49392919089889, + -16.107744107744104, + -16.72808897051321, + -17.3549637792062, + -17.98836853382308, + -18.628303234363838, + -19.274767880828485, + -19.92776247321702, + -20.587287011529437, + -21.253341495765735, + -21.92592592592593, + -22.605040302009996, + -23.290684624017953, + -23.982858891949803, + -24.681563105805527, + -25.386797265585148, + -26.098561371288646, + -26.816855422916024, + -27.5416794204673, + -28.273033363942456, + -29.01091725334149, + -29.75533108866442, + -30.50627486991123, + -31.263748597081936, + -32.02775227017651, + -32.79828588919497, + -33.57534945413733, + -34.35894296500357, + -35.149066421793705, + -35.945719824507705 + ], + [ + 10.834812774206709, + 10.691153963881236, + 10.54096520763187, + 10.384246505458623, + 10.220997857361493, + 10.051219263340473, + 9.87491072339557, + 9.692072237526784, + 9.502703805734107, + 9.30680542801755, + 9.104377104377102, + 8.895418834812773, + 8.679930619324558, + 8.457912457912457, + 8.22936435057647, + 7.9942862973166, + 7.752678298132844, + 7.504540353025201, + 7.249872461993673, + 6.988674625038262, + 6.720946842158961, + 6.446689113355779, + 6.16590143862871, + 5.878583817977756, + 5.584736251402917, + 5.284358738904194, + 4.977451280481583, + 4.664013876135088, + 4.344046525864707, + 4.017549229670442, + 3.6845219875522903, + 3.3449647995102545, + 2.9988776655443328, + 2.646260585654524, + 2.2871135598408325, + 1.921436588103254, + 1.5492296704417918, + 1.1704928068564429, + 0.78522599734721, + 0.3934292419140901, + -0.004897459442915197, + -0.40975410672380197, + -0.821140699928578, + -1.2390572390572392, + -1.6635037241097854, + -2.094480155086214, + -2.5319865319865307, + -2.9760228548107337, + -3.426589123558821, + -3.883685338230794, + -4.347311498826649, + -4.817467605346392, + -5.294153657790022, + -5.7773696561575365, + -6.267115600448932, + -6.763391490664217, + -7.266197326803388, + -7.775533108866443, + -8.29139883685338, + -8.813794510764206, + -9.342720130598918, + -9.878175696357514, + -10.420161208039993, + -10.96867666564636, + -11.523722069176612, + -12.085297418630752, + -12.653402714008775, + -13.228037955310679, + -13.809203142536475, + -14.396898275686155, + -14.991123354759718, + -15.591878379757166, + -16.1991633506785, + -16.81297826752372, + -17.433323130292827, + -18.060197938985812, + -18.693602693602692, + -19.333537394143455, + -19.9800020406081, + -20.63299663299663, + -21.292521171309055, + -21.958575655545353, + -22.63116008570553, + -23.310274461789618, + -23.995918783797567, + -24.688093051729417, + -25.386797265585145, + -26.092031425364752, + -26.80379553106826, + -27.522089582695642, + -28.246913580246904, + -28.97826752372207, + -29.716151413121107, + -30.460565248444038, + -31.211509029690845, + -31.968982756861536, + -32.73298642995613, + -33.50352004897459, + -34.280583613916946, + -35.064177124783185 + ], + [ + 10.416896235078053, + 10.286297316600345, + 10.149168452198754, + 10.005509641873278, + 9.855320885623916, + 9.698602183450669, + 9.535353535353535, + 9.365574941332516, + 9.189266401387613, + 9.006427915518824, + 8.81705948372615, + 8.621161106009591, + 8.418732782369148, + 8.209774512804817, + 7.994286297316599, + 7.7722681359045, + 7.543720028568515, + 7.308641975308641, + 7.067033976124884, + 6.818896031017244, + 6.564228139985714, + 6.303030303030303, + 6.035302520151005, + 5.761044791347821, + 5.480257116620752, + 5.192939495969799, + 4.8990919293949595, + 4.598714416896235, + 4.291806958473625, + 3.9783695541271307, + 3.658402203856749, + 3.331904907662484, + 2.9988776655443328, + 2.6593204775022947, + 2.313233343536374, + 1.960616263646566, + 1.6014692378328745, + 1.235792266095296, + 0.8635853484338339, + 0.4848484848484844, + 0.09958167533924978, + -0.2922150800938663, + -0.6905417814508716, + -1.0953984287317624, + -1.5067850219365382, + -1.924701561065196, + -2.349148046117742, + -2.7801244770941738, + -3.217630853994491, + -3.6616671768186935, + -4.112233445566778, + -4.5693296602387505, + -5.032955820834609, + -5.503111927354354, + -5.979797979797978, + -6.463013978165492, + -6.952759922456893, + -7.449035812672178, + -7.951841648811342, + -8.4611774308744, + -8.977043158861342, + -9.499438832772167, + -10.028364452606873, + -10.563820018365472, + -11.105805530047954, + -11.654320987654321, + -12.209366391184577, + -12.770941740638708, + -13.339047036016733, + -13.913682277318642, + -14.494847464544435, + -15.08254259769411, + -15.676767676767678, + -16.277522701765125, + -16.884807672686463, + -17.498622589531678, + -18.118967452300783, + -18.745842260993776, + -19.37924701561065, + -20.019181716151408, + -20.665646362616066, + -21.31864095500459, + -21.978165493317007, + -22.644219977553313, + -23.316804407713498, + -23.995918783797578, + -24.68156310580553, + -25.37373737373737, + -26.072441587593104, + -26.777675747372715, + -27.48943985307621, + -28.207733904703602, + -28.93255790225487, + -29.66391184573003, + -30.401795735129067, + -31.14620957045199, + -31.89715335169881, + -32.6546270788695, + -33.418630751964095, + -34.18916437098255 + ], + [ + 9.992449750025509, + 9.874910723395573, + 9.75084175084175, + 9.620242832364045, + 9.483113967962453, + 9.339455157636978, + 9.189266401387613, + 9.032547699214366, + 8.869299051117235, + 8.699520457096215, + 8.523211917151313, + 8.340373431282522, + 8.15100499948985, + 7.9551066217732895, + 7.752678298132842, + 7.543720028568514, + 7.3282318130803, + 7.106213651668197, + 6.877665544332212, + 6.642587491072341, + 6.400979491888583, + 6.152841546780941, + 5.898173655749414, + 5.636975818794001, + 5.369248035914702, + 5.09499030711152, + 4.8142026323844505, + 4.526885011733497, + 4.233037445158658, + 3.9326599326599334, + 3.6257524742373226, + 3.312315069890828, + 2.9923477196204478, + 2.66585042342618, + 2.3328231813080302, + 1.993265993265993, + 1.647178859300072, + 1.2945617794102642, + 0.9354147535965726, + 0.5697377818589938, + 0.19753086419752952, + -0.18120599938781612, + -0.5664728088970505, + -0.9582695643301706, + -1.3565962656871762, + -1.7614529129680632, + -2.1728395061728385, + -2.5907560453014997, + -3.0152025303540464, + -3.4461789613304785, + -3.883685338230792, + -4.327721661054994, + -4.778287929803083, + -5.235384144475056, + -5.69901030507091, + -6.169166411590654, + -6.6458524640342835, + -7.129068462401797, + -7.618814406693193, + -8.115090296908479, + -8.617896133047648, + -9.127231915110706, + -9.64309764309764, + -10.165493317008467, + -10.694418936843181, + -11.229874502601776, + -11.77186001428426, + -12.320375471890625, + -12.875420875420875, + -13.436996224875015, + -14.005101520253039, + -14.57973676155494, + -15.160901948780737, + -15.748597081930416, + -16.34282216100398, + -16.943577186001427, + -17.55086215692276, + -18.164677073767983, + -18.785021936537092, + -19.411896745230077, + -20.04530149984696, + -20.685236200387717, + -21.331700846852357, + -21.984695439240898, + -22.644219977553313, + -23.310274461789618, + -23.982858891949803, + -24.661973268033872, + -25.347617590041835, + -26.039791857973675, + -26.738496071829402, + -27.44373023160902, + -28.15549433731252, + -28.873788388939907, + -29.598612386491176, + -30.329966329966325, + -31.067850219365376, + -31.812264054688292, + -32.56320783593512, + -33.32068156310581 + ], + [ + 9.561473319049075, + 9.456994184266913, + 9.34598510356086, + 9.228446076930924, + 9.104377104377104, + 8.973778185899397, + 8.836649321497806, + 8.69299051117233, + 8.542801754922968, + 8.386083052749719, + 8.222834404652586, + 8.053055810631568, + 7.876747270686666, + 7.693908784817876, + 7.5045403530252, + 7.308641975308642, + 7.106213651668199, + 6.897255382103866, + 6.681767166615651, + 6.459749005203552, + 6.231200897867564, + 5.996122844607694, + 5.7545148454239365, + 5.506376900316294, + 5.251709009284767, + 4.990511172329354, + 4.722783389450056, + 4.448525660646872, + 4.167737985919803, + 3.8804203652688507, + 3.586572798694011, + 3.286195286195287, + 2.9792878277726764, + 2.66585042342618, + 2.3458830731558002, + 2.019385776961534, + 1.6863585348433834, + 1.3468013468013467, + 1.0007142128354252, + 0.6480971329456174, + 0.28895010713192404, + -0.07672686460565115, + -0.4489337822671149, + -0.8276706458524643, + -1.2129374553616987, + -1.6047342107948155, + -2.0030609121518204, + -2.4079175594327107, + -2.819304152637487, + -3.2372206917661477, + -3.6616671768186912, + -4.0926436077951225, + -4.53014998469544, + -4.974186307519642, + -5.424752576267727, + -5.881848790939699, + -6.345474951535558, + -6.815631058055303, + -7.292317110498926, + -7.7755331088664414, + -8.265279053157842, + -8.761554943373127, + -9.264360779512293, + -9.773696561575347, + -10.289562289562289, + -10.811957963473116, + -11.340883583307827, + -11.876339149066421, + -12.418324660748901, + -12.96684011835527, + -13.521885521885524, + -14.083460871339657, + -14.651566166717682, + -15.226201408019591, + -15.807366595245384, + -16.39506172839506, + -16.989286807468623, + -17.590041832466074, + -18.197326803387412, + -18.811141720232627, + -19.43148658300174, + -20.058361391694724, + -20.691766146311597, + -21.331700846852364, + -21.978165493317007, + -22.631160085705545, + -23.290684624017956, + -23.956739108254254, + -24.629323538414454, + -25.30843791449852, + -25.994082236506472, + -26.686256504438326, + -27.384960718294046, + -28.090194878073667, + -28.80195898377717, + -29.520253035404544, + -30.24507703295582, + -30.976430976430976, + -31.714314865830026, + -32.45872870115294 + ], + [ + 9.123966942148758, + 9.032547699214364, + 8.934598510356086, + 8.830119375573922, + 8.71911029486787, + 8.601571268237935, + 8.477502295684113, + 8.346903377206408, + 8.209774512804817, + 8.066115702479339, + 7.915926946229976, + 7.759208244056728, + 7.595959595959597, + 7.426181001938579, + 7.2498724619936725, + 7.067033976124884, + 6.877665544332212, + 6.681767166615651, + 6.479338842975206, + 6.270380573410877, + 6.05489235792266, + 5.832874196510561, + 5.604326089174574, + 5.369248035914702, + 5.127640036730946, + 4.879502091623304, + 4.624834200591776, + 4.363636363636364, + 4.095908580757065, + 3.8216508519538834, + 3.540863177226814, + 3.253545556575861, + 2.959697990001021, + 2.6593204775022956, + 2.3524130190796866, + 2.0389756147331908, + 1.7190082644628106, + 1.3925109682685444, + 1.059483726150394, + 0.7199265381083565, + 0.3738394041424339, + 0.021222324252629265, + -0.3379247015610639, + -0.7036016732986424, + -1.0758085909601065, + -1.4545454545454524, + -1.8398122640546868, + -2.2316090194878067, + -2.629935720844812, + -3.0347923681257023, + -3.4461789613304745, + -3.8640955004591357, + -4.2885419855116815, + -4.719518416488114, + -5.157024793388428, + -5.601061116212629, + -6.051627384960718, + -6.508723599632691, + -6.972349760228545, + -7.442505866748289, + -7.919191919191919, + -8.402407917559433, + -8.89215386185083, + -9.388429752066113, + -9.891235588205284, + -10.400571370268338, + -10.91643709825528, + -11.438832772166103, + -11.967758392000814, + -12.50321395775941, + -13.045199469441894, + -13.593714927048257, + -14.148760330578508, + -14.71033568003265, + -15.278440975410673, + -15.853076216712576, + -16.434241403938373, + -17.021936537088052, + -17.616161616161616, + -18.216916641159063, + -18.824201612080405, + -19.438016528925615, + -20.058361391694717, + -20.685236200387717, + -21.31864095500459, + -21.958575655545356, + -22.605040302009996, + -23.258034894398527, + -23.917559432710952, + -24.583613916947247, + -25.25619834710743, + -25.935312723191515, + -26.62095704519946, + -27.313131313131315, + -28.011835526987042, + -28.71706968676665, + -29.428833792470154, + -30.14712784409754, + -30.871951841648816, + -31.603305785123965 + ], + [ + 8.679930619324557, + 8.601571268237935, + 8.516681971227426, + 8.425262728293031, + 8.32731353943475, + 8.222834404652586, + 8.111825323946535, + 7.9942862973166005, + 7.8702173247627805, + 7.739618406285073, + 7.6024895418834815, + 7.458830731558004, + 7.3086419753086425, + 7.151923273135395, + 6.988674625038261, + 6.8188960310172435, + 6.642587491072341, + 6.45974900520355, + 6.270380573410876, + 6.074482195694317, + 5.872053872053871, + 5.663095602489542, + 5.447607387001327, + 5.225589225589225, + 4.997041118253239, + 4.761963064993369, + 4.520355065809611, + 4.27221712070197, + 4.017549229670442, + 3.75635139271503, + 3.4886236098357313, + 3.2143658810325486, + 2.93357820630548, + 2.6462605856545247, + 2.352413019079686, + 2.0520355065809612, + 1.7451280481583518, + 1.431690643811856, + 1.1117232935414763, + 0.7852259973472093, + 0.4521987552290574, + 0.11264156718702323, + -0.23344556677889916, + -0.5860626466687072, + -0.9452096724824005, + -1.3108866442199756, + -1.68309356188144, + -2.061830425466789, + -2.4470972349760234, + -2.8388939904091437, + -3.237220691766145, + -3.642077339047036, + -4.053463932251812, + -4.471380471380472, + -4.895826956433016, + -5.326803387409448, + -5.764309764309764, + -6.208346087133966, + -6.658912355882052, + -7.116008570554024, + -7.579634731149882, + -8.049790837669626, + -8.526476890113251, + -9.009692888480766, + -9.499438832772167, + -9.99571472298745, + -10.498520559126622, + -11.007856341189672, + -11.523722069176614, + -12.046117743087441, + -12.575043362922152, + -13.110498928680745, + -13.652484440363228, + -14.200999897969595, + -14.75604530149985, + -15.317620650953982, + -15.885725946332007, + -16.460361187633914, + -17.04152637485971, + -17.629221508009383, + -18.223446587082954, + -18.8242016120804, + -19.43148658300173, + -20.045301499846957, + -20.66564636261606, + -21.292521171309055, + -21.92592592592593, + -22.56586062646668, + -23.212325272931338, + -23.865319865319865, + -24.524844403632276, + -25.190898887868585, + -25.86348331802877, + -26.54259769411285, + -27.228242016120802, + -27.920416284052642, + -28.61912049790838, + -29.32435465768799, + -30.036118763391492, + -30.754412815018878 + ], + [ + 8.229364350576471, + 8.164064891337619, + 8.09223548617488, + 8.013876135088257, + 7.928986838077746, + 7.837567595143353, + 7.739618406285073, + 7.635139271502908, + 7.524130190796858, + 7.4065911641669215, + 7.282522191613101, + 7.151923273135394, + 7.0147944087338026, + 6.871135598408326, + 6.720946842158963, + 6.564228139985715, + 6.4009794918885845, + 6.231200897867564, + 6.054892357922661, + 5.872053872053873, + 5.6826854402611975, + 5.486787062544638, + 5.284358738904194, + 5.075400469339863, + 4.859912253851647, + 4.637894092439548, + 4.409345985103561, + 4.17426793184369, + 3.9326599326599325, + 3.6845219875522908, + 3.4298540965207636, + 3.168656259565352, + 2.9009284766860532, + 2.6266707478828684, + 2.3458830731558007, + 2.0585654525048467, + 1.7647178859300077, + 1.4643403734312828, + 1.1574329150086733, + 0.8439955106621775, + 0.5240281603917962, + 0.19753086419753263, + -0.1354963779206192, + -0.4750535659626566, + -0.8211406999285791, + -1.173757779818384, + -1.5329048056320769, + -1.8985817773696554, + -2.2707886950311194, + -2.6495255586164688, + -3.0347923681256996, + -3.4265891235588195, + -3.8249158249158244, + -4.229772472196716, + -4.641159065401487, + -5.059075604530149, + -5.483522089582696, + -5.914498520559128, + -6.35200489745944, + -6.7960412202836435, + -7.246607489031731, + -7.703703703703704, + -8.167329864299559, + -8.637485970819302, + -9.114172023262931, + -9.597388021630445, + -10.087133965921847, + -10.583409856137127, + -11.086215692276298, + -11.595551474339354, + -12.111417202326294, + -12.633812876237116, + -13.162738496071828, + -13.698194061830424, + -14.240179573512908, + -14.78869503111927, + -15.343740434649524, + -15.905315784103662, + -16.473421079481685, + -17.04805632078359, + -17.629221508009387, + -18.216916641159063, + -18.811141720232623, + -19.41189674523008, + -20.019181716151408, + -20.632996632996637, + -21.25334149576574, + -21.880216304458724, + -22.513621059075607, + -23.153555759616363, + -23.80002040608101, + -24.453014998469545, + -25.11253953678196, + -25.778594021018264, + -26.45117845117845, + -27.130292827262515, + -27.815937149270486, + -28.508111417202322, + -29.20681563105806, + -29.91204979083767 + ], + [ + 7.772268135904499, + 7.720028568513417, + 7.661259055198449, + 7.595959595959596, + 7.524130190796857, + 7.445770839710234, + 7.360881542699724, + 7.269462299765331, + 7.171513110907051, + 7.067033976124885, + 6.956024895418835, + 6.838485868788899, + 6.714416896235079, + 6.583817977757373, + 6.446689113355779, + 6.303030303030303, + 6.152841546780942, + 5.996122844607693, + 5.83287419651056, + 5.663095602489543, + 5.4867870625446375, + 5.303948576675849, + 5.114580144883175, + 4.918681767166615, + 4.7162534435261705, + 4.507295173961841, + 4.291806958473625, + 4.069788797061525, + 3.841240689725538, + 3.606162636465667, + 3.3645546372819104, + 3.116416692174269, + 2.861748801142741, + 2.6005509641873275, + 2.3328231813080302, + 2.0585654525048462, + 1.7777777777777781, + 1.4904601571268237, + 1.196612590551985, + 0.8962350780532597, + 0.5893276196306492, + 0.275890215284156, + -0.04407713498622512, + -0.3705744311804918, + -0.7036016732986438, + -1.043158861340678, + -1.3892459953066008, + -1.7418630751964086, + -2.1010101010101017, + -2.46668707274768, + -2.8388939904091406, + -3.2176308539944904, + -3.6028976635037244, + -3.9946944189368443, + -4.393021120293846, + -4.797877767574737, + -5.209264360779512, + -5.627180899908174, + -6.0516273849607165, + -6.482603815937148, + -6.920110192837465, + -7.36414651566167, + -7.814712784409752, + -8.271808999081724, + -8.735435159677584, + -9.205591266197327, + -9.682277318640956, + -10.165493317008467, + -10.655239261299867, + -11.151515151515152, + -11.654320987654321, + -12.163656769717374, + -12.679522497704315, + -13.201918171615143, + -13.730843791449853, + -14.266299357208446, + -14.80828486889093, + -15.356800326497297, + -15.91184573002755, + -16.473421079481685, + -17.041526374859714, + -17.616161616161616, + -18.197326803387405, + -18.785021936537092, + -19.37924701561065, + -19.980002040608106, + -20.58728701152944, + -21.20110192837465, + -21.821446791143764, + -22.448321599836753, + -23.08172635445362, + -23.72166105499439, + -24.368125701459032, + -25.02112029384757, + -25.680644832159985, + -26.346699316396283, + -27.019283746556475, + -27.698398122640548, + -28.384042444648514, + -29.076216712580347 + ], + [ + 7.308641975308641, + 7.26946229976533, + 7.2237526782981325, + 7.17151311090705, + 7.112743597592082, + 7.047444138353229, + 6.975614733190491, + 6.897255382103867, + 6.812366085093358, + 6.7209468421589635, + 6.622997653300684, + 6.518518518518518, + 6.407509437812468, + 6.289970411182533, + 6.16590143862871, + 6.035302520151005, + 5.898173655749415, + 5.754514845423936, + 5.604326089174574, + 5.447607387001327, + 5.284358738904192, + 5.114580144883175, + 4.938271604938272, + 4.755433119069482, + 4.566064687276809, + 4.37016630956025, + 4.167737985919804, + 3.9587797163554743, + 3.7432915008672585, + 3.521273339455158, + 3.292725232119172, + 3.057647178859301, + 2.8160391796755437, + 2.567901234567901, + 2.313233343536374, + 2.0520355065809612, + 1.7843077237016636, + 1.5100499948984798, + 1.229262320171412, + 0.9419446995204571, + 0.6480971329456171, + 0.34771962044689475, + 0.04081216202428417, + -0.27262524232221175, + -0.592592592592593, + -0.9190898887868569, + -1.2521171309050083, + -1.5916743189470457, + -1.9377614529129683, + -2.2903785328027766, + -2.649525558616466, + -3.015202530354045, + -3.387409448015508, + -3.766146311600858, + -4.151413121110089, + -4.543209876543209, + -4.941536577900214, + -5.346393225181105, + -5.757779818385876, + -6.175696357514537, + -6.6001428425670845, + -7.031119273543517, + -7.46862565044383, + -7.9126619732680314, + -8.36322824201612, + -8.820324456688093, + -9.283950617283951, + -9.754106723803691, + -10.23079277624732, + -10.714008774614834, + -11.203754718906236, + -11.700030609121516, + -12.202836445260687, + -12.712172227323743, + -13.228037955310683, + -13.750433629221504, + -14.279359249056217, + -14.814814814814813, + -15.356800326497297, + -15.90531578410366, + -16.46036118763392, + -17.021936537088052, + -17.59004183246607, + -18.164677073767983, + -18.745842260993772, + -19.33353739414346, + -19.92776247321702, + -20.528517498214462, + -21.135802469135804, + -21.749617385981022, + -22.36996224875012, + -22.996837057443116, + -23.630241812059992, + -24.270176512600756, + -24.9166411590654, + -25.56963575145393, + -26.229160289766355, + -26.89521477400265, + -27.567799204162846, + -28.246913580246915 + ], + [ + 6.838485868788899, + 6.812366085093358, + 6.779716355473932, + 6.74053667993062, + 6.694827058463423, + 6.642587491072341, + 6.583817977757373, + 6.518518518518519, + 6.446689113355781, + 6.368329762269157, + 6.283440465258648, + 6.192021222324252, + 6.094072033465974, + 5.989592898683809, + 5.8785838179777565, + 5.761044791347821, + 5.636975818794002, + 5.506376900316294, + 5.369248035914702, + 5.225589225589227, + 5.075400469339863, + 4.918681767166616, + 4.755433119069483, + 4.585654525048464, + 4.409345985103561, + 4.226507499234772, + 4.037139067442098, + 3.8412406897255384, + 3.6388123660850935, + 3.4298540965207636, + 3.214365881032548, + 2.9923477196204478, + 2.7637996122844615, + 2.5287215590245893, + 2.287113559840833, + 2.0389756147331903, + 1.7843077237016636, + 1.5231098867462505, + 1.2553821038669528, + 0.981124375063769, + 0.7003367003366995, + 0.4130190796857476, + 0.11917151311090768, + -0.18120599938781767, + -0.48811345781042836, + -0.8015508621569215, + -1.1215182124273029, + -1.4480155086215694, + -1.781042750739721, + -2.1205999387817585, + -2.466687072747678, + -2.819304152637486, + -3.178451178451179, + -3.5441281501887576, + -3.9163350678502185, + -4.295071931435568, + -4.680338740944802, + -5.072135496377922, + -5.470462197734923, + -5.875318845015814, + -6.28670543822059, + -6.704621977349252, + -7.1290684624017935, + -7.560044893378225, + -7.997551270278544, + -8.441587593102746, + -8.892153861850833, + -9.349250076522804, + -9.812876237118662, + -10.283032343638405, + -10.759718396082034, + -11.242934394449545, + -11.732680338740945, + -12.228956228956228, + -12.7317620650954, + -13.24109784715845, + -13.756963575145392, + -14.27935924905622, + -14.808284868890933, + -15.343740434649522, + -15.885725946332013, + -16.434241403938373, + -16.989286807468623, + -17.55086215692277, + -18.118967452300783, + -18.6936026936027, + -19.274767880828488, + -19.862463013978164, + -20.45668809305173, + -21.05744311804918, + -21.66472808897051, + -22.278543005815735, + -22.898887868584836, + -23.525762677277832, + -24.159167431894705, + -24.799102132435465, + -25.445566778900115, + -26.098561371288643, + -26.758085909601068, + -27.424140393837362 + ], + [ + 6.36179981634527, + 6.348739924497501, + 6.329150086725845, + 6.303030303030303, + 6.2703805734108755, + 6.231200897867565, + 6.1854912764003664, + 6.133251709009285, + 6.074482195694317, + 6.009182736455465, + 5.937353331292726, + 5.858993980206101, + 5.774104683195594, + 5.682685440261198, + 5.5847362514029175, + 5.480257116620753, + 5.369248035914704, + 5.251709009284767, + 5.127640036730946, + 4.99704111825324, + 4.859912253851648, + 4.716253443526171, + 4.566064687276809, + 4.409345985103561, + 4.246097337006428, + 4.07631874298541, + 3.900010203040506, + 3.717171717171717, + 3.527803285379043, + 3.331904907662484, + 3.1294765840220387, + 2.920518314457709, + 2.7050300989694938, + 2.483011937557392, + 2.254463830221406, + 2.0193857769615344, + 1.7777777777777781, + 1.529639832670136, + 1.2749719416386087, + 1.0137741046831956, + 0.746046321803897, + 0.47178859300071563, + 0.1910009182736464, + -0.09631670237730827, + -0.3901642689521483, + -0.6905417814508708, + -0.9974492398734811, + -1.3108866442199771, + -1.6308539944903586, + -1.957351290684625, + -2.290378532802774, + -2.629935720844811, + -2.9760228548107333, + -3.3286399347005418, + -3.6877869605142317, + -4.05346393225181, + -4.425670849913274, + -4.804407713498624, + -5.189674523007854, + -5.581471278440974, + -5.97979797979798, + -6.38465462707887, + -6.796041220283643, + -7.213957759412303, + -7.63840424446485, + -8.069380675441282, + -8.5068870523416, + -8.950923375165797, + -9.401489643913886, + -9.85858585858586, + -10.322212019181716, + -10.792368125701458, + -11.269054178145087, + -11.7522701765126, + -12.242016120804, + -12.738292011019281, + -13.241097847158454, + -13.750433629221508, + -14.26629935720845, + -14.788695031119271, + -15.317620650953987, + -15.85307621671258, + -16.395061728395056, + -16.943577186001427, + -17.498622589531678, + -18.060197938985823, + -18.62830323436384, + -19.202938475665746, + -19.784103662891543, + -20.37179879604122, + -20.96602387511478, + -21.566778900112233, + -22.174063871033567, + -22.78787878787879, + -23.40822365064789, + -24.03509845934088, + -24.66850321395776, + -25.30843791449852, + -25.954902560963173, + -26.6078971533517 + ], + [ + 5.878583817977757, + 5.878583817977759, + 5.872053872053873, + 5.858993980206102, + 5.8394041424344465, + 5.813284358738905, + 5.780634629119478, + 5.741454953576166, + 5.695745332108969, + 5.6435057647178875, + 5.584736251402918, + 5.519436792164066, + 5.4476073870013275, + 5.369248035914703, + 5.284358738904192, + 5.192939495969799, + 5.09499030711152, + 4.990511172329354, + 4.879502091623304, + 4.761963064993369, + 4.637894092439547, + 4.507295173961841, + 4.37016630956025, + 4.2265074992347715, + 4.07631874298541, + 3.9196000408121625, + 3.75635139271503, + 3.586572798694011, + 3.4102642587491077, + 3.227425772880319, + 3.0380573410876446, + 2.8421589633710855, + 2.63973063973064, + 2.4307723701663093, + 2.2152841546780944, + 1.9932659932659933, + 1.7647178859300074, + 1.5296398326701357, + 1.2880318334863794, + 1.0398938883787368, + 0.7852259973472087, + 0.5240281603917978, + 0.2563003775124993, + -0.017957351290684764, + -0.2987450260177541, + -0.586062646668706, + -0.8799102132435462, + -1.1802877257422715, + -1.487195184164882, + -1.800632588511378, + -2.1205999387817562, + -2.4470972349760225, + -2.7801244770941747, + -3.119681665136212, + -3.4657687991021318, + -3.8183858789919394, + -4.177532904805632, + -4.543209876543211, + -4.915416794204672, + -5.294153657790021, + -5.679420467299256, + -6.0712172227323755, + -6.469543924089377, + -6.874400571370268, + -7.285787164575044, + -7.703703703703706, + -8.128150188756251, + -8.55912661973268, + -8.996632996632997, + -9.4406693194572, + -9.891235588205287, + -10.348331802877258, + -10.811957963473114, + -11.282114069992858, + -11.758800122436488, + -12.242016120804, + -12.731762065095399, + -13.228037955310683, + -13.730843791449855, + -14.240179573512906, + -14.756045301499853, + -15.278440975410673, + -15.80736659524538, + -16.342822161003983, + -16.88480767268646, + -17.433323130292834, + -17.98836853382308, + -18.549943883277216, + -19.118049178655244, + -19.692684419957146, + -20.27384960718294, + -20.861544740332622, + -21.45576981940618, + -22.056524844403636, + -22.663809815324967, + -23.27762473217018, + -23.897969594939294, + -24.52484440363228, + -25.158249158249166, + -25.79818385878992 + ], + [ + 5.388837873686358, + 5.401897765534129, + 5.408427711458015, + 5.408427711458014, + 5.4018977655341285, + 5.388837873686359, + 5.369248035914703, + 5.343128252219161, + 5.310478522599736, + 5.271298847056423, + 5.225589225589226, + 5.173349658198143, + 5.114580144883176, + 5.049280685644323, + 4.977451280481582, + 4.8990919293949595, + 4.814202632384451, + 4.722783389450056, + 4.624834200591776, + 4.520355065809611, + 4.409345985103561, + 4.291806958473625, + 4.167737985919804, + 4.037139067442098, + 3.900010203040506, + 3.75635139271503, + 3.6061626364656667, + 3.449443934292419, + 3.2861952861952863, + 3.116416692174268, + 2.9401081522293646, + 2.7572696663605765, + 2.567901234567902, + 2.372002856851341, + 2.169574533210897, + 1.9606162636465667, + 1.7451280481583515, + 1.5231098867462505, + 1.2945617794102646, + 1.0594837261503929, + 0.8178757269666355, + 0.5697377818589953, + 0.31506989082746734, + 0.05387205387205396, + -0.2138557290072446, + -0.4881134578104262, + -0.7689011325374953, + -1.0562187531884497, + -1.3500663197632898, + -1.650443832262015, + -1.9573512906846229, + -2.270788695031119, + -2.5907560453015, + -2.9172533414957664, + -3.2502805836139155, + -3.5898377716559526, + -3.9359249056218752, + -4.288541985511683, + -4.647689011325372, + -5.013365983062952, + -5.385572900724416, + -5.764309764309766, + -6.149576573818996, + -6.5413733292521155, + -6.939700030609122, + -7.3445566778900115, + -7.755943271094788, + -8.173859810223446, + -8.598306295275991, + -9.029282726252424, + -9.466789103152742, + -9.910825425976938, + -10.361391694725027, + -10.818487909397, + -11.282114069992858, + -11.752270176512598, + -12.228956228956228, + -12.712172227323741, + -13.20191817161514, + -13.698194061830423, + -14.200999897969599, + -14.71033568003265, + -15.226201408019586, + -15.748597081930416, + -16.277522701765122, + -16.812978267523725, + -17.3549637792062, + -17.903479236812565, + -18.458524640342823, + -19.02009998979696, + -19.588205285174976, + -20.16284052647689, + -20.74400571370268, + -21.331700846852364, + -21.925925925925924, + -22.52668095092337, + -23.133965921844712, + -23.747780838689927, + -24.368125701459043, + -24.995000510152025 + ], + [ + 4.892561983471075, + 4.918681767166617, + 4.938271604938272, + 4.951331496786043, + 4.957861442709928, + 4.957861442709929, + 4.951331496786043, + 4.938271604938272, + 4.918681767166617, + 4.892561983471075, + 4.859912253851649, + 4.820732578308337, + 4.7750229568411395, + 4.722783389450057, + 4.664013876135088, + 4.598714416896236, + 4.526885011733498, + 4.448525660646872, + 4.363636363636364, + 4.27221712070197, + 4.17426793184369, + 4.069788797061525, + 3.9587797163554743, + 3.8412406897255384, + 3.717171717171717, + 3.5865727986940117, + 3.4494439342924195, + 3.3057851239669427, + 3.15559636771758, + 2.9988776655443328, + 2.8356290174471996, + 2.665850423426182, + 2.489541883481278, + 2.3067033976124884, + 2.117334965819815, + 1.921436588103255, + 1.7190082644628104, + 1.5100499948984798, + 1.2945617794102646, + 1.0725436179981633, + 0.8439955106621766, + 0.6089174574023068, + 0.36730945821854966, + 0.11917151311090696, + -0.13549637792062108, + -0.39669421487603207, + -0.6644219977553306, + -0.9386797265585145, + -1.2194674012855837, + -1.5067850219365386, + -1.8006325885113759, + -2.101010101010101, + -2.407917559432712, + -2.7213549637792074, + -3.0413223140495864, + -3.3678196102438527, + -3.7008468523620044, + -4.040404040404042, + -4.3864911743699615, + -4.739108254259769, + -5.098255280073463, + -5.463932251811041, + -5.836139169472501, + -6.21487603305785, + -6.600142842567086, + -6.991939598000205, + -7.3902662993572115, + -7.795122946638098, + -8.206509539842873, + -8.624426078971535, + -9.048872564024082, + -9.47984899500051, + -9.917355371900825, + -10.361391694725029, + -10.811957963473118, + -11.269054178145087, + -11.732680338740945, + -12.20283644526069, + -12.679522497704319, + -13.162738496071828, + -13.652484440363235, + -14.148760330578515, + -14.651566166717679, + -15.16090194878074, + -15.676767676767676, + -16.199163350678507, + -16.72808897051322, + -17.263544536271805, + -17.805530047954292, + -18.35404550556066, + -18.909090909090907, + -19.470666258545048, + -20.03877155392307, + -20.613406795224982, + -21.194571982450775, + -21.782267115600447, + -22.376492194674015, + -22.97724721967146, + -23.584532190592803, + -24.198347107438018 + ], + [ + 4.389756147331904, + 4.428935822875218, + 4.461585552494644, + 4.487705336190184, + 4.5072951739618405, + 4.520355065809611, + 4.526885011733497, + 4.526885011733496, + 4.520355065809612, + 4.507295173961841, + 4.487705336190185, + 4.461585552494644, + 4.428935822875218, + 4.389756147331906, + 4.344046525864707, + 4.291806958473625, + 4.233037445158659, + 4.167737985919804, + 4.095908580757066, + 4.0175492296704425, + 3.9326599326599325, + 3.841240689725539, + 3.743291500867259, + 3.6388123660850935, + 3.5278032853790426, + 3.4102642587491077, + 3.2861952861952863, + 3.15559636771758, + 3.0184675033159882, + 2.874808692990512, + 2.724619936741149, + 2.567901234567902, + 2.404652586470769, + 2.23487399244975, + 2.0585654525048467, + 1.8757269666360576, + 1.6863585348433836, + 1.490460157126824, + 1.2880318334863794, + 1.0790735639220488, + 0.8635853484338327, + 0.6415671870217335, + 0.413019079685747, + 0.177941026425875, + -0.06366697275788225, + -0.3118049178655227, + -0.5664728088970508, + -0.8276706458524639, + -1.0953984287317626, + -1.3696561575349466, + -1.6504438322620132, + -1.9377614529129679, + -2.231609019487808, + -2.531986531986533, + -2.838893990409141, + -3.1523313947556364, + -3.472298745026018, + -3.798796041220285, + -4.131823283338433, + -4.471380471380471, + -4.817467605346393, + -5.170084685236201, + -5.529231711049891, + -5.89490868278747, + -6.267115600448934, + -6.645852464034283, + -7.031119273543518, + -7.422916028976634, + -7.821242730333639, + -8.226099377614531, + -8.637485970819306, + -9.055402509947964, + -9.47984899500051, + -9.910825425976942, + -10.34833180287726, + -10.792368125701458, + -11.242934394449545, + -11.70003060912152, + -12.163656769717377, + -12.633812876237117, + -13.11049892868075, + -13.59371492704826, + -14.083460871339655, + -14.579736761554948, + -15.082542597694111, + -15.591878379757173, + -16.107744107744107, + -16.630139781654933, + -17.15906540148965, + -17.694520967248238, + -18.236506478930718, + -18.785021936537092, + -19.340067340067336, + -19.90164268952148, + -20.4697479848995, + -21.044383226201404, + -21.625548413427204, + -22.213243546576876, + -22.80746862565045, + -23.408223650647894 + ], + [ + 3.8804203652688516, + 3.9326599326599334, + 3.9783695541271316, + 4.0175492296704425, + 4.050198959289869, + 4.0763187429854115, + 4.095908580757067, + 4.108968472604837, + 4.115498418528723, + 4.115498418528722, + 4.108968472604838, + 4.095908580757066, + 4.076318742985411, + 4.050198959289871, + 4.0175492296704425, + 3.9783695541271316, + 3.9326599326599343, + 3.8804203652688507, + 3.821650851953883, + 3.7563513927150303, + 3.684521987552291, + 3.606162636465667, + 3.5212733394551585, + 3.4298540965207636, + 3.3319049076624836, + 3.227425772880319, + 3.116416692174268, + 2.9988776655443328, + 2.8748086929905114, + 2.7442097745128056, + 2.607080910111214, + 2.463422099785737, + 2.3132333435363748, + 2.156514641363126, + 1.9932659932659935, + 1.823487399244975, + 1.6471788593000718, + 1.4643403734312825, + 1.2749719416386087, + 1.0790735639220488, + 0.8766452402816035, + 0.6676869707172748, + 0.45219875522905884, + 0.2301805938169575, + 0.0016324864809708073, + -0.23344556677889916, + -0.4750535659626564, + -0.7231915110702989, + -0.977859402101827, + -1.23905723905724, + -1.5067850219365364, + -1.7810427507397204, + -2.06183042546679, + -2.3491480461177443, + -2.6429956126925815, + -2.943373125191307, + -3.2502805836139177, + -3.5637179879604135, + -3.883685338230792, + -4.210182634425058, + -4.5432098765432105, + -4.882767064585248, + -5.228854198551167, + -5.581471278440974, + -5.940618304254668, + -6.306295275992246, + -6.678502193653711, + -7.057239057239057, + -7.442505866748291, + -7.834302622181411, + -8.232629323538415, + -8.637485970819302, + -9.04887256402408, + -9.466789103152742, + -9.891235588205287, + -10.322212019181716, + -10.759718396082032, + -11.203754718906236, + -11.654320987654323, + -12.111417202326294, + -12.575043362922155, + -13.045199469441895, + -13.521885521885519, + -14.005101520253039, + -14.494847464544433, + -14.991123354759722, + -15.49392919089889, + -16.003264972961944, + -16.519130700948885, + -17.041526374859707, + -17.570451994694416, + -18.10590756045302, + -18.647893072135496, + -19.196408529741866, + -19.751453933272117, + -20.313029282726248, + -20.881134578104277, + -21.455769819406182, + -22.036935006631985, + -22.624630139781658 + ], + [ + 3.364554637281909, + 3.429854096520763, + 3.4886236098357317, + 3.540863177226813, + 3.5865727986940104, + 3.625752474237323, + 3.658402203856749, + 3.6845219875522908, + 3.704111825323947, + 3.7171717171717176, + 3.7237016630956026, + 3.723701663095602, + 3.717171717171718, + 3.704111825323947, + 3.68452198755229, + 3.658402203856749, + 3.625752474237323, + 3.5865727986940104, + 3.540863177226814, + 3.4886236098357317, + 3.4298540965207627, + 3.3645546372819104, + 3.292725232119172, + 3.2143658810325473, + 3.1294765840220387, + 3.038057341087644, + 2.9401081522293646, + 2.835629017447199, + 2.7246199367411488, + 2.607080910111214, + 2.483011937557392, + 2.352413019079686, + 2.2152841546780944, + 2.0716253443526167, + 1.921436588103255, + 1.764717885930007, + 1.6014692378328745, + 1.431690643811856, + 1.2553821038669528, + 1.0725436179981633, + 0.8831751862054887, + 0.6872768084889306, + 0.4848484848484853, + 0.27589021528415464, + 0.06040199979593869, + -0.16161616161616071, + -0.39016426895214723, + -0.625242322212019, + -0.8668503213957764, + -1.114988266503419, + -1.3696561575349446, + -1.630853994490358, + -1.8985817773696565, + -2.1728395061728403, + -2.453627180899907, + -2.7409448015508615, + -3.034792368125702, + -3.335169880624427, + -3.6420773390470345, + -3.9555147433935307, + -4.275482093663912, + -4.601979389858179, + -4.935006631976328, + -5.274563820018365, + -5.6206509539842875, + -5.973268033874095, + -6.332415059687788, + -6.6980920314253645, + -7.070298949086828, + -7.449035812672176, + -7.834302622181411, + -8.226099377614528, + -8.624426078971533, + -9.029282726252424, + -9.4406693194572, + -9.858585858585856, + -10.283032343638403, + -10.714008774614836, + -11.151515151515152, + -11.595551474339352, + -12.046117743087443, + -12.50321395775941, + -12.966840118355266, + -13.436996224875015, + -13.913682277318639, + -14.396898275686159, + -14.886644219977555, + -15.382920110192835, + -15.885725946332009, + -16.395061728395063, + -16.910927456381998, + -17.433323130292827, + -17.962248750127536, + -18.49770431588614, + -19.039689827568615, + -19.58820528517498, + -20.143250688705237, + -20.704826038159368, + -21.2729313335374, + -21.847566574839302 + ], + [ + 2.842158963371085, + 2.9205183144577105, + 2.992347719620448, + 3.0576471788593005, + 3.1164166921742695, + 3.1686562595653514, + 3.21436588103255, + 3.253545556575861, + 3.2861952861952877, + 3.312315069890829, + 3.3319049076624845, + 3.3449647995102554, + 3.3514947454341417, + 3.35149474543414, + 3.3449647995102545, + 3.3319049076624836, + 3.3123150698908286, + 3.2861952861952863, + 3.2535455565758604, + 3.214365881032549, + 3.168656259565351, + 3.1164166921742686, + 3.057647178859301, + 2.9923477196204473, + 2.920518314457709, + 2.8421589633710855, + 2.757269666360576, + 2.6658504234261815, + 2.567901234567902, + 2.463422099785737, + 2.352413019079686, + 2.2348739924497507, + 2.11080501989593, + 1.9802061014182226, + 1.8430772370166313, + 1.699418426691154, + 1.549229670441792, + 1.3925109682685441, + 1.2292623201714115, + 1.0594837261503929, + 0.8831751862054888, + 0.7003367003367013, + 0.5109682685440265, + 0.31506989082746656, + 0.11264156718702123, + -0.09631670237730755, + -0.31180491786552345, + -0.5338230792776246, + -0.7623711866136114, + -0.9974492398734836, + -1.2390572390572385, + -1.4871951841648812, + -1.741863075196409, + -2.0030609121518226, + -2.2707886950311185, + -2.545046423834303, + -2.825834098561372, + -3.1131517192123264, + -3.406999285787164, + -3.707376798285889, + -4.0142842567085, + -4.327721661054996, + -4.647689011325374, + -4.97418630751964, + -5.307213549637792, + -5.64677073767983, + -5.992857871645753, + -6.345474951535557, + -6.704621977349251, + -7.07029894908683, + -7.442505866748293, + -7.82124273033364, + -8.206509539842873, + -8.598306295275993, + -8.996632996633, + -9.401489643913884, + -9.812876237118662, + -10.230792776247323, + -10.655239261299869, + -11.086215692276298, + -11.52372206917662, + -11.967758392000816, + -12.418324660748901, + -12.875420875420879, + -13.339047036016733, + -13.809203142536482, + -14.285889194980106, + -14.769105193347615, + -15.258851137639022, + -15.755127027854302, + -16.257932863993467, + -16.76726864605653, + -17.283134374043467, + -17.805530047954292, + -18.334455667789, + -18.869911233547594, + -19.41189674523008, + -19.960412202836444, + -20.515457606366702, + -21.077032955820837 + ], + [ + 2.313233343536374, + 2.4046525864707693, + 2.489541883481278, + 2.5679012345679006, + 2.6397306397306393, + 2.7050300989694938, + 2.7637996122844615, + 2.816039179675543, + 2.861748801142741, + 2.900928476686053, + 2.9335782063054796, + 2.959697990001021, + 2.9792878277726764, + 2.9923477196204473, + 2.998877665544332, + 2.9988776655443323, + 2.9923477196204473, + 2.979287827772676, + 2.9596979900010205, + 2.933578206305479, + 2.9009284766860524, + 2.861748801142741, + 2.8160391796755433, + 2.7637996122844606, + 2.705030098969493, + 2.6397306397306397, + 2.5679012345679015, + 2.4895418834812775, + 2.4046525864707684, + 2.3132333435363743, + 2.215284154678095, + 2.1108050198959294, + 1.999795939189879, + 1.8822569125599429, + 1.7581879400061222, + 1.6275890215284154, + 1.4904601571268241, + 1.3468013468013469, + 1.196612590551985, + 1.039893888378737, + 0.8766452402816037, + 0.7068666462605866, + 0.5305581063156826, + 0.3477196204468933, + 0.15835118865421866, + -0.03754718906233956, + -0.23997551270278483, + -0.4489337822671154, + -0.6644219977553314, + -0.8864401591674327, + -1.1149882665034172, + -1.3500663197632892, + -1.5916743189470464, + -1.8398122640546888, + -2.094480155086215, + -2.355677992041628, + -2.6234057749209265, + -2.8976635037241105, + -3.1784511784511773, + -3.4657687991021318, + -3.7596163656769717, + -4.059993878175698, + -4.366901336598304, + -4.6803387409448005, + -5.000306091215182, + -5.3268033874094485, + -5.6598306295276, + -5.999387817569635, + -6.345474951535557, + -6.698092031425365, + -7.057239057239058, + -7.422916028976633, + -7.795122946638097, + -8.173859810223448, + -8.559126619732682, + -8.950923375165797, + -9.349250076522804, + -9.754106723803694, + -10.165493317008469, + -10.583409856137127, + -11.00785634118968, + -11.438832772166105, + -11.876339149066418, + -12.320375471890625, + -12.770941740638708, + -13.228037955310686, + -13.69166411590654, + -14.16182022242628, + -14.638506274869915, + -15.121722273237424, + -15.61146821752882, + -16.10774410774411, + -16.610549943883274, + -17.119885725946336, + -17.635751453933274, + -18.158147127844096, + -18.687072747678812, + -19.2225283134374, + -19.76451382511989, + -20.313029282726255 + ], + [ + 1.7777777777777768, + 1.882256912559943, + 1.9802061014182226, + 2.071625344352616, + 2.156514641363125, + 2.2348739924497494, + 2.306703397612489, + 2.372002856851341, + 2.4307723701663098, + 2.483011937557392, + 2.5287215590245893, + 2.5679012345679, + 2.6005509641873275, + 2.6266707478828693, + 2.6462605856545243, + 2.6593204775022956, + 2.665850423426181, + 2.6658504234261806, + 2.6593204775022956, + 2.646260585654525, + 2.626670747882869, + 2.600550964187328, + 2.567901234567901, + 2.528721559024589, + 2.483011937557392, + 2.4307723701663098, + 2.372002856851341, + 2.3067033976124884, + 2.23487399244975, + 2.156514641363126, + 2.0716253443526167, + 1.9802061014182228, + 1.882256912559943, + 1.7777777777777772, + 1.6667686970717273, + 1.5492296704417914, + 1.4251606978879707, + 1.2945617794102642, + 1.1574329150086728, + 1.0137741046831956, + 0.8635853484338329, + 0.7068666462605864, + 0.5436179981634531, + 0.3738394041424345, + 0.19753086419753052, + 0.014692378328742872, + -0.1746760534639317, + -0.37057443118049155, + -0.5730027548209369, + -0.7819610243852675, + -0.9974492398734814, + -1.2194674012855826, + -1.4480155086215691, + -1.6830935618814409, + -1.9247015610651963, + -2.172839506172839, + -2.427507397204367, + -2.68870523415978, + -2.956433017039076, + -3.2306907458422605, + -3.511478420569329, + -3.798796041220284, + -4.092643607795122, + -4.393021120293846, + -4.699928578716457, + -5.013365983062952, + -5.333333333333334, + -5.6598306295275975, + -5.992857871645749, + -6.332415059687786, + -6.67850219365371, + -7.0311192735435135, + -7.390266299357208, + -7.755943271094786, + -8.12815018875625, + -8.506887052341595, + -8.892153861850831, + -9.28395061728395, + -9.682277318640955, + -10.087133965921842, + -10.498520559126622, + -10.916437098255278, + -11.340883583307821, + -11.771860014284258, + -12.20936639118457, + -12.653402714008777, + -13.10396898275686, + -13.561065197428828, + -14.024691358024693, + -14.494847464544435, + -14.971533516988057, + -15.454749515355577, + -15.944495459646973, + -16.44077134986226, + -16.943577186001427, + -17.452912968064478, + -17.968778696051423, + -18.491174369962245, + -19.02009998979696, + -19.555555555555554 + ], + [ + 1.235792266095297, + 1.3533312927252328, + 1.4643403734312836, + 1.5688195082134473, + 1.6667686970717277, + 1.7581879400061227, + 1.8430772370166313, + 1.921436588103255, + 1.993265993265994, + 2.0585654525048476, + 2.117334965819815, + 2.1695745332108975, + 2.215284154678095, + 2.2544638302214066, + 2.287113559840832, + 2.313233343536374, + 2.3328231813080302, + 2.3458830731558002, + 2.3524130190796866, + 2.352413019079686, + 2.3458830731558007, + 2.3328231813080302, + 2.3132333435363743, + 2.2871135598408325, + 2.254463830221406, + 2.215284154678095, + 2.1695745332108975, + 2.117334965819814, + 2.0585654525048467, + 1.993265993265994, + 1.9214365881032553, + 1.8430772370166317, + 1.7581879400061222, + 1.6667686970717275, + 1.5688195082134477, + 1.4643403734312825, + 1.3533312927252326, + 1.2357922660952965, + 1.1117232935414758, + 0.9811243750637693, + 0.843995510662177, + 0.7003367003367011, + 0.5501479440873385, + 0.39342924191409046, + 0.2301805938169572, + 0.06040199979594002, + -0.1159065401489639, + -0.2987450260177531, + -0.4881134578104278, + -0.6840118355269879, + -0.8864401591674312, + -1.095398428731762, + -1.3108866442199778, + -1.5329048056320789, + -1.7614529129680638, + -1.9965309662279354, + -2.238138965411693, + -2.4862769105193356, + -2.740944801550861, + -3.0021426385062746, + -3.2698704213855727, + -3.544128150188757, + -3.8249158249158235, + -4.112233445566778, + -4.406081012141618, + -4.706458524640343, + -5.013365983062954, + -5.326803387409448, + -5.646770737679828, + -5.973268033874095, + -6.306295275992246, + -6.645852464034281, + -6.991939598000204, + -7.3445566778900115, + -7.703703703703705, + -8.06938067544128, + -8.441587593102746, + -8.820324456688093, + -9.205591266197327, + -9.597388021630444, + -9.995714722987454, + -10.40057137026834, + -10.811957963473112, + -11.229874502601778, + -11.65432098765432, + -12.085297418630756, + -12.522803795531068, + -12.966840118355268, + -13.41740638710336, + -13.87450260177533, + -14.338128762371184, + -14.808284868890931, + -15.284970921334555, + -15.768186919702073, + -16.257932863993467, + -16.75420875420875, + -17.257014590347925, + -17.766350372410976, + -18.282216100397925, + -18.804611774308743 + ], + [ + 0.687276808488928, + 0.8178757269666361, + 0.941944699520457, + 1.059483726150391, + 1.170492806856442, + 1.2749719416386078, + 1.3729211304968878, + 1.464340373431281, + 1.5492296704417914, + 1.627589021528415, + 1.6994184266911536, + 1.7647178859300063, + 1.8234873992449745, + 1.8757269666360572, + 1.9214365881032538, + 1.960616263646566, + 1.9932659932659929, + 2.019385776961534, + 2.0389756147331903, + 2.052035506580961, + 2.058565452504846, + 2.0585654525048462, + 2.052035506580961, + 2.03897561473319, + 2.0193857769615344, + 1.9932659932659933, + 1.9606162636465665, + 1.9214365881032545, + 1.8757269666360572, + 1.823487399244975, + 1.764717885930007, + 1.699418426691154, + 1.6275890215284154, + 1.5492296704417914, + 1.4643403734312825, + 1.3729211304968878, + 1.2749719416386083, + 1.170492806856443, + 1.0594837261503929, + 0.941944699520457, + 0.8178757269666357, + 0.6872768084889302, + 0.5501479440873384, + 0.4064891337618611, + 0.2563003775124984, + 0.09958167533925186, + -0.06366697275788136, + -0.2334455667788999, + -0.40975410672380386, + -0.592592592592593, + -0.781961024385266, + -0.9778594021018259, + -1.1802877257422713, + -1.3892459953066016, + -1.6047342107948157, + -1.8267523722069172, + -2.0553004795429035, + -2.2903785328027757, + -2.5319865319865307, + -2.7801244770941733, + -3.034792368125701, + -3.2959902050811145, + -3.56371798796041, + -3.837975716763594, + -4.118763391490663, + -4.406081012141618, + -4.699928578716458, + -5.00030609121518, + -5.307213549637791, + -5.6206509539842875, + -5.940618304254668, + -6.267115600448932, + -6.6001428425670845, + -6.939700030609121, + -7.2857871645750425, + -7.638404244464848, + -7.997551270278541, + -8.36322824201612, + -8.735435159677582, + -9.11417202326293, + -9.499438832772167, + -9.891235588205284, + -10.289562289562285, + -10.69441893684318, + -11.105805530047952, + -11.523722069176618, + -11.94816855422916, + -12.379144985205588, + -12.816651362105908, + -13.260687684930108, + -13.711253953678192, + -14.168350168350168, + -14.631976328946022, + -15.102132435465771, + -15.578818487909395, + -16.062034486276907, + -16.55178043056831, + -17.04805632078359, + -17.55086215692277, + -18.060197938985816 + ], + [ + 0.13223140495867725, + 0.27589021528415625, + 0.41301907968574714, + 0.5436179981634526, + 0.6676869707172739, + 0.7852259973472102, + 0.8962350780532606, + 1.0007142128354247, + 1.0986634016937056, + 1.1900826446280997, + 1.2749719416386087, + 1.353331292725232, + 1.425160697887971, + 1.4904601571268241, + 1.5492296704417914, + 1.6014692378328743, + 1.6471788593000716, + 1.686358534843383, + 1.7190082644628104, + 1.7451280481583515, + 1.7647178859300072, + 1.7777777777777781, + 1.7843077237016636, + 1.7843077237016627, + 1.7777777777777777, + 1.7647178859300072, + 1.7451280481583515, + 1.7190082644628097, + 1.6863585348433834, + 1.647178859300072, + 1.6014692378328745, + 1.5492296704417918, + 1.4904601571268241, + 1.4251606978879705, + 1.3533312927252323, + 1.2749719416386085, + 1.1900826446280994, + 1.098663401693705, + 1.0007142128354252, + 0.89623507805326, + 0.7852259973472092, + 0.6676869707172743, + 0.543617998163453, + 0.41301907968574636, + 0.2758902152841544, + 0.13223140495867836, + -0.017957351290684292, + -0.1746760534639322, + -0.3379247015610655, + -0.5077032955820842, + -0.6840118355269865, + -0.8668503213957759, + -1.0562187531884506, + -1.2521171309050103, + -1.454545454545454, + -1.6635037241097845, + -1.8789919395980004, + -2.1010101010101017, + -2.329558208346086, + -2.564636261605958, + -2.8062442607897156, + -3.054382205897358, + -3.3090500969288836, + -3.5702479338842967, + -3.8379757167635957, + -4.11223344556678, + -4.393021120293849, + -4.680338740944801, + -4.974186307519641, + -5.274563820018366, + -5.581471278440976, + -5.89490868278747, + -6.214876033057851, + -6.541373329252117, + -6.87440057137027, + -7.213957759412303, + -7.560044893378227, + -7.912661973268034, + -8.271808999081728, + -8.637485970819302, + -9.009692888480771, + -9.388429752066116, + -9.773696561575347, + -10.16549331700847, + -10.563820018365472, + -10.968676665646367, + -11.380063258851138, + -11.797979797979796, + -12.222426283032346, + -12.653402714008774, + -13.090909090909088, + -13.534945413733293, + -13.985511682481377, + -14.442607897153355, + -14.906234057749211, + -15.376390164268948, + -15.853076216712584, + -16.336292215080093, + -16.826038159371496, + -17.32231404958678 + ], + [ + -0.42934394449546076, + -0.27262524232221264, + -0.12243648607284996, + 0.02122232425262638, + 0.15835118865421727, + 0.28895010713192537, + 0.41301907968574625, + 0.5305581063156808, + 0.6415671870217321, + 0.7460463218038975, + 0.843995510662177, + 0.9354147535965716, + 1.0203040506070806, + 1.0986634016937047, + 1.1704928068564426, + 1.235792266095296, + 1.2945617794102642, + 1.3468013468013462, + 1.3925109682685441, + 1.431690643811856, + 1.464340373431282, + 1.4904601571268237, + 1.51004999489848, + 1.5231098867462496, + 1.5296398326701353, + 1.5296398326701355, + 1.52310988674625, + 1.5100499948984794, + 1.4904601571268237, + 1.4643403734312825, + 1.4316906438118557, + 1.3925109682685441, + 1.3468013468013469, + 1.294561779410264, + 1.2357922660952965, + 1.170492806856443, + 1.0986634016937047, + 1.0203040506070808, + 0.9354147535965719, + 0.8439955106621773, + 0.7460463218038973, + 0.641567187021733, + 0.5305581063156823, + 0.41301907968574636, + 0.28895010713192504, + 0.1583511886542196, + 0.021222324252627656, + -0.1224364860728496, + -0.2726252423222122, + -0.4293439444954601, + -0.592592592592592, + -0.7623711866136105, + -0.9386797265585146, + -1.1215182124273038, + -1.3108866442199765, + -1.5067850219365366, + -1.7092133455769818, + -1.9181716151413126, + -2.1336598306295267, + -2.3556779920416275, + -2.5842260993776147, + -2.8193041526374865, + -3.060912151821241, + -3.3090500969288836, + -3.5637179879604117, + -3.824915824915825, + -4.092643607795123, + -4.366901336598305, + -4.647689011325374, + -4.935006631976329, + -5.2288541985511685, + -5.529231711049891, + -5.836139169472502, + -6.149576573818997, + -6.469543924089379, + -6.796041220283643, + -7.129068462401795, + -7.4686256504438315, + -7.814712784409755, + -8.167329864299559, + -8.526476890113255, + -8.892153861850831, + -9.264360779512291, + -9.643097643097644, + -10.028364452606874, + -10.420161208039998, + -10.818487909397, + -11.223344556677887, + -11.634731149882667, + -12.052647689011323, + -12.477094174063867, + -12.908070605040301, + -13.345576981940614, + -13.78961330476482, + -14.240179573512906, + -14.697275788184875, + -15.160901948780737, + -15.631058055300475, + -16.10774410774411, + -16.590960106111623 + ], + [ + -0.9974492398734824, + -0.8276706458524625, + -0.6644219977553298, + -0.5077032955820839, + -0.35751453933272126, + -0.2138557290072436, + -0.07672686460565137, + 0.05387205387205363, + 0.1779410264258754, + 0.2954800530558117, + 0.4064891337618617, + 0.5109682685440267, + 0.6089174574023062, + 0.7003367003367007, + 0.7852259973472093, + 0.8635853484338334, + 0.9354147535965724, + 1.0007142128354247, + 1.0594837261503935, + 1.1117232935414758, + 1.1574329150086728, + 1.1966125905519844, + 1.2292623201714115, + 1.2553821038669524, + 1.2749719416386083, + 1.2880318334863792, + 1.2945617794102646, + 1.2945617794102642, + 1.2880318334863792, + 1.2749719416386087, + 1.2553821038669526, + 1.2292623201714112, + 1.1966125905519847, + 1.1574329150086726, + 1.1117232935414756, + 1.059483726150393, + 1.0007142128354252, + 0.9354147535965719, + 0.8635853484338336, + 0.7852259973472095, + 0.7003367003367001, + 0.6089174574023064, + 0.5109682685440264, + 0.4064891337618611, + 0.2954800530558104, + 0.17794102642587545, + 0.053872053872054154, + -0.07672686460565245, + -0.21385572900724442, + -0.35751453933272176, + -0.507703295582083, + -0.6644219977553311, + -0.8276706458524643, + -0.9974492398734829, + -1.1737577798183854, + -1.3565962656871746, + -1.5459646974798493, + -1.7418630751964095, + -1.9442913988368526, + -2.153249668401183, + -2.3687378838893993, + -2.590756045301501, + -2.8193041526374847, + -3.054382205897357, + -3.2959902050811145, + -3.544128150188757, + -3.798796041220285, + -4.059993878175696, + -4.327721661054994, + -4.601979389858178, + -4.882767064585247, + -5.1700846852361995, + -5.463932251811039, + -5.764309764309765, + -6.0712172227323755, + -6.384654627078869, + -6.70462197734925, + -7.031119273543517, + -7.364146515661668, + -7.703703703703702, + -8.049790837669628, + -8.402407917559433, + -8.761554943373124, + -9.127231915110706, + -9.499438832772165, + -9.878175696357518, + -10.263442505866749, + -10.655239261299865, + -11.053565962656874, + -11.458422609937763, + -11.869809203142534, + -12.2877257422712, + -12.712172227323741, + -13.143148658300177, + -13.58065503520049, + -14.02469135802469, + -14.47525762677278, + -14.932353841444751, + -15.395980002040613, + -15.866136108560353 + ], + [ + -1.572084481175391, + -1.389245995306601, + -1.2129374553616974, + -1.0431588613406801, + -0.8799102132435475, + -0.7231915110702993, + -0.5730027548209367, + -0.42934394449546076, + -0.2922150800938681, + -0.16161616161616177, + -0.03754718906234089, + 0.07999183756759498, + 0.1910009182736454, + 0.2954800530558104, + 0.3934292419140899, + 0.4848484848484844, + 0.5697377818589939, + 0.6480971329456173, + 0.7199265381083564, + 0.7852259973472093, + 0.8439955106621773, + 0.8962350780532597, + 0.9419446995204572, + 0.9811243750637687, + 1.0137741046831954, + 1.0398938883787368, + 1.0594837261503927, + 1.0725436179981633, + 1.0790735639220486, + 1.0790735639220486, + 1.0725436179981633, + 1.0594837261503927, + 1.039893888378737, + 1.0137741046831954, + 0.981124375063769, + 0.941944699520457, + 0.8962350780532599, + 0.8439955106621773, + 0.7852259973472095, + 0.7199265381083563, + 0.6480971329456175, + 0.5697377818589944, + 0.4848484848484851, + 0.39342924191409046, + 0.2954800530558105, + 0.1910009182736461, + 0.07999183756759548, + -0.03754718906234042, + -0.16161616161616174, + -0.2922150800938684, + -0.4293439444954591, + -0.5730027548209363, + -0.723191511070299, + -0.879910213243547, + -1.0431588613406788, + -1.2129374553616974, + -1.3892459953066014, + -1.5720844811753905, + -1.7614529129680634, + -1.9573512906846235, + -2.1597796143250685, + -2.3687378838893993, + -2.584226099377613, + -2.8062442607897147, + -3.034792368125701, + -3.2698704213855727, + -3.51147842056933, + -3.7596163656769708, + -4.014284256708498, + -4.275482093663912, + -4.5432098765432105, + -4.817467605346391, + -5.098255280073461, + -5.385572900724416, + -5.679420467299256, + -5.9797979797979774, + -6.286705438220588, + -6.6001428425670845, + -6.920110192837465, + -7.24660748903173, + -7.579634731149886, + -7.919191919191918, + -8.265279053157839, + -8.61789613304765, + -8.977043158861338, + -9.34272013059892, + -9.714927048260382, + -10.093663911845727, + -10.478930721354965, + -10.870727476788081, + -11.269054178145083, + -11.673910825425978, + -12.085297418630748, + -12.503213957759414, + -12.927660442811959, + -13.358636873788384, + -13.796143250688708, + -14.240179573512904, + -14.690745842260995, + -15.147842056932967 + ], + [ + -2.1532496684011853, + -1.9573512906846253, + -1.7679828588919504, + -1.5851443730231631, + -1.408835833078259, + -1.2390572390572396, + -1.0758085909601065, + -0.9190898887868602, + -0.768901132537497, + -0.6252423222120198, + -0.48811345781042803, + -0.3575145393327226, + -0.23344556677890127, + -0.1159065401489654, + -0.0048974594429154195, + 0.09958167533925, + 0.19753086419752997, + 0.28895010713192426, + 0.3738394041424342, + 0.45219875522905784, + 0.524028160391796, + 0.589327619630649, + 0.6480971329456173, + 0.7003367003366994, + 0.7460463218038967, + 0.7852259973472087, + 0.8178757269666354, + 0.8439955106621765, + 0.8635853484338327, + 0.8766452402816033, + 0.8831751862054886, + 0.8831751862054888, + 0.8766452402816037, + 0.8635853484338327, + 0.8439955106621769, + 0.8178757269666357, + 0.7852259973472092, + 0.7460463218038972, + 0.7003367003367001, + 0.6480971329456178, + 0.5893276196306496, + 0.5240281603917969, + 0.4521987552290584, + 0.37383940414243444, + 0.28895010713192515, + 0.1975308641975313, + 0.0995816753392514, + -0.0048974594429138235, + -0.11590654014896445, + -0.23344556677890038, + -0.3575145393327206, + -0.4881134578104271, + -0.625242322212019, + -0.7689011325374963, + -0.9190898887868575, + -1.0758085909601054, + -1.2390572390572387, + -1.4088358330782573, + -1.5851443730231596, + -1.767982858891949, + -1.9573512906846235, + -2.1532496684011835, + -2.3556779920416266, + -2.5646362616059575, + -2.7801244770941733, + -3.0021426385062746, + -3.230690745842261, + -3.465768799102131, + -3.707376798285888, + -3.9555147433935307, + -4.210182634425059, + -4.47138047138047, + -4.739108254259768, + -5.013365983062952, + -5.294153657790021, + -5.581471278440973, + -5.875318845015813, + -6.175696357514537, + -6.482603815937148, + -6.796041220283642, + -7.116008570554026, + -7.44250586674829, + -7.775533108866439, + -8.115090296908479, + -8.461177430874397, + -8.81379451076421, + -9.172941536577898, + -9.538618508315475, + -9.910825425976942, + -10.289562289562287, + -10.67482909907152, + -11.066625854504641, + -11.464952555861643, + -11.869809203142536, + -12.281195796347308, + -12.699112335475967, + -13.123558820528517, + -13.554535251504946, + -13.992041628405268, + -14.436077951229464 + ], + [ + -2.7409448015508597, + -2.5319865319865285, + -2.329558208346084, + -2.133659830629526, + -1.9442913988368513, + -1.7614529129680618, + -1.5851443730231578, + -1.415365779002141, + -1.2521171309050074, + -1.0953984287317593, + -0.9452096724823975, + -0.8015508621569207, + -0.664421997755329, + -0.5338230792776226, + -0.40975410672380175, + -0.2922150800938663, + -0.1812059993878159, + -0.07672686460565092, + 0.021222324252629488, + 0.11264156718702356, + 0.1975308641975324, + 0.27589021528415625, + 0.34771962044689464, + 0.41301907968574736, + 0.4717885930007155, + 0.5240281603917978, + 0.5697377818589949, + 0.6089174574023066, + 0.6415671870217334, + 0.6676869707172746, + 0.6872768084889305, + 0.7003367003367011, + 0.7068666462605866, + 0.7068666462605863, + 0.7003367003367009, + 0.6872768084889302, + 0.6676869707172742, + 0.641567187021733, + 0.6089174574023063, + 0.5697377818589944, + 0.5240281603917969, + 0.47178859300071474, + 0.4130190796857467, + 0.3477196204468933, + 0.2758902152841546, + 0.19753086419753127, + 0.11264156718702191, + 0.02122232425262726, + -0.0767268646056528, + -0.18120599938781815, + -0.29221508009386793, + -0.40975410672380386, + -0.5338230792776253, + -0.6644219977553318, + -0.8015508621569227, + -0.9452096724824, + -1.0953984287317629, + -1.2521171309050108, + -1.4153657790021428, + -1.5851443730231614, + -1.7614529129680652, + -1.9442913988368544, + -2.1336598306295276, + -2.3295582083460875, + -2.531986531986533, + -2.7409448015508633, + -2.9564330170390796, + -3.178451178451179, + -3.406999285787166, + -3.6420773390470376, + -3.8836853382307943, + -4.131823283338435, + -4.386491174369963, + -4.647689011325377, + -4.915416794204675, + -5.189674523007856, + -5.470462197734927, + -5.757779818385881, + -6.05162738496072, + -6.352004897459443, + -6.658912355882057, + -6.97234976022855, + -7.292317110498928, + -7.618814406693197, + -7.951841648811346, + -8.291398836853386, + -8.637485970819306, + -8.990103050709111, + -9.349250076522807, + -9.714927048260384, + -10.087133965921844, + -10.465870829507196, + -10.851137639016427, + -11.24293439444955, + -11.641261095806552, + -12.04611774308744, + -12.457504336292217, + -12.875420875420877, + -13.299867360473428, + -13.730843791449855 + ], + [ + -3.3351698806244254, + -3.1131517192123237, + -2.897663503724108, + -2.6887052341597797, + -2.486276910519334, + -2.290378532802774, + -2.1010101010100994, + -1.9181716151413117, + -1.7418630751964073, + -1.5720844811753891, + -1.408835833078256, + -1.2521171309050088, + -1.1019283746556465, + -0.9582695643301693, + -0.8211406999285782, + -0.6905417814508714, + -0.5664728088970508, + -0.4489337822671151, + -0.33792470156106424, + -0.23344556677889972, + -0.13549637792061953, + -0.044077134986225674, + 0.04081216202428406, + 0.11917151311090746, + 0.19100091827364607, + 0.25630037751249923, + 0.31506989082746706, + 0.3673094582185493, + 0.4130190796857467, + 0.4521987552290586, + 0.4848484848484853, + 0.5109682685440265, + 0.5305581063156826, + 0.543617998163453, + 0.5501479440873384, + 0.5501479440873385, + 0.543617998163453, + 0.5305581063156823, + 0.5109682685440264, + 0.48484848484848503, + 0.4521987552290584, + 0.4130190796857467, + 0.3673094582185494, + 0.31506989082746667, + 0.2563003775124987, + 0.1910009182736459, + 0.11917151311090722, + 0.04081216202428327, + -0.044077134986226084, + -0.13549637792062075, + -0.2334455667788999, + -0.3379247015610652, + -0.44893378226711583, + -0.5664728088970519, + -0.6905417814508721, + -0.8211406999285789, + -0.9582695643301706, + -1.101928374655648, + -1.2521171309050092, + -1.4088358330782573, + -1.5720844811753907, + -1.741863075196409, + -1.9181716151413113, + -2.1010101010101008, + -2.2903785328027757, + -2.486276910519335, + -2.688705234159781, + -2.8976635037241096, + -3.1131517192123255, + -3.335169880624427, + -3.5637179879604135, + -3.7987960412202835, + -4.040404040404041, + -4.288541985511683, + -4.543209876543211, + -4.804407713498622, + -5.072135496377921, + -5.346393225181105, + -5.627180899908174, + -5.9144985205591265, + -6.208346087133969, + -6.508723599632691, + -6.815631058055299, + -7.129068462401798, + -7.449035812672177, + -7.775533108866446, + -8.108560350984595, + -8.44811753902663, + -8.794204672992555, + -9.14682175288236, + -9.50596877869605, + -9.87164575043363, + -10.24385266809509, + -10.622589531680443, + -11.007856341189676, + -11.399653096622792, + -11.797979797979801, + -12.202836445260688, + -12.614223038465468, + -13.032139577594126 + ], + [ + -3.9359249056218757, + -3.7008468523620026, + -3.472298745026017, + -3.2502805836139173, + -3.0347923681257014, + -2.8258340985613706, + -2.6234057749209256, + -2.4275073972043675, + -2.238138965411693, + -2.0553004795429035, + -1.878991939598, + -1.7092133455769818, + -1.5459646974798489, + -1.3892459953066014, + -1.2390572390572392, + -1.0953984287317622, + -0.9582695643301706, + -0.8276706458524643, + -0.7036016732986425, + -0.5860626466687073, + -0.4750535659626567, + -0.37057443118049216, + -0.2726252423222115, + -0.18120599938781812, + -0.09631670237730838, + -0.017957351290684764, + 0.05387205387205385, + 0.11917151311090668, + 0.17794102642587495, + 0.23018059381695744, + 0.2758902152841546, + 0.3150698908274665, + 0.34771962044689336, + 0.37383940414243433, + 0.3934292419140904, + 0.406489133761861, + 0.41301907968574636, + 0.41301907968574636, + 0.4064891337618611, + 0.39342924191409046, + 0.3738394041424344, + 0.3477196204468933, + 0.31506989082746667, + 0.2758902152841547, + 0.23018059381695735, + 0.17794102642587517, + 0.11917151311090718, + 0.05387205387205392, + -0.01795735129068475, + -0.09631670237730873, + -0.18120599938781728, + -0.2726252423222119, + -0.3705744311804919, + -0.47505356596265713, + -0.5860626466687069, + -0.7036016732986428, + -0.8276706458524641, + -0.9582695643301706, + -1.0953984287317615, + -1.2390572390572387, + -1.3892459953066014, + -1.545964697479849, + -1.709213345576981, + -1.8789919395979997, + -2.0553004795429035, + -2.2381389654116925, + -2.4275073972043675, + -2.6234057749209256, + -2.825834098561371, + -3.034792368125702, + -3.2502805836139177, + -3.4722987450260168, + -3.7008468523620035, + -3.9359249056218752, + -4.177532904805632, + -4.425670849913272, + -4.680338740944801, + -4.941536577900214, + -5.209264360779512, + -5.483522089582694, + -5.7643097643097665, + -6.051627384960718, + -6.3454749515355555, + -6.6458524640342835, + -6.952759922456891, + -7.26619732680339, + -7.586164677073769, + -7.9126619732680314, + -8.245689215386186, + -8.585246403428222, + -8.93133353739414, + -9.283950617283951, + -9.643097643097642, + -10.008774614835223, + -10.380981532496683, + -10.759718396082029, + -11.144985205591269, + -11.536781961024385, + -11.935108662381392, + -12.33996530966228 + ], + [ + -4.543209876543212, + -4.295071931435567, + -4.053463932251811, + -3.8183858789919416, + -3.5898377716559553, + -3.3678196102438527, + -3.1523313947556373, + -2.9433731251913087, + -2.740944801550863, + -2.545046423834303, + -2.355677992041629, + -2.1728395061728403, + -1.996530966227937, + -1.8267523722069186, + -1.6635037241097854, + -1.5067850219365377, + -1.3565962656871755, + -1.2129374553616987, + -1.0758085909601063, + -0.9452096724824008, + -0.8211406999285791, + -0.7036016732986439, + -0.5925925925925928, + -0.4881134578104285, + -0.39016426895214806, + -0.2987450260177542, + -0.2138557290072447, + -0.1354963779206212, + -0.06366697275788247, + 0.0016324864809706963, + 0.06040199979593863, + 0.11264156718702123, + 0.1583511886542186, + 0.19753086419753046, + 0.2301805938169571, + 0.25630037751249846, + 0.27589021528415436, + 0.2889501071319251, + 0.2954800530558104, + 0.2954800530558105, + 0.28895010713192515, + 0.2758902152841546, + 0.2563003775124987, + 0.23018059381695738, + 0.19753086419753071, + 0.1583511886542191, + 0.11264156718702183, + 0.06040199979593924, + 0.0016324864809712653, + -0.06366697275788202, + -0.13549637792062003, + -0.21385572900724392, + -0.2987450260177532, + -0.39016426895214784, + -0.4881134578104269, + -0.5925925925925922, + -0.7036016732986428, + -0.8211406999285787, + -0.9452096724823988, + -1.0758085909601056, + -1.2129374553616974, + -1.3565962656871746, + -1.506785021936536, + -1.6635037241097839, + -1.826752372206917, + -1.9965309662279354, + -2.17283950617284, + -2.3556779920416275, + -2.5450464238343016, + -2.740944801550862, + -2.9433731251913073, + -3.1523313947556355, + -3.367819610243852, + -3.589837771655953, + -3.818385878991939, + -4.053463932251809, + -4.295071931435567, + -4.543209876543209, + -4.797877767574736, + -5.059075604530148, + -5.3268033874094485, + -5.60106111621263, + -5.8818487909396975, + -6.169166411590654, + -6.463013978165491, + -6.76339149066422, + -7.070298949086827, + -7.383736353433321, + -7.703703703703704, + -8.030200999897968, + -8.363228242016117, + -8.702785430058157, + -9.048872564024077, + -9.401489643913887, + -9.760636669727578, + -10.126313641465153, + -10.49852055912662, + -10.877257422711967, + -11.262524232221203, + -11.654320987654321 + ], + [ + -5.157024793388427, + -4.895826956433012, + -4.641159065401485, + -4.393021120293845, + -4.151413121110088, + -3.9163350678502162, + -3.68778696051423, + -3.465768799102131, + -3.2502805836139146, + -3.0413223140495838, + -2.8388939904091393, + -2.6429956126925798, + -2.4536271808999066, + -2.2707886950311176, + -2.094480155086214, + -1.9247015610651956, + -1.7614529129680632, + -1.6047342107948157, + -1.4545454545454526, + -1.310886644219976, + -1.173757779818384, + -1.0431588613406784, + -0.9190898887868567, + -0.8015508621569215, + -0.6905417814508709, + -0.5860626466687061, + -0.48811345781042637, + -0.39669421487603207, + -0.3118049178655228, + -0.23344556677889916, + -0.16161616161616066, + -0.0963167023773076, + -0.03754718906233956, + 0.014692378328742817, + 0.060401999795939965, + 0.099581675339252, + 0.13223140495867836, + 0.15835118865421963, + 0.17794102642587548, + 0.1910009182736461, + 0.19753086419753133, + 0.19753086419753127, + 0.1910009182736459, + 0.17794102642587517, + 0.15835118865421913, + 0.13223140495867797, + 0.09958167533925125, + 0.060401999795939236, + 0.014692378328741847, + -0.03754718906234087, + -0.0963167023773084, + -0.16161616161616177, + -0.23344556677890047, + -0.3118049178655245, + -0.3966942148760332, + -0.4881134578104278, + -0.5860626466687078, + -0.6905417814508732, + -0.801550862156923, + -0.919089888786859, + -1.0431588613406801, + -1.173757779818387, + -1.3108866442199778, + -1.454545454545455, + -1.6047342107948177, + -1.7614529129680656, + -1.9247015610651992, + -2.094480155086216, + -2.2707886950311202, + -2.4536271808999097, + -2.642995612692584, + -2.8388939904091424, + -3.0413223140495877, + -3.2502805836139186, + -3.4657687991021344, + -3.6877869605142335, + -3.9163350678502207, + -4.151413121110092, + -4.39302112029385, + -4.6411590654014905, + -4.895826956433021, + -5.157024793388431, + -5.4247525762677276, + -5.699010305070914, + -5.979797979797981, + -6.267115600448938, + -6.560963167023776, + -6.861340679522499, + -7.168248137945112, + -7.481685542291605, + -7.801652892561983, + -8.128150188756253, + -8.461177430874402, + -8.800734618916442, + -9.146821752882362, + -9.499438832772167, + -9.858585858585862, + -10.224262830323438, + -10.596469747984905, + -10.975206611570252 + ], + [ + -5.777369656157533, + -5.503111927354349, + -5.23538414447505, + -4.97418630751964, + -4.719518416488112, + -4.471380471380469, + -4.2297724721967125, + -3.9946944189368425, + -3.7661463116008553, + -3.544128150188754, + -3.328639934700539, + -3.119681665136209, + -2.9172533414957647, + -2.7213549637792047, + -2.531986531986531, + -2.349148046117742, + -2.1728395061728385, + -2.003060912151821, + -1.839812264054687, + -1.6830935618814398, + -1.5329048056320773, + -1.3892459953066005, + -1.2521171309050088, + -1.1215182124273029, + -0.9974492398734816, + -0.879910213243546, + -0.7689011325374954, + -0.6644219977553307, + -0.5664728088970507, + -0.47505356596265647, + -0.3901642689521473, + -0.3118049178655235, + -0.23997551270278483, + -0.17467605346393178, + -0.11590654014896401, + -0.06366697275788125, + -0.017957351290684265, + 0.02122232425262771, + 0.05387205387205418, + 0.07999183756759551, + 0.09958167533925141, + 0.11264156718702195, + 0.11917151311090726, + 0.11917151311090722, + 0.11264156718702184, + 0.09958167533925126, + 0.07999183756759526, + 0.05387205387205393, + 0.021222324252627225, + -0.017957351290684813, + -0.06366697275788176, + -0.11590654014896443, + -0.17467605346393245, + -0.2399755127027858, + -0.3118049178655239, + -0.39016426895214784, + -0.4750535659626572, + -0.5664728088970519, + -0.664421997755331, + -0.7689011325374964, + -0.8799102132435469, + -0.9974492398734829, + -1.121518212427303, + -1.2521171309050096, + -1.3892459953066019, + -1.532904805632079, + -1.6830935618814418, + -1.8398122640546883, + -2.0030609121518217, + -2.1728395061728403, + -2.3491480461177443, + -2.531986531986532, + -2.7213549637792065, + -2.9172533414957664, + -3.1196816651362123, + -3.328639934700541, + -3.544128150188757, + -3.766146311600858, + -3.9946944189368447, + -4.229772472196714, + -4.471380471380474, + -4.719518416488114, + -4.9741863075196395, + -5.235384144475056, + -5.503111927354352, + -5.777369656157539, + -6.0581573308846055, + -6.345474951535557, + -6.6393225181104, + -6.939700030609123, + -7.246607489031731, + -7.560044893378229, + -7.880012243648608, + -8.206509539842877, + -8.539536781961026, + -8.87909397000306, + -9.225181103968985, + -9.577798183858791, + -9.936945209672487, + -10.302622181410062 + ], + [ + -6.404244464850525, + -6.11692684419957, + -5.836139169472501, + -5.561881440669319, + -5.294153657790021, + -5.032955820834608, + -4.77828792980308, + -4.53014998469544, + -4.288541985511682, + -4.053463932251811, + -3.8249158249158235, + -3.602897663503723, + -3.387409448015508, + -3.1784511784511777, + -2.9760228548107333, + -2.7801244770941738, + -2.5907560453015, + -2.407917559432711, + -2.2316090194878067, + -2.0618304254667885, + -1.8985817773696556, + -1.7418630751964086, + -1.5916743189470457, + -1.4480155086215694, + -1.3108866442199774, + -1.1802877257422713, + -1.0562187531884502, + -0.9386797265585147, + -0.8276706458524641, + -0.7231915110702991, + -0.6252423222120191, + -0.5338230792776248, + -0.44893378226711544, + -0.3705744311804916, + -0.2987450260177532, + -0.23344556677889988, + -0.17467605346393222, + -0.12243648607284952, + -0.07672686460565248, + -0.03754718906234042, + -0.004897459442913865, + 0.02122232425262724, + 0.04081216202428328, + 0.053872053872053925, + 0.060401999795939236, + 0.06040199979593923, + 0.05387205387205392, + 0.04081216202428327, + 0.021222324252627253, + -0.004897459442914093, + -0.037547189062340475, + -0.07672686460565245, + -0.12243648607284978, + -0.17467605346393245, + -0.23344556677889994, + -0.2987450260177532, + -0.3705744311804919, + -0.4489337822671159, + -0.5338230792776244, + -0.6252423222120191, + -0.7231915110702989, + -0.8276706458524643, + -0.938679726558514, + -1.05621875318845, + -1.1802877257422713, + -1.3108866442199778, + -1.4480155086215698, + -1.591674318947046, + -1.7418630751964086, + -1.8985817773696565, + -2.0618304254667894, + -2.2316090194878067, + -2.4079175594327107, + -2.5907560453014997, + -2.7801244770941747, + -2.976022854810733, + -3.178451178451178, + -3.387409448015509, + -3.6028976635037244, + -3.824915824915824, + -4.0534639322518125, + -4.288541985511682, + -4.530149984695438, + -4.778287929803083, + -5.032955820834609, + -5.294153657790024, + -5.561881440669321, + -5.836139169472502, + -6.116926844199574, + -6.4042444648505255, + -6.698092031425363, + -6.99846954392409, + -7.305377002346698, + -7.618814406693198, + -7.938781756963576, + -8.265279053157839, + -8.598306295275995, + -8.937863483318027, + -9.283950617283955, + -9.63656769717376 + ], + [ + -7.0376492194674025, + -6.737271706968675, + -6.443424140393837, + -6.156106519742885, + -5.875318845015816, + -5.601061116212631, + -5.333333333333333, + -5.072135496377922, + -4.817467605346393, + -4.569329660238751, + -4.327721661054994, + -4.092643607795123, + -3.864095500459137, + -3.6420773390470362, + -3.426589123558821, + -3.217630853994491, + -3.0152025303540464, + -2.819304152637487, + -2.629935720844812, + -2.447097234976024, + -2.2707886950311194, + -2.1010101010101017, + -1.937761452912968, + -1.7810427507397213, + -1.6308539944903584, + -1.4871951841648818, + -1.3500663197632898, + -1.219467401285584, + -1.0953984287317626, + -0.9778594021018269, + -0.8668503213957763, + -0.7623711866136115, + -0.6644219977553314, + -0.5730027548209369, + -0.4881134578104278, + -0.40975410672380386, + -0.3379247015610655, + -0.2726252423222122, + -0.21385572900724448, + -0.16161616161616177, + -0.11590654014896447, + -0.07672686460565281, + -0.04407713498622608, + -0.01795735129068475, + 0.0016324864809712653, + 0.014692378328741845, + 0.021222324252627222, + 0.021222324252627257, + 0.014692378328741939, + 0.0016324864809712785, + -0.017957351290684525, + -0.04407713498622581, + -0.07672686460565245, + -0.11590654014896444, + -0.16161616161616132, + -0.21385572900724398, + -0.2726252423222119, + -0.3379247015610652, + -0.4097541067238032, + -0.48811345781042714, + -0.5730027548209363, + -0.6644219977553311, + -0.76237118661361, + -0.8668503213957753, + -0.977859402101826, + -1.0953984287317617, + -1.2194674012855833, + -1.3500663197632885, + -1.4871951841648805, + -1.630853994490358, + -1.7810427507397204, + -1.9377614529129672, + -2.1010101010101003, + -2.270788695031119, + -2.4470972349760225, + -2.62993572084481, + -2.819304152637485, + -3.0152025303540446, + -3.21763085399449, + -3.426589123558819, + -3.6420773390470367, + -3.864095500459136, + -4.092643607795121, + -4.327721661054995, + -4.56932966023875, + -4.817467605346395, + -5.07213549637792, + -5.333333333333331, + -5.601061116212633, + -5.875318845015814, + -6.156106519742881, + -6.443424140393837, + -6.7372717069686745, + -7.0376492194674025, + -7.344556677890011, + -7.657994082236503, + -7.977961432506888, + -8.304458728701151, + -8.637485970819307, + -8.97704315886134 + ], + [ + -7.677583920008165, + -7.364146515661668, + -7.057239057239058, + -6.756861544740335, + -6.463013978165495, + -6.17569635751454, + -5.894908682787472, + -5.62065095398429, + -5.352923171104991, + -5.091725334149578, + -4.83705744311805, + -4.588919498010409, + -4.3473114988266515, + -4.112233445566781, + -3.883685338230794, + -3.6616671768186935, + -3.446178961330478, + -3.237220691766148, + -3.0347923681257023, + -2.8388939904091433, + -2.6495255586164688, + -2.4666870727476806, + -2.290378532802776, + -2.1205999387817585, + -1.957351290684625, + -1.8006325885113779, + -1.6504438322620152, + -1.5067850219365386, + -1.3696561575349464, + -1.23905723905724, + -1.114988266503419, + -0.9974492398734834, + -0.8864401591674327, + -0.7819610243852675, + -0.6840118355269877, + -0.5925925925925931, + -0.5077032955820842, + -0.42934394449546015, + -0.35751453933272176, + -0.2922150800938684, + -0.2334455667789004, + -0.18120599938781817, + -0.13549637792062075, + -0.09631670237730873, + -0.06366697275788202, + -0.03754718906234088, + -0.017957351290684813, + -0.004897459442914092, + 0.0016324864809712783, + 0.0016324864809713078, + -0.004897459442913922, + -0.017957351290684525, + -0.037547189062340475, + -0.06366697275788177, + -0.09631670237730808, + -0.13549637792062003, + -0.18120599938781728, + -0.23344556677889988, + -0.2922150800938673, + -0.3575145393327205, + -0.4293439444954591, + -0.507703295582083, + -0.5925925925925916, + -0.6840118355269861, + -0.7819610243852659, + -0.8864401591674314, + -0.9974492398734819, + -1.1149882665034168, + -1.239057239057238, + -1.3696561575349446, + -1.5067850219365364, + -1.6504438322620127, + -1.800632588511375, + -1.9573512906846229, + -2.1205999387817562, + -2.290378532802773, + -2.4666870727476775, + -2.649525558616466, + -2.8388939904091406, + -3.0347923681256987, + -3.2372206917661464, + -3.446178961330475, + -3.6616671768186886, + -3.8836853382307925, + -4.112233445566777, + -4.347311498826651, + -4.588919498010406, + -4.837057443118046, + -5.091725334149577, + -5.352923171104988, + -5.620650953984284, + -5.894908682787469, + -6.175696357514536, + -6.463013978165494, + -6.756861544740331, + -7.057239057239053, + -7.364146515661667, + -7.677583920008159, + -7.997551270278544, + -8.324048566472808 + ], + [ + -8.324048566472808, + -7.9975512702785405, + -7.677583920008159, + -7.364146515661667, + -7.057239057239056, + -6.756861544740331, + -6.463013978165491, + -6.175696357514539, + -5.894908682787469, + -5.620650953984286, + -5.352923171104988, + -5.091725334149576, + -4.837057443118048, + -4.588919498010406, + -4.347311498826649, + -4.112233445566778, + -3.8836853382307925, + -3.6616671768186912, + -3.446178961330475, + -3.237220691766145, + -3.0347923681256996, + -2.8388939904091406, + -2.649525558616466, + -2.466687072747678, + -2.290378532802774, + -2.1205999387817562, + -1.9573512906846229, + -1.8006325885113759, + -1.6504438322620132, + -1.5067850219365364, + -1.3696561575349446, + -1.2390572390572385, + -1.1149882665034172, + -0.9974492398734814, + -0.8864401591674314, + -0.7819610243852659, + -0.6840118355269865, + -0.5925925925925919, + -0.507703295582083, + -0.4293439444954591, + -0.3575145393327205, + -0.2922150800938679, + -0.23344556677889988, + -0.18120599938781728, + -0.13549637792062003, + -0.0963167023773084, + -0.06366697275788177, + -0.037547189062340475, + -0.017957351290684525, + -0.004897459442913922, + 0.0016324864809713078, + 0.0016324864809712783, + -0.004897459442914092, + -0.017957351290684813, + -0.03754718906234068, + -0.06366697275788202, + -0.09631670237730873, + -0.13549637792062075, + -0.18120599938781773, + -0.2334455667789004, + -0.2922150800938684, + -0.35751453933272176, + -0.4293439444954598, + -0.5077032955820838, + -0.5925925925925931, + -0.6840118355269877, + -0.7819610243852678, + -0.8864401591674322, + -0.997449239873483, + -1.114988266503419, + -1.23905723905724, + -1.369656157534946, + -1.5067850219365377, + -1.6504438322620152, + -1.8006325885113779, + -1.9573512906846242, + -2.1205999387817576, + -2.290378532802776, + -2.4666870727476806, + -2.6495255586164683, + -2.8388939904091446, + -3.0347923681257023, + -3.2372206917661455, + -3.446178961330478, + -3.661667176818692, + -3.8836853382307956, + -4.112233445566781, + -4.34731149882665, + -4.58891949801041, + -4.83705744311805, + -5.091725334149576, + -5.352923171104991, + -5.620650953984287, + -5.894908682787473, + -6.17569635751454, + -6.463013978165492, + -6.756861544740335, + -7.057239057239058, + -7.364146515661671, + -7.677583920008165 + ], + [ + -8.97704315886134, + -8.637485970819304, + -8.304458728701151, + -7.977961432506888, + -7.657994082236507, + -7.344556677890011, + -7.037649219467401, + -6.737271706968678, + -6.443424140393837, + -6.156106519742883, + -5.875318845015814, + -5.601061116212631, + -5.333333333333333, + -5.07213549637792, + -4.817467605346393, + -4.5693296602387505, + -4.327721661054995, + -4.092643607795123, + -3.864095500459136, + -3.642077339047036, + -3.42658912355882, + -3.21763085399449, + -3.0152025303540446, + -2.8193041526374856, + -2.629935720844811, + -2.4470972349760225, + -2.270788695031119, + -2.1010101010101008, + -1.9377614529129676, + -1.7810427507397204, + -1.630853994490358, + -1.487195184164881, + -1.3500663197632892, + -1.2194674012855828, + -1.0953984287317617, + -0.977859402101826, + -0.8668503213957758, + -0.7623711866136105, + -0.6644219977553311, + -0.5730027548209363, + -0.48811345781042714, + -0.40975410672380386, + -0.3379247015610652, + -0.2726252423222119, + -0.21385572900724398, + -0.16161616161616177, + -0.11590654014896444, + -0.07672686460565245, + -0.04407713498622581, + -0.017957351290684525, + 0.0016324864809712785, + 0.014692378328741939, + 0.021222324252627257, + 0.021222324252627222, + 0.014692378328741922, + 0.0016324864809712653, + -0.01795735129068475, + -0.04407713498622608, + -0.0767268646056525, + -0.11590654014896447, + -0.16161616161616177, + -0.21385572900724448, + -0.27262524232221197, + -0.33792470156106524, + -0.40975410672380386, + -0.4881134578104278, + -0.5730027548209372, + -0.664421997755331, + -0.7623711866136111, + -0.8668503213957763, + -0.9778594021018269, + -1.0953984287317622, + -1.2194674012855833, + -1.3500663197632898, + -1.4871951841648818, + -1.630853994490358, + -1.7810427507397204, + -1.937761452912968, + -2.1010101010101017, + -2.2707886950311185, + -2.4470972349760243, + -2.629935720844812, + -2.8193041526374847, + -3.0152025303540464, + -3.2176308539944896, + -3.4265891235588226, + -3.6420773390470362, + -3.8640955004591353, + -4.092643607795124, + -4.327721661054994, + -4.569329660238749, + -4.817467605346393, + -5.072135496377919, + -5.333333333333335, + -5.601061116212631, + -5.875318845015812, + -6.156106519742885, + -6.443424140393837, + -6.737271706968679, + -7.0376492194674025 + ], + [ + -9.63656769717376, + -9.283950617283951, + -8.937863483318027, + -8.598306295275995, + -8.265279053157842, + -7.938781756963576, + -7.618814406693195, + -7.3053770023467015, + -6.99846954392409, + -6.698092031425365, + -6.4042444648505255, + -6.116926844199572, + -5.836139169472504, + -5.561881440669321, + -5.294153657790022, + -5.0329558208346095, + -4.778287929803083, + -4.5301499846954405, + -4.288541985511682, + -4.053463932251812, + -3.8249158249158253, + -3.6028976635037244, + -3.387409448015509, + -3.178451178451179, + -2.9760228548107337, + -2.7801244770941747, + -2.5907560453014997, + -2.4079175594327116, + -2.2316090194878075, + -2.0618304254667894, + -1.8985817773696565, + -1.741863075196409, + -1.5916743189470464, + -1.4480155086215691, + -1.3108866442199778, + -1.1802877257422713, + -1.0562187531884504, + -0.9386797265585146, + -0.8276706458524643, + -0.7231915110702989, + -0.6252423222120191, + -0.5338230792776253, + -0.4489337822671159, + -0.3705744311804919, + -0.2987450260177532, + -0.23344556677890044, + -0.17467605346393245, + -0.12243648607284978, + -0.07672686460565245, + -0.037547189062340475, + -0.004897459442914093, + 0.021222324252627253, + 0.04081216202428327, + 0.05387205387205392, + 0.060401999795939194, + 0.060401999795939236, + 0.053872053872053925, + 0.04081216202428328, + 0.021222324252627434, + -0.004897459442913865, + -0.03754718906234042, + -0.07672686460565248, + -0.12243648607284935, + -0.17467605346393206, + -0.23344556677889988, + -0.2987450260177532, + -0.37057443118049194, + -0.4489337822671152, + -0.5338230792776246, + -0.6252423222120191, + -0.7231915110702991, + -0.8276706458524635, + -0.9386797265585141, + -1.0562187531884502, + -1.1802877257422713, + -1.310886644219977, + -1.4480155086215687, + -1.5916743189470457, + -1.7418630751964086, + -1.8985817773696552, + -2.06183042546679, + -2.2316090194878067, + -2.407917559432709, + -2.5907560453015, + -2.780124477094173, + -2.9760228548107346, + -3.1784511784511777, + -3.3874094480155064, + -3.602897663503725, + -3.8249158249158235, + -4.053463932251808, + -4.288541985511682, + -4.530149984695436, + -4.778287929803082, + -5.032955820834608, + -5.294153657790019, + -5.561881440669319, + -5.836139169472501, + -6.116926844199573, + -6.404244464850525 + ], + [ + -10.302622181410062, + -9.936945209672484, + -9.577798183858791, + -9.225181103968985, + -8.879093970003064, + -8.539536781961026, + -8.206509539842875, + -7.880012243648611, + -7.560044893378229, + -7.246607489031733, + -6.939700030609123, + -6.639322518110399, + -6.34547495153556, + -6.0581573308846055, + -5.7773696561575365, + -5.503111927354354, + -5.235384144475056, + -4.974186307519642, + -4.719518416488114, + -4.471380471380472, + -4.229772472196715, + -3.9946944189368447, + -3.766146311600858, + -3.5441281501887576, + -3.3286399347005418, + -3.1196816651362123, + -2.9172533414957664, + -2.7213549637792074, + -2.531986531986533, + -2.3491480461177443, + -2.1728395061728403, + -2.003060912151822, + -1.839812264054689, + -1.683093561881441, + -1.532904805632079, + -1.3892459953066019, + -1.2521171309050103, + -1.1215182124273038, + -0.9974492398734829, + -0.8799102132435469, + -0.7689011325374964, + -0.6644219977553318, + -0.5664728088970519, + -0.4750535659626572, + -0.39016426895214784, + -0.31180491786552456, + -0.2399755127027858, + -0.17467605346393245, + -0.11590654014896443, + -0.06366697275788176, + -0.017957351290684813, + 0.021222324252627225, + 0.05387205387205393, + 0.07999183756759526, + 0.09958167533925112, + 0.11264156718702184, + 0.11917151311090722, + 0.11917151311090726, + 0.112641567187022, + 0.09958167533925141, + 0.07999183756759551, + 0.05387205387205418, + 0.021222324252627878, + -0.017957351290684154, + -0.06366697275788125, + -0.11590654014896401, + -0.17467605346393195, + -0.2399755127027846, + -0.31180491786552333, + -0.3901642689521473, + -0.47505356596265647, + -0.5664728088970504, + -0.6644219977553302, + -0.7689011325374954, + -0.879910213243546, + -0.997449239873481, + -1.1215182124273024, + -1.2521171309050088, + -1.3892459953066005, + -1.5329048056320764, + -1.6830935618814404, + -1.839812264054687, + -2.0030609121518186, + -2.1728395061728385, + -2.349148046117741, + -2.5319865319865325, + -2.7213549637792047, + -2.917253341495763, + -3.119681665136211, + -3.328639934700539, + -3.5441281501887527, + -3.7661463116008553, + -3.9946944189368394, + -4.229772472196714, + -4.471380471380469, + -4.719518416488109, + -4.97418630751964, + -5.23538414447505, + -5.503111927354352, + -5.777369656157533 + ], + [ + -10.975206611570245, + -10.596469747984896, + -10.224262830323433, + -9.858585858585856, + -9.499438832772164, + -9.146821752882357, + -8.800734618916433, + -8.4611774308744, + -8.128150188756248, + -7.801652892561982, + -7.481685542291601, + -7.168248137945106, + -6.861340679522496, + -6.560963167023772, + -6.267115600448932, + -5.979797979797978, + -5.69901030507091, + -5.424752576267727, + -5.157024793388428, + -4.895826956433016, + -4.641159065401488, + -4.393021120293846, + -4.151413121110089, + -3.916335067850218, + -3.6877869605142317, + -3.4657687991021318, + -3.2502805836139155, + -3.041322314049586, + -2.838893990409141, + -2.642995612692582, + -2.4536271808999075, + -2.2707886950311185, + -2.094480155086215, + -1.924701561065196, + -1.7614529129680636, + -1.604734210794816, + -1.4545454545454537, + -1.3108866442199767, + -1.1737577798183854, + -1.0431588613406788, + -0.9190898887868576, + -0.8015508621569227, + -0.6905417814508721, + -0.5860626466687069, + -0.48811345781042703, + -0.3966942148760331, + -0.3118049178655239, + -0.2334455667788999, + -0.16161616161616132, + -0.09631670237730809, + -0.037547189062340676, + 0.014692378328741934, + 0.06040199979593921, + 0.09958167533925111, + 0.13223140495867744, + 0.15835118865421874, + 0.1779410264258747, + 0.19100091827364532, + 0.19753086419753046, + 0.19753086419753052, + 0.1910009182736451, + 0.17794102642587445, + 0.15835118865421857, + 0.13223140495867713, + 0.0995816753392505, + 0.06040199979593858, + 0.014692378328741151, + -0.03754718906234111, + -0.09631670237730916, + -0.16161616161616255, + -0.23344556677890116, + -0.3118049178655248, + -0.39669421487603407, + -0.48811345781042836, + -0.5860626466687088, + -0.6905417814508734, + -0.8015508621569236, + -0.9190898887868595, + -1.043158861340681, + -1.173757779818387, + -1.31088664421998, + -1.4545454545454555, + -1.6047342107948166, + -1.7614529129680663, + -1.924701561065198, + -2.0944801550862184, + -2.270788695031121, + -2.453627180899909, + -2.642995612692585, + -2.8388939904091437, + -3.041322314049587, + -3.250280583613919, + -3.465768799102133, + -3.687786960514236, + -3.916335067850221, + -4.151413121110091, + -4.3930211202938505, + -4.6411590654014905, + -4.895826956433022, + -5.157024793388432 + ], + [ + -11.654320987654321, + -11.2625242322212, + -10.877257422711967, + -10.49852055912662, + -10.126313641465156, + -9.760636669727578, + -9.401489643913884, + -9.04887256402408, + -8.702785430058157, + -8.36322824201612, + -8.030200999897968, + -7.703703703703702, + -7.3837363534333225, + -7.070298949086827, + -6.763391490664216, + -6.463013978165493, + -6.169166411590654, + -5.8818487909397, + -5.60106111621263, + -5.326803387409447, + -5.059075604530149, + -4.797877767574736, + -4.543209876543209, + -4.295071931435567, + -4.05346393225181, + -3.818385878991939, + -3.589837771655953, + -3.3678196102438527, + -3.152331394755637, + -2.9433731251913073, + -2.740944801550862, + -2.545046423834303, + -2.355677992041628, + -2.1728395061728385, + -1.9965309662279354, + -1.826752372206917, + -1.6635037241097845, + -1.5067850219365366, + -1.3565962656871746, + -1.2129374553616974, + -1.0758085909601056, + -0.9452096724824001, + -0.8211406999285787, + -0.7036016732986428, + -0.5925925925925922, + -0.48811345781042786, + -0.39016426895214784, + -0.2987450260177532, + -0.21385572900724392, + -0.13549637792062003, + -0.06366697275788202, + 0.0016324864809712653, + 0.06040199979593924, + 0.11264156718702183, + 0.1583511886542187, + 0.19753086419753071, + 0.23018059381695738, + 0.2563003775124987, + 0.27589021528415447, + 0.28895010713192515, + 0.2954800530558105, + 0.2954800530558104, + 0.28895010713192515, + 0.27589021528415436, + 0.25630037751249846, + 0.2301805938169571, + 0.1975308641975304, + 0.1583511886542187, + 0.11264156718702134, + 0.06040199979593863, + 0.0016324864809706963, + -0.06366697275788225, + -0.13549637792062064, + -0.2138557290072447, + -0.2987450260177542, + -0.3901642689521483, + -0.4881134578104276, + -0.5925925925925928, + -0.7036016732986439, + -0.8211406999285786, + -0.9452096724824015, + -1.0758085909601063, + -1.2129374553616967, + -1.3565962656871755, + -1.506785021936537, + -1.6635037241097868, + -1.8267523722069186, + -1.9965309662279356, + -2.172839506172841, + -2.355677992041629, + -2.545046423834302, + -2.740944801550863, + -2.9433731251913064, + -3.152331394755639, + -3.3678196102438527, + -3.589837771655952, + -3.8183858789919416, + -4.053463932251811, + -4.2950719314355705, + -4.543209876543212 + ], + [ + -12.33996530966228, + -11.935108662381388, + -11.536781961024385, + -11.144985205591269, + -10.759718396082032, + -10.380981532496683, + -10.00877461483522, + -9.643097643097644, + -9.283950617283951, + -8.931333537394144, + -8.585246403428222, + -8.245689215386186, + -7.912661973268035, + -7.586164677073769, + -7.266197326803387, + -6.9527599224568934, + -6.6458524640342835, + -6.345474951535559, + -6.051627384960718, + -5.764309764309765, + -5.483522089582696, + -5.209264360779512, + -4.941536577900214, + -4.680338740944801, + -4.425670849913274, + -4.177532904805632, + -3.9359249056218752, + -3.7008468523620044, + -3.472298745026018, + -3.2502805836139177, + -3.034792368125702, + -2.825834098561372, + -2.6234057749209265, + -2.4275073972043666, + -2.2381389654116925, + -2.0553004795429035, + -1.8789919395980004, + -1.7092133455769818, + -1.545964697479849, + -1.3892459953066014, + -1.2390572390572387, + -1.0953984287317629, + -0.9582695643301706, + -0.8276706458524641, + -0.7036016732986428, + -0.5860626466687078, + -0.47505356596265713, + -0.3705744311804919, + -0.2726252423222119, + -0.18120599938781728, + -0.09631670237730873, + -0.01795735129068475, + 0.05387205387205392, + 0.11917151311090718, + 0.17794102642587467, + 0.23018059381695735, + 0.2758902152841547, + 0.31506989082746667, + 0.347719620446893, + 0.3738394041424344, + 0.39342924191409046, + 0.4064891337618611, + 0.4130190796857463, + 0.41301907968574625, + 0.406489133761861, + 0.3934292419140904, + 0.3738394041424344, + 0.3477196204468933, + 0.3150698908274666, + 0.2758902152841546, + 0.23018059381695744, + 0.17794102642587484, + 0.11917151311090712, + 0.05387205387205385, + -0.017957351290684764, + -0.09631670237730838, + -0.18120599938781723, + -0.2726252423222115, + -0.37057443118049216, + -0.47505356596265647, + -0.586062646668708, + -0.7036016732986425, + -0.8276706458524623, + -0.9582695643301706, + -1.095398428731761, + -1.2390572390572399, + -1.3892459953066014, + -1.5459646974798478, + -1.709213345576983, + -1.878991939598, + -2.055300479542902, + -2.238138965411693, + -2.4275073972043653, + -2.623405774920927, + -2.8258340985613706, + -3.034792368125699, + -3.2502805836139173, + -3.472298745026017, + -3.7008468523620057, + -3.9359249056218757 + ], + [ + -13.032139577594126, + -12.614223038465463, + -12.202836445260688, + -11.797979797979801, + -11.399653096622796, + -11.007856341189676, + -10.622589531680442, + -10.243852668095094, + -9.87164575043363, + -9.505968778696053, + -9.14682175288236, + -8.794204672992553, + -8.448117539026631, + -8.108560350984595, + -7.775533108866444, + -7.449035812672178, + -7.129068462401798, + -6.815631058055303, + -6.508723599632691, + -6.208346087133966, + -5.9144985205591265, + -5.627180899908174, + -5.346393225181105, + -5.072135496377922, + -4.804407713498623, + -4.543209876543211, + -4.288541985511683, + -4.0404040404040416, + -3.7987960412202844, + -3.5637179879604135, + -3.335169880624427, + -3.1131517192123264, + -2.89766350372411, + -2.6887052341597797, + -2.486276910519335, + -2.2903785328027757, + -2.1010101010101017, + -1.9181716151413124, + -1.741863075196409, + -1.5720844811753907, + -1.4088358330782573, + -1.2521171309050108, + -1.101928374655648, + -0.9582695643301706, + -0.8211406999285789, + -0.6905417814508732, + -0.5664728088970519, + -0.44893378226711583, + -0.3379247015610652, + -0.2334455667788999, + -0.13549637792062075, + -0.044077134986226084, + 0.04081216202428327, + 0.11917151311090722, + 0.19100091827364526, + 0.2563003775124987, + 0.31506989082746667, + 0.3673094582185494, + 0.41301907968574625, + 0.4521987552290584, + 0.48484848484848503, + 0.5109682685440264, + 0.5305581063156822, + 0.5436179981634529, + 0.5501479440873385, + 0.5501479440873384, + 0.543617998163453, + 0.5305581063156826, + 0.5109682685440264, + 0.4848484848484853, + 0.4521987552290586, + 0.4130190796857469, + 0.36730945821854977, + 0.31506989082746706, + 0.25630037751249923, + 0.1910009182736463, + 0.1191715131109079, + 0.04081216202428406, + -0.044077134986225674, + -0.1354963779206193, + -0.23344556677890016, + -0.33792470156106424, + -0.44893378226711356, + -0.5664728088970508, + -0.690541781450871, + -0.8211406999285789, + -0.9582695643301693, + -1.1019283746556456, + -1.2521171309050096, + -1.408835833078256, + -1.5720844811753882, + -1.7418630751964073, + -1.9181716151413095, + -2.1010101010101008, + -2.290378532802774, + -2.4862769105193316, + -2.6887052341597797, + -2.897663503724108, + -3.1131517192123255, + -3.3351698806244254 + ], + [ + -13.730843791449848, + -13.299867360473415, + -12.875420875420872, + -12.457504336292214, + -12.046117743087438, + -11.641261095806547, + -11.242934394449543, + -10.851137639016425, + -10.46587082950719, + -10.087133965921842, + -9.714927048260378, + -9.3492500765228, + -8.99010305070911, + -8.637485970819302, + -8.291398836853379, + -7.951841648811344, + -7.618814406693193, + -7.292317110498927, + -6.972349760228545, + -6.658912355882051, + -6.352004897459441, + -6.0516273849607165, + -5.7577798183858775, + -5.470462197734923, + -5.189674523007854, + -4.915416794204671, + -4.647689011325373, + -4.3864911743699615, + -4.131823283338433, + -3.8836853382307917, + -3.6420773390470345, + -3.406999285787164, + -3.1784511784511773, + -2.956433017039076, + -2.740944801550861, + -2.531986531986531, + -2.3295582083460866, + -2.1336598306295267, + -1.944291398836853, + -1.7614529129680636, + -1.5851443730231596, + -1.4153657790021428, + -1.2521171309050094, + -1.0953984287317615, + -0.945209672482399, + -0.801550862156923, + -0.664421997755331, + -0.5338230792776245, + -0.40975410672380325, + -0.2922150800938673, + -0.18120599938781773, + -0.07672686460565248, + 0.02122232425262744, + 0.112641567187022, + 0.19753086419753046, + 0.27589021528415447, + 0.3477196204468931, + 0.4130190796857463, + 0.47178859300071363, + 0.5240281603917963, + 0.5697377818589936, + 0.6089174574023055, + 0.6415671870217318, + 0.667686970717273, + 0.6872768084889291, + 0.7003367003366997, + 0.706866646260585, + 0.7068666462605848, + 0.7003367003366993, + 0.6872768084889289, + 0.667686970717273, + 0.6415671870217313, + 0.608917457402305, + 0.5697377818589928, + 0.5240281603917953, + 0.4717885930007131, + 0.41301907968574514, + 0.347719620446892, + 0.27589021528415314, + 0.19753086419752997, + 0.11264156718701956, + 0.021222324252625713, + -0.07672686460565314, + -0.18120599938781945, + -0.29221508009386943, + -0.40975410672380663, + -0.5338230792776266, + -0.6644219977553325, + -0.8015508621569256, + -0.945209672482402, + -1.0953984287317633, + -1.2521171309050119, + -1.4153657790021432, + -1.5851443730231645, + -1.7614529129680667, + -1.944291398836854, + -2.1336598306295307, + -2.329558208346089, + -2.531986531986536, + -2.7409448015508655 + ], + [ + -14.436077951229464, + -13.99204162840526, + -13.554535251504946, + -13.123558820528517, + -12.69911233547597, + -12.281195796347308, + -11.869809203142534, + -11.464952555861647, + -11.066625854504641, + -10.674829099071522, + -10.289562289562287, + -9.91082542597694, + -9.538618508315476, + -9.172941536577898, + -8.813794510764206, + -8.4611774308744, + -8.115090296908479, + -7.7755331088664414, + -7.44250586674829, + -7.116008570554024, + -6.796041220283643, + -6.482603815937148, + -6.175696357514537, + -5.875318845015814, + -5.581471278440974, + -5.294153657790021, + -5.013365983062952, + -4.73910825425977, + -4.471380471380471, + -4.210182634425059, + -3.9555147433935307, + -3.707376798285889, + -3.4657687991021318, + -3.23069074584226, + -3.0021426385062746, + -2.7801244770941733, + -2.5646362616059584, + -2.3556779920416275, + -2.1532496684011835, + -1.9573512906846235, + -1.767982858891949, + -1.5851443730231614, + -1.4088358330782573, + -1.2390572390572387, + -1.0758085909601054, + -0.9190898887868588, + -0.7689011325374963, + -0.625242322212019, + -0.4881134578104271, + -0.3575145393327206, + -0.23344556677890038, + -0.11590654014896445, + -0.0048974594429138235, + 0.0995816753392514, + 0.19753086419753046, + 0.28895010713192515, + 0.37383940414243444, + 0.4521987552290584, + 0.5240281603917962, + 0.5893276196306496, + 0.6480971329456178, + 0.7003367003367001, + 0.7460463218038971, + 0.7852259973472089, + 0.8178757269666357, + 0.8439955106621769, + 0.8635853484338329, + 0.8766452402816035, + 0.8831751862054886, + 0.8831751862054886, + 0.8766452402816033, + 0.8635853484338326, + 0.8439955106621769, + 0.8178757269666354, + 0.7852259973472087, + 0.7460463218038967, + 0.7003367003366998, + 0.6480971329456173, + 0.589327619630649, + 0.5240281603917967, + 0.4521987552290574, + 0.3738394041424342, + 0.2889501071319258, + 0.19753086419752997, + 0.09958167533925089, + -0.0048974594429158635, + -0.1159065401489654, + -0.23344556677890038, + -0.35751453933272304, + -0.48811345781042803, + -0.6252423222120189, + -0.768901132537497, + -0.9190898887868579, + -1.0758085909601078, + -1.2390572390572396, + -1.4088358330782569, + -1.5851443730231631, + -1.7679828588919504, + -1.957351290684627, + -2.1532496684011853 + ], + [ + -15.147842056932967, + -14.690745842260993, + -14.240179573512904, + -13.796143250688708, + -13.35863687378839, + -12.927660442811959, + -12.50321395775941, + -12.085297418630752, + -11.673910825425978, + -11.269054178145087, + -10.870727476788081, + -10.478930721354963, + -10.09366391184573, + -9.714927048260382, + -9.342720130598916, + -8.977043158861342, + -8.61789613304765, + -8.26527905315784, + -7.919191919191918, + -7.579634731149882, + -7.24660748903173, + -6.920110192837465, + -6.6001428425670845, + -6.28670543822059, + -5.979797979797979, + -5.679420467299256, + -5.385572900724416, + -5.098255280073461, + -4.817467605346393, + -4.5432098765432105, + -4.275482093663912, + -4.0142842567085, + -3.7596163656769717, + -3.511478420569329, + -3.2698704213855727, + -3.034792368125701, + -2.8062442607897156, + -2.5842260993776143, + -2.3687378838893993, + -2.1597796143250685, + -1.9573512906846235, + -1.7614529129680654, + -1.5720844811753905, + -1.3892459953066014, + -1.2129374553616974, + -1.0431588613406801, + -0.879910213243547, + -0.723191511070299, + -0.5730027548209363, + -0.4293439444954591, + -0.2922150800938684, + -0.16161616161616174, + -0.03754718906234042, + 0.07999183756759548, + 0.19100091827364513, + 0.2954800530558105, + 0.39342924191409046, + 0.4848484848484851, + 0.5697377818589936, + 0.6480971329456175, + 0.7199265381083563, + 0.7852259973472095, + 0.843995510662177, + 0.8962350780532595, + 0.941944699520457, + 0.981124375063769, + 1.0137741046831956, + 1.0398938883787368, + 1.0594837261503924, + 1.0725436179981633, + 1.0790735639220486, + 1.0790735639220486, + 1.0725436179981633, + 1.0594837261503927, + 1.0398938883787368, + 1.0137741046831954, + 0.9811243750637691, + 0.9419446995204572, + 0.8962350780532597, + 0.8439955106621779, + 0.7852259973472089, + 0.7199265381083564, + 0.6480971329456187, + 0.5697377818589939, + 0.48484848484848486, + 0.39342924191408946, + 0.2954800530558104, + 0.1910009182736463, + 0.07999183756759409, + -0.03754718906234089, + -0.16161616161616088, + -0.2922150800938681, + -0.42934394449545854, + -0.573002754820938, + -0.7231915110702993, + -0.8799102132435452, + -1.0431588613406801, + -1.2129374553616974, + -1.3892459953066036, + -1.572084481175391 + ], + [ + -15.866136108560353, + -15.39598000204061, + -14.932353841444751, + -14.47525762677278, + -14.024691358024693, + -13.58065503520049, + -13.143148658300174, + -12.712172227323745, + -12.2877257422712, + -11.869809203142538, + -11.458422609937763, + -11.053565962656872, + -10.655239261299869, + -10.263442505866749, + -9.878175696357514, + -9.499438832772167, + -9.127231915110706, + -8.761554943373127, + -8.402407917559433, + -8.049790837669626, + -7.703703703703704, + -7.364146515661668, + -7.031119273543517, + -6.704621977349252, + -6.38465462707887, + -6.0712172227323755, + -5.764309764309765, + -5.463932251811041, + -5.170084685236201, + -4.882767064585247, + -4.601979389858178, + -4.327721661054996, + -4.059993878175698, + -3.7987960412202835, + -3.544128150188757, + -3.2959902050811145, + -3.054382205897358, + -2.8193041526374865, + -2.590756045301501, + -2.3687378838893993, + -2.153249668401183, + -1.9442913988368549, + -1.7418630751964095, + -1.5459646974798493, + -1.3565962656871746, + -1.173757779818387, + -0.9974492398734829, + -0.8276706458524643, + -0.6644219977553311, + -0.507703295582083, + -0.35751453933272176, + -0.21385572900724442, + -0.07672686460565245, + 0.053872053872054154, + 0.17794102642587437, + 0.2954800530558104, + 0.4064891337618611, + 0.5109682685440264, + 0.6089174574023055, + 0.7003367003367001, + 0.7852259973472095, + 0.8635853484338336, + 0.9354147535965716, + 1.0007142128354247, + 1.059483726150393, + 1.1117232935414756, + 1.1574329150086728, + 1.1966125905519844, + 1.229262320171411, + 1.2553821038669526, + 1.2749719416386087, + 1.2880318334863787, + 1.2945617794102648, + 1.2945617794102646, + 1.2880318334863792, + 1.2749719416386083, + 1.2553821038669528, + 1.2292623201714115, + 1.1966125905519844, + 1.1574329150086735, + 1.1117232935414758, + 1.0594837261503935, + 1.0007142128354263, + 0.9354147535965724, + 0.863585348433834, + 0.7852259973472093, + 0.7003367003367007, + 0.6089174574023066, + 0.5109682685440258, + 0.4064891337618617, + 0.2954800530558117, + 0.1779410264258754, + 0.0538720538720554, + -0.0767268646056527, + -0.2138557290072436, + -0.35751453933271904, + -0.5077032955820839, + -0.6644219977553298, + -0.8276706458524643, + -0.9974492398734824 + ], + [ + -16.59096010611162, + -16.107744107744104, + -15.631058055300475, + -15.160901948780733, + -14.697275788184877, + -14.240179573512904, + -13.789613304764815, + -13.345576981940617, + -12.908070605040297, + -12.477094174063868, + -12.052647689011321, + -11.634731149882661, + -11.223344556677887, + -10.818487909396998, + -10.420161208039993, + -10.028364452606874, + -9.643097643097642, + -9.264360779512293, + -8.89215386185083, + -8.526476890113251, + -8.167329864299557, + -7.8147127844097515, + -7.46862565044383, + -7.1290684624017935, + -6.796041220283643, + -6.469543924089377, + -6.149576573818996, + -5.836139169472501, + -5.52923171104989, + -5.228854198551167, + -4.935006631976327, + -4.647689011325374, + -4.366901336598305, + -4.092643607795121, + -3.8249158249158235, + -3.563717987960411, + -3.3090500969288836, + -3.060912151821241, + -2.8193041526374856, + -2.584226099377613, + -2.3556779920416266, + -2.1336598306295276, + -1.9181716151413117, + -1.7092133455769811, + -1.5067850219365357, + -1.3108866442199778, + -1.121518212427303, + -0.938679726558514, + -0.7623711866136101, + -0.5925925925925916, + -0.4293439444954598, + -0.2726252423222119, + -0.12243648607284938, + 0.021222324252627822, + 0.15835118865421852, + 0.28895010713192515, + 0.41301907968574636, + 0.5305581063156823, + 0.6415671870217318, + 0.7460463218038971, + 0.843995510662177, + 0.9354147535965716, + 1.0203040506070802, + 1.0986634016937038, + 1.1704928068564426, + 1.2357922660952958, + 1.2945617794102637, + 1.3468013468013456, + 1.3925109682685428, + 1.431690643811855, + 1.4643403734312819, + 1.4904601571268223, + 1.5100499948984787, + 1.5231098867462491, + 1.5296398326701341, + 1.5296398326701341, + 1.5231098867462491, + 1.5100499948984782, + 1.4904601571268221, + 1.464340373431281, + 1.431690643811854, + 1.3925109682685421, + 1.3468013468013456, + 1.2945617794102624, + 1.2357922660952945, + 1.1704928068564406, + 1.0986634016937025, + 1.0203040506070788, + 0.9354147535965684, + 0.8439955106621748, + 0.7460463218038953, + 0.6415671870217299, + 0.5305581063156808, + 0.4130190796857427, + 0.28895010713192226, + 0.15835118865421727, + 0.021222324252622826, + -0.12243648607285262, + -0.2726252423222162, + -0.4293439444954634 + ], + [ + -17.322314049586772, + -16.82603815937149, + -16.336292215080093, + -15.853076216712576, + -15.376390164268951, + -14.906234057749208, + -14.442607897153348, + -13.985511682481377, + -13.53494541373329, + -13.090909090909088, + -12.653402714008772, + -12.222426283032341, + -11.797979797979796, + -11.380063258851136, + -10.96867666564636, + -10.563820018365472, + -10.165493317008469, + -9.773696561575349, + -9.388429752066113, + -9.009692888480766, + -8.637485970819302, + -8.271808999081726, + -7.9126619732680314, + -7.560044893378225, + -7.213957759412303, + -6.874400571370268, + -6.5413733292521155, + -6.214876033057851, + -5.894908682787469, + -5.581471278440975, + -5.274563820018365, + -4.97418630751964, + -4.680338740944801, + -4.393021120293846, + -4.112233445566778, + -3.8379757167635944, + -3.570247933884297, + -3.3090500969288836, + -3.0543822058973573, + -2.8062442607897142, + -2.5646362616059575, + -2.3295582083460875, + -2.1010101010101008, + -1.878991939598, + -1.6635037241097839, + -1.454545454545455, + -1.2521171309050099, + -1.05621875318845, + -0.8668503213957754, + -0.6840118355269862, + -0.5077032955820838, + -0.33792470156106524, + -0.17467605346393203, + -0.017957351290684126, + 0.13223140495867716, + 0.27589021528415447, + 0.41301907968574636, + 0.5436179981634529, + 0.667686970717273, + 0.7852259973472091, + 0.8962350780532597, + 1.000714212835425, + 1.0986634016937038, + 1.1900826446280983, + 1.2749719416386078, + 1.3533312927252317, + 1.4251606978879705, + 1.490460157126823, + 1.5492296704417907, + 1.6014692378328736, + 1.6471788593000707, + 1.6863585348433823, + 1.719008264462809, + 1.7451280481583504, + 1.7647178859300063, + 1.7777777777777763, + 1.7843077237016622, + 1.7843077237016622, + 1.7777777777777768, + 1.7647178859300063, + 1.74512804815835, + 1.7190082644628093, + 1.6863585348433832, + 1.64717885930007, + 1.6014692378328732, + 1.5492296704417896, + 1.4904601571268223, + 1.4251606978879696, + 1.3533312927252297, + 1.2749719416386065, + 1.1900826446280983, + 1.098663401693703, + 1.0007142128354247, + 0.8962350780532571, + 0.7852259973472075, + 0.6676869707172726, + 0.5436179981634499, + 0.4130190796857445, + 0.2758902152841518, + 0.13223140495867547 + ], + [ + -18.060197938985816, + -17.550862156922758, + -17.04805632078359, + -16.55178043056831, + -16.062034486276907, + -15.578818487909395, + -15.102132435465768, + -14.631976328946028, + -14.168350168350168, + -13.711253953678195, + -13.260687684930108, + -12.816651362105906, + -12.379144985205592, + -11.94816855422916, + -11.523722069176614, + -11.105805530047952, + -10.69441893684318, + -10.289562289562289, + -9.891235588205284, + -9.499438832772167, + -9.114172023262931, + -8.735435159677582, + -8.36322824201612, + -7.997551270278542, + -7.63840424446485, + -7.2857871645750425, + -6.939700030609121, + -6.6001428425670845, + -6.267115600448934, + -5.940618304254668, + -5.6206509539842875, + -5.307213549637792, + -5.000306091215181, + -4.699928578716457, + -4.406081012141618, + -4.118763391490663, + -3.8379757167635953, + -3.5637179879604117, + -3.2959902050811145, + -3.034792368125701, + -2.7801244770941733, + -2.531986531986533, + -2.2903785328027757, + -2.0553004795429035, + -1.8267523722069172, + -1.6047342107948177, + -1.3892459953066016, + -1.1802877257422713, + -0.9778594021018259, + -0.781961024385266, + -0.592592592592593, + -0.40975410672380386, + -0.2334455667788999, + -0.06366697275788136, + 0.09958167533925047, + 0.2563003775124984, + 0.4064891337618611, + 0.5501479440873384, + 0.6872768084889289, + 0.8178757269666357, + 0.941944699520457, + 1.0594837261503929, + 1.1704928068564426, + 1.2749719416386078, + 1.3729211304968878, + 1.4643403734312825, + 1.5492296704417918, + 1.627589021528415, + 1.6994184266911536, + 1.764717885930007, + 1.823487399244975, + 1.8757269666360568, + 1.9214365881032545, + 1.9606162636465665, + 1.9932659932659933, + 2.019385776961534, + 2.0389756147331903, + 2.052035506580961, + 2.0585654525048462, + 2.0585654525048462, + 2.0520355065809612, + 2.0389756147331903, + 2.019385776961535, + 1.9932659932659929, + 1.9606162636465665, + 1.9214365881032538, + 1.8757269666360572, + 1.8234873992449745, + 1.7647178859300063, + 1.6994184266911536, + 1.627589021528415, + 1.5492296704417914, + 1.4643403734312836, + 1.3729211304968865, + 1.2749719416386078, + 1.1704928068564437, + 1.059483726150391, + 0.941944699520457, + 0.8178757269666335, + 0.687276808488928 + ], + [ + -18.804611774308743, + -18.282216100397918, + -17.766350372410976, + -17.257014590347925, + -16.754208754208754, + -16.257932863993467, + -15.768186919702071, + -15.28497092133456, + -14.808284868890931, + -14.338128762371188, + -13.87450260177533, + -13.417406387103357, + -12.966840118355272, + -12.522803795531068, + -12.085297418630752, + -11.654320987654323, + -11.229874502601778, + -10.811957963473116, + -10.40057137026834, + -9.99571472298745, + -9.597388021630445, + -9.205591266197327, + -8.820324456688093, + -8.441587593102746, + -8.06938067544128, + -7.703703703703705, + -7.3445566778900115, + -6.991939598000205, + -6.645852464034283, + -6.306295275992246, + -5.973268033874095, + -5.64677073767983, + -5.3268033874094485, + -5.013365983062952, + -4.706458524640343, + -4.406081012141618, + -4.11223344556678, + -3.824915824915825, + -3.544128150188757, + -3.2698704213855727, + -3.0021426385062746, + -2.7409448015508637, + -2.4862769105193356, + -2.238138965411693, + -1.9965309662279354, + -1.7614529129680658, + -1.5329048056320789, + -1.3108866442199778, + -1.095398428731762, + -0.8864401591674312, + -0.6840118355269879, + -0.4881134578104278, + -0.2987450260177531, + -0.1159065401489639, + 0.060401999795938494, + 0.2301805938169572, + 0.39342924191409046, + 0.5501479440873385, + 0.7003367003366997, + 0.843995510662177, + 0.9811243750637693, + 1.1117232935414758, + 1.235792266095296, + 1.3533312927252317, + 1.4643403734312825, + 1.5688195082134477, + 1.6667686970717281, + 1.7581879400061218, + 1.8430772370166308, + 1.9214365881032553, + 1.993265993265994, + 2.0585654525048462, + 2.117334965819815, + 2.1695745332108975, + 2.215284154678095, + 2.2544638302214057, + 2.287113559840833, + 2.3132333435363743, + 2.3328231813080302, + 2.345883073155801, + 2.3524130190796866, + 2.3524130190796866, + 2.345883073155801, + 2.3328231813080302, + 2.3132333435363743, + 2.2871135598408325, + 2.2544638302214066, + 2.215284154678095, + 2.1695745332108967, + 2.117334965819815, + 2.058565452504847, + 1.993265993265994, + 1.9214365881032567, + 1.8430772370166308, + 1.7581879400061227, + 1.6667686970717295, + 1.5688195082134473, + 1.4643403734312836, + 1.353331292725232, + 1.235792266095297 + ], + [ + -19.555555555555557, + -19.02009998979696, + -18.49117436996225, + -17.968778696051427, + -17.45291296806449, + -16.94357718600143, + -16.44077134986226, + -15.94449545964698, + -15.454749515355578, + -14.971533516988064, + -14.494847464544435, + -14.024691358024693, + -13.561065197428837, + -13.103968982756864, + -12.653402714008774, + -12.209366391184576, + -11.77186001428426, + -11.340883583307829, + -10.916437098255281, + -10.498520559126622, + -10.087133965921847, + -9.682277318640958, + -9.283950617283953, + -8.892153861850833, + -8.506887052341598, + -8.128150188756251, + -7.755943271094788, + -7.39026629935721, + -7.031119273543518, + -6.67850219365371, + -6.332415059687788, + -5.992857871645752, + -5.659830629527601, + -5.333333333333334, + -5.013365983062954, + -4.699928578716459, + -4.393021120293849, + -4.092643607795123, + -3.7987960412202852, + -3.511478420569331, + -3.230690745842261, + -2.9564330170390796, + -2.6887052341597806, + -2.4275073972043675, + -2.1728395061728394, + -1.924701561065199, + -1.683093561881442, + -1.4480155086215698, + -1.219467401285583, + -0.9974492398734819, + -0.7819610243852679, + -0.5730027548209371, + -0.3705744311804918, + -0.1746760534639319, + 0.01469237832874104, + 0.1975308641975304, + 0.37383940414243444, + 0.5436179981634531, + 0.7068666462605849, + 0.8635853484338329, + 1.0137741046831956, + 1.157432915008673, + 1.2945617794102637, + 1.4251606978879703, + 1.5492296704417918, + 1.6667686970717277, + 1.7777777777777786, + 1.882256912559943, + 1.9802061014182228, + 2.0716253443526176, + 2.156514641363127, + 2.2348739924497503, + 2.306703397612489, + 2.3720028568513425, + 2.43077237016631, + 2.4830119375573925, + 2.52872155902459, + 2.5679012345679024, + 2.600550964187329, + 2.62667074788287, + 2.6462605856545265, + 2.6593204775022965, + 2.665850423426182, + 2.665850423426183, + 2.6593204775022965, + 2.6462605856545265, + 2.626670747882871, + 2.600550964187329, + 2.567901234567903, + 2.528721559024592, + 2.4830119375573934, + 2.4307723701663115, + 2.3720028568513443, + 2.3067033976124898, + 2.2348739924497525, + 2.1565146413631293, + 2.071625344352619, + 1.9802061014182253, + 1.882256912559943, + 1.777777777777779 + ], + [ + -20.313029282726248, + -19.76451382511988, + -19.2225283134374, + -18.68707274767881, + -18.158147127844096, + -17.635751453933267, + -17.11988572594633, + -16.610549943883278, + -16.107744107744107, + -15.61146821752882, + -15.121722273237424, + -14.638506274869908, + -14.161820222426282, + -13.691664115906539, + -13.22803795531068, + -12.770941740638708, + -12.320375471890625, + -11.876339149066421, + -11.438832772166101, + -11.007856341189672, + -10.583409856137125, + -10.165493317008467, + -9.754106723803691, + -9.349250076522802, + -8.950923375165797, + -8.55912661973268, + -8.173859810223444, + -7.795122946638098, + -7.422916028976633, + -7.057239057239057, + -6.698092031425363, + -6.345474951535557, + -5.999387817569635, + -5.6598306295275975, + -5.326803387409447, + -5.00030609121518, + -4.680338740944801, + -4.366901336598305, + -4.059993878175696, + -3.7596163656769703, + -3.465768799102131, + -3.1784511784511786, + -2.897663503724109, + -2.6234057749209256, + -2.3556779920416275, + -2.094480155086216, + -1.8398122640546886, + -1.5916743189470457, + -1.3500663197632887, + -1.1149882665034168, + -0.8864401591674322, + -0.664421997755331, + -0.4489337822671151, + -0.23997551270278455, + -0.03754718906234117, + 0.1583511886542188, + 0.34771962044689336, + 0.5305581063156826, + 0.7068666462605849, + 0.8766452402816036, + 1.0398938883787368, + 1.1966125905519847, + 1.346801346801346, + 1.490460157126823, + 1.627589021528415, + 1.7581879400061218, + 1.882256912559943, + 1.9997959391898779, + 2.1108050198959285, + 2.215284154678094, + 2.3132333435363734, + 2.404652586470767, + 2.4895418834812766, + 2.5679012345679006, + 2.6397306397306393, + 2.705030098969491, + 2.7637996122844597, + 2.816039179675543, + 2.8617488011427397, + 2.9009284766860515, + 2.9335782063054783, + 2.9596979900010196, + 2.979287827772676, + 2.9923477196204455, + 2.9988776655443314, + 2.9988776655443306, + 2.9923477196204455, + 2.979287827772675, + 2.959697990001018, + 2.933578206305478, + 2.9009284766860515, + 2.861748801142739, + 2.8160391796755424, + 2.7637996122844584, + 2.705030098969491, + 2.6397306397306393, + 2.567901234567899, + 2.4895418834812757, + 2.404652586470766, + 2.313233343536371 + ], + [ + -21.077032955820833, + -20.515457606366695, + -19.960412202836444, + -19.41189674523008, + -18.869911233547597, + -18.334455667789, + -17.805530047954285, + -17.283134374043467, + -16.76726864605652, + -16.257932863993467, + -15.755127027854297, + -15.258851137639017, + -14.769105193347617, + -14.285889194980104, + -13.809203142536473, + -13.339047036016733, + -12.875420875420875, + -12.418324660748903, + -11.967758392000814, + -11.523722069176614, + -11.086215692276296, + -10.655239261299867, + -10.23079277624732, + -9.812876237118662, + -9.401489643913886, + -8.996632996632997, + -8.598306295275993, + -8.206509539842873, + -7.821242730333639, + -7.4425058667482915, + -7.070298949086828, + -6.70462197734925, + -6.345474951535557, + -5.99285787164575, + -5.646770737679828, + -5.307213549637791, + -4.974186307519641, + -4.647689011325375, + -4.327721661054994, + -4.014284256708499, + -3.707376798285888, + -3.4069992857871654, + -3.1131517192123255, + -2.8258340985613715, + -2.545046423834302, + -2.2707886950311202, + -2.0030609121518217, + -1.7418630751964084, + -1.4871951841648807, + -1.239057239057238, + -0.9974492398734831, + -0.7623711866136111, + -0.5338230792776244, + -0.3118049178655232, + -0.09631670237730927, + 0.1126415671870214, + 0.3150698908274667, + 0.5109682685440265, + 0.7003367003366994, + 0.8831751862054888, + 1.0594837261503929, + 1.2292623201714115, + 1.3925109682685433, + 1.549229670441791, + 1.6994184266911538, + 1.8430772370166308, + 1.980206101418223, + 2.1108050198959285, + 2.2348739924497494, + 2.3524130190796857, + 2.463422099785736, + 2.5679012345679006, + 2.6658504234261806, + 2.757269666360575, + 2.8421589633710846, + 2.9205183144577074, + 2.9923477196204464, + 3.0576471788593, + 3.1164166921742678, + 3.16865625956535, + 3.214365881032548, + 3.2535455565758595, + 3.2861952861952863, + 3.3123150698908277, + 3.331904907662483, + 3.3449647995102536, + 3.3514947454341395, + 3.351494745434138, + 3.3449647995102536, + 3.3319049076624827, + 3.3123150698908272, + 3.286195286195286, + 3.2535455565758604, + 3.2143658810325464, + 3.1686562595653505, + 3.116416692174268, + 3.057647178859299, + 2.9923477196204464, + 2.9205183144577065, + 2.8421589633710833 + ], + [ + -21.847566574839302, + -21.272931333537393, + -20.704826038159368, + -20.143250688705237, + -19.588205285174983, + -19.039689827568615, + -18.497704315886132, + -17.962248750127543, + -17.433323130292827, + -16.910927456382, + -16.395061728395063, + -15.885725946332007, + -15.382920110192838, + -14.886644219977555, + -14.396898275686155, + -13.913682277318642, + -13.436996224875015, + -12.96684011835527, + -12.50321395775941, + -12.046117743087441, + -11.595551474339352, + -11.151515151515152, + -10.714008774614836, + -10.283032343638403, + -9.858585858585858, + -9.4406693194572, + -9.029282726252424, + -8.624426078971535, + -8.22609937761453, + -7.834302622181411, + -7.449035812672176, + -7.07029894908683, + -6.698092031425365, + -6.332415059687786, + -5.973268033874095, + -5.6206509539842875, + -5.274563820018366, + -4.9350066319763295, + -4.601979389858179, + -4.275482093663912, + -3.9555147433935307, + -3.6420773390470376, + -3.335169880624427, + -3.034792368125702, + -2.7409448015508615, + -2.4536271808999093, + -2.1728395061728403, + -1.8985817773696565, + -1.630853994490358, + -1.3696561575349446, + -1.114988266503419, + -0.8668503213957764, + -0.625242322212019, + -0.39016426895214723, + -0.16161616161616266, + 0.06040199979593869, + 0.27589021528415464, + 0.4848484848484853, + 0.6872768084889287, + 0.8831751862054887, + 1.0725436179981633, + 1.2553821038669528, + 1.431690643811855, + 1.6014692378328734, + 1.764717885930007, + 1.921436588103255, + 2.0716253443526176, + 2.2152841546780935, + 2.3524130190796853, + 2.483011937557392, + 2.607080910111214, + 2.724619936741148, + 2.835629017447199, + 2.9401081522293646, + 3.038057341087644, + 3.1294765840220378, + 3.2143658810325473, + 3.292725232119172, + 3.3645546372819104, + 3.429854096520763, + 3.4886236098357317, + 3.540863177226814, + 3.586572798694011, + 3.625752474237323, + 3.658402203856749, + 3.6845219875522908, + 3.704111825323947, + 3.717171717171717, + 3.7237016630956017, + 3.7237016630956026, + 3.717171717171717, + 3.704111825323947, + 3.6845219875522917, + 3.6584022038567485, + 3.625752474237323, + 3.5865727986940117, + 3.540863177226813, + 3.4886236098357317, + 3.4298540965207622, + 3.364554637281909 + ], + [ + -22.624630139781658, + -22.03693500663198, + -21.455769819406182, + -20.881134578104277, + -20.313029282726255, + -19.751453933272117, + -19.196408529741866, + -18.647893072135503, + -18.10590756045302, + -17.570451994694423, + -17.041526374859707, + -16.519130700948885, + -16.003264972961947, + -15.49392919089889, + -14.991123354759718, + -14.494847464544435, + -14.005101520253039, + -13.521885521885523, + -13.045199469441895, + -12.575043362922154, + -12.111417202326294, + -11.654320987654323, + -11.203754718906236, + -10.759718396082034, + -10.322212019181716, + -9.891235588205287, + -9.466789103152742, + -9.04887256402408, + -8.637485970819306, + -8.232629323538415, + -7.834302622181411, + -7.442505866748293, + -7.057239057239058, + -6.67850219365371, + -6.306295275992246, + -5.940618304254668, + -5.581471278440977, + -5.2288541985511685, + -4.882767064585248, + -4.5432098765432105, + -4.210182634425058, + -3.8836853382307948, + -3.5637179879604135, + -3.2502805836139177, + -2.943373125191307, + -2.642995612692584, + -2.3491480461177443, + -2.06183042546679, + -1.7810427507397204, + -1.5067850219365364, + -1.23905723905724, + -0.977859402101827, + -0.7231915110702989, + -0.4750535659626564, + -0.23344556677890121, + 0.0016324864809708073, + 0.2301805938169575, + 0.45219875522905884, + 0.6676869707172728, + 0.8766452402816035, + 1.0790735639220488, + 1.2749719416386087, + 1.4643403734312819, + 1.647178859300071, + 1.823487399244975, + 1.9932659932659935, + 2.156514641363127, + 2.3132333435363734, + 2.463422099785736, + 2.607080910111214, + 2.7442097745128056, + 2.8748086929905106, + 2.9988776655443328, + 3.116416692174268, + 3.227425772880319, + 3.3319049076624827, + 3.429854096520764, + 3.5212733394551585, + 3.606162636465667, + 3.684521987552291, + 3.7563513927150303, + 3.821650851953883, + 3.880420365268851, + 3.9326599326599343, + 3.97836955412713, + 4.017549229670443, + 4.050198959289871, + 4.07631874298541, + 4.095908580757067, + 4.108968472604838, + 4.115498418528722, + 4.115498418528723, + 4.108968472604839, + 4.095908580757067, + 4.0763187429854115, + 4.050198959289871, + 4.0175492296704425, + 3.9783695541271316, + 3.9326599326599334, + 3.8804203652688516 + ], + [ + -23.40822365064789, + -22.80746862565044, + -22.213243546576876, + -21.625548413427204, + -21.044383226201408, + -20.4697479848995, + -19.901642689521474, + -19.34006734006734, + -18.785021936537085, + -18.23650647893072, + -17.694520967248238, + -17.15906540148964, + -16.630139781654933, + -16.107744107744107, + -15.591878379757166, + -15.082542597694111, + -14.579736761554944, + -14.083460871339659, + -13.593714927048257, + -13.110498928680745, + -12.633812876237116, + -12.163656769717374, + -11.700030609121516, + -11.242934394449545, + -10.792368125701458, + -10.348331802877256, + -9.910825425976938, + -9.47984899500051, + -9.055402509947964, + -8.637485970819304, + -8.226099377614528, + -7.82124273033364, + -7.422916028976635, + -7.0311192735435135, + -6.645852464034281, + -6.267115600448932, + -5.89490868278747, + -5.529231711049891, + -5.1700846852362, + -4.817467605346392, + -4.47138047138047, + -4.131823283338436, + -3.7987960412202835, + -3.4722987450260168, + -3.152331394755636, + -2.838893990409143, + -2.531986531986532, + -2.231609019487807, + -1.9377614529129672, + -1.6504438322620125, + -1.369656157534946, + -1.095398428731762, + -0.8276706458524635, + -0.5664728088970503, + -0.3118049178655247, + -0.06366697275788208, + 0.17794102642587517, + 0.4130190796857471, + 0.6415671870217315, + 0.8635853484338327, + 1.0790735639220488, + 1.2880318334863792, + 1.4904601571268226, + 1.6863585348433823, + 1.8757269666360572, + 2.0585654525048462, + 2.2348739924497503, + 2.4046525864707675, + 2.5679012345679, + 2.7246199367411483, + 2.874808692990511, + 3.0184675033159865, + 3.155596367717579, + 3.2861952861952854, + 3.4102642587491068, + 3.5278032853790413, + 3.638812366085092, + 3.7432915008672576, + 3.841240689725537, + 3.9326599326599316, + 4.017549229670442, + 4.095908580757064, + 4.1677379859198025, + 4.233037445158657, + 4.291806958473623, + 4.344046525864706, + 4.389756147331904, + 4.428935822875215, + 4.461585552494642, + 4.487705336190183, + 4.507295173961838, + 4.5203550658096106, + 4.526885011733496, + 4.526885011733495, + 4.52035506580961, + 4.50729517396184, + 4.487705336190182, + 4.4615855524946415, + 4.428935822875214, + 4.3897561473319024 + ], + [ + -24.198347107438018, + -23.584532190592796, + -22.97724721967146, + -22.376492194674015, + -21.782267115600447, + -21.194571982450768, + -20.613406795224975, + -20.03877155392307, + -19.470666258545045, + -18.909090909090907, + -18.354045505560656, + -17.80553004795429, + -17.26354453627181, + -16.728088970513213, + -16.199163350678504, + -15.676767676767676, + -15.160901948780737, + -14.65156616671768, + -14.14876033057851, + -13.652484440363228, + -13.162738496071828, + -12.679522497704315, + -12.202836445260687, + -11.732680338740945, + -11.269054178145087, + -10.811957963473116, + -10.361391694725029, + -9.917355371900825, + -9.47984899500051, + -9.04887256402408, + -8.624426078971533, + -8.206509539842873, + -7.795122946638097, + -7.390266299357208, + -6.9919395980002035, + -6.600142842567084, + -6.214876033057851, + -5.836139169472502, + -5.463932251811039, + -5.098255280073461, + -4.739108254259769, + -4.386491174369963, + -4.040404040404041, + -3.700846852362004, + -3.367819610243852, + -3.041322314049588, + -2.7213549637792065, + -2.407917559432711, + -2.1010101010101003, + -1.800632588511375, + -1.5067850219365377, + -1.2194674012855833, + -0.938679726558514, + -0.6644219977553301, + -0.39669421487603385, + -0.13549637792062053, + 0.11917151311090735, + 0.36730945821855, + 0.6089174574023049, + 0.8439955106621769, + 1.0725436179981636, + 1.2945617794102648, + 1.5100499948984787, + 1.719008264462809, + 1.921436588103255, + 2.1173349658198144, + 2.3067033976124893, + 2.489541883481277, + 2.6658504234261806, + 2.835629017447199, + 2.9988776655443323, + 3.155596367717579, + 3.305785123966942, + 3.4494439342924186, + 3.5865727986940112, + 3.7171717171717162, + 3.8412406897255384, + 3.9587797163554743, + 4.069788797061524, + 4.17426793184369, + 4.27221712070197, + 4.363636363636363, + 4.448525660646872, + 4.526885011733497, + 4.598714416896235, + 4.664013876135089, + 4.722783389450056, + 4.775022956841139, + 4.820732578308336, + 4.859912253851648, + 4.892561983471074, + 4.918681767166616, + 4.938271604938272, + 4.951331496786041, + 4.957861442709928, + 4.957861442709929, + 4.951331496786041, + 4.938271604938271, + 4.918681767166615, + 4.892561983471074 + ], + [ + -24.995000510152025, + -24.368125701459032, + -23.747780838689927, + -23.133965921844712, + -22.526680950923378, + -21.925925925925924, + -21.331700846852364, + -20.744005713702684, + -20.16284052647689, + -19.588205285174983, + -19.02009998979696, + -18.458524640342823, + -17.903479236812572, + -17.3549637792062, + -16.81297826752372, + -16.27752270176513, + -15.748597081930416, + -15.226201408019591, + -14.71033568003265, + -14.200999897969595, + -13.698194061830424, + -13.20191817161514, + -12.712172227323741, + -12.228956228956228, + -11.7522701765126, + -11.282114069992858, + -10.818487909397, + -10.361391694725029, + -9.910825425976942, + -9.466789103152742, + -9.029282726252424, + -8.598306295275993, + -8.173859810223448, + -7.755943271094786, + -7.3445566778900115, + -6.939700030609122, + -6.541373329252117, + -6.149576573818998, + -5.764309764309766, + -5.385572900724416, + -5.013365983062952, + -4.647689011325377, + -4.288541985511683, + -3.9359249056218752, + -3.5898377716559526, + -3.250280583613918, + -2.9172533414957664, + -2.5907560453015, + -2.270788695031119, + -1.9573512906846229, + -1.650443832262015, + -1.3500663197632898, + -1.0562187531884497, + -0.7689011325374953, + -0.4881134578104286, + -0.2138557290072446, + 0.05387205387205396, + 0.31506989082746734, + 0.5697377818589928, + 0.8178757269666355, + 1.0594837261503929, + 1.2945617794102646, + 1.5231098867462494, + 1.7451280481583504, + 1.9606162636465667, + 2.169574533210897, + 2.372002856851343, + 2.5679012345679006, + 2.7572696663605747, + 2.9401081522293646, + 3.116416692174268, + 3.2861952861952854, + 3.449443934292419, + 3.6061626364656667, + 3.75635139271503, + 3.900010203040505, + 4.037139067442098, + 4.167737985919804, + 4.291806958473625, + 4.409345985103561, + 4.520355065809612, + 4.624834200591776, + 4.722783389450056, + 4.814202632384451, + 4.8990919293949595, + 4.977451280481584, + 5.049280685644323, + 5.114580144883175, + 5.173349658198143, + 5.225589225589226, + 5.271298847056422, + 5.310478522599736, + 5.343128252219163, + 5.369248035914703, + 5.388837873686359, + 5.40189776553413, + 5.408427711458014, + 5.408427711458015, + 5.401897765534129, + 5.388837873686358 + ], + [ + -25.79818385878992, + -25.15824915824916, + -24.52484440363228, + -23.897969594939294, + -23.27762473217019, + -22.663809815324967, + -22.056524844403633, + -21.45576981940619, + -20.861544740332622, + -20.273849607182942, + -19.692684419957146, + -19.11804917865524, + -18.549943883277223, + -17.98836853382308, + -17.433323130292827, + -16.884807672686463, + -16.342822161003983, + -15.807366595245384, + -15.278440975410673, + -14.75604530149985, + -14.240179573512908, + -13.730843791449855, + -13.228037955310683, + -12.7317620650954, + -12.242016120804, + -11.758800122436488, + -11.282114069992858, + -10.811957963473116, + -10.348331802877258, + -9.891235588205287, + -9.4406693194572, + -8.996632996633, + -8.559126619732682, + -8.12815018875625, + -7.703703703703706, + -7.285787164575044, + -6.87440057137027, + -6.469543924089379, + -6.0712172227323755, + -5.679420467299256, + -5.294153657790021, + -4.915416794204676, + -4.543209876543211, + -4.177532904805632, + -3.8183858789919394, + -3.465768799102135, + -3.119681665136212, + -2.7801244770941747, + -2.4470972349760225, + -2.1205999387817562, + -1.800632588511378, + -1.487195184164882, + -1.1802877257422715, + -0.8799102132435462, + -0.5860626466687087, + -0.2987450260177541, + -0.017957351290684764, + 0.2563003775124993, + 0.5240281603917953, + 0.7852259973472087, + 1.0398938883787368, + 1.2880318334863794, + 1.5296398326701344, + 1.7647178859300061, + 1.9932659932659933, + 2.2152841546780944, + 2.43077237016631, + 2.6397306397306393, + 2.842158963371084, + 3.0380573410876446, + 3.227425772880319, + 3.4102642587491063, + 3.5865727986940112, + 3.75635139271503, + 3.9196000408121625, + 4.076318742985409, + 4.226507499234772, + 4.37016630956025, + 4.507295173961841, + 4.637894092439547, + 4.7619630649933695, + 4.879502091623304, + 4.990511172329354, + 5.09499030711152, + 5.192939495969799, + 5.284358738904195, + 5.369248035914703, + 5.447607387001326, + 5.519436792164066, + 5.584736251402918, + 5.643505764717886, + 5.695745332108969, + 5.7414549535761665, + 5.780634629119478, + 5.813284358738905, + 5.8394041424344465, + 5.858993980206102, + 5.872053872053873, + 5.878583817977757, + 5.878583817977757 + ], + [ + -26.607897153351693, + -25.95490256096316, + -25.308437914498516, + -24.668503213957756, + -24.03509845934088, + -23.40822365064789, + -22.787878787878782, + -22.174063871033567, + -21.566778900112233, + -20.96602387511478, + -20.37179879604122, + -19.78410366289154, + -19.202938475665746, + -18.628303234363838, + -18.060197938985816, + -17.498622589531678, + -16.943577186001427, + -16.39506172839506, + -15.853076216712576, + -15.317620650953984, + -14.78869503111927, + -14.266299357208446, + -13.750433629221504, + -13.24109784715845, + -12.738292011019281, + -12.242016120804, + -11.752270176512598, + -11.269054178145087, + -10.792368125701458, + -10.322212019181714, + -9.858585858585858, + -9.401489643913886, + -8.950923375165798, + -8.506887052341595, + -8.06938067544128, + -7.638404244464848, + -7.213957759412304, + -6.796041220283643, + -6.384654627078869, + -5.979797979797978, + -5.581471278440973, + -5.189674523007858, + -4.804407713498622, + -4.425670849913272, + -4.05346393225181, + -3.687786960514234, + -3.328639934700541, + -2.976022854810733, + -2.62993572084481, + -2.290378532802773, + -1.9573512906846247, + -1.630853994490358, + -1.3108866442199767, + -0.9974492398734811, + -0.6905417814508732, + -0.39016426895214795, + -0.09631670237730794, + 0.19100091827364662, + 0.4717885930007132, + 0.7460463218038971, + 1.0137741046831958, + 1.274971941638609, + 1.5296398326701346, + 1.7777777777777768, + 2.0193857769615344, + 2.2544638302214057, + 2.483011937557393, + 2.705030098969492, + 2.9205183144577074, + 3.129476584022038, + 3.331904907662483, + 3.5278032853790413, + 3.7171717171717162, + 3.9000102030405057, + 4.076318742985409, + 4.246097337006425, + 4.40934598510356, + 4.566064687276808, + 4.71625344352617, + 4.859912253851646, + 4.9970411182532395, + 5.127640036730944, + 5.251709009284765, + 5.369248035914702, + 5.480257116620751, + 5.584736251402917, + 5.682685440261197, + 5.774104683195589, + 5.858993980206099, + 5.937353331292724, + 6.009182736455461, + 6.074482195694316, + 6.133251709009283, + 6.185491276400365, + 6.231200897867563, + 6.270380573410875, + 6.3030303030303, + 6.329150086725842, + 6.348739924497497, + 6.361799816345268 + ], + [ + -27.424140393837362, + -26.758085909601057, + -26.09856137128864, + -25.445566778900115, + -24.799102132435465, + -24.1591674318947, + -23.525762677277825, + -22.89888786858484, + -22.278543005815735, + -21.664728088970513, + -21.057443118049175, + -20.456688093051728, + -19.862463013978164, + -19.274767880828485, + -18.693602693602692, + -18.118967452300787, + -17.550862156922765, + -16.989286807468623, + -16.434241403938373, + -15.885725946332006, + -15.343740434649522, + -14.80828486889093, + -14.279359249056217, + -13.756963575145392, + -13.241097847158452, + -12.731762065095399, + -12.228956228956228, + -11.732680338740945, + -11.242934394449545, + -10.759718396082032, + -10.283032343638403, + -9.812876237118662, + -9.349250076522804, + -8.89215386185083, + -8.441587593102746, + -7.9975512702785405, + -7.560044893378227, + -7.129068462401795, + -6.70462197734925, + -6.286705438220588, + -5.875318845015813, + -5.470462197734926, + -5.07213549637792, + -4.680338740944801, + -4.295071931435567, + -3.9163350678502207, + -3.544128150188757, + -3.1784511784511786, + -2.819304152637485, + -2.4666870727476775, + -2.1205999387817576, + -1.7810427507397204, + -1.4480155086215687, + -1.1215182124273022, + -0.8015508621569237, + -0.48811345781042803, + -0.18120599938781734, + 0.1191715131109079, + 0.41301907968574497, + 0.7003367003366996, + 0.981124375063769, + 1.255382103866953, + 1.523109886746249, + 1.784307723701662, + 2.0389756147331903, + 2.2871135598408325, + 2.52872155902459, + 2.7637996122844597, + 2.992347719620446, + 3.2143658810325473, + 3.4298540965207636, + 3.6388123660850917, + 3.841240689725537, + 4.037139067442097, + 4.226507499234772, + 4.409345985103559, + 4.585654525048463, + 4.755433119069482, + 4.918681767166616, + 5.075400469339862, + 5.225589225589227, + 5.369248035914702, + 5.506376900316293, + 5.636975818794, + 5.76104479134782, + 5.8785838179777565, + 5.989592898683807, + 6.094072033465971, + 6.192021222324252, + 6.2834404652586455, + 6.368329762269155, + 6.446689113355778, + 6.518518518518517, + 6.58381797775737, + 6.642587491072338, + 6.694827058463421, + 6.740536679930617, + 6.779716355473929, + 6.812366085093358, + 6.838485868788896 + ], + [ + -28.246913580246915, + -27.56779920416284, + -26.89521477400265, + -26.229160289766355, + -25.569635751453937, + -24.9166411590654, + -24.270176512600752, + -23.630241812059996, + -22.996837057443116, + -22.369962248750127, + -21.749617385981022, + -21.1358024691358, + -20.52851749821447, + -19.92776247321702, + -19.333537394143452, + -18.745842260993776, + -18.164677073767983, + -17.590041832466078, + -17.021936537088052, + -16.460361187633914, + -15.90531578410366, + -15.356800326497297, + -14.814814814814813, + -14.279359249056217, + -13.750433629221508, + -13.228037955310683, + -12.712172227323743, + -12.202836445260688, + -11.700030609121518, + -11.203754718906236, + -10.714008774614834, + -10.230792776247323, + -9.754106723803694, + -9.28395061728395, + -8.820324456688093, + -8.36322824201612, + -7.912661973268034, + -7.4686256504438315, + -7.031119273543517, + -6.6001428425670845, + -6.175696357514537, + -5.757779818385881, + -5.346393225181105, + -4.941536577900214, + -4.543209876543209, + -4.151413121110092, + -3.766146311600858, + -3.387409448015508, + -3.015202530354045, + -2.649525558616466, + -2.2903785328027766, + -1.9377614529129683, + -1.5916743189470457, + -1.2521171309050083, + -0.9190898887868596, + -0.592592592592593, + -0.27262524232221175, + 0.04081216202428417, + 0.3477196204468921, + 0.6480971329456171, + 0.9419446995204571, + 1.229262320171412, + 1.5100499948984785, + 1.784307723701662, + 2.0520355065809612, + 2.313233343536374, + 2.567901234567902, + 2.816039179675543, + 3.0576471788592996, + 3.292725232119172, + 3.521273339455158, + 3.743291500867257, + 3.9587797163554734, + 4.167737985919804, + 4.37016630956025, + 4.566064687276807, + 4.755433119069482, + 4.938271604938272, + 5.114580144883175, + 5.284358738904193, + 5.4476073870013275, + 5.604326089174574, + 5.754514845423936, + 5.898173655749415, + 6.035302520151005, + 6.165901438628712, + 6.289970411182533, + 6.407509437812466, + 6.518518518518519, + 6.622997653300684, + 6.720946842158962, + 6.812366085093358, + 6.897255382103867, + 6.975614733190491, + 7.047444138353229, + 7.1127435975920825, + 7.17151311090705, + 7.2237526782981325, + 7.269462299765329, + 7.308641975308641 + ], + [ + -29.076216712580347, + -28.384042444648504, + -27.698398122640548, + -27.019283746556475, + -26.34669931639629, + -25.680644832159985, + -25.021120293847567, + -24.368125701459036, + -23.72166105499439, + -23.08172635445363, + -22.448321599836753, + -21.821446791143764, + -21.20110192837466, + -20.58728701152944, + -19.9800020406081, + -19.37924701561065, + -18.785021936537092, + -18.197326803387412, + -17.616161616161616, + -17.04152637485971, + -16.473421079481685, + -15.91184573002755, + -15.356800326497297, + -14.808284868890931, + -14.266299357208448, + -13.730843791449853, + -13.201918171615143, + -12.679522497704319, + -12.163656769717377, + -11.654320987654321, + -11.151515151515152, + -10.655239261299869, + -10.16549331700847, + -9.682277318640955, + -9.205591266197327, + -8.735435159677584, + -8.271808999081728, + -7.814712784409754, + -7.36414651566167, + -6.920110192837465, + -6.482603815937148, + -6.051627384960721, + -5.627180899908174, + -5.209264360779512, + -4.797877767574737, + -4.3930211202938505, + -3.9946944189368443, + -3.6028976635037244, + -3.2176308539944904, + -2.8388939904091406, + -2.46668707274768, + -2.1010101010101017, + -1.7418630751964086, + -1.3892459953066008, + -1.043158861340681, + -0.7036016732986438, + -0.3705744311804918, + -0.04407713498622512, + 0.27589021528415303, + 0.5893276196306492, + 0.8962350780532597, + 1.196612590551985, + 1.4904601571268223, + 1.7777777777777768, + 2.0585654525048462, + 2.3328231813080302, + 2.600550964187329, + 2.8617488011427397, + 3.1164166921742673, + 3.3645546372819104, + 3.606162636465667, + 3.841240689725537, + 4.069788797061524, + 4.291806958473625, + 4.507295173961841, + 4.716253443526169, + 4.918681767166616, + 5.114580144883175, + 5.303948576675849, + 5.4867870625446375, + 5.663095602489543, + 5.83287419651056, + 5.996122844607692, + 6.152841546780942, + 6.303030303030303, + 6.446689113355782, + 6.583817977757373, + 6.714416896235077, + 6.838485868788899, + 6.956024895418835, + 7.0670339761248835, + 7.171513110907051, + 7.269462299765331, + 7.360881542699724, + 7.445770839710234, + 7.524130190796858, + 7.595959595959596, + 7.661259055198449, + 7.720028568513419, + 7.772268135904499 + ], + [ + -29.912049790837667, + -29.20681563105805, + -28.50811141720232, + -27.81593714927048, + -27.130292827262522, + -26.451178451178446, + -25.778594021018257, + -25.11253953678196, + -24.45301499846954, + -23.800020406081007, + -23.15355575961636, + -22.513621059075597, + -21.880216304458727, + -21.25334149576574, + -20.63299663299663, + -20.019181716151408, + -19.411896745230077, + -18.811141720232627, + -18.216916641159063, + -17.629221508009387, + -17.04805632078359, + -16.47342107948168, + -15.90531578410366, + -15.343740434649522, + -14.78869503111927, + -14.240179573512906, + -13.69819406183042, + -13.162738496071828, + -12.633812876237116, + -12.11141720232629, + -11.595551474339352, + -11.086215692276298, + -10.583409856137127, + -10.087133965921842, + -9.597388021630444, + -9.114172023262931, + -8.637485970819302, + -8.167329864299559, + -7.703703703703702, + -7.24660748903173, + -6.796041220283641, + -6.352004897459444, + -5.914498520559126, + -5.483522089582694, + -5.059075604530147, + -4.6411590654014905, + -4.229772472196714, + -3.824915824915824, + -3.426589123558819, + -3.034792368125699, + -2.649525558616468, + -2.2707886950311185, + -1.898581777369655, + -1.5329048056320769, + -1.1737577798183865, + -0.8211406999285789, + -0.47505356596265613, + -0.13549637792061897, + 0.19753086419752985, + 0.5240281603917963, + 0.8439955106621777, + 1.1574329150086737, + 1.4643403734312814, + 1.764717885930006, + 2.0585654525048462, + 2.3458830731558007, + 2.62667074788287, + 2.900928476686051, + 3.1686562595653496, + 3.429854096520763, + 3.6845219875522908, + 3.9326599326599307, + 4.174267931843689, + 4.40934598510356, + 4.637894092439547, + 4.859912253851645, + 5.075400469339862, + 5.284358738904192, + 5.4867870625446375, + 5.682685440261196, + 5.872053872053872, + 6.054892357922659, + 6.231200897867563, + 6.400979491888583, + 6.564228139985714, + 6.720946842158963, + 6.871135598408324, + 7.014794408733799, + 7.1519232731353926, + 7.282522191613099, + 7.406591164166918, + 7.524130190796856, + 7.635139271502906, + 7.739618406285071, + 7.8375675951433506, + 7.928986838077745, + 8.013876135088253, + 8.092235486174877, + 8.164064891337617, + 8.229364350576468 + ], + [ + -30.75441281501888, + -30.036118763391492, + -29.32435465768799, + -28.619120497908384, + -27.920416284052656, + -27.22824201612081, + -26.54259769411285, + -25.863483318028784, + -25.19089888786859, + -24.524844403632287, + -23.86531986531987, + -23.212325272931338, + -22.565860626466694, + -21.92592592592593, + -21.292521171309055, + -20.665646362616066, + -20.04530149984696, + -19.43148658300174, + -18.8242016120804, + -18.223446587082954, + -17.629221508009387, + -17.041526374859714, + -16.460361187633918, + -15.885725946332009, + -15.317620650953987, + -14.756045301499853, + -14.200999897969597, + -13.652484440363231, + -13.110498928680748, + -12.575043362922155, + -12.046117743087443, + -11.523722069176618, + -11.007856341189678, + -10.498520559126622, + -9.995714722987453, + -9.499438832772167, + -9.009692888480771, + -8.526476890113257, + -8.049790837669628, + -7.579634731149885, + -7.116008570554026, + -6.658912355882056, + -6.208346087133968, + -5.7643097643097665, + -5.3268033874094485, + -4.89582695643302, + -4.471380471380474, + -4.053463932251813, + -3.6420773390470362, + -3.237220691766146, + -2.8388939904091446, + -2.4470972349760247, + -2.06183042546679, + -1.6830935618814409, + -1.31088664421998, + -0.9452096724824013, + -0.5860626466687079, + -0.23344556677889994, + 0.11264156718701945, + 0.45219875522905684, + 0.785225997347209, + 1.1117232935414756, + 1.4316906438118537, + 1.7451280481583495, + 2.052035506580961, + 2.3524130190796857, + 2.646260585654526, + 2.9335782063054783, + 3.2143658810325473, + 3.4886236098357317, + 3.75635139271503, + 4.017549229670441, + 4.272217120701969, + 4.520355065809611, + 4.7619630649933695, + 4.997041118253239, + 5.225589225589227, + 5.4476073870013275, + 5.663095602489543, + 5.872053872053873, + 6.074482195694319, + 6.270380573410878, + 6.459749005203551, + 6.642587491072343, + 6.8188960310172435, + 6.988674625038264, + 7.151923273135397, + 7.3086419753086425, + 7.458830731558006, + 7.602489541883483, + 7.739618406285073, + 7.870217324762782, + 7.994286297316603, + 8.111825323946539, + 8.22283440465259, + 8.327313539434753, + 8.425262728293033, + 8.516681971227428, + 8.601571268237937, + 8.67993061932456 + ], + [ + -31.603305785123965, + -30.87195184164881, + -30.14712784409754, + -29.428833792470154, + -28.717069686766656, + -28.011835526987042, + -27.31313131313131, + -26.62095704519947, + -25.935312723191515, + -25.256198347107436, + -24.583613916947247, + -23.917559432710945, + -23.25803489439853, + -22.605040302009996, + -21.958575655545353, + -21.318640955004593, + -20.685236200387717, + -20.058361391694724, + -19.438016528925615, + -18.8242016120804, + -18.216916641159067, + -17.616161616161616, + -17.021936537088052, + -16.434241403938373, + -15.85307621671258, + -15.278440975410673, + -14.71033568003265, + -14.148760330578511, + -13.593714927048259, + -13.045199469441894, + -12.50321395775941, + -11.967758392000817, + -11.438832772166105, + -10.91643709825528, + -10.400571370268338, + -9.891235588205284, + -9.388429752066116, + -8.89215386185083, + -8.402407917559433, + -7.919191919191919, + -7.442505866748289, + -6.97234976022855, + -6.508723599632691, + -6.051627384960718, + -5.601061116212629, + -5.157024793388431, + -4.719518416488114, + -4.2885419855116815, + -3.8640955004591357, + -3.4461789613304745, + -3.0347923681257023, + -2.629935720844812, + -2.2316090194878067, + -1.8398122640546868, + -1.4545454545454557, + -1.0758085909601065, + -0.7036016732986424, + -0.3379247015610639, + 0.021222324252625935, + 0.3738394041424339, + 0.7199265381083565, + 1.059483726150394, + 1.3925109682685428, + 1.7190082644628089, + 2.0389756147331908, + 2.3524130190796866, + 2.659320477502297, + 2.959697990001019, + 3.253545556575859, + 3.540863177226814, + 3.8216508519538834, + 4.095908580757064, + 4.363636363636363, + 4.624834200591776, + 4.879502091623304, + 5.127640036730944, + 5.369248035914702, + 5.604326089174574, + 5.832874196510561, + 6.05489235792266, + 6.270380573410878, + 6.479338842975206, + 6.68176716661565, + 6.877665544332212, + 7.067033976124884, + 7.249872461993675, + 7.426181001938579, + 7.595959595959594, + 7.75920824405673, + 7.915926946229976, + 8.066115702479337, + 8.209774512804817, + 8.346903377206408, + 8.477502295684115, + 8.601571268237935, + 8.719110294867871, + 8.830119375573922, + 8.934598510356086, + 9.032547699214366, + 9.123966942148758 + ], + [ + -32.458728701152936, + -31.714314865830005, + -30.97643097643097, + -30.245077032955813, + -29.520253035404544, + -28.80195898377716, + -28.09019487807366, + -27.384960718294046, + -26.68625650443832, + -25.994082236506472, + -25.308437914498516, + -24.62932353841444, + -23.956739108254254, + -23.290684624017953, + -22.631160085705535, + -21.978165493317004, + -21.331700846852357, + -20.691766146311593, + -20.058361391694717, + -19.43148658300173, + -18.811141720232623, + -18.197326803387405, + -17.59004183246607, + -16.98928680746862, + -16.395061728395056, + -15.80736659524538, + -15.226201408019584, + -14.651566166717679, + -14.083460871339655, + -13.521885521885517, + -12.966840118355268, + -12.418324660748901, + -11.87633914906642, + -11.340883583307821, + -10.811957963473112, + -10.289562289562285, + -9.773696561575345, + -9.264360779512291, + -8.761554943373122, + -8.265279053157837, + -7.775533108866439, + -7.292317110498928, + -6.815631058055299, + -6.3454749515355555, + -5.881848790939697, + -5.424752576267727, + -4.9741863075196395, + -4.530149984695437, + -4.09264360779512, + -3.661667176818689, + -3.2372206917661455, + -2.8193041526374847, + -2.4079175594327085, + -2.0030609121518186, + -1.604734210794817, + -1.212937455361697, + -0.8276706458524626, + -0.44893378226711356, + -0.07672686460565337, + 0.28895010713192526, + 0.6480971329456187, + 1.0007142128354263, + 1.3468013468013456, + 1.6863585348433825, + 2.019385776961535, + 2.3458830731558007, + 2.6658504234261824, + 2.979287827772675, + 3.2861952861952854, + 3.586572798694011, + 3.8804203652688507, + 4.1677379859198025, + 4.4485256606468715, + 4.722783389450055, + 4.990511172329354, + 5.251709009284764, + 5.506376900316293, + 5.754514845423936, + 5.996122844607692, + 6.231200897867563, + 6.459749005203551, + 6.68176716661565, + 6.8972553821038645, + 7.106213651668197, + 7.308641975308639, + 7.504540353025201, + 7.693908784817875, + 7.876747270686661, + 8.053055810631566, + 8.222834404652584, + 8.386083052749715, + 8.542801754922966, + 8.692990511172328, + 8.836649321497804, + 8.973778185899395, + 9.104377104377102, + 9.228446076930922, + 9.345985103560857, + 9.45699418426691, + 9.561473319049071 + ], + [ + -33.32068156310581, + -32.56320783593511, + -31.812264054688292, + -31.067850219365376, + -30.329966329966332, + -29.598612386491176, + -28.873788388939907, + -28.155494337312525, + -27.44373023160902, + -26.73849607182941, + -26.039791857973675, + -25.347617590041835, + -24.661973268033876, + -23.982858891949803, + -23.31027446178961, + -22.644219977553313, + -21.984695439240898, + -21.331700846852364, + -20.685236200387717, + -20.045301499846957, + -19.41189674523008, + -18.785021936537092, + -18.164677073767983, + -17.550862156922765, + -16.943577186001427, + -16.34282216100398, + -15.748597081930416, + -15.160901948780738, + -14.579736761554944, + -14.005101520253039, + -13.436996224875015, + -12.875420875420879, + -12.320375471890625, + -11.771860014284258, + -11.229874502601776, + -10.694418936843181, + -10.16549331700847, + -9.643097643097644, + -9.127231915110706, + -8.617896133047648, + -8.115090296908479, + -7.618814406693198, + -7.129068462401797, + -6.6458524640342835, + -6.169166411590654, + -5.699010305070914, + -5.235384144475056, + -4.778287929803083, + -4.327721661054994, + -3.883685338230792, + -3.4461789613304785, + -3.0152025303540464, + -2.5907560453014997, + -2.1728395061728385, + -1.7614529129680665, + -1.3565962656871762, + -0.9582695643301706, + -0.5664728088970505, + -0.18120599938781967, + 0.19753086419752952, + 0.5697377818589938, + 0.9354147535965726, + 1.2945617794102624, + 1.6471788593000698, + 1.993265993265993, + 2.3328231813080302, + 2.665850423426182, + 2.9923477196204455, + 3.3123150698908264, + 3.6257524742373226, + 3.9326599326599334, + 4.233037445158656, + 4.526885011733496, + 4.8142026323844505, + 5.09499030711152, + 5.369248035914701, + 5.636975818794001, + 5.898173655749414, + 6.152841546780941, + 6.400979491888583, + 6.642587491072343, + 6.877665544332212, + 7.106213651668196, + 7.3282318130803, + 7.543720028568513, + 7.752678298132846, + 7.9551066217732895, + 8.151004999489846, + 8.340373431282524, + 8.523211917151313, + 8.699520457096213, + 8.869299051117235, + 9.032547699214367, + 9.189266401387615, + 9.339455157636978, + 9.483113967962455, + 9.620242832364045, + 9.75084175084175, + 9.874910723395574, + 9.992449750025509 + ], + [ + -34.18916437098255, + -33.41863075196408, + -32.654627078869495, + -31.897153351698805, + -31.146209570451994, + -30.401795735129063, + -29.66391184573002, + -28.93255790225487, + -28.207733904703602, + -27.489439853076213, + -26.77767574737271, + -26.072441587593097, + -25.373737373737374, + -24.68156310580553, + -23.995918783797567, + -23.316804407713498, + -22.644219977553313, + -21.978165493317007, + -21.31864095500459, + -20.66564636261606, + -20.019181716151408, + -19.379247015610648, + -18.745842260993772, + -18.118967452300783, + -17.498622589531678, + -16.88480767268646, + -16.277522701765122, + -15.676767676767676, + -15.082542597694111, + -14.494847464544435, + -13.913682277318639, + -13.339047036016732, + -12.77094174063871, + -12.20936639118457, + -11.65432098765432, + -11.10580553004795, + -10.563820018365472, + -10.028364452606874, + -9.499438832772164, + -8.977043158861338, + -8.461177430874397, + -7.951841648811347, + -7.449035812672176, + -6.952759922456891, + -6.463013978165491, + -5.979797979797981, + -5.503111927354352, + -5.032955820834608, + -4.56932966023875, + -4.112233445566776, + -3.661667176818692, + -3.21763085399449, + -2.780124477094173, + -2.3491480461177408, + -1.924701561065198, + -1.506785021936537, + -1.095398428731761, + -0.6905417814508708, + -0.29221508009386943, + 0.09958167533925044, + 0.4848484848484851, + 0.8635853484338342, + 1.2357922660952945, + 1.601469237832873, + 1.9606162636465667, + 2.313233343536374, + 2.659320477502297, + 2.998877665544331, + 3.3319049076624827, + 3.658402203856749, + 3.9783695541271302, + 4.291806958473623, + 4.598714416896234, + 4.8990919293949595, + 5.192939495969799, + 5.48025711662075, + 5.761044791347821, + 6.035302520151005, + 6.303030303030303, + 6.5642281399857145, + 6.818896031017244, + 7.067033976124884, + 7.308641975308641, + 7.543720028568514, + 7.772268135904498, + 7.9942862973166005, + 8.209774512804815, + 8.418732782369144, + 8.62116110600959, + 8.817059483726148, + 9.006427915518822, + 9.189266401387611, + 9.365574941332516, + 9.535353535353533, + 9.698602183450665, + 9.855320885623913, + 10.005509641873276, + 10.149168452198753, + 10.286297316600347, + 10.416896235078049 + ], + [ + -35.064177124783185, + -34.280583613916946, + -33.5035200489746, + -32.732986429956135, + -31.96898275686155, + -31.211509029690852, + -30.46056524844404, + -29.716151413121118, + -28.978267523722074, + -28.24691358024692, + -27.52208958269565, + -26.80379553106826, + -26.092031425364766, + -25.38679726558515, + -24.688093051729417, + -23.995918783797578, + -23.310274461789618, + -22.631160085705545, + -21.958575655545356, + -21.292521171309055, + -20.632996632996637, + -19.980002040608106, + -19.333537394143455, + -18.6936026936027, + -18.060197938985823, + -17.433323130292834, + -16.812978267523725, + -16.199163350678507, + -15.591878379757173, + -14.991123354759722, + -14.396898275686159, + -13.809203142536479, + -13.228037955310686, + -12.653402714008777, + -12.085297418630756, + -11.523722069176618, + -10.968676665646365, + -10.42016120804, + -9.878175696357518, + -9.34272013059892, + -8.81379451076421, + -8.291398836853388, + -7.775533108866446, + -7.26619732680339, + -6.763391490664219, + -6.267115600448938, + -5.777369656157538, + -5.294153657790023, + -4.817467605346394, + -4.347311498826651, + -3.8836853382307956, + -3.4265891235588226, + -2.9760228548107346, + -2.531986531986532, + -2.094480155086219, + -1.6635037241097872, + -1.2390572390572403, + -0.8211406999285786, + -0.40975410672380663, + -0.004897459442916086, + 0.39342924191408946, + 0.7852259973472095, + 1.1704928068564406, + 1.5492296704417894, + 1.921436588103254, + 2.2871135598408325, + 2.646260585654526, + 2.9988776655443306, + 3.3449647995102527, + 3.6845219875522908, + 4.0175492296704425, + 4.344046525864706, + 4.664013876135089, + 4.977451280481583, + 5.284358738904195, + 5.584736251402917, + 5.878583817977757, + 6.165901438628712, + 6.446689113355781, + 6.720946842158963, + 6.988674625038264, + 7.249872461993674, + 7.5045403530252015, + 7.752678298132846, + 7.9942862973166005, + 8.229364350576475, + 8.45791245791246, + 8.679930619324558, + 8.895418834812777, + 9.104377104377106, + 9.306805428017547, + 9.50270380573411, + 9.692072237526785, + 9.874910723395574, + 10.051219263340478, + 10.220997857361496, + 10.384246505458629, + 10.540965207631876, + 10.69115396388124, + 10.834812774206716 + ], + [ + -35.945719824507705, + -35.14906642179369, + -34.35894296500357, + -33.57534945413733, + -32.79828588919498, + -32.02775227017651, + -31.26374859708193, + -30.506274869911234, + -29.75533108866442, + -29.010917253341496, + -28.273033363942456, + -27.541679420467297, + -26.81685542291603, + -26.098561371288646, + -25.386797265585145, + -24.68156310580553, + -23.982858891949803, + -23.290684624017956, + -22.605040302009996, + -21.925925925925927, + -21.25334149576574, + -20.587287011529437, + -19.92776247321702, + -19.274767880828488, + -18.62830323436384, + -17.98836853382308, + -17.3549637792062, + -16.728088970513213, + -16.107744107744107, + -15.49392919089889, + -14.886644219977555, + -14.285889194980104, + -13.69166411590654, + -13.10396898275686, + -12.522803795531068, + -11.94816855422916, + -11.38006325885114, + -10.818487909397, + -10.263442505866749, + -9.714927048260382, + -9.172941536577898, + -8.637485970819307, + -8.108560350984595, + -7.586164677073768, + -7.070298949086826, + -6.560963167023775, + -6.058157330884605, + -5.561881440669319, + -5.07213549637792, + -4.588919498010406, + -4.112233445566781, + -3.6420773390470367, + -3.178451178451178, + -2.7213549637792047, + -2.270788695031121, + -1.826752372206919, + -1.3892459953066014, + -0.9582695643301697, + -0.5338230792776271, + -0.11590654014896562, + 0.2954800530558104, + 0.7003367003367007, + 1.0986634016937025, + 1.490460157126822, + 1.875726966636057, + 2.2544638302214057, + 2.62667074788287, + 2.992347719620445, + 3.3514947454341386, + 3.7041118253239462, + 4.050198959289869, + 4.3897561473319024, + 4.722783389450056, + 5.049280685644321, + 5.369248035914703, + 5.682685440261196, + 5.9895928986838065, + 6.289970411182532, + 6.583817977757372, + 6.871135598408324, + 7.151923273135395, + 7.426181001938577, + 7.693908784817875, + 7.9551066217732895, + 8.209774512804813, + 8.457912457912458, + 8.699520457096215, + 8.934598510356084, + 9.163146617692073, + 9.385164779104173, + 9.600652994592386, + 9.809611264156718, + 10.012039587797162, + 10.207937965513722, + 10.397306397306398, + 10.580144883175185, + 10.756453423120089, + 10.926232017141107, + 11.089480665238241, + 11.246199367411487 + ], + [ + -36.8337924701561, + -36.02407917559432, + -35.22089582695642, + -34.42424242424242, + -33.634118967452295, + -32.850525456586055, + -32.0734618916437, + -31.30292827262524, + -30.538924599530656, + -29.781450872359954, + -29.030507091113144, + -28.28609325579022, + -27.548209366391177, + -26.816855422916028, + -26.092031425364752, + -25.37373737373737, + -24.661973268033872, + -23.956739108254254, + -23.258034894398527, + -22.565860626466684, + -21.88021630445872, + -21.20110192837465, + -20.528517498214462, + -19.86246301397816, + -19.202938475665743, + -18.549943883277216, + -17.903479236812565, + -17.26354453627181, + -16.63013978165493, + -16.00326497296194, + -15.382920110192835, + -14.769105193347615, + -14.161820222426282, + -13.56106519742883, + -12.966840118355266, + -12.379144985205588, + -11.797979797979794, + -11.223344556677889, + -10.655239261299865, + -10.093663911845727, + -9.538618508315475, + -8.990103050709111, + -8.44811753902663, + -7.912661973268032, + -7.383736353433319, + -6.861340679522498, + -6.345474951535557, + -5.836139169472501, + -5.333333333333331, + -4.837057443118047, + -4.347311498826651, + -3.8640955004591357, + -3.3874094480155073, + -2.917253341495763, + -2.453627180899909, + -1.9965309662279358, + -1.545964697479848, + -1.1019283746556454, + -0.6644219977553323, + -0.2334455667789006, + 0.19100091827364585, + 0.6089174574023073, + 1.0203040506070793, + 1.4251606978879694, + 1.823487399244975, + 2.2152841546780944, + 2.6005509641873292, + 2.979287827772675, + 3.351494745434138, + 3.717171717171717, + 4.076318742985411, + 4.428935822875214, + 4.775022956841138, + 5.114580144883174, + 5.447607387001327, + 5.7741046831955884, + 6.094072033465972, + 6.407509437812466, + 6.714416896235077, + 7.014794408733801, + 7.3086419753086425, + 7.595959595959594, + 7.876747270686662, + 8.151004999489848, + 8.418732782369144, + 8.679930619324558, + 8.934598510356086, + 9.182736455463726, + 9.424344454647484, + 9.659422507907355, + 9.887970615243336, + 10.109988776655442, + 10.325476992143656, + 10.534435261707987, + 10.73686358534843, + 10.93276196306499, + 11.122130394857665, + 11.304968880726454, + 11.481277420671358, + 11.651056014692374 + ], + [ + -37.7283950617284, + -36.90562187531884, + -36.08937863483318, + -35.27966534027141, + -34.47648199163351, + -33.6798285889195, + -32.88970513212938, + -32.106111621263146, + -31.329048056320786, + -30.55851443730232, + -29.794510764207736, + -29.03703703703704, + -28.286093255790234, + -27.5416794204673, + -26.803795531068257, + -26.072441587593104, + -25.347617590041835, + -24.62932353841445, + -23.917559432710952, + -23.212325272931338, + -22.513621059075604, + -21.821446791143764, + -21.135802469135804, + -20.456688093051735, + -19.784103662891543, + -19.118049178655244, + -18.458524640342823, + -17.805530047954292, + -17.15906540148965, + -16.519130700948885, + -15.885725946332009, + -15.25885113763902, + -14.638506274869913, + -14.024691358024693, + -13.417406387103359, + -12.81665136210591, + -12.222426283032346, + -11.634731149882667, + -11.053565962656876, + -10.478930721354965, + -9.910825425976942, + -9.349250076522809, + -8.794204672992555, + -8.245689215386188, + -7.703703703703705, + -7.1682481379451115, + -6.6393225181104, + -6.116926844199574, + -5.601061116212632, + -5.091725334149577, + -4.5889194980104095, + -4.092643607795125, + -3.6028976635037244, + -3.1196816651362105, + -2.6429956126925855, + -2.1728395061728416, + -1.709213345576983, + -1.2521171309050096, + -0.8015508621569261, + -0.35751453933272326, + 0.07999183756759409, + 0.510968268544026, + 0.9354147535965687, + 1.3533312927252297, + 1.7647178859300063, + 2.169574533210896, + 2.567901234567902, + 2.9596979900010183, + 3.3449647995102527, + 3.7237016630956026, + 4.095908580757066, + 4.461585552494641, + 4.820732578308336, + 5.173349658198143, + 5.519436792164065, + 5.858993980206098, + 6.192021222324252, + 6.518518518518519, + 6.838485868788899, + 7.151923273135393, + 7.458830731558007, + 7.759208244056729, + 8.053055810631566, + 8.340373431282524, + 8.62116110600959, + 8.895418834812777, + 9.163146617692075, + 9.424344454647484, + 9.679012345679013, + 9.927150290786654, + 10.168758289970409, + 10.403836343230285, + 10.63238445056627, + 10.854402611978372, + 11.069890827466587, + 11.278849097030916, + 11.481277420671361, + 11.677175798387921, + 11.866544230180594, + 12.049382716049383 + ], + [ + -38.629527599224566, + -37.79369452096724, + -36.964391388633814, + -36.141618202224265, + -35.325374961738596, + -34.515661667176815, + -33.71247831853892, + -32.91582491582491, + -32.125701459034794, + -31.342107948168554, + -30.5650443832262, + -29.79451076420773, + -29.03050709111315, + -28.273033363942453, + -27.522089582695642, + -26.77767574737272, + -26.039791857973675, + -25.30843791449852, + -24.583613916947247, + -23.865319865319865, + -23.15355575961636, + -22.448321599836753, + -21.749617385981022, + -21.05744311804918, + -20.37179879604122, + -19.69268441995715, + -19.020099989796957, + -18.35404550556066, + -17.694520967248238, + -17.041526374859707, + -16.395061728395063, + -15.755127027854302, + -15.121722273237424, + -14.494847464544431, + -13.87450260177533, + -13.260687684930106, + -12.653402714008775, + -12.052647689011325, + -11.458422609937761, + -10.870727476788083, + -10.289562289562287, + -9.714927048260384, + -9.146821752882358, + -8.585246403428222, + -8.030200999897968, + -7.481685542291605, + -6.9397000306091225, + -6.4042444648505255, + -5.875318845015814, + -5.352923171104988, + -4.83705744311805, + -4.327721661054994, + -3.824915824915824, + -3.328639934700539, + -2.8388939904091437, + -2.3556779920416293, + -1.878991939598, + -1.408835833078256, + -0.9452096724824017, + -0.4881134578104287, + -0.03754718906234045, + 0.4064891337618619, + 0.843995510662175, + 1.2749719416386065, + 1.699418426691154, + 2.1173349658198144, + 2.528721559024591, + 2.9335782063054774, + 3.3319049076624827, + 3.7237016630956026, + 4.108968472604837, + 4.4877053361901815, + 4.859912253851647, + 5.225589225589225, + 5.584736251402919, + 5.937353331292722, + 6.283440465258646, + 6.622997653300684, + 6.956024895418835, + 7.2825221916131, + 7.602489541883484, + 7.915926946229976, + 8.222834404652584, + 8.523211917151311, + 8.81705948372615, + 9.104377104377106, + 9.385164779104173, + 9.659422507907353, + 9.927150290786654, + 10.188348127742067, + 10.44301601877359, + 10.691153963881236, + 10.932761963064992, + 11.167840016324863, + 11.396388123660849, + 11.618406285072949, + 11.833894500561165, + 12.042852770125494, + 12.245281093765945, + 12.4411794714825 + ], + [ + -39.53719008264462, + -38.68829711253953, + -37.84593408835832, + -37.01010101010101, + -36.18079787776757, + -35.35802469135802, + -34.54178145087235, + -33.732068156310575, + -32.92888480767268, + -32.132231404958674, + -31.342107948168547, + -30.55851443730231, + -29.78145087235996, + -29.01091725334149, + -28.246913580246904, + -27.48943985307621, + -26.738496071829402, + -25.994082236506472, + -25.256198347107432, + -24.52484440363228, + -23.800020406081003, + -23.08172635445362, + -22.36996224875012, + -21.66472808897051, + -20.966023875114775, + -20.27384960718294, + -19.58820528517498, + -18.909090909090903, + -18.236506478930718, + -17.570451994694416, + -16.910927456381998, + -16.257932863993467, + -15.611468217528818, + -14.971533516988059, + -14.338128762371182, + -13.711253953678192, + -13.090909090909086, + -12.477094174063868, + -11.869809203142534, + -11.269054178145083, + -10.674829099071518, + -10.087133965921844, + -9.50596877869605, + -8.93133353739414, + -8.363228242016117, + -7.801652892561983, + -7.246607489031731, + -6.698092031425363, + -6.15610651974288, + -5.620650953984283, + -5.091725334149576, + -4.56932966023875, + -4.053463932251808, + -3.5441281501887527, + -3.0413223140495873, + -2.545046423834302, + -2.055300479542902, + -1.5720844811753878, + -1.095398428731763, + -0.6252423222120194, + -0.16161616161616066, + 0.2954800530558124, + 0.7460463218038962, + 1.1900826446280979, + 1.627589021528416, + 2.058565452504847, + 2.483011937557394, + 2.900928476686051, + 3.3123150698908264, + 3.7171717171717176, + 4.1154984185287224, + 4.507295173961838, + 4.892561983471073, + 5.271298847056422, + 5.643505764717887, + 6.009182736455461, + 6.3683297622691555, + 6.720946842158963, + 7.067033976124884, + 7.406591164166919, + 7.739618406285074, + 8.066115702479337, + 8.386083052749717, + 8.699520457096215, + 9.006427915518822, + 9.306805428017551, + 9.600652994592387, + 9.887970615243338, + 10.168758289970409, + 10.44301601877359, + 10.710743801652887, + 10.971941638608305, + 11.22660952963983, + 11.474747474747474, + 11.71635547393123, + 11.951433527191101, + 12.179981634527087, + 12.401999795939187, + 12.617488011427403, + 12.826446280991732 + ], + [ + -40.45138251198857, + -39.58942965003571, + -38.734006734006726, + -37.88511376390164, + -37.04275073972044, + -36.206917661463116, + -35.37761452912968, + -34.55484134272014, + -33.73859810223446, + -32.92888480767269, + -32.125701459034794, + -31.329048056320786, + -30.538924599530667, + -29.755331088664423, + -28.978267523722067, + -28.207733904703602, + -27.443730231609024, + -26.686256504438326, + -25.93531272319151, + -25.190898887868588, + -24.45301499846954, + -23.721661054994392, + -22.996837057443116, + -22.278543005815735, + -21.566778900112233, + -20.86154474033262, + -20.16284052647689, + -19.470666258545048, + -18.785021936537092, + -18.105907560453016, + -17.433323130292827, + -16.76726864605653, + -16.107744107744107, + -15.454749515355577, + -14.80828486889093, + -14.16835016835017, + -13.534945413733293, + -12.908070605040303, + -12.2877257422712, + -11.673910825425978, + -11.06662585450464, + -10.465870829507198, + -9.871645750433629, + -9.283950617283951, + -8.702785430058157, + -8.128150188756251, + -7.560044893378229, + -6.99846954392409, + -6.443424140393836, + -5.89490868278747, + -5.352923171104991, + -4.817467605346394, + -4.2885419855116815, + -3.7661463116008553, + -3.250280583613919, + -2.740944801550863, + -2.238138965411692, + -1.7418630751964068, + -1.2521171309050119, + -0.7689011325374973, + -0.2922150800938679, + 0.17794102642587606, + 0.6415671870217301, + 1.098663401693703, + 1.5492296704417918, + 1.9932659932659935, + 2.4307723701663115, + 2.861748801142739, + 3.2861952861952863, + 3.704111825323947, + 4.115498418528723, + 4.52035506580961, + 4.918681767166616, + 5.310478522599736, + 5.69574533210897, + 6.074482195694315, + 6.446689113355781, + 6.812366085093359, + 7.171513110907052, + 7.524130190796857, + 7.870217324762783, + 8.209774512804817, + 8.542801754922966, + 8.869299051117235, + 9.189266401387613, + 9.50270380573411, + 9.80961126415672, + 10.109988776655442, + 10.403836343230285, + 10.691153963881238, + 10.971941638608303, + 11.246199367411492, + 11.513927150290789, + 11.775124987246203, + 12.029792878277728, + 12.277930823385372, + 12.519538822569128, + 12.754616875828999, + 12.983164983164984, + 13.205183144577084 + ], + [ + -41.3721048872564, + -40.497092133455766, + -39.62860932557901, + -38.76665646362616, + -37.91123354759718, + -37.06234057749209, + -36.219977553310876, + -35.38414447505356, + -34.554841342720124, + -33.732068156310575, + -32.915824915824906, + -32.10611162126313, + -31.302928272625238, + -30.50627486991123, + -29.716151413121104, + -28.93255790225487, + -28.15549433731252, + -27.384960718294046, + -26.62095704519946, + -25.86348331802877, + -25.112539536781952, + -24.368125701459032, + -23.630241812059992, + -22.898887868584833, + -22.174063871033564, + -21.455769819406182, + -20.744005713702677, + -20.038771553923066, + -19.340067340067336, + -18.647893072135496, + -17.962248750127536, + -17.283134374043463, + -16.610549943883278, + -15.944495459646971, + -15.284970921334557, + -14.63197632894602, + -13.985511682481377, + -13.345576981940614, + -12.71217222732374, + -12.085297418630748, + -11.464952555861643, + -10.851137639016425, + -10.24385266809509, + -9.643097643097642, + -9.048872564024077, + -8.4611774308744, + -7.880012243648607, + -7.305377002346698, + -6.737271706968674, + -6.1756963575145365, + -5.6206509539842875, + -5.0721354963779195, + -4.530149984695436, + -3.99469441893684, + -3.465768799102133, + -2.943373125191307, + -2.4275073972043653, + -1.9181716151413097, + -1.4153657790021439, + -0.9190898887868586, + -0.42934394449545876, + 0.053872053872055625, + 0.5305581063156806, + 1.0007142128354238, + 1.4643403734312828, + 1.9214365881032553, + 2.372002856851344, + 2.816039179675542, + 3.253545556575859, + 3.684521987552291, + 4.108968472604837, + 4.526885011733494, + 4.938271604938271, + 5.343128252219161, + 5.7414549535761665, + 6.133251709009281, + 6.518518518518517, + 6.897255382103866, + 7.26946229976533, + 7.635139271502906, + 7.994286297316603, + 8.346903377206406, + 8.692990511172326, + 9.032547699214367, + 9.365574941332515, + 9.692072237526784, + 10.012039587797164, + 10.325476992143654, + 10.632384450566269, + 10.932761963064992, + 11.226609529639827, + 11.513927150290787, + 11.794714825017852, + 12.068972553821038, + 12.336700336700334, + 12.597898173655745, + 12.852566064687274, + 13.100704009794914, + 13.342312008978677, + 13.577390062238543 + ], + [ + -42.29935720844812, + -41.411284562799715, + -40.5297418630752, + -39.65472910927457, + -38.786246301397824, + -37.92429343944496, + -37.06887052341598, + -36.2199775533109, + -35.37761452912969, + -34.541781450872364, + -33.71247831853893, + -32.88970513212938, + -32.07346189164372, + -31.263748597081936, + -30.46056524844404, + -29.66391184573003, + -28.87378838893991, + -28.09019487807367, + -27.313131313131315, + -26.54259769411285, + -25.778594021018264, + -25.021120293847574, + -24.270176512600756, + -23.525762677277832, + -22.787878787878793, + -22.05652484440364, + -21.331700846852364, + -20.613406795224982, + -19.90164268952148, + -19.196408529741866, + -18.49770431588614, + -17.805530047954296, + -17.119885725946336, + -16.44077134986226, + -15.768186919702075, + -15.102132435465771, + -14.442607897153355, + -13.789613304764822, + -13.143148658300177, + -12.503213957759415, + -11.869809203142536, + -11.24293439444955, + -10.622589531680447, + -10.008774614835223, + -9.401489643913887, + -8.800734618916442, + -8.206509539842877, + -7.618814406693196, + -7.037649219467402, + -6.463013978165494, + -5.894908682787474, + -5.333333333333336, + -4.778287929803082, + -4.229772472196714, + -3.6877869605142366, + -3.152331394755639, + -2.6234057749209274, + -2.1010101010101003, + -1.5851443730231642, + -1.075808590960108, + -0.5730027548209373, + -0.07672686460565226, + 0.41301907968574314, + 0.8962350780532575, + 1.3729211304968876, + 1.8430772370166308, + 2.30670339761249, + 2.7637996122844593, + 3.214365881032547, + 3.65840220385675, + 4.095908580757067, + 4.526885011733494, + 4.951331496786042, + 5.369248035914703, + 5.780634629119479, + 6.185491276400365, + 6.583817977757372, + 6.975614733190492, + 7.360881542699726, + 7.7396184062850715, + 8.11182532394654, + 8.477502295684115, + 8.836649321497806, + 9.189266401387616, + 9.535353535353535, + 9.874910723395576, + 10.207937965513725, + 10.534435261707989, + 10.854402611978372, + 11.167840016324867, + 11.474747474747472, + 11.775124987246201, + 12.068972553821041, + 12.356290174471996, + 12.637077849199065, + 12.911335578002245, + 13.179063360881544, + 13.440261197836957, + 13.694929088868488, + 13.943067033976126 + ], + [ + -43.23313947556372, + -42.332006938067536, + -41.43740434649525, + -40.54933170084686, + -39.66778900112233, + -38.7927762473217, + -37.92429343944495, + -37.062340577492094, + -36.20691766146311, + -35.358024691358025, + -34.51566166717682, + -33.6798285889195, + -32.85052545658606, + -32.027752270176514, + -31.21150902969085, + -30.401795735129063, + -29.598612386491176, + -28.80195898377717, + -28.011835526987042, + -27.228242016120802, + -26.451178451178446, + -25.680644832159985, + -24.9166411590654, + -24.1591674318947, + -23.40822365064789, + -22.663809815324967, + -21.925925925925924, + -21.19457198245077, + -20.4697479848995, + -19.751453933272117, + -19.039689827568615, + -18.334455667789, + -17.635751453933274, + -16.943577186001427, + -16.257932863993467, + -15.578818487909396, + -14.90623405774921, + -14.240179573512904, + -13.58065503520049, + -12.927660442811957, + -12.28119579634731, + -11.641261095806552, + -11.007856341189676, + -10.380981532496683, + -9.760636669727576, + -9.14682175288236, + -8.539536781961026, + -7.938781756963574, + -7.34455667789001, + -6.756861544740331, + -6.17569635751454, + -5.601061116212632, + -5.032955820834609, + -4.471380471380469, + -3.9163350678502216, + -3.367819610243853, + -2.825834098561371, + -2.290378532802774, + -1.761452912968067, + -1.23905723905724, + -0.7231915110702989, + -0.21385572900724314, + 0.2889501071319225, + 0.7852259973472078, + 1.274971941638608, + 1.7581879400061218, + 2.2348739924497516, + 2.705030098969491, + 3.1686562595653496, + 3.625752474237323, + 4.076318742985411, + 4.520355065809609, + 4.957861442709927, + 5.388837873686358, + 5.813284358738905, + 6.231200897867561, + 6.642587491072339, + 7.047444138353229, + 7.445770839710233, + 7.8375675951433506, + 8.22283440465259, + 8.601571268237935, + 8.973778185899395, + 9.339455157636978, + 9.698602183450665, + 10.051219263340476, + 10.397306397306398, + 10.73686358534843, + 11.069890827466585, + 11.396388123660849, + 11.716355473931227, + 12.029792878277728, + 12.336700336700336, + 12.637077849199061, + 12.930925415773899, + 13.218243036424852, + 13.499030711151923, + 13.773288439955104, + 14.041016222834406, + 14.302214059789815 + ], + [ + -44.173451688603194, + -43.25925925925925, + -42.351596775839184, + -41.45046423834302, + -40.55586164677074, + -39.66778900112233, + -38.7862463013978, + -37.911233547597185, + -37.04275073972043, + -36.18079787776757, + -35.32537496173859, + -34.476481991633506, + -33.634118967452295, + -32.79828588919497, + -31.968982756861536, + -31.146209570451987, + -30.329966329966325, + -29.520253035404544, + -28.71706968676665, + -27.920416284052642, + -27.130292827262515, + -26.346699316396283, + -25.56963575145393, + -24.799102132435458, + -24.03509845934088, + -23.277624732170185, + -22.52668095092337, + -21.782267115600447, + -21.044383226201404, + -20.313029282726248, + -19.58820528517498, + -18.869911233547594, + -18.158147127844096, + -17.452912968064474, + -16.75420875420875, + -16.062034486276907, + -15.376390164268948, + -14.697275788184875, + -14.02469135802469, + -13.358636873788384, + -12.699112335475967, + -12.04611774308744, + -11.399653096622792, + -10.759718396082029, + -10.126313641465153, + -9.499438832772165, + -8.879093970003058, + -8.265279053157839, + -7.6579940822365025, + -7.057239057239053, + -6.463013978165492, + -5.875318845015813, + -5.2941536577900195, + -4.71951841648811, + -4.151413121110091, + -3.5898377716559526, + -3.0347923681256996, + -2.486276910519331, + -1.9442913988368544, + -1.4088358330782569, + -0.8799102132435452, + -0.3575145393327186, + 0.1583511886542177, + 0.667686970717273, + 1.1704928068564442, + 1.6667686970717286, + 2.1565146413631293, + 2.639730639730639, + 3.1164166921742678, + 3.586572798694012, + 4.050198959289871, + 4.507295173961839, + 4.957861442709927, + 5.401897765534129, + 5.8394041424344465, + 6.270380573410874, + 6.694827058463422, + 7.1127435975920825, + 7.524130190796857, + 7.928986838077745, + 8.327313539434755, + 8.71911029486787, + 9.104377104377102, + 9.483113967962455, + 9.855320885623913, + 10.220997857361496, + 10.580144883175187, + 10.932761963064989, + 11.278849097030914, + 11.61840628507295, + 11.9514335271911, + 12.277930823385368, + 12.597898173655746, + 12.911335578002245, + 13.218243036424852, + 13.518620548923575, + 13.812468115498415, + 14.099785736149368, + 14.380573410876442, + 14.65483113967962 + ], + [ + -45.12029384756657, + -44.193041526374856, + -43.27231915110703, + -42.358126721763085, + -41.45046423834303, + -40.54933170084685, + -39.65472910927456, + -38.76665646362617, + -37.88511376390164, + -37.01010101010101, + -36.141618202224265, + -35.2796653402714, + -34.42424242424243, + -33.57534945413734, + -32.73298642995613, + -31.897153351698808, + -31.067850219365376, + -30.24507703295582, + -29.428833792470158, + -28.61912049790838, + -27.815937149270482, + -27.01928374655648, + -26.229160289766348, + -25.445566778900115, + -24.668503213957756, + -23.897969594939294, + -23.133965921844712, + -22.376492194674015, + -21.625548413427204, + -20.88113457810428, + -20.143250688705237, + -19.411896745230084, + -18.687072747678812, + -17.968778696051423, + -17.257014590347925, + -16.55178043056831, + -15.853076216712584, + -15.160901948780737, + -14.475257626772784, + -13.796143250688706, + -13.123558820528517, + -12.457504336292219, + -11.7979797979798, + -11.144985205591269, + -10.49852055912662, + -9.858585858585862, + -9.225181103968985, + -8.598306295275995, + -7.977961432506888, + -7.364146515661666, + -6.756861544740335, + -6.156106519742885, + -5.561881440669319, + -4.97418630751964, + -4.3930211202938505, + -3.8183858789919407, + -3.250280583613918, + -2.6887052341597792, + -2.133659830629531, + -1.5851443730231631, + -1.0431588613406806, + -0.507703295582083, + 0.021222324252623714, + 0.5436179981634499, + 1.0594837261503918, + 1.568819508213447, + 2.0716253443526185, + 2.567901234567899, + 3.0576471788592983, + 3.5408631772268135, + 4.0175492296704425, + 4.4877053361901815, + 4.951331496786041, + 5.408427711458014, + 5.858993980206102, + 6.303030303030299, + 6.740536679930618, + 7.17151311090705, + 7.595959595959595, + 8.013876135088253, + 8.425262728293035, + 8.83011937557392, + 9.228446076930922, + 9.620242832364045, + 10.005509641873276, + 10.384246505458629, + 10.75645342312009, + 11.122130394857665, + 11.481277420671361, + 11.833894500561167, + 12.179981634527085, + 12.519538822569126, + 12.852566064687275, + 13.179063360881544, + 13.499030711151924, + 13.812468115498419, + 14.11937557392103, + 14.419753086419753, + 14.713600652994593, + 15.000918273645546 + ], + [ + -46.07366595245383, + -45.13335373941434, + -44.19957147229874, + -43.27231915110703, + -42.3515967758392, + -41.437404346495256, + -40.52974186307519, + -39.62860932557902, + -38.73400673400673, + -37.84593408835833, + -36.964391388633814, + -36.089378634833174, + -35.22089582695643, + -34.35894296500357, + -33.50352004897459, + -32.6546270788695, + -31.8122640546883, + -30.976430976430976, + -30.14712784409754, + -29.32435465768799, + -28.508111417202322, + -27.698398122640548, + -26.895214774002653, + -26.09856137128864, + -25.30843791449852, + -24.524844403632283, + -23.747780838689927, + -22.977247219671465, + -22.213243546576876, + -21.455769819406182, + -20.70482603815937, + -19.960412202836444, + -19.222528313437405, + -18.491174369962245, + -17.766350372410976, + -17.04805632078359, + -16.336292215080093, + -15.631058055300477, + -14.93235384144475, + -14.240179573512904, + -13.554535251504944, + -12.875420875420875, + -12.202836445260687, + -11.536781961024385, + -10.877257422711967, + -10.224262830323436, + -9.577798183858791, + -8.93786348331803, + -8.304458728701151, + -7.67758392000816, + -7.057239057239058, + -6.443424140393837, + -5.836139169472501, + -5.23538414447505, + -4.641159065401491, + -4.053463932251811, + -3.4722987450260163, + -2.897663503724108, + -2.3295582083460893, + -1.7679828588919504, + -1.212937455361697, + -0.6644219977553298, + -0.12243648607285218, + 0.4130190796857445, + 0.9419446995204572, + 1.4643403734312832, + 1.9802061014182248, + 2.4895418834812757, + 2.992347719620446, + 3.4886236098357317, + 3.978369554127131, + 4.461585552494641, + 4.938271604938271, + 5.408427711458014, + 5.872053872053873, + 6.329150086725841, + 6.77971635547393, + 7.223752678298133, + 7.66125905519845, + 8.092235486174879, + 8.516681971227428, + 8.934598510356086, + 9.345985103560858, + 9.750841750841753, + 10.149168452198753, + 10.540965207631876, + 10.926232017141107, + 11.304968880726452, + 11.677175798387921, + 12.042852770125496, + 12.401999795939187, + 12.754616875828997, + 13.100704009794917, + 13.440261197836955, + 13.773288439955104, + 14.099785736149368, + 14.419753086419751, + 14.733190490766244, + 15.04009794918886, + 15.34047546168758 + ], + [ + -47.033568003264975, + -46.080195898377724, + -45.133353739414346, + -44.19304152637487, + -43.25925925925927, + -42.33200693806755, + -41.41128456279972, + -40.49709213345578, + -39.58942965003572, + -38.688297112539544, + -37.79369452096726, + -36.90562187531886, + -36.02407917559434, + -35.149066421793705, + -34.280583613916946, + -33.418630751964095, + -32.56320783593512, + -31.71431486583002, + -30.871951841648816, + -30.036118763391492, + -29.20681563105806, + -28.384042444648514, + -27.567799204162846, + -26.758085909601068, + -25.95490256096317, + -25.158249158249163, + -24.368125701459036, + -23.584532190592803, + -22.807468625650447, + -22.036935006631982, + -21.2729313335374, + -20.515457606366702, + -19.76451382511989, + -19.02009998979696, + -18.28221610039792, + -17.550862156922765, + -16.826038159371496, + -16.10774410774411, + -15.395980002040613, + -14.690745842260998, + -13.992041628405266, + -13.299867360473428, + -12.614223038465468, + -11.935108662381392, + -11.262524232221203, + -10.596469747984905, + -9.936945209672487, + -9.283950617283953, + -8.637485970819306, + -7.997551270278544, + -7.364146515661671, + -6.73727170696868, + -6.116926844199574, + -5.503111927354352, + -4.895826956433022, + -4.295071931435572, + -3.7008468523620057, + -3.1131517192123255, + -2.5319865319865373, + -1.9573512906846273, + -1.3892459953066032, + -0.8276706458524647, + -0.27262524232221663, + 0.2758902152841509, + 0.8178757269666339, + 1.3533312927252308, + 1.8822569125599433, + 2.4046525864707653, + 2.920518314457706, + 3.4298540965207622, + 3.932659932659933, + 4.4289358228752125, + 4.918681767166614, + 5.4018977655341285, + 5.878583817977757, + 6.348739924497496, + 6.812366085093356, + 7.26946229976533, + 7.720028568513417, + 8.164064891337617, + 8.601571268237937, + 9.032547699214366, + 9.45699418426691, + 9.874910723395574, + 10.286297316600345, + 10.691153963881238, + 11.089480665238241, + 11.481277420671358, + 11.866544230180594, + 12.245281093765943, + 12.617488011427401, + 12.983164983164983, + 13.342312008978675, + 13.694929088868484, + 14.041016222834404, + 14.38057341087644, + 14.713600652994593, + 15.040097949188858, + 15.360065299459242, + 15.673502703805735 + ], + [ + -48, + -47.033568003264975, + -46.07366595245383, + -45.12029384756658, + -44.17345168860321, + -43.23313947556372, + -42.299357208448114, + -41.372104887256405, + -40.45138251198858, + -39.53719008264463, + -38.629527599224566, + -37.72839506172839, + -36.83379247015611, + -35.945719824507705, + -35.06417712478318, + -34.18916437098256, + -33.32068156310581, + -32.45872870115294, + -31.603305785123965, + -30.754412815018878, + -29.912049790837667, + -29.07621671258035, + -28.24691358024691, + -27.424140393837362, + -26.6078971533517, + -25.79818385878992, + -24.995000510152025, + -24.19834710743802, + -23.408223650647894, + -22.624630139781658, + -21.847566574839302, + -21.077032955820837, + -20.313029282726255, + -19.555555555555557, + -18.804611774308746, + -18.060197938985816, + -17.32231404958678, + -16.59096010611162, + -15.866136108560353, + -15.147842056932967, + -14.436077951229466, + -13.730843791449855, + -13.032139577594126, + -12.339965309662281, + -11.65432098765432, + -10.97520661157025, + -10.302622181410062, + -9.636567697173758, + -8.97704315886134, + -8.324048566472806, + -7.677583920008165, + -7.0376492194674025, + -6.404244464850526, + -5.777369656157533, + -5.157024793388432, + -4.543209876543212, + -3.9359249056218752, + -3.335169880624425, + -2.740944801550865, + -2.153249668401185, + -1.5720844811753905, + -0.9974492398734816, + -0.429343944495463, + 0.13223140495867503, + 0.6872768084889289, + 1.235792266095296, + 1.7777777777777792, + 2.3132333435363717, + 2.8421589633710833, + 3.36455463728191, + 3.8804203652688507, + 4.389756147331902, + 4.892561983471073, + 5.388837873686358, + 5.878583817977757, + 6.361799816345267, + 6.838485868788898, + 7.3086419753086425, + 7.7722681359045, + 8.22936435057647, + 8.679930619324562, + 9.123966942148758, + 9.561473319049075, + 9.99244975002551, + 10.416896235078053, + 10.834812774206716, + 11.246199367411489, + 11.651056014692376, + 12.049382716049383, + 12.441179471482503, + 12.826446280991732, + 13.205183144577084, + 13.577390062238546, + 13.943067033976126, + 14.302214059789817, + 14.654831139679622, + 15.000918273645546, + 15.340475461687582, + 15.673502703805735, + 16 + ] + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + }, + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + }, + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "autotypenumbers": "strict", + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "trace = go.Surface(x=mx, y=my, z=mz)\n", + "fig = go.Figure(data=[trace])\n", + "py.iplot(fig, show_link=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On a un superbe point selle.\n", + "\n", + "Bien sûr avec une autre graine aléatoire nous aurions autre chose. Imaginez ce que vous pourriez avoir si toutes\n", + "les valeurs de A sont positives." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Optimisons\n", + "\n", + "Si on doit faire ce calcul de nombreuses fois en grande dimension, il serait bien de trouver la solution\n", + "optimale. Si la notation d'Einstein aide bien ici, elle n'est pas toujours la plus rapide. Donc comparons avec\n", + "d'autres méthodes.\n", + "\n", + "### Passer par une fonction J" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def J(x):\n", + " return x @ A @ x\n", + "\n", + "mz2 = np.array([J(x) for line in M for x in line]).reshape([M.shape[0], M.shape[1]])\n", + "\n", + "np.max(np.square(mz2 - mz)) # pour vérifier qu'on obtient la même chose" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "143 µs ± 1.99 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "# comparons les temps calculs :\n", + "\n", + "%timeit np.einsum(\"ijk, ijk -> ij\", np.einsum(\"ijk, ka -> ija\", M, A), M)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "19.7 ms ± 494 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "%timeit np.array([J(x) for line in M for x in line]).reshape([M.shape[0], M.shape[1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On est plus de 100 fois plus rapide avec la sommation d'Einstein." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Notons qu'avec `apply_along_axis` c'est pire :" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "34.6 ms ± 989 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "%timeit np.array([np.apply_along_axis(J, 1, line) for line in M]).reshape([M.shape[0], M.shape[1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Utiliser `np.tensordot`\n", + "\n", + "Un tensor est une matrice en N dimension donc voici une fonction qui devrait pouvoir servir puisque notre ensemble de point est en 3 dimensions." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100 µs ± 1.15 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" + ] + } + ], + "source": [ + "%%timeit # pour calculer le temps d'execution de toute la cellule %%\n", + "\n", + "MA = np.tensordot(M, A, axes=(2,1)) # on somme sur l'axe 2 de M (les points) et l'axe 1 de A (les colonnes)\n", + "np.einsum(\"ijk, ijk -> ij\", MA, M) # je n'arrive pas à faire cette opération autrement" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "On a un gain de 30 % par rapport à `einsum`.\n", + "\n", + "Pour avoir de bonne mesures il faudrait utiliser des cas plus gros que 100x100 et lancer les tests\n", + "sur une machine qui ne fait que cela, donc en mode single user sous Linux.\n", + "\n", + "### Conclusion\n", + "\n", + "Grosso modo on a :\n", + "\n", + "| Méthode | Temps |\n", + "| --- | --: |\n", + "|`einsum` | 140 µs|\n", + "|`tensordot` | 100 µs|\n", + "|boucle `for` | 20 000 µs|" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma52 M\303\251thode du gradiant pour syst\303\250me matriciel.ipynb" "b/PVCM/cama/fr/ma52 M\303\251thode du gradiant pour syst\303\250me matriciel.ipynb" new file mode 100644 index 0000000..ecfffc6 --- /dev/null +++ "b/PVCM/cama/fr/ma52 M\303\251thode du gradiant pour syst\303\250me matriciel.ipynb" @@ -0,0 +1,31807 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# A x = b vu comme un problème d'optimisation\n", + "\n", + "Pour résoudre $A {\\bf x} = {\\bf b}$ on va chercher le minimum de la fonctionnelle\n", + "\n", + "$$\n", + "J({\\bf x}) = \\frac{1}{2} \\, {\\bf x}^T \\, A \\, {\\bf x} - {\\bf b}\\, . {\\bf x}\n", + "$$\n", + "\n", + "En ce point la dérivée s'annule et dans un cas précis la dérivée est justement $A {\\bf x} - {\\bf b}$.\n", + "\n", + "## Calcul de dérivée\n", + "\n", + "La notion de dérivée en dimension supérieure à 1 doit être manipulée avec précaution car il y a différents\n", + "types de dérivées, les dérivées partielles et la dérivée totale.\n", + "\n", + "Ce qui nous intéresse est la dérivée dans une direction ce qui correpond à la dérivée partielle en $y$ si on\n", + "va dans la direction de l'axe $y$.\n", + "\n", + "### Définition\n", + "\n", + "On dit que $f : \\Omega \\subset X \\rightarrow Y$ ($\\Omega$ ouvert) est dérivable en ${\\bf p} \\in \\Omega$ si\n", + "\n", + "$$\n", + "\\exists \\; f'({\\bf p}) \\in L(X,Y) \\textrm{ tel que} \\\\\n", + "f ({\\bf p} + {\\bf h}) = f({\\bf p}) + f'({\\bf p}) ( {\\bf h} ) + {\\bf h} \\; \\varepsilon({\\bf h}) \\quad\n", + "\\textrm{ avec } \\lim_{\\bf h \\rightarrow 0} \\varepsilon({\\bf h}) = {\\bf 0}\n", + "$$\n", + "\n", + "où $L(X,Y)$ représente l'espace des applications linéraires continues de $X$ dans $Y$. Attention c'est\n", + "$f'(p) \\in L(X,Y)$ et non $f'$.\n", + "\n", + "\n", + "On note que si $f$ est dérivable en ${\\bf p}$ alors $\\forall \\; {\\bf h} \\in X$\n", + "\n", + "$$\n", + "f'({\\bf p}) ({\\bf h})= \\lim_{\\theta \\rightarrow 0} \\frac{f({\\bf p} + \\theta \\, {\\bf h}) - f({\\bf p})}{\\theta}\n", + "$$\n", + "\n", + "Attention à bien regarder le type de chaque terme. Pour bien visualiser j'ai considéré que $f$ est une \n", + "fonction scalaire donc $Y = ℝ$. Par contre $X = ℝ^n$ avec $n > 1$. \n", + "\n", + "#### Autre notation\n", + "\n", + "Je trouve la notation avec le gradient plus claire. On voit mieux où sont les vecteurs et les scalaires :\n", + "\n", + "$$\n", + "f ({\\bf p} + {\\bf h}) = f({\\bf p}) + \\nabla \\! f\\,({\\bf p})^T \\; {\\bf h} + {\\bf h}^T \\; \\varepsilon({\\bf h}) \\quad\n", + "$$\n", + "\n", + "Comme j'ai pris $Y = ℝ$ l'application $f$ est scalaire. $\\nabla \\! f \\, ({\\bf p})$ est un vecteur dont le\n", + "produit scalaire avec ${\\bf h}$ donne un réel.\n", + "\n", + "### Calculons la dérivée de J suivant une direction\n", + "\n", + "On calcule la dérivée de $J({\\bf x})$ au point ${\\bf p}$ suivant la direction donnée par le vecteur $\\bf h$ :\n", + "\n", + "$$\n", + "\\begin{align}\n", + "J'({\\bf p}) ({\\bf h}) &= \\lim_{\\theta \\rightarrow 0} \\; \\frac{J({\\bf p} + \\theta \\, {\\bf h}) - J({\\bf p})}{\\theta} \\\\\n", + " &= \\lim_{\\theta \\rightarrow 0} \\; \\frac{1}{\\theta} \\; \n", + " \\left( \\frac{1}{2} \\; ({\\bf p} + \\theta {\\bf h})^T \\, A \\; ({\\bf p} + \\theta {\\bf h})\n", + " - {\\bf b}^T \\, ({\\bf p} + \\theta {\\bf h})\n", + " - \\frac{1}{2} \\; {\\bf p}^T \\, A \\; {\\bf p} + {\\bf b}^T \\, {\\bf p}\n", + " \\right) \\\\\n", + " &= \\lim_{\\theta \\rightarrow 0} \\; \\frac{1}{\\theta} \\; \n", + " \\left( \\frac{1}{2} \\left( \\theta \\, {\\bf p}^T \\, A \\; {\\bf h} \n", + " + \\theta \\, {\\bf h}^T \\, A \\; {\\bf p} \n", + " + \\theta^2 \\, {\\bf h}^T \\, A \\; {\\bf h} \\right) \n", + " - \\theta \\, {\\bf b}^T \\, {\\bf h}\n", + " \\right) \\\\\n", + " &= \\frac{1}{2} \\left( {\\bf p}^T \\, A \\; {\\bf h} +{\\bf h}^T \\, A \\; {\\bf p} \\right) - {\\bf b}^T \\, {\\bf h} \\\\\n", + " &= \\frac{1}{2} \\left( {\\bf p}^T \\, A \\; {\\bf h} +{\\bf p}^T \\, A^T \\; {\\bf h} \\right) - {\\bf b}^T \\, {\\bf h} \\\\\n", + " &= \\frac{1}{2} \\left( {\\bf p}^T \\, ( A + A^T ) - {\\bf b}^T \\right) \\, {\\bf h} \\\\\n", + " &= \\frac{1}{2} \\left( ( A + A^T ) \\, {\\bf p} - {\\bf b} \\right) \\, . \\, {\\bf h}\n", + "\\end{align}\n", + "$$\n", + "\n", + "donc\n", + "\n", + "$$\n", + "\\begin{align}\n", + "J' : \\; & {\\bf x} \\in \\Omega \\subset ℝ^n \\longrightarrow \\;L(ℝ^n, ℝ) \\\\\n", + " & {\\bf x} \\; \\longmapsto \\; \\frac{1}{2} ( A + A^T ) \\, {\\bf x}^T - {\\bf b}\n", + "\\end{align}\n", + "$$\n", + "\n", + "### A symétrique\n", + "\n", + "Dans le cas où A est symétrique on a\n", + "\n", + "$$\n", + "J'({\\bf x}) = A \\; {\\bf x} - {\\bf b}\n", + "$$\n", + "\n", + "On note que si la dérivée s'annule alors on a résolu notre système matriciel !\n", + "\n", + "Il faut donc que\n", + "\n", + "* A soit symétrique\n", + "* J ait un minimum (par certain, on a vu un cas de point selle)\n", + "\n", + "et dans ce cas on peut utiliser une méthode de gradient pour trouver le minimum qui sera la solution de \n", + "notre système matriciel.\n", + "\n", + "#### Propriété\n", + "\n", + "Si A est symétrique et définie positive alors $J$ est convexe strictement et coervice (c.a.d. \n", + "$\\lim_{||{\\bf p}|| \\rightarrow \\infty} J({\\bf p}) = + \\infty$) ce qui garantit qu'elle a un minimum." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gradient et dérivée\n", + "\n", + "Le gradient est composé des dérivées partielles suivant chaque direction de la base. On peut rérouler les calculs et calculer $\\nabla J$ facilement (mais c'est long). Faisons le pour une matrice sur la partie compliquée :\n", + "\n", + "$$ \n", + "\\begin{align}\n", + "\\frac{1}{2} {\\bf x}^T A {\\bf x} &= \\frac{1}{2} \\begin{pmatrix} x_1 & x_2 \\end{pmatrix} \\begin{pmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\end{pmatrix} \\begin{pmatrix} x_1 \\\\ x_2 \\end{pmatrix} \\\\\n", + "&= \\frac{1}{2} \\left( x_1 a_{11} x_1 + x_1 a_{12} x_2 + x_2 a_{21} x_1 + x_2 a_{22} x_2 \\right) \\\\\n", + "& = \\frac{1}{2} \\left( a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2 \\right)\n", + "\\end{align}\n", + "$$\n", + "\n", + "Calcul des dérivées partielles de $ \\frac{1}{2} x^T A x $ :\n", + "\n", + "$$\n", + "\\frac{\\partial}{\\partial x_1} \\left( \\frac{1}{2} (a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2) \\right)\n", + " = \\frac{1}{2} (2 a_{11} x_1 + (a_{12} + a_{21}) x_2) = a_{11} x_1 + \\frac{a_{12} + a_{21}}{2} x_2\n", + "$$\n", + "\n", + "$$\n", + " \\frac{\\partial}{\\partial x_2} \\left( \\frac{1}{2} (a_{11} x_1^2 + (a_{12} + a_{21}) x_1 x_2 + a_{22} x_2^2) \\right)\n", + " = \\frac{1}{2} ((a_{12} + a_{21}) x_1 + 2 a_{22} x_2) = \\frac{a_{12} + a_{21}}{2} x_1 + a_{22} x_2\n", + "$$\n", + "\n", + "\n", + "Donc le gradient de $\\frac{1}{2} {\\bf x}^T A {\\bf x}$ est :\n", + "\n", + "$$\n", + "\\nabla \\left( \\frac{1}{2} x^T A x \\right) = \\begin{pmatrix} a_{11} x_1 + \\frac{a_{12} + a_{21}}{2} x_2 \\\\ \\frac{a_{12} + a_{21}}{2} x_1 + a_{22} x_2 \\end{pmatrix} = \\frac{1}{2} (A + A^T) \\, {\\bf x}\n", + "$$\n", + "\n", + "Il faut faire le calcul pour une matrice $n \\times n$ mais on arrive au même résultat\n", + "et donc\n", + "\n", + "$$\n", + "J'({\\bf x}) = \\nabla J({\\bf x})\n", + "$$\n", + "\n", + "Ainsi on peut aussi calculer la dérivée suivant la direction $\\bf h$ avec le gradient :\n", + "\n", + "$$\n", + "J'({\\bf x})({\\bf h}) = \\nabla J({\\bf x}) \\, . \\, {\\bf h}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import plotly.offline as py\n", + "import plotly.graph_objects as go\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([[2,1], [1,2]])\n", + "b = np.array([-1, 0.5])\n", + "\n", + "# lets make the mesh\n", + "x = np.linspace(-20,20,100)\n", + "y = np.linspace(-20,20,100)\n", + "mx, my = np.meshgrid(x,y) \n", + "M = np.array(np.meshgrid(x,y)).swapaxes(0,2)\n", + "\n", + "# and compute 0.5 x.T A x - b x on each node of the mesh\n", + "MA = np.einsum(\"ijk, ka -> ija\", M, A)\n", + "mz = 0.5 * np.einsum(\"ijk, ijk -> ij\", MA, M) - M @ b" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "linkText": "Export to plot.ly", + "plotlyServerURL": "https://plot.ly", + "showLink": false + }, + "data": [ + { + "type": "surface", + "x": [ + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ], + [ + -20, + -19.595959595959595, + -19.19191919191919, + -18.78787878787879, + -18.383838383838384, + -17.97979797979798, + -17.575757575757574, + -17.171717171717173, + -16.767676767676768, + -16.363636363636363, + -15.959595959595958, + -15.555555555555555, + -15.151515151515152, + -14.747474747474747, + -14.343434343434343, + -13.93939393939394, + -13.535353535353536, + -13.131313131313131, + -12.727272727272727, + -12.323232323232324, + -11.919191919191919, + -11.515151515151516, + -11.11111111111111, + -10.707070707070708, + -10.303030303030303, + -9.8989898989899, + -9.494949494949495, + -9.090909090909092, + -8.686868686868687, + -8.282828282828284, + -7.878787878787879, + -7.474747474747476, + -7.070707070707071, + -6.666666666666666, + -6.262626262626263, + -5.858585858585858, + -5.454545454545455, + -5.05050505050505, + -4.646464646464647, + -4.242424242424242, + -3.8383838383838373, + -3.434343434343436, + -3.030303030303031, + -2.6262626262626263, + -2.2222222222222214, + -1.8181818181818201, + -1.4141414141414153, + -1.0101010101010104, + -0.6060606060606055, + -0.20202020202020066, + 0.20202020202020066, + 0.6060606060606055, + 1.0101010101010104, + 1.4141414141414153, + 1.8181818181818166, + 2.2222222222222214, + 2.6262626262626263, + 3.030303030303031, + 3.4343434343434325, + 3.8383838383838373, + 4.242424242424242, + 4.646464646464647, + 5.050505050505048, + 5.454545454545453, + 5.858585858585858, + 6.262626262626263, + 6.666666666666668, + 7.070707070707069, + 7.474747474747474, + 7.878787878787879, + 8.282828282828284, + 8.686868686868685, + 9.09090909090909, + 9.494949494949495, + 9.8989898989899, + 10.303030303030301, + 10.707070707070706, + 11.11111111111111, + 11.515151515151516, + 11.919191919191917, + 12.323232323232325, + 12.727272727272727, + 13.131313131313128, + 13.535353535353536, + 13.939393939393938, + 14.343434343434346, + 14.747474747474747, + 15.151515151515149, + 15.555555555555557, + 15.959595959595958, + 16.36363636363636, + 16.767676767676768, + 17.17171717171717, + 17.575757575757578, + 17.97979797979798, + 18.38383838383838, + 18.78787878787879, + 19.19191919191919, + 19.5959595959596, + 20 + ] + ], + "y": [ + [ + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20, + -20 + ], + [ + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595, + -19.595959595959595 + ], + [ + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919, + -19.19191919191919 + ], + [ + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879, + -18.78787878787879 + ], + [ + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384, + -18.383838383838384 + ], + [ + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798, + -17.97979797979798 + ], + [ + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574, + -17.575757575757574 + ], + [ + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173, + -17.171717171717173 + ], + [ + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768, + -16.767676767676768 + ], + [ + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363, + -16.363636363636363 + ], + [ + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958, + -15.959595959595958 + ], + [ + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555, + -15.555555555555555 + ], + [ + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152, + -15.151515151515152 + ], + [ + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747, + -14.747474747474747 + ], + [ + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343, + -14.343434343434343 + ], + [ + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394, + -13.93939393939394 + ], + [ + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536, + -13.535353535353536 + ], + [ + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131, + -13.131313131313131 + ], + [ + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727, + -12.727272727272727 + ], + [ + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324, + -12.323232323232324 + ], + [ + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919, + -11.919191919191919 + ], + [ + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516, + -11.515151515151516 + ], + [ + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111, + -11.11111111111111 + ], + [ + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708, + -10.707070707070708 + ], + [ + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303, + -10.303030303030303 + ], + [ + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899, + -9.8989898989899 + ], + [ + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495, + -9.494949494949495 + ], + [ + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092, + -9.090909090909092 + ], + [ + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687, + -8.686868686868687 + ], + [ + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284, + -8.282828282828284 + ], + [ + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879, + -7.878787878787879 + ], + [ + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476, + -7.474747474747476 + ], + [ + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071, + -7.070707070707071 + ], + [ + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666, + -6.666666666666666 + ], + [ + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263, + -6.262626262626263 + ], + [ + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858, + -5.858585858585858 + ], + [ + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455, + -5.454545454545455 + ], + [ + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505, + -5.05050505050505 + ], + [ + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647, + -4.646464646464647 + ], + [ + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242, + -4.242424242424242 + ], + [ + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373, + -3.8383838383838373 + ], + [ + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436, + -3.434343434343436 + ], + [ + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031, + -3.030303030303031 + ], + [ + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263, + -2.6262626262626263 + ], + [ + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214, + -2.2222222222222214 + ], + [ + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201, + -1.8181818181818201 + ], + [ + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153, + -1.4141414141414153 + ], + [ + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104, + -1.0101010101010104 + ], + [ + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055, + -0.6060606060606055 + ], + [ + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066, + -0.20202020202020066 + ], + [ + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066, + 0.20202020202020066 + ], + [ + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055, + 0.6060606060606055 + ], + [ + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104, + 1.0101010101010104 + ], + [ + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153, + 1.4141414141414153 + ], + [ + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166, + 1.8181818181818166 + ], + [ + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214, + 2.2222222222222214 + ], + [ + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263, + 2.6262626262626263 + ], + [ + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031, + 3.030303030303031 + ], + [ + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325, + 3.4343434343434325 + ], + [ + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373, + 3.8383838383838373 + ], + [ + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242, + 4.242424242424242 + ], + [ + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647, + 4.646464646464647 + ], + [ + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048, + 5.050505050505048 + ], + [ + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453, + 5.454545454545453 + ], + [ + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858, + 5.858585858585858 + ], + [ + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263, + 6.262626262626263 + ], + [ + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668, + 6.666666666666668 + ], + [ + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069, + 7.070707070707069 + ], + [ + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474, + 7.474747474747474 + ], + [ + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879, + 7.878787878787879 + ], + [ + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284, + 8.282828282828284 + ], + [ + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685, + 8.686868686868685 + ], + [ + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909, + 9.09090909090909 + ], + [ + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495, + 9.494949494949495 + ], + [ + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899, + 9.8989898989899 + ], + [ + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301, + 10.303030303030301 + ], + [ + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706, + 10.707070707070706 + ], + [ + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111, + 11.11111111111111 + ], + [ + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516, + 11.515151515151516 + ], + [ + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917, + 11.919191919191917 + ], + [ + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325, + 12.323232323232325 + ], + [ + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727, + 12.727272727272727 + ], + [ + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128, + 13.131313131313128 + ], + [ + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536, + 13.535353535353536 + ], + [ + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938, + 13.939393939393938 + ], + [ + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346, + 14.343434343434346 + ], + [ + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747, + 14.747474747474747 + ], + [ + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149, + 15.151515151515149 + ], + [ + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557, + 15.555555555555557 + ], + [ + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958, + 15.959595959595958 + ], + [ + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636, + 16.36363636363636 + ], + [ + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768, + 16.767676767676768 + ], + [ + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717, + 17.17171717171717 + ], + [ + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578, + 17.575757575757578 + ], + [ + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798, + 17.97979797979798 + ], + [ + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838, + 18.38383838383838 + ], + [ + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879, + 18.78787878787879 + ], + [ + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919, + 19.19191919191919 + ], + [ + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596, + 19.5959595959596 + ], + [ + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20, + 20 + ] + ], + "z": [ + [ + 1190, + 1165.7188042036528, + 1141.7641057034996, + 1118.135904499541, + 1094.8342005917764, + 1071.8589939802062, + 1049.21028466483, + 1026.8880726456487, + 1004.892357922661, + 983.2231404958677, + 961.8804203652687, + 940.8641975308642, + 920.1744719926538, + 899.8112437506377, + 879.7745128048158, + 860.0642791551882, + 840.680542801755, + 821.623303744516, + 802.8925619834711, + 784.4883175186205, + 766.4105703499642, + 748.6593204775023, + 731.2345679012345, + 714.1363126211611, + 697.3645546372819, + 680.919293949597, + 664.8005305581063, + 649.00826446281, + 633.5424956637077, + 618.4032241607999, + 603.5904499540864, + 589.104173043567, + 574.944393429242, + 561.1111111111111, + 547.6043260891746, + 534.4240383634323, + 521.5702479338843, + 509.04295480053054, + 496.84215896337116, + 484.9678604224059, + 473.42005917763487, + 462.19875522905824, + 451.30394857667585, + 440.73563922048777, + 430.4938271604938, + 420.5785123966943, + 410.98969492908884, + 401.7273747576778, + 392.791551882461, + 384.1822263034384, + 375.89939802061014, + 367.94306703397604, + 360.31323334353635, + 353.0098969492909, + 346.03305785123973, + 339.38271604938274, + 333.05887154372, + 327.0615243342516, + 321.3906744209775, + 316.0463218038976, + 311.0284664830119, + 306.3371084583205, + 301.97224772982344, + 297.9338842975207, + 294.22201816141217, + 290.8366493214978, + 287.7777777777777, + 285.04540353025203, + 282.63952657892054, + 280.56014692378335, + 278.8072645648403, + 277.38087950209166, + 276.2809917355372, + 275.507601265177, + 275.06070809101107, + 274.94031221303953, + 275.14641363126213, + 275.67901234567904, + 276.5381083562902, + 277.7237016630956, + 279.2357922660953, + 281.07438016528926, + 283.2394653606774, + 285.73104785225996, + 288.54912764003666, + 291.6937047240078, + 295.1647791041731, + 298.9623507805326, + 303.08641975308643, + 307.5369860218345, + 312.3140495867768, + 317.4176104479135, + 322.8476686052443, + 328.6042240587695, + 334.68727680848895, + 341.0968268544026, + 347.8328741965106, + 354.89541883481274, + 362.2844607693093, + 370 + ], + [ + 1166.3248648097133, + 1142.2069176614627, + 1118.4154678094071, + 1094.9505152535457, + 1071.8120599938782, + 1049.000102030405, + 1026.514641363126, + 1004.3556779920416, + 982.5232119171512, + 961.0172431384552, + 939.8377716559532, + 918.9847974696457, + 898.4583205795326, + 878.2583409856137, + 858.384858687889, + 838.8378736863585, + 819.6173859810225, + 800.7233955718802, + 782.1559024589327, + 763.9149066421794, + 746.0004081216201, + 728.4124068972554, + 711.1509029690847, + 694.2158963371085, + 677.6073870013264, + 661.3253749617386, + 645.369860218345, + 629.7408427711458, + 614.4383226201406, + 599.46229976533, + 584.8127742067135, + 570.4897459442914, + 556.4932149780635, + 542.8231813080298, + 529.4796449341904, + 516.4626058565453, + 503.7720640750943, + 491.4080195898378, + 479.3704724007754, + 467.6594225079074, + 456.2748699112335, + 445.21681461075406, + 434.48525660646874, + 424.0801958983776, + 414.0016324864809, + 404.2495663707785, + 394.8239975512703, + 385.7249260279563, + 376.9523518008366, + 368.5062748699112, + 360.38669523518007, + 352.59361289664326, + 345.12702785430054, + 337.9869401081521, + 331.1733496581981, + 324.6862565044383, + 318.5256606468728, + 312.69156208550146, + 307.1839608203245, + 302.0028568513417, + 297.1482501785532, + 292.62014080195894, + 288.418528721559, + 284.5434139373533, + 280.99479644934183, + 277.77267625752467, + 274.87705336190186, + 272.30792776247324, + 270.0652994592389, + 268.14916845219875, + 266.55953474135293, + 265.2963983267013, + 264.35975920824404, + 263.74961738598097, + 263.4659728599122, + 263.50882563003773, + 263.8781756963575, + 264.57402305887155, + 265.5963677175799, + 266.94520967248235, + 268.6205489235792, + 270.6223854708703, + 272.95071931435564, + 275.60555045403527, + 278.58687888990914, + 281.8947046219773, + 285.52902765023975, + 289.48984797469643, + 293.7771655953474, + 298.3909805121926, + 303.33129272523206, + 308.5981022344659, + 314.1914090398938, + 320.1112131415162, + 326.3575145393327, + 332.93031323334344, + 339.8296092235487, + 347.05540250994795, + 354.6076930925416, + 362.48648097132946 + ], + [ + 1142.9762269156208, + 1119.0215284154676, + 1095.393327211509, + 1072.0916233037444, + 1049.1164166921742, + 1026.4677073767982, + 1004.1454953576164, + 982.1497806346291, + 960.480563207836, + 939.1378430772369, + 918.1216202428323, + 897.4318947046219, + 877.0686664626057, + 857.0319355167838, + 837.3217018671563, + 817.937965513723, + 798.880726456484, + 780.1499846954392, + 761.7457402305887, + 743.6679930619324, + 725.9167431894704, + 708.4919906132027, + 691.3937353331293, + 674.6219773492501, + 658.176716661565, + 642.0579532700744, + 626.265687174778, + 610.7999183756759, + 595.660646872768, + 580.8478726660544, + 566.361595755535, + 552.20181614121, + 538.3685338230791, + 524.8617488011425, + 511.68146107540036, + 498.8276706458524, + 486.30037751249864, + 474.0995816753392, + 462.22528313437397, + 450.6774818896031, + 439.4561779410263, + 428.56137128864395, + 417.9930619324558, + 407.751249872462, + 397.83593510866234, + 388.247117641057, + 378.9847974696459, + 370.04897459442907, + 361.43964901540653, + 353.15682073257824, + 345.20048974594425, + 337.57065605550446, + 330.26731966125897, + 323.29048056320784, + 316.64013876135084, + 310.31629425568815, + 304.31894704621965, + 298.6480971329455, + 293.3037445158657, + 288.2858891949801, + 283.59453117028875, + 279.22967044179154, + 275.19130700948875, + 271.4794408733802, + 268.094072033466, + 265.03520048974593, + 262.30282624222014, + 259.8969492908886, + 257.8175696357514, + 256.06468727680846, + 254.63830221405973, + 253.53841444750532, + 252.76502397714512, + 252.31813080297923, + 252.19773492500758, + 252.40383634323024, + 252.93643505764717, + 253.79553106825833, + 254.98112437506373, + 256.4932149780634, + 258.3318028772574, + 260.4968880726456, + 262.98847056422807, + 265.8065503520049, + 268.9511274359759, + 272.4222018161412, + 276.21977349250074, + 280.3438424650545, + 284.7944087338027, + 289.571472298745, + 294.6750331598816, + 300.1050913172125, + 305.86164677073765, + 311.9446995204571, + 318.3542495663707, + 325.09029690847865, + 332.1528415467809, + 339.54188348127735, + 347.25742271196816, + 355.29945923885316 + ], + [ + 1119.9540863177228, + 1096.1626364656668, + 1072.6976839098052, + 1049.5592286501378, + 1026.7472706866647, + 1004.2618100193858, + 982.1028466483012, + 960.2703805734111, + 938.764411794715, + 917.584940312213, + 896.7319661259055, + 876.2054892357922, + 856.0055096418733, + 836.1320273441486, + 816.5850423426181, + 797.3645546372819, + 778.4705642281401, + 759.9030711151925, + 741.6620752984389, + 723.7475767778799, + 706.159575553515, + 688.8980716253444, + 671.9630649933681, + 655.354555657586, + 639.0725436179982, + 623.1170288746047, + 607.4880114274054, + 592.1854912764004, + 577.2094684215897, + 562.5599428629732, + 548.2369146005509, + 534.240383634323, + 520.5703499642893, + 507.22681359045004, + 494.20977451280487, + 481.51923273135395, + 469.1551882460974, + 457.11764105703503, + 445.40659116416697, + 434.02203856749315, + 422.96398326701353, + 412.2324252627284, + 401.82736455463737, + 391.7488011427406, + 381.9967350270381, + 372.57116620753, + 363.4720946842159, + 354.69952045709624, + 346.2534435261709, + 338.13386389143966, + 330.3407815529028, + 322.8741965105602, + 315.73410876441187, + 308.9205183144578, + 302.433425160698, + 296.27282930313237, + 290.438730741761, + 284.93112947658403, + 279.7500255076013, + 274.89541883481286, + 270.36730945821853, + 266.16569737781856, + 262.2905825936129, + 258.74196510560154, + 255.51984491378437, + 252.62422201816145, + 250.05509641873277, + 247.81246811549846, + 245.89633710845834, + 244.3067033976125, + 243.04356698296098, + 242.10692786450366, + 241.4967860422406, + 241.21314151617185, + 241.25599428629738, + 241.6253443526171, + 242.32119171513114, + 243.3435363738394, + 244.692378328742, + 246.3677175798388, + 248.36955412712993, + 250.69788797061526, + 253.35271911029488, + 256.3340475461688, + 259.6418732782369, + 263.2761963064994, + 267.2370166309561, + 271.52433425160694, + 276.13814916845223, + 281.0784613814917, + 286.3452708907254, + 291.9385776961535, + 297.85838179777573, + 304.1046831955924, + 310.67748188960314, + 317.57677787980816, + 324.80257116620754, + 332.3548617488011, + 340.23364962758905, + 348.43893480257117 + ], + [ + 1097.2584430160189, + 1073.63024181206, + 1050.3285379042954, + 1027.3533312927252, + 1004.7046219773493, + 982.3824099581675, + 960.38669523518, + 938.717477808387, + 917.374757677788, + 896.3585348433834, + 875.6688093051728, + 855.3055810631569, + 835.268850117335, + 815.5586164677073, + 796.174880114274, + 777.117641057035, + 758.3868992959901, + 739.9826548311396, + 721.9049076624833, + 704.1536577900215, + 686.7289052137537, + 669.6306499336803, + 652.8588919498011, + 636.4136312621162, + 620.2948678706255, + 604.5026017753291, + 589.036832976227, + 573.8975614733191, + 559.0847872666054, + 544.5985103560861, + 530.4387307417611, + 516.6054484236303, + 503.09866340169367, + 489.91837567595144, + 477.0645852464035, + 464.5372921130498, + 452.3364962758902, + 440.46219773492504, + 428.91439649015405, + 417.69309254157736, + 406.798285889195, + 396.2299765330069, + 385.988164473013, + 376.0728497092133, + 366.484032241608, + 357.221712070197, + 348.2858891949802, + 339.67656361595755, + 331.39373533312926, + 323.43740434649527, + 315.8075706560555, + 308.50423426181004, + 301.5273951637588, + 294.87705336190174, + 288.55320885623917, + 282.5558616467708, + 276.88501173349664, + 271.5406591164167, + 266.5228037955311, + 261.8314457708397, + 257.4665850423426, + 253.4282216100398, + 249.71635547393126, + 246.33098663401697, + 243.27211509029692, + 240.53974084277115, + 238.13386389143966, + 236.05448423630241, + 234.30160187735942, + 232.87521681461078, + 231.77532904805634, + 231.0019385776962, + 230.55504540353027, + 230.43464952555863, + 230.64075094378126, + 231.17334965819816, + 232.03244566880932, + 233.21803897561472, + 234.73012957861442, + 236.56871747780838, + 238.73380267319664, + 241.2253851647791, + 244.0434649525558, + 247.18804203652692, + 250.65911641669217, + 254.45668809305175, + 258.58075706560555, + 263.0313233343536, + 267.808386899296, + 272.91194776043255, + 278.34200591776346, + 284.0985613712886, + 290.181614121008, + 296.5911641669218, + 303.3272115090297, + 310.38975614733187, + 317.77879808182837, + 325.4943373125191, + 333.5363738394042, + 341.9049076624834 + ], + [ + 1074.8892970105092, + 1051.4243444546473, + 1028.28588919498, + 1005.4739312315071, + 982.9884705642281, + 960.8295071931435, + 938.9970411182533, + 917.4910723395573, + 896.3116008570555, + 875.4586266707478, + 854.9321497806345, + 834.7321701867156, + 814.858687888991, + 795.3117028874605, + 776.0912151821242, + 757.1972247729822, + 738.6297316600346, + 720.3887358432813, + 702.474237322722, + 684.8862360983572, + 667.6247321701867, + 650.6897255382105, + 634.0812162024283, + 617.7992041628405, + 601.8436894194471, + 586.2146719722477, + 570.9121518212427, + 555.9361289664321, + 541.2866034078155, + 526.9635751453934, + 512.9670441791653, + 499.2970105091317, + 485.9534741352923, + 472.93643505764715, + 460.2458932761963, + 447.8818487909396, + 435.84430160187736, + 424.1332517090093, + 412.74869911233554, + 401.6906438118559, + 390.95908580757055, + 380.5540250994796, + 370.4754616875829, + 360.7233955718804, + 351.29782675237215, + 342.1987552290583, + 333.4261810019386, + 324.98010407101316, + 316.86052443628205, + 309.06744209774513, + 301.60085705540246, + 294.4607693092541, + 287.6471788593, + 281.1600857055402, + 274.9994898479747, + 269.16539128660344, + 263.65779002142637, + 258.4766860524436, + 253.62207937965513, + 249.09397000306097, + 244.89235792266095, + 241.01724313845523, + 237.4686256504438, + 234.24650545862667, + 231.35088256300375, + 228.78175696357513, + 226.53912866034077, + 224.62299765330067, + 223.03336394245486, + 221.77022752780329, + 220.83358840934596, + 220.22344658708292, + 219.93980206101418, + 219.98265483113968, + 220.35200489745944, + 221.04785225997344, + 222.07019691868175, + 223.41903887358433, + 225.09437812468116, + 227.09621467197223, + 229.4245485154576, + 232.0793796551372, + 235.0607080910111, + 238.36853382307928, + 242.00285685134165, + 245.96367717579838, + 250.2509947964493, + 254.86480971329456, + 259.80512192633404, + 265.07193143556776, + 270.66523824099573, + 276.58504234261807, + 282.8313437404346, + 289.4041424344455, + 296.3034384246505, + 303.5292317110498, + 311.08152229364356, + 318.9603101724313, + 327.16559534741356, + 335.6973778185899 + ], + [ + 1052.8466483011937, + 1029.544944393429, + 1006.5697377818587, + 983.9210284664831, + 961.5988164473013, + 939.6031017243139, + 917.9338842975205, + 896.5911641669217, + 875.574941332517, + 854.8852157943066, + 834.5219875522905, + 814.4852566064686, + 794.775022956841, + 775.3912866034078, + 756.3340475461687, + 737.6033057851239, + 719.1990613202735, + 701.121314151617, + 683.370064279155, + 665.9453117028874, + 648.8470564228138, + 632.0752984389347, + 615.6300377512498, + 599.5112743597592, + 583.7190082644628, + 568.2532394653607, + 553.1139679624528, + 538.3011937557392, + 523.8149168452198, + 509.65513723089475, + 495.82185491276397, + 482.31506989082743, + 469.1347821650852, + 456.2809917355371, + 443.7536986021834, + 431.55290276502393, + 419.67860422405863, + 408.1308029792878, + 396.9094990307111, + 386.0146923783287, + 375.44638302214054, + 365.20457096214676, + 355.2892561983471, + 345.7004387307417, + 336.4381185593306, + 327.5022956841138, + 318.8929701050913, + 310.610141822263, + 302.653810835629, + 295.02397714518924, + 287.72064075094374, + 280.74380165289256, + 274.09345985103556, + 267.7696153453728, + 261.7722681359044, + 256.1014182226303, + 250.75706560555042, + 245.73921028466478, + 241.04785225997344, + 236.68299153147632, + 232.64462809917353, + 228.93276196306493, + 225.54739312315067, + 222.4885215794306, + 219.75614733190486, + 217.35027038057336, + 215.27089072543615, + 213.51800836649318, + 212.09162330374448, + 210.99173553719004, + 210.21834506682987, + 209.77145189266398, + 209.65105601469233, + 209.85715743291496, + 210.38975614733187, + 211.24885215794302, + 212.43444546474845, + 213.94653606774816, + 215.7851239669421, + 217.95020916233034, + 220.44179165391284, + 223.2598714416896, + 226.4044485256606, + 229.8755229058259, + 233.67309458218543, + 237.79716355473929, + 242.2477298234874, + 247.02479338842969, + 252.12835424956634, + 257.5584124068972, + 263.3149678604223, + 269.39802061014177, + 275.8075706560554, + 282.5436179981634, + 289.60616263646557, + 296.9952045709621, + 304.71074380165294, + 312.7527803285379, + 321.12131415161724, + 329.81634527089074 + ], + [ + 1031.130496888073, + 1007.9920416284052, + 985.1800836649321, + 962.6946229976535, + 940.5356596265688, + 918.7031935516785, + 897.1972247729823, + 876.0177532904806, + 855.1647791041732, + 834.6383022140599, + 814.4383226201409, + 794.5648403224162, + 775.0178553208857, + 755.7973676155495, + 736.9033772064075, + 718.3358840934599, + 700.0948882767066, + 682.1803897561473, + 664.5923885317825, + 647.3308846036119, + 630.3958779716355, + 613.7873686358536, + 597.5053565962656, + 581.5498418528722, + 565.9208244056729, + 550.618304254668, + 535.6422813998573, + 520.9927558412409, + 506.6697275788186, + 492.6731966125907, + 479.00316294255697, + 465.65962656871756, + 452.6425874910724, + 439.9520457096215, + 427.5880012243649, + 415.55045403530255, + 403.8394041424345, + 392.4548515457607, + 381.3967962452811, + 370.6652382409959, + 360.2601775329049, + 350.1816141210082, + 340.42954800530566, + 331.0039791857974, + 321.9049076624835, + 313.1323334353638, + 304.6862565044384, + 296.56667686970724, + 288.77359453117026, + 281.3070094888277, + 274.16692174267945, + 267.35333129272533, + 260.86623813896546, + 254.7056422813999, + 248.87154372002863, + 243.3639424548516, + 238.18283848586884, + 233.32823181308032, + 228.8001224364861, + 224.59851035608617, + 220.72339557188045, + 217.17477808386906, + 213.95265789205192, + 211.05703499642897, + 208.48790939700032, + 206.24528109376595, + 204.32915008672586, + 202.73951637588004, + 201.47637996122847, + 200.53974084277118, + 199.92959902050814, + 199.64595449443937, + 199.6888072645649, + 200.05815733088465, + 200.75400469339868, + 201.77634935210696, + 203.12519130700952, + 204.80053055810635, + 206.80236710539745, + 209.13070094888278, + 211.7855320885624, + 214.7668605244363, + 218.07468625650444, + 221.70900928476692, + 225.66982960922354, + 229.95714722987455, + 234.57096214671975, + 239.5112743597592, + 244.77808386899304, + 250.371390674421, + 256.29119477604326, + 262.53749617385984, + 269.1102948678706, + 276.00959085807574, + 283.23538414447506, + 290.78767472706863, + 298.66646260585657, + 306.87174778083863, + 315.4035302520152, + 324.2618100193858 + ], + [ + 1009.7408427711458, + 986.7656361595755, + 964.1169268441996, + 941.794714825018, + 919.7990001020304, + 898.1297826752373, + 876.7870625446382, + 855.7708397102339, + 835.0811141720234, + 814.7178859300071, + 794.6811549841852, + 774.9709213345577, + 755.5871849811244, + 736.5299459238853, + 717.7992041628405, + 699.39495969799, + 681.3172125293338, + 663.5659626568718, + 646.141210080604, + 629.0429548005305, + 612.2711968166514, + 595.8259361289664, + 579.7071727374757, + 563.9149066421794, + 548.4491378430772, + 533.3098663401694, + 518.4970921334557, + 504.0108152229365, + 489.8510356086114, + 476.0177532904806, + 462.510968268544, + 449.3306805428018, + 436.47689011325383, + 423.94959697990004, + 411.7488011427406, + 399.8745026017753, + 388.32670135700437, + 377.10539740842773, + 366.21059075604535, + 355.64228139985715, + 345.4004693398632, + 335.48515457606374, + 325.89633710845834, + 316.6340169370473, + 307.6981940618304, + 299.088868482808, + 290.80604019997963, + 282.8497092133456, + 275.21987552290585, + 267.9165391286603, + 260.9397000306092, + 254.28935822875215, + 247.96551372308951, + 241.9681665136211, + 236.29731660034693, + 230.95296398326704, + 225.93510866238142, + 221.24375063769003, + 216.878889909193, + 212.84052647689015, + 209.12866034078155, + 205.7432915008673, + 202.68441995714727, + 199.95204570962147, + 197.54616875829, + 195.46678910315276, + 193.7139067442098, + 192.28752168146107, + 191.18763391490666, + 190.41424344454649, + 189.9673502703806, + 189.84695439240895, + 190.05305581063158, + 190.58565452504848, + 191.44475053565967, + 192.63034384246507, + 194.14243444546474, + 195.9810223446587, + 198.14610754004696, + 200.63769003162943, + 203.4557698194062, + 206.6003469033772, + 210.07142128354243, + 213.86899295990207, + 217.99306193245587, + 222.443628201204, + 227.22069176614633, + 232.32425262728287, + 237.75431078461384, + 243.51086623813896, + 249.59391898785836, + 256.0034690337721, + 262.73951637588, + 269.8020610141823, + 277.1911029486787, + 284.9066421793694, + 292.9486787062545, + 301.3172125293337, + 310.01224364860735, + 319.0337720640751 + ], + [ + 988.6776859504132, + 965.8657279869401, + 943.3802673196611, + 921.2213039485766, + 899.3888378736864, + 877.8828690949902, + 856.7033976124884, + 835.850423426181, + 815.3239465360678, + 795.1239669421489, + 775.250484644424, + 755.7034996428937, + 736.4830119375574, + 717.5890215284154, + 699.0215284154679, + 680.7805325987144, + 662.8660340781553, + 645.2780328537905, + 628.0165289256197, + 611.0815222936435, + 594.4730129578613, + 578.1910009182736, + 562.2354861748801, + 546.6064687276809, + 531.3039485766758, + 516.3279257218652, + 501.6784001632487, + 487.35537190082647, + 473.3588409345985, + 459.6888072645648, + 446.3452708907255, + 433.3282318130803, + 420.6376900316294, + 408.2736455463728, + 396.2360983573105, + 384.5250484644424, + 373.14049586776855, + 362.08244056728904, + 351.3508825630038, + 340.94582185491277, + 330.867258443016, + 321.1151923273136, + 311.6896235078053, + 302.59055198449136, + 293.8179777573717, + 285.3719008264463, + 277.2523211917152, + 269.45923885317825, + 261.9926538108356, + 254.8525660646872, + 248.0389756147332, + 241.55188246097342, + 235.3912866034078, + 229.5571880420365, + 224.0495867768595, + 218.86848280787677, + 214.01387613508825, + 209.485766758494, + 205.28415467809407, + 201.40903989388838, + 197.86042240587693, + 194.6383022140598, + 191.7426793184369, + 189.17355371900828, + 186.93092541577388, + 185.0147944087338, + 183.42516069788795, + 182.1620242832364, + 181.22538516477908, + 180.61524334251604, + 180.3315988164473, + 180.3744515865728, + 180.74380165289256, + 181.4396490154066, + 182.46199367411486, + 183.81083562901745, + 185.48617488011428, + 187.48801142740535, + 189.8163452708907, + 192.4711764105703, + 195.45250484644424, + 198.7603305785124, + 202.3946536067748, + 206.3554739312315, + 210.64279155188242, + 215.25660646872768, + 220.1969186817672, + 225.46372819100088, + 231.05703499642897, + 236.9768390980512, + 243.22314049586768, + 249.79593918987857, + 256.6952351800836, + 263.92102846648305, + 271.4733190490766, + 279.35210692786444, + 287.5573921028467, + 296.08917457402305, + 304.9474543413938, + 314.1322314049587 + ], + [ + 967.9410264258748, + 945.2923171104987, + 922.9701050913171, + 900.9743903683298, + 879.3051729415364, + 857.9624528109375, + 836.9462299765329, + 816.2565044383226, + 795.8932761963064, + 775.8565452504845, + 756.146311600857, + 736.7625752474238, + 717.7053361901848, + 698.9745944291399, + 680.5703499642893, + 662.4926027956329, + 644.7413529231711, + 627.3166003469033, + 610.2183450668299, + 593.4465870829507, + 577.0013263952657, + 560.8825630037751, + 545.0902969084786, + 529.6245281093765, + 514.4852566064686, + 499.6724823997551, + 485.18620548923576, + 471.0264258749108, + 457.19314355677983, + 443.68635853484335, + 430.50607080910106, + 417.6522803795531, + 405.12498724619934, + 392.9241914090398, + 381.0498928680746, + 369.5020916233037, + 358.28078767472704, + 347.38598102234465, + 336.8176716661565, + 326.5758596061626, + 316.6605448423629, + 307.07172737475764, + 297.80940720334655, + 288.8735843281297, + 280.26425874910717, + 271.981430466279, + 264.0250994796449, + 256.39526578920515, + 249.09192939495966, + 242.11509029690842, + 235.4647484950515, + 229.1409039893888, + 223.1435567799204, + 217.47270686664623, + 212.12835424956634, + 207.11049892868073, + 202.41914090398933, + 198.05428017549224, + 194.01591674318945, + 190.3040506070809, + 186.9186817671666, + 183.85981022344654, + 181.12743597592083, + 178.7215590245893, + 176.6421793694521, + 174.8892970105091, + 173.46291194776038, + 172.36302418120596, + 171.58963371084582, + 171.14274053667992, + 171.02234465870825, + 171.2284460769309, + 171.76104479134779, + 172.62014080195897, + 173.8057341087644, + 175.31782471176408, + 177.15641261095803, + 179.32149780634626, + 181.8130802979288, + 184.63116008570552, + 187.77573716967655, + 191.24681154984182, + 195.04438322620135, + 199.16845219875523, + 203.61901846750325, + 208.3960820324457, + 213.49964289358226, + 218.9297010509131, + 224.68625650443835, + 230.7693092541577, + 237.17885930007134, + 243.91490664217935, + 250.97745128048152, + 258.3664932149781, + 266.0820324456688, + 274.1240689725538, + 282.49260279563316, + 291.1876339149066, + 300.2091623303745, + 309.5571880420365 + ], + [ + 947.5308641975308, + 925.0454035302519, + 902.8864401591674, + 881.0539740842771, + 859.5480053055811, + 838.3685338230792, + 817.5155596367716, + 796.9890827466586, + 776.7891031527395, + 756.9156208550148, + 737.3686358534843, + 718.148148148148, + 699.2541577390064, + 680.6866646260586, + 662.4456688093052, + 644.531170288746, + 626.9431690643813, + 609.6816651362107, + 592.7466585042342, + 576.1381491684522, + 559.8561371288645, + 543.9006223854709, + 528.2716049382716, + 512.9690847872666, + 497.9930619324558, + 483.3435363738394, + 469.02050811141714, + 455.0239771451893, + 441.35394347515563, + 428.01040710131616, + 414.9933680236711, + 402.3028262422202, + 389.9387817569636, + 377.9012345679012, + 366.19018467503315, + 354.80563207835934, + 343.7475767778798, + 333.0160187735945, + 322.61095806550355, + 312.53239465360673, + 302.78032853790427, + 293.3547597183961, + 284.25568819508214, + 275.4831139679624, + 267.037037037037, + 258.9174574023059, + 251.124375063769, + 243.6577900214264, + 236.51770227527803, + 229.7041118253239, + 223.21701867156415, + 217.05642281399858, + 211.22232425262726, + 205.71472298745024, + 200.5336190184675, + 195.67901234567904, + 191.15090296908477, + 186.94929088868483, + 183.07417610447914, + 179.52555861646772, + 176.30343842465055, + 173.40781552902763, + 170.83868992959904, + 168.59606162636464, + 166.67993061932458, + 165.0902969084787, + 163.82716049382717, + 162.89052137536987, + 162.2803795531068, + 161.99673502703808, + 162.03958779716356, + 162.40893786348332, + 163.10478522599732, + 164.12712988470562, + 165.47597183960823, + 167.151311090705, + 169.1531476379961, + 171.48148148148147, + 174.1363126211611, + 177.11764105703497, + 180.42546678910318, + 184.05978981736558, + 188.0206101418222, + 192.30792776247324, + 196.9217426793184, + 201.86205489235797, + 207.12886440159167, + 212.72217120701964, + 218.641975308642, + 224.8882767064585, + 231.46107540046927, + 238.3603713906744, + 245.58616467707367, + 253.1384552596674, + 261.01724313845517, + 269.2225283134373, + 277.75431078461384, + 286.61259055198445, + 295.7973676155495, + 305.30864197530866 + ], + [ + 927.4471992653811, + 905.1249872461992, + 883.1292725232119, + 861.4600550964188, + 840.1173349658199, + 819.1011121314152, + 798.4113865932046, + 778.0481583511887, + 758.0114274053668, + 738.3011937557392, + 718.9174574023059, + 699.8602183450669, + 681.129476584022, + 662.7252321191716, + 644.6474849505151, + 626.8962350780533, + 609.4714825017857, + 592.3732272217121, + 575.6014692378329, + 559.1562085501481, + 543.0374451586573, + 527.245179063361, + 511.7794102642588, + 496.6401387613509, + 481.82736455463737, + 467.34108764411803, + 453.1813080297929, + 439.3480257116621, + 425.8412406897255, + 412.6609529639834, + 399.80716253443535, + 387.27986940108156, + 375.0790735639221, + 363.2047750229568, + 351.6569737781859, + 340.43566982960925, + 329.5408631772268, + 318.9725538210387, + 308.7307417610448, + 298.81542699724514, + 289.2266095296399, + 279.9642893582289, + 271.028466483012, + 262.4191409039894, + 254.1363126211611, + 246.17998163452717, + 238.55014794408737, + 231.24681154984188, + 224.26997245179066, + 217.6196306499337, + 211.295786144271, + 205.2984389348026, + 199.62758902152845, + 194.28323640444856, + 189.26538108356294, + 184.57402305887157, + 180.20916233037445, + 176.17079889807167, + 172.4589327619631, + 169.0735639220488, + 166.01469237832876, + 163.282318130803, + 160.87644117947153, + 158.79706152433428, + 157.0441791653913, + 155.6177941026426, + 154.51790633608817, + 153.74451586572803, + 153.2976226915621, + 153.17722681359047, + 153.3833282318131, + 153.91592694623, + 154.77502295684118, + 155.96061626364659, + 157.47270686664626, + 159.31129476584022, + 161.47637996122842, + 163.96796245281095, + 166.7860422405877, + 169.9306193245587, + 173.401693704724, + 177.1992653810836, + 181.3233343536374, + 185.7739006223855, + 190.55096418732782, + 195.65452504846448, + 201.08458320579535, + 206.84113865932045, + 212.92419140903993, + 219.33374145495355, + 226.06978879706148, + 233.13233343536376, + 240.5213753698602, + 248.23691460055102, + 256.27895112743596, + 264.6474849505152, + 273.3425160697888, + 282.36404448525656, + 291.7120701969187, + 301.38659320477507 + ], + [ + 907.6900316294256, + 885.531068258341, + 863.6986021834506, + 842.1926334047547, + 821.0131619222528, + 800.1601877359453, + 779.6337108458321, + 759.4337312519132, + 739.5602489541883, + 720.0132639526578, + 700.7927762473216, + 681.8987858381797, + 663.3312927252322, + 645.0902969084786, + 627.1757983879195, + 609.5877971635547, + 592.3262932353841, + 575.3912866034078, + 558.7827772676258, + 542.500765228038, + 526.5452504846444, + 510.9162330374452, + 495.61371288644017, + 480.6376900316295, + 465.98816447301294, + 451.66513621059073, + 437.66860524436277, + 423.99857157432916, + 410.6550352004897, + 397.6379961228446, + 384.9474543413937, + 372.5834098561371, + 360.54586266707486, + 348.8348127742067, + 337.4502601775329, + 326.3922048770533, + 315.6606468727681, + 305.2555861646771, + 295.1770227527804, + 285.42495663707786, + 275.9993878175696, + 266.90031629425573, + 258.12774206713607, + 249.68166513621057, + 241.56208550147943, + 233.7690031629426, + 226.30241812059995, + 219.16233037445159, + 212.34873992449747, + 205.86164677073768, + 199.70105091317214, + 193.86695235180085, + 188.3593510866238, + 183.17824711764104, + 178.32364044485257, + 173.79553106825836, + 169.59391898785836, + 165.71880420365267, + 162.17018671564125, + 158.9480665238241, + 156.05244362820122, + 153.48331802877257, + 151.24068972553823, + 149.3245587184981, + 147.73492500765227, + 146.4717885930007, + 145.5351494745434, + 144.92500765228036, + 144.64136312621162, + 144.68421589633712, + 145.05356596265688, + 145.7494133251709, + 146.77175798387918, + 148.12059993878177, + 149.7959391898786, + 151.79777573716967, + 154.12610958065503, + 156.78094072033463, + 159.76226915620856, + 163.0700948882767, + 166.70441791653914, + 170.66523824099582, + 174.95255586164672, + 179.566370778492, + 184.50668299153148, + 189.77349250076526, + 195.36679930619323, + 201.28660340781548, + 207.53290480563209, + 214.10570349964289, + 221.0049994898479, + 228.23079277624734, + 235.78308335884086, + 243.66187123762887, + 251.86715641261094, + 260.39893888378725, + 269.2572186511581, + 278.44199571472296, + 287.95327007448225, + 297.79104173043567 + ], + [ + 888.2593612896643, + 866.2636465666769, + 844.5944291398836, + 823.2517090092848, + 802.2354861748801, + 781.5457606366697, + 761.1825323946535, + 741.1458014488318, + 721.4355677992041, + 702.0518314457709, + 682.9945923885317, + 664.2638506274869, + 645.8596061626364, + 627.7818589939801, + 610.0306091215182, + 592.6058565452504, + 575.507601265177, + 558.7358432812978, + 542.2905825936127, + 526.1718192021223, + 510.37955310682577, + 494.9137843077237, + 479.77451280481574, + 464.9617385981022, + 450.4754616875829, + 436.3156820732579, + 422.48239975512695, + 408.9756147331905, + 395.7953270074481, + 382.94153657790025, + 370.41424344454646, + 358.21344760738697, + 346.3391490664217, + 334.7913478216508, + 323.5700438730742, + 312.67523722069177, + 302.1069278645036, + 291.86511580450974, + 281.9498010407101, + 272.36098357310476, + 263.09866340169367, + 254.1628405264769, + 245.55351494745432, + 237.27068666462603, + 229.314355677992, + 221.68452198755233, + 214.3811855933068, + 207.40434649525557, + 200.7540046933986, + 194.4301601877359, + 188.43281297826752, + 182.76196306499335, + 177.41761044791346, + 172.39975512702782, + 167.70839710233648, + 163.34353637383936, + 159.30517294153657, + 155.59330680542797, + 152.2079379655137, + 149.14906642179366, + 146.41669217426795, + 144.01081522293643, + 141.9314355677992, + 140.17855320885621, + 138.75216814610752, + 137.65228037955308, + 136.87888990919294, + 136.431996735027, + 136.31160085705537, + 136.517702275278, + 137.0503009896949, + 137.90939700030606, + 139.0949903071115, + 140.6070809101112, + 142.44566880930518, + 144.61075400469338, + 147.10233649627588, + 149.92041628405264, + 153.06499336802366, + 156.5360677481889, + 160.3336394245485, + 164.45770839710232, + 168.90827466585037, + 173.68533823079278, + 178.78889909192935, + 184.2189572492603, + 189.97551270278544, + 196.0585654525048, + 202.4681154984185, + 209.20416284052646, + 216.26670747882864, + 223.6557494133252, + 231.37128864401583, + 239.413325170901, + 247.7818589939802, + 256.47689011325366, + 265.4984185287216, + 274.8464442403836, + 284.52096724824, + 294.52198755229057 + ], + [ + 869.1551882460972, + 847.322722171207, + 825.8167533925109, + 804.6372819100093, + 783.7843077237018, + 763.2578308335883, + 743.0578512396694, + 723.1843689419447, + 703.6373839404142, + 684.4168962350781, + 665.5229058259359, + 646.9554127129884, + 628.7144168962351, + 610.7999183756759, + 593.211917151311, + 575.9504132231405, + 559.0154065911642, + 542.4068972553821, + 526.1248852157943, + 510.1693704724008, + 494.54035302520145, + 479.2378328741965, + 464.2618100193858, + 449.61228446076933, + 435.2892561983471, + 421.2927252321192, + 407.6226915620855, + 394.27915518824614, + 381.262116110601, + 368.57157432915017, + 356.2075298438935, + 344.1699826548312, + 332.45893276196307, + 321.07438016528926, + 310.01632486480975, + 299.2847668605244, + 288.87970615243347, + 278.8011427405367, + 269.04907662483424, + 259.623507805326, + 250.524436282012, + 241.75186205489237, + 233.30578512396696, + 225.18620548923582, + 217.3931231506989, + 209.9265381083563, + 202.78645036220797, + 195.97285991225385, + 189.48576675849404, + 183.32517090092847, + 177.4910723395572, + 171.9834710743802, + 166.8023671053974, + 161.9477604326089, + 157.41965105601471, + 153.21803897561475, + 149.34292419140903, + 145.79430670339758, + 142.57218651158047, + 139.67656361595755, + 137.10743801652893, + 134.86480971329456, + 132.9486787062545, + 131.35904499540865, + 130.09590858075708, + 129.15926946229976, + 128.54912764003672, + 128.26548311396795, + 128.30833588409345, + 128.67768595041323, + 129.37353331292726, + 130.39587797163554, + 131.7447199265381, + 133.42005917763493, + 135.42189572492603, + 137.75022956841138, + 140.40506070809099, + 143.3863891439649, + 146.69421487603307, + 150.32853790429544, + 154.28935822875218, + 158.5766758494031, + 163.19049076624827, + 168.13080297928784, + 173.39761248852156, + 178.99091929394964, + 184.91072339557186, + 191.15702479338842, + 197.7298234873993, + 204.62911947760432, + 211.85491276400361, + 219.40720334659733, + 227.2859912253851, + 235.4912764003674, + 244.02305887154372, + 252.8813386389143, + 262.0661157024794, + 271.5773900622385, + 281.4151617181921, + 291.5794306703398 + ], + [ + 850.3775124987246, + 828.7082950719315, + 807.3655749413324, + 786.349352106928, + 765.6596265687175, + 745.2963983267014, + 725.2596673808796, + 705.5494337312521, + 686.1656973778187, + 667.1084583205795, + 648.3777165595347, + 629.9734720946843, + 611.895724926028, + 594.144475053566, + 576.7197224772982, + 559.6214671972248, + 542.8497092133456, + 526.4044485256607, + 510.28568513417, + 494.4934190388737, + 479.02765023977145, + 463.8883787368637, + 449.07560453015, + 434.5893276196307, + 420.42954800530566, + 406.5962656871748, + 393.0894806652382, + 379.90919293949605, + 367.055402509948, + 354.52810937659433, + 342.3273135394348, + 330.4530149984696, + 318.90521375369866, + 307.6839098051219, + 296.7891031527396, + 286.22079379655133, + 275.9789817365575, + 266.0636669727579, + 256.4748495051526, + 247.21252933374146, + 238.27670645852467, + 229.66738087950216, + 221.38455259667387, + 213.42822161003983, + 205.79838791960003, + 198.49505152535463, + 191.51821242730338, + 184.86787062544641, + 178.54402611978372, + 172.54667891031525, + 166.8758289970412, + 161.53147637996128, + 156.5136210590756, + 151.82226303438426, + 147.45740230588717, + 143.41903887358436, + 139.70717273747582, + 136.3218038975615, + 133.26293235384145, + 130.5305581063157, + 128.12468115498422, + 126.045301499847, + 124.29241914090403, + 122.86603407815531, + 121.76614631160088, + 120.99275584124071, + 120.54586266707483, + 120.42546678910318, + 120.63156820732578, + 121.1641669217427, + 122.02326293235386, + 123.20885623915927, + 124.72094684215898, + 126.55953474135293, + 128.7246199367412, + 131.21620242832367, + 134.0342822161004, + 137.17885930007142, + 140.64993368023673, + 144.44750535659625, + 148.57157432915014, + 153.0221405978982, + 157.7992041628405, + 162.90276502397717, + 168.33282318130802, + 174.08937863483325, + 180.1724313845526, + 186.58198143046624, + 193.31802877257425, + 200.38057341087642, + 207.76961534537287, + 215.48515457606368, + 223.52719110294862, + 231.89572492602798, + 240.59075604530148, + 249.61228446076925, + 258.9603101724314, + 268.6348331802877, + 278.63585348433844, + 288.96337108458323 + ], + [ + 831.9263340475462, + 810.4203652688499, + 789.2408937863482, + 768.3879196000408, + 747.8614427099275, + 727.6614631160087, + 707.7879808182837, + 688.2409958167534, + 669.0205081114173, + 650.1265177022754, + 631.5590245893276, + 613.3180287725743, + 595.4035302520151, + 577.8155290276502, + 560.5540250994796, + 543.6190184675033, + 527.0105091317213, + 510.72849709213335, + 494.7729823487399, + 479.1439649015407, + 463.8414447505357, + 448.865421895725, + 434.2158963371084, + 419.8928680746863, + 405.89633710845834, + 392.2263034384247, + 378.88276706458527, + 365.86572798694016, + 353.1751862054892, + 340.8111417202326, + 328.7735945311704, + 317.06254463830226, + 305.67799204162844, + 294.6199367411489, + 283.8883787368636, + 273.4833180287726, + 263.40475461687583, + 253.6526885011734, + 244.22711968166516, + 235.1280481583512, + 226.35547393123147, + 217.90939700030614, + 209.78981736557498, + 201.99673502703808, + 194.5301499846954, + 187.39006223854713, + 180.576471788593, + 174.0893786348332, + 167.92878277726763, + 162.0946842158963, + 156.58708295071935, + 151.40597898173655, + 146.5513723089481, + 142.02326293235382, + 137.8216508519539, + 133.94653606774818, + 130.39791857973677, + 127.17579838791958, + 124.28017549229673, + 121.71104989286806, + 119.46842158963372, + 117.55229058259361, + 115.9626568717478, + 114.69952045709624, + 113.76288133863892, + 113.15273951637587, + 112.86909499030712, + 112.91194776043261, + 113.2812978267524, + 113.9771451892664, + 114.9994898479747, + 116.34833180287727, + 118.02367105397408, + 120.02550760126519, + 122.35384144475054, + 125.00867258443014, + 127.99000102030404, + 131.2978267523722, + 134.93214978063466, + 138.89297010509128, + 143.1802877257423, + 147.79410264258752, + 152.73441485562694, + 158.00122436486075, + 163.59453117028872, + 169.51433527191108, + 175.76063666972755, + 182.33343536373835, + 189.2327313539435, + 196.4585246403428, + 204.01081522293634, + 211.88960310172433, + 220.09488827670643, + 228.6266707478829, + 237.48495051525356, + 246.66972757881837, + 256.1810019385777, + 266.0187735945311, + 276.18304254667896, + 286.673808795021 + ], + [ + 813.801652892562, + 792.458932761963, + 771.4427099275583, + 750.752984389348, + 730.3897561473318, + 710.3530252015099, + 690.6427915518823, + 671.2590551984492, + 652.2018161412101, + 633.4710743801652, + 615.0668299153148, + 596.9890827466585, + 579.2378328741966, + 561.8130802979288, + 544.7148250178552, + 527.9430670339761, + 511.4978063462912, + 495.3790429548005, + 479.5867768595041, + 464.12100806040195, + 448.98173655749406, + 434.1689623507805, + 419.6826854402612, + 405.5229058259361, + 391.68962350780527, + 378.1828384858688, + 365.00255076012644, + 352.1487603305785, + 339.6214671972247, + 327.4206713600653, + 315.5463728191, + 303.99857157432916, + 292.77726762575253, + 281.88246097337003, + 271.3141516171819, + 261.072339557188, + 251.15702479338842, + 241.56820732578305, + 232.305887154372, + 223.37006427915517, + 214.76073870013258, + 206.47791041730437, + 198.52157943067033, + 190.89174574023056, + 183.58840934598507, + 176.6115702479339, + 169.96122844607692, + 163.63738394041422, + 157.64003673094578, + 151.96918681767164, + 146.62483420059178, + 141.60697887970613, + 136.91562085501477, + 132.55076012651767, + 128.51239669421489, + 124.80053055810632, + 121.41516171819202, + 118.35629017447195, + 115.62391592694622, + 113.21803897561473, + 111.13865932047749, + 109.38577696153452, + 107.95939189878584, + 106.8595041322314, + 106.08611366187122, + 105.63922048770533, + 105.5188246097337, + 105.72492602795631, + 106.2575247423732, + 107.11662075298437, + 108.3022140597898, + 109.81430466278948, + 111.65289256198346, + 113.81797775737168, + 116.3095602489542, + 119.12764003673092, + 122.27221712070195, + 125.74329150086723, + 129.5408631772268, + 133.6649321497806, + 138.11549841852874, + 142.89256198347107, + 147.99612284460764, + 153.42618100193857, + 159.18273645546373, + 165.26578920518318, + 171.67533925109683, + 178.41138659320472, + 185.47393123150698, + 192.86297316600346, + 200.57851239669415, + 208.6205489235792, + 216.98908274665845, + 225.6841138659321, + 234.70564228139983, + 244.05366799306182, + 253.7281910009183, + 263.7292113049688, + 274.0567289052138, + 284.7107438016529 + ], + [ + 796.003469033772, + 774.8239975512703, + 753.9710233649627, + 733.4445464748495, + 713.2445668809305, + 693.3710845832057, + 673.8240995816752, + 654.6036118763392, + 635.7096214671972, + 617.1421283542496, + 598.9011325374962, + 580.986634016937, + 563.3986327925724, + 546.1371288644016, + 529.2021222324253, + 512.5936128966432, + 496.3116008570555, + 480.35608611366195, + 464.72706866646257, + 449.4245485154576, + 434.44852566064685, + 419.79900010203045, + 405.4759718396082, + 391.47944087338027, + 377.8094072033466, + 364.46587082950725, + 351.4488317518621, + 338.7582899704112, + 326.3942454851546, + 314.35669829609225, + 302.6456484032242, + 291.2610958065504, + 280.2030405060708, + 269.47148250178554, + 259.0664217936946, + 248.98785838179774, + 239.23579226609533, + 229.81022344658706, + 220.71115192327318, + 211.93857769615346, + 203.49250076522802, + 195.37292113049696, + 187.57983879196001, + 180.1132537496174, + 172.973166003469, + 166.15957555351497, + 159.67248239975515, + 153.5118865421896, + 147.6777879808183, + 142.17018671564125, + 136.9890827466585, + 132.13447607387002, + 127.6063666972758, + 123.40475461687583, + 119.52963983267017, + 115.98102234465874, + 112.75890215284156, + 109.86327925721865, + 107.29415365779003, + 105.05152535455568, + 103.13539434751557, + 101.54576063666973, + 100.28262422201817, + 99.34598510356086, + 98.73584328129783, + 98.45219875522908, + 98.49505152535455, + 98.86440159167432, + 99.56024895418835, + 100.58259361289663, + 101.93143556779921, + 103.60677481889604, + 105.60861136618712, + 107.93694520967247, + 110.5917763493521, + 113.573104785226, + 116.88093051729416, + 120.51525354555656, + 124.47607387001327, + 128.76339149066416, + 133.37720640750945, + 138.31751862054892, + 143.58432812978262, + 149.1776349352107, + 155.09743903683292, + 161.3437404346496, + 167.91653912866033, + 174.81583511886535, + 182.0416284052648, + 189.59391898785833, + 197.47270686664615, + 205.6779920416284, + 214.20977451280478, + 223.06805428017552, + 232.25283134374038, + 241.76410570349958, + 251.60187735945317, + 261.7661463116008, + 272.2569125599429, + 283.0741761044791 + ], + [ + 778.5317824711764, + 757.5155596367716, + 736.8258340985612, + 716.4626058565452, + 696.4258749107233, + 676.7156412610957, + 657.3319049076623, + 638.2746658504234, + 619.5439240893786, + 601.139679624528, + 583.0619324558717, + 565.31068258341, + 547.8859300071422, + 530.7876747270686, + 514.0159167431895, + 497.57065605550446, + 481.4518926640139, + 465.6596265687175, + 450.1938577696153, + 435.0545862667075, + 420.2418120599939, + 405.7555351494745, + 391.59575553514946, + 377.7624732170187, + 364.2556881950821, + 351.0754004693398, + 338.22161003979187, + 325.69431690643813, + 313.49352106927864, + 301.6192225283135, + 290.07142128354246, + 278.8501173349659, + 267.9553106825834, + 257.38700132639525, + 247.1451892664014, + 237.22987450260175, + 227.64105703499644, + 218.37873686358532, + 209.44291398836853, + 200.83358840934596, + 192.55076012651767, + 184.5944291398837, + 176.96459544944392, + 169.66125905519843, + 162.68441995714718, + 156.0340781552903, + 149.71023364962758, + 143.71288644015914, + 138.042036526885, + 132.6976839098051, + 127.67982858891949, + 122.98847056422812, + 118.62360983573105, + 114.5852464034282, + 110.87338026731966, + 107.48801142740537, + 104.42913988368531, + 101.69676563615955, + 99.29088868482808, + 97.21150902969084, + 95.45862667074786, + 94.03224160799917, + 92.93235384144474, + 92.15896337108457, + 91.71207019691869, + 91.59167431894704, + 91.79777573716967, + 92.33037445158656, + 93.18947046219772, + 94.37506376900316, + 95.88715437200285, + 97.7257422711968, + 99.89082746658504, + 102.38240995816753, + 105.20048974594428, + 108.34506682991528, + 111.81614121008059, + 115.61371288644015, + 119.737781858994, + 124.18834812774202, + 128.96541169268443, + 134.06897255382103, + 139.49903071115187, + 145.2555861646771, + 151.33863891439645, + 157.74818896031022, + 164.4842363024181, + 171.54678094072028, + 178.93582287521684, + 186.65136210590754, + 194.69339863279248, + 203.06193245587184, + 211.75696357514533, + 220.77849199061328, + 230.1265177022753, + 239.80104071013156, + 249.80206101418227, + 260.1295786144271, + 270.78359351086635, + 281.76410570349964 + ], + [ + 761.3865932047751, + 740.5336190184676, + 720.0071421283542, + 699.8071625344353, + 679.9336802367105, + 660.3866952351801, + 641.1662075298439, + 622.2722171207021, + 603.7047240077543, + 585.4637281910009, + 567.5492296704417, + 549.9612284460769, + 532.6997245179064, + 515.76471788593, + 499.15620855014794, + 482.8741965105601, + 466.9186817671667, + 451.28966431996736, + 435.98714416896235, + 421.0111213141517, + 406.3615957555351, + 392.03856749311296, + 378.042036526885, + 364.37200285685134, + 351.0284664830119, + 338.0114274053668, + 325.3208856239159, + 312.95684113865934, + 300.91929394959703, + 289.208244056729, + 277.82369146005516, + 266.7656361595756, + 256.0340781552903, + 245.62901744719926, + 235.55045403530255, + 225.79838791960006, + 216.37281910009185, + 207.27374757677788, + 198.50117334965822, + 190.0550964187328, + 181.93551678400163, + 174.1424344454648, + 166.67584940312216, + 159.53576165697376, + 152.7221712070197, + 146.23507805325994, + 140.07448219569434, + 134.24038363432305, + 128.73278236914598, + 123.55167840016325, + 118.69707172737479, + 114.16896235078056, + 109.96735027038058, + 106.09223548617489, + 102.54361799816348, + 99.3214978063463, + 96.42587491072342, + 93.85674931129476, + 91.61412100806041, + 89.69799000102032, + 88.10835629017448, + 86.84521987552291, + 85.90858075706561, + 85.29843893480259, + 85.0147944087338, + 85.05764717885931, + 85.42699724517907, + 86.1228446076931, + 87.14518926640139, + 88.49403122130396, + 90.16937047240079, + 92.17120701969188, + 94.49954086317723, + 97.15437200285686, + 100.13570043873075, + 103.44352617079889, + 107.07784919906132, + 111.038669523518, + 115.32598714416898, + 119.93980206101416, + 124.8801142740537, + 130.1469237832874, + 135.74023058871538, + 141.66003469033774, + 147.90633608815426, + 154.47913478216515, + 161.37843077237017, + 168.60422405876946, + 176.15651464136317, + 184.035302520151, + 192.2405876951331, + 200.77237016630957, + 209.6306499336802, + 218.81542699724523, + 228.32670135700437, + 238.1644730129578, + 248.32874196510565, + 258.8195082134476, + 269.636771757984, + 280.78053259871444 + ], + [ + 744.5679012345679, + 723.8781756963574, + 703.5149474543414, + 683.4782165085196, + 663.767982858892, + 644.3842465054586, + 625.3270074482194, + 606.5962656871748, + 588.1920212223242, + 570.1142740536679, + 552.3630241812059, + 534.9382716049382, + 517.8400163248648, + 501.0682583409856, + 484.6229976533006, + 468.50423426181004, + 452.7119681665136, + 437.2461993674114, + 422.1069278645036, + 407.29415365779, + 392.8078767472707, + 378.6480971329456, + 364.8148148148148, + 351.3080297928783, + 338.127742067136, + 325.273951637588, + 312.74665850423423, + 300.5458626670748, + 288.67156412610956, + 277.1237628813386, + 265.902458932762, + 255.00765228037957, + 244.43934292419144, + 234.1975308641975, + 224.2822161003979, + 214.69339863279254, + 205.43107846138145, + 196.49525558616466, + 187.88593000714215, + 179.60310172431383, + 171.64677073767982, + 164.01693704724008, + 156.71360065299461, + 149.73676155494337, + 143.0864197530864, + 136.76257524742374, + 130.76522803795532, + 125.09437812468114, + 119.75002550760126, + 114.73217018671562, + 110.04081216202428, + 105.67595143352719, + 101.63758800122436, + 97.92572186511579, + 94.54035302520151, + 91.4814814814815, + 88.74910723395571, + 86.3432302826242, + 84.26385062748699, + 82.51096826854402, + 81.08458320579533, + 79.9846954392409, + 79.21130496888071, + 78.76441179471482, + 78.64401591674319, + 78.85011733496583, + 79.38271604938272, + 80.24181205999386, + 81.4274053667993, + 82.93949596979898, + 84.77808386899295, + 86.94316906438117, + 89.43475155596366, + 92.25283134374044, + 95.39740842771145, + 98.86848280787672, + 102.66605448423628, + 106.79012345679013, + 111.2406897255382, + 116.01775329048053, + 121.12131415161721, + 126.55137230894805, + 132.30792776247318, + 138.39098051219264, + 144.8005305581063, + 151.5365779002143, + 158.59912253851644, + 165.98816447301292, + 173.70370370370372, + 181.74574023058867, + 190.1142740536679, + 198.80930517294155, + 207.8308335884093, + 217.17885930007148, + 226.85338230792775, + 236.8544026119783, + 247.18192021222325, + 257.83593510866234, + 268.81644730129585, + 280.1234567901235 + ], + [ + 728.0757065605551, + 707.5492296704418, + 687.3492500765228, + 667.4757677787982, + 647.9287827772677, + 628.7082950719314, + 609.8143046627895, + 591.2468115498419, + 573.0058157330885, + 555.0913172125294, + 537.5033159881643, + 520.2418120599939, + 503.3068054280176, + 486.6982960922356, + 470.4162840526477, + 454.4607693092542, + 438.83175186205494, + 423.52923171104993, + 408.5532088562391, + 393.9036832976227, + 379.5806550352005, + 365.5841240689725, + 351.9140903989389, + 338.57055402509957, + 325.55351494745435, + 312.8629731660035, + 300.49892868074687, + 288.46138149168456, + 276.75033159881644, + 265.36577900214263, + 254.3077237016631, + 243.5761656973779, + 233.17110498928682, + 223.09254157739005, + 213.34047546168762, + 203.91490664217937, + 194.81583511886546, + 186.04326089174572, + 177.59718396082033, + 169.4776043260892, + 161.6845219875523, + 154.21793694520971, + 147.07784919906132, + 140.26425874910723, + 133.7771655953474, + 127.6165697377819, + 121.78247117641061, + 116.27486991123357, + 111.0937659422508, + 106.23915926946229, + 101.7110498928681, + 97.50943781246814, + 93.63432302826243, + 90.085705540251, + 86.86358534843386, + 83.96796245281097, + 81.39883685338232, + 79.15620855014794, + 77.24007754310787, + 75.65044383226203, + 74.38730741761046, + 73.45066829915315, + 72.84052647689012, + 72.55688195082136, + 72.59973472094684, + 72.96908478726661, + 73.66493214978064, + 74.68727680848895, + 76.0361187633915, + 77.71145801448831, + 79.71329456177942, + 82.04162840526476, + 84.69645954494439, + 87.67778798081828, + 90.98561371288646, + 94.61993674114885, + 98.58075706560555, + 102.8680746862565, + 107.48188960310173, + 112.42220181614118, + 117.68901132537499, + 123.28231813080296, + 129.2021222324252, + 135.44842363024185, + 142.02122232425262, + 148.92051831445778, + 156.14631160085708, + 163.69860218345062, + 171.57739006223858, + 179.7826752372207, + 188.31445770839704, + 197.1727374757678, + 206.35751453933267, + 215.868788899092, + 225.70656055504543, + 235.8708295071931, + 246.36159575553518, + 257.1788593000714, + 268.32262014080203, + 279.7928782777268 + ], + [ + 711.9100091827365, + 691.5467809407204, + 671.5100499948984, + 651.799816345271, + 632.4160799918376, + 613.3588409345986, + 594.6280991735537, + 576.2238547087032, + 558.146107540047, + 540.3948576675849, + 522.9701050913171, + 505.8718498112437, + 489.1000918273646, + 472.6548311396796, + 456.53606774818894, + 440.7438016528926, + 425.27803285379053, + 410.1387613508826, + 395.3259871441689, + 380.8397102336496, + 366.6799306193245, + 352.84664830119374, + 339.3398632792572, + 326.1595755535149, + 313.3057851239669, + 300.77849199061325, + 288.57769615345376, + 276.7033976124885, + 265.1555963677176, + 253.9342924191409, + 243.0394857667585, + 232.4711764105704, + 222.22936435057645, + 212.31404958677686, + 202.72523211917152, + 193.4629119477604, + 184.52708907254365, + 175.91776349352105, + 167.6349352106928, + 159.67860422405874, + 152.04877053361898, + 144.74543413937357, + 137.76859504132233, + 131.11825323946536, + 124.79440873380267, + 118.79706152433427, + 113.1262116110601, + 107.78185899398021, + 102.76400367309458, + 98.0726456484032, + 93.70778491990615, + 89.6694214876033, + 85.95755535149473, + 82.57218651158044, + 79.51331496786042, + 76.78094072033466, + 74.37506376900316, + 72.29568411386593, + 70.54280175492298, + 69.11641669217425, + 68.01652892561984, + 67.24313845525965, + 66.79624528109376, + 66.67584940312213, + 66.88195082134476, + 67.41454953576167, + 68.2736455463728, + 69.45923885317825, + 70.97132945617793, + 72.80991735537191, + 74.97500255076012, + 77.4665850423426, + 80.28466483011937, + 83.4292419140904, + 86.9003162942557, + 90.69788797061521, + 94.82195694316904, + 99.27252321191716, + 104.0495867768595, + 109.15314763799608, + 114.58320579532703, + 120.33976124885217, + 126.42281399857151, + 132.83236404448527, + 139.56841138659314, + 146.63095602489545, + 154.01999795939187, + 161.7355371900826, + 169.77757371696768, + 178.14610754004687, + 186.8411386593204, + 195.8626670747883, + 205.2106927864503, + 214.88521579430673, + 224.88623609835727, + 235.2137536986021, + 245.86776859504135, + 256.84828078767464, + 268.15529027650246, + 279.7887970615243 + ], + [ + 696.0708091011121, + 675.8708295071932, + 655.9973472094684, + 636.450362207938, + 617.2298745026019, + 598.3358840934599, + 579.7683909805122, + 561.5273951637589, + 543.6128966431997, + 526.024895418835, + 508.76339149066416, + 491.8283848586879, + 475.2198755229059, + 458.937863483318, + 442.98234873992453, + 427.3533312927252, + 412.0508111417203, + 397.07478828690955, + 382.42526272829303, + 368.1022344658709, + 354.10570349964286, + 340.43566982960925, + 327.09213345576984, + 314.0750943781247, + 301.3845525966738, + 289.0205081114172, + 276.9829609223549, + 265.2719110294869, + 253.88735843281302, + 242.8293031323335, + 232.0977451280482, + 221.69268441995717, + 211.6141210080604, + 201.86205489235792, + 192.43648607284976, + 183.33741454953577, + 174.5648403224161, + 166.11876339149066, + 157.99918375675955, + 150.20610141822266, + 142.73951637588002, + 135.5994286297317, + 128.78583817977758, + 122.29874502601776, + 116.1381491684522, + 110.30405060708095, + 104.79644934190391, + 99.61534537292115, + 94.76073870013265, + 90.23262932353842, + 86.03101724313849, + 82.15590245893277, + 78.60728497092134, + 75.38516477910417, + 72.48954188348131, + 69.92041628405266, + 67.6777879808183, + 65.7616569737782, + 64.17202326293237, + 62.908886848280794, + 61.97224772982349, + 61.36210590756047, + 61.07846138149169, + 61.121314151617185, + 61.49066421793696, + 62.186511580451, + 63.20885623915928, + 64.55769819406183, + 66.23303744515866, + 68.23487399244976, + 70.56320783593512, + 73.21803897561472, + 76.19936741148862, + 79.50719314355678, + 83.14151617181922, + 87.10233649627588, + 91.38965411692683, + 96.00346903377206, + 100.94378124681155, + 106.21059075604528, + 111.80389756147335, + 117.7237016630956, + 123.9700030609121, + 130.542801754923, + 137.44209774512802, + 144.66789103152743, + 152.220181614121, + 160.09896949290885, + 168.30425466789106, + 176.83603713906743, + 185.69431690643802, + 194.87909397000308, + 204.39036832976223, + 214.2281399857158, + 224.39240893786348, + 234.88317518620542, + 245.7004387307418, + 256.84419957147225, + 268.3144577083972, + 280.11121314151615 + ], + [ + 680.558106315682, + 660.5213753698602, + 640.8111417202325, + 621.4274053667993, + 602.3701663095603, + 583.6394245485154, + 565.2351800836649, + 547.1574329150088, + 529.4061830425467, + 511.981430466279, + 494.88317518620545, + 478.11141720232627, + 461.6661565146414, + 445.54739312315064, + 429.7551270278542, + 414.2893582287521, + 399.1500867258443, + 384.3373125191307, + 369.8510356086113, + 355.69125599428634, + 341.8579736761555, + 328.35118865421896, + 315.17090092847667, + 302.3171104989287, + 289.78981736557495, + 277.58902152841546, + 265.7147229874502, + 254.16692174267936, + 242.94561779410262, + 232.05081114172023, + 221.4825017855321, + 211.24068972553823, + 201.32537496173862, + 191.73655749413322, + 182.47423732272216, + 173.53841444750535, + 164.9290888684828, + 156.64626058565452, + 148.6899295990205, + 141.06009590858073, + 133.75675951433527, + 126.77992041628409, + 120.12957861442712, + 113.8057341087644, + 107.80838689929597, + 102.13753698602186, + 96.79318436894197, + 91.77532904805632, + 87.08397102336495, + 82.71911029486785, + 78.68074686256506, + 74.96888072645649, + 71.58351188654218, + 68.52464034282214, + 65.79226609529641, + 63.386389143964905, + 61.30700948882767, + 59.554127129884705, + 58.127742067136005, + 57.02785430058158, + 56.25446383022141, + 55.807570656055496, + 55.68717477808386, + 55.893276196306495, + 56.425874910723394, + 57.28497092133456, + 58.470564228139985, + 59.98265483113967, + 61.82124273033363, + 63.98632792572187, + 66.47791041730436, + 69.2959902050811, + 72.44056728905213, + 75.91164166921743, + 79.70921334557698, + 83.83328231813077, + 88.28384858687888, + 93.06091215182124, + 98.16447301295787, + 103.59453117028872, + 109.35108662381393, + 115.4341393735333, + 121.84368941944695, + 128.57973676155495, + 135.6422813998571, + 143.0313233343537, + 150.74686256504438, + 158.78889909192932, + 167.1574329150087, + 175.8524640342822, + 184.87399244974995, + 194.22201816141214, + 203.89654116926837, + 213.89756147331912, + 224.2250790735639, + 234.87909397000297, + 245.85960616263648, + 257.1666156514641, + 268.80012243648616, + 280.7601265177023 + ], + [ + 665.3719008264463, + 645.4984185287216, + 625.951433527191, + 606.7309458218549, + 587.836955412713, + 569.2694622997655, + 551.0284664830119, + 533.113967962453, + 515.5259667380881, + 498.26446280991735, + 481.3294561779411, + 464.72094684215904, + 448.4389348025712, + 432.48342005917766, + 416.8544026119784, + 401.5518824609734, + 386.5758596061627, + 371.9263340475462, + 357.60330578512395, + 343.60677481889604, + 329.9367411488624, + 316.593204775023, + 303.57616569737786, + 290.885623915927, + 278.52157943067033, + 266.4840322416081, + 254.77298234873996, + 243.38842975206614, + 232.3303744515866, + 221.59881644730135, + 211.19375573921033, + 201.11519232731357, + 191.36312621161107, + 181.93755739210286, + 172.83848586878895, + 164.06591164166923, + 155.61983471074382, + 147.50025507601268, + 139.70717273747582, + 132.24058769513317, + 125.10049994898478, + 118.28690949903076, + 111.79981634527091, + 105.63922048770536, + 99.80512192633405, + 94.29752066115707, + 89.1164166921743, + 84.26181001938579, + 79.73370064279155, + 75.53208856239159, + 71.65697377818591, + 68.1083562901745, + 64.88623609835732, + 61.990613202734416, + 59.42148760330582, + 57.178859300071444, + 55.262728293031344, + 53.6730945821855, + 52.409958167533944, + 51.473319049076636, + 50.8631772268136, + 50.579532700744835, + 50.62238547087033, + 50.99173553719009, + 51.68758289970412, + 52.70992755841241, + 54.058769513314985, + 55.7341087644118, + 57.735945311702885, + 60.06427915518826, + 62.71911029486788, + 65.70043873074177, + 69.00826446280992, + 72.64258749107235, + 76.60340781552904, + 80.89072543617996, + 85.50454035302519, + 90.44485256606468, + 95.71166207529845, + 101.30496888072642, + 107.22477298234877, + 113.47107438016526, + 120.04387307417603, + 126.94316906438121, + 134.1689623507805, + 141.72125293337416, + 149.60004081216204, + 157.8053259871441, + 166.3371084583206, + 175.1953882256912, + 184.38016528925607, + 193.8914396490154, + 203.72921130496883, + 213.89348025711666, + 224.38424650545858, + 235.2015100499948, + 246.34527089072543, + 257.81552902765014, + 269.6122844607694, + 281.7355371900826 + ], + [ + 650.5121926334047, + 630.801958983777, + 611.4182226303437, + 592.3609835731048, + 573.6302418120599, + 555.2259973472094, + 537.1482501785531, + 519.3970003060914, + 501.97224772982355, + 484.87399244975, + 468.1022344658707, + 451.6569737781859, + 435.53821038669525, + 419.7459442913988, + 404.2801754922966, + 389.1409039893889, + 374.32812978267526, + 359.84185287215587, + 345.6820732578308, + 331.84879093970005, + 318.34200591776346, + 305.1617181920212, + 292.30792776247324, + 279.7806346291195, + 267.57983879196, + 255.70554025099483, + 244.15773900622384, + 232.9364350576472, + 222.04162840526476, + 211.47331904907665, + 201.23150698908276, + 191.31619222528317, + 181.72737475767778, + 172.4650545862667, + 163.52923171104993, + 154.91990613202734, + 146.63707784919907, + 138.68074686256503, + 131.0509131721253, + 123.74757677787979, + 116.77073767982858, + 110.12039587797167, + 103.79655137230895, + 97.79920416284052, + 92.12835424956636, + 86.78400163248651, + 81.76614631160088, + 77.0747882869095, + 72.70992755841242, + 68.67156412610956, + 64.95969799000103, + 61.574329150086726, + 58.5154576063667, + 55.78308335884094, + 53.37720640750945, + 51.29782675237222, + 49.54494439342923, + 48.11855933068054, + 47.018671564126116, + 46.24528109376594, + 45.79838791960004, + 45.67799204162841, + 45.88409345985103, + 46.416692174267936, + 47.27578818487909, + 48.46138149168452, + 49.973472094684226, + 51.81205999387817, + 53.977145189266395, + 56.468727680848886, + 59.28680746862566, + 62.431384552596654, + 65.90245893276196, + 69.70003060912153, + 73.82409958167534, + 78.2746658504234, + 83.05172941536577, + 88.1552902765024, + 93.58534843383329, + 99.3419038873584, + 105.42495663707788, + 111.83450668299153, + 118.57055402509944, + 125.63309866340173, + 133.0221405978982, + 140.73767982858897, + 148.77971635547397, + 157.14825017855316, + 165.84328129782682, + 174.86480971329456, + 184.21283542495655, + 193.887358432813, + 203.88837873686353, + 214.21589633710852, + 224.8699112335476, + 235.85042342618095, + 247.1574329150087, + 258.79093970003055, + 270.75094378124686, + 283.0374451586573 + ], + [ + 635.9789817365576, + 616.431996735027, + 597.2115090296908, + 578.317518620549, + 559.7500255076012, + 541.5090296908479, + 523.5945311702886, + 506.006529945924, + 488.74502601775333, + 471.8100193857769, + 455.20151004999485, + 438.91949801040704, + 422.96398326701365, + 407.3349658198143, + 392.0324456688094, + 377.05642281399867, + 362.4068972553822, + 348.08386899295994, + 334.08733802673197, + 320.4173043566983, + 307.07376798285895, + 294.0567289052138, + 281.36618712376287, + 269.00214263850626, + 256.96459544944395, + 245.25354555657592, + 233.86899295990207, + 222.81093765942256, + 212.07937965513725, + 201.67431894704626, + 191.5957555351495, + 181.84368941944703, + 172.41812059993882, + 163.31904907662485, + 154.5464748495052, + 146.10039791857974, + 137.98081828384863, + 130.18773594531172, + 122.72115090296913, + 115.58106315682075, + 108.76747270686666, + 102.28037955310687, + 96.11978369554129, + 90.28568513417, + 84.77808386899295, + 79.59697990001025, + 74.74237322722175, + 70.2142638506275, + 66.01265177022754, + 62.13753698602183, + 58.588919498010426, + 55.366799306193265, + 52.471176410570365, + 49.90205081114173, + 47.65942250790738, + 45.74329150086727, + 44.15365779002144, + 42.890521375369865, + 41.95388225691258, + 41.34374043464954, + 41.06009590858076, + 41.10294867870626, + 41.47229874502602, + 42.16814610754005, + 43.19049076624835, + 44.53933272115091, + 46.21467197224774, + 48.21650851953881, + 50.54484236302419, + 53.19967350270381, + 56.18100193857771, + 59.48882767064585, + 63.12315069890827, + 67.08397102336497, + 71.37128864401592, + 75.98510356086112, + 80.92541577390061, + 86.19222528313438, + 91.7855320885624, + 97.70533619018465, + 103.95163758800126, + 110.52443628201202, + 117.42373227221705, + 124.64952555861649, + 132.20181614121003, + 140.080604019998, + 148.28588919498011, + 156.81767166615646, + 165.67595143352722, + 174.86072849709208, + 184.37200285685122, + 194.20977451280484, + 204.3740434649525, + 214.86480971329462, + 225.6820732578308, + 236.8258340985613, + 248.29609223548624, + 260.0928476686052, + 272.2161003979187, + 284.66585042342615 + ], + [ + 621.7722681359045, + 602.3885317824711, + 583.331292725232, + 564.6005509641873, + 546.1963064993369, + 528.1185593306805, + 510.36730945821853, + 492.9425568819509, + 475.84430160187736, + 459.07254361799824, + 442.6272829303132, + 426.5085195388226, + 410.7162534435262, + 395.25048464442403, + 380.11121314151615, + 365.29843893480256, + 350.8121620242833, + 336.65238240995825, + 322.8191000918273, + 309.3123150698909, + 296.1320273441485, + 283.2782369146006, + 270.7509437812468, + 258.5501479440873, + 246.67584940312216, + 235.12804815835122, + 223.9067442097745, + 213.01193755739214, + 202.44362820120398, + 192.20181614121012, + 182.28650137741047, + 172.69768390980516, + 163.43536373839405, + 154.49954086317723, + 145.8902152841547, + 137.6073870013264, + 129.6510560146924, + 122.02122232425263, + 114.71788593000716, + 107.74104683195591, + 101.09070503009896, + 94.7668605244363, + 88.76951331496788, + 83.0986634016937, + 77.7543107846138, + 72.7364554637282, + 68.04509743903684, + 63.680236710539745, + 59.641873278236915, + 55.930007142128346, + 52.544638302214075, + 49.48576675849404, + 46.75339251096827, + 44.34751555963677, + 42.26813590449955, + 40.51525354555658, + 39.08886848280788, + 37.98898071625345, + 37.21559024589328, + 36.768697071727374, + 36.64830119375574, + 36.85440261197837, + 37.387001326395264, + 38.24609733700643, + 39.431690643811855, + 40.943781246811554, + 42.78236914600552, + 44.94745434139373, + 47.43903683297623, + 50.25711662075298, + 53.40169370472401, + 56.87276808488928, + 60.67033976124884, + 64.79440873380267, + 69.24497500255077, + 74.02203856749308, + 79.12559942862973, + 84.5556575859606, + 90.31221303948577, + 96.39526578920514, + 102.8048158351189, + 109.54086317722681, + 116.60340781552897, + 123.99244975002553, + 131.7079889807162, + 139.75002550760132, + 148.11855933068054, + 156.813590449954, + 165.83511886542192, + 175.18314457708397, + 184.85766758494023, + 194.85868788899091, + 205.1862054892357, + 215.840220385675, + 226.82073257830834, + 238.12774206713593, + 249.76124885215793, + 261.7212529333741, + 274.0077543107847, + 286.6207529843894 + ], + [ + 607.8920518314458, + 588.6715641261096, + 569.7775737169676, + 551.21008060402, + 532.9690847872666, + 515.0545862667075, + 497.46658504234256, + 480.20508111417206, + 463.27007448219575, + 446.6615651464137, + 430.3795531068258, + 414.4240383634323, + 398.79502091623306, + 383.49250076522804, + 368.5164779104173, + 353.8669523518009, + 339.54392408937866, + 325.5473931231507, + 311.87735945311704, + 298.5338230792777, + 285.5167840016326, + 272.82624222018165, + 260.46219773492504, + 248.42465054586273, + 236.71360065299461, + 225.3290480563208, + 214.27099275584126, + 203.539434751556, + 193.134374043465, + 183.05581063156822, + 173.3037445158658, + 163.87817569635757, + 154.7791041730436, + 146.0065299459239, + 137.56045301499847, + 129.4408733802673, + 121.64779104173046, + 114.18120599938783, + 107.04111825323949, + 100.22752780328541, + 93.74043464952557, + 87.57983879196004, + 81.74574023058875, + 76.23813896541171, + 71.05703499642895, + 66.20242832364048, + 61.67431894704625, + 57.47270686664628, + 53.59759208244057, + 50.04897459442914, + 46.826854402612, + 43.9312315069891, + 41.36210590756047, + 39.11947760432609, + 37.203346597286014, + 35.61371288644017, + 34.35057647178861, + 33.413937353331306, + 32.803795531068275, + 32.520151004999505, + 32.56300377512499, + 32.93235384144476, + 33.62820120395878, + 34.65054586266708, + 35.99938781756964, + 37.67472706866647, + 39.67656361595757, + 42.004897459442915, + 44.65972859912254, + 47.641057034996436, + 50.9488827670646, + 54.583205795327, + 58.544026119783695, + 62.831343740434654, + 67.44515865727989, + 72.38547087031934, + 77.6522803795531, + 83.24558718498112, + 89.16539128660341, + 95.41169268441993, + 101.98449137843082, + 108.88378736863586, + 116.10958065503516, + 123.66187123762884, + 131.54065911641666, + 139.7459442913989, + 148.27772676257527, + 157.13600652994586, + 166.32078359351092, + 175.83205795327004, + 185.66982960922346, + 195.83409856137132, + 206.32486480971323, + 217.14212835424965, + 228.2858891949801, + 239.75614733190483, + 251.55290276502402, + 263.6761554943373, + 276.12590551984505, + 288.9021528415468 + ], + [ + 594.3383328231814, + 575.2810937659423, + 556.5503520048974, + 538.146107540047, + 520.0683603713907, + 502.3171104989287, + 484.89235792266095, + 467.7941026425875, + 451.02234465870833, + 434.57708397102334, + 418.4583205795327, + 402.6660544842363, + 387.20028568513425, + 372.06101418222636, + 357.24823997551266, + 342.7619630649934, + 328.60218345066835, + 314.7689011325375, + 301.26211611060097, + 288.0818283848587, + 275.2280379553107, + 262.70074482195696, + 250.49994898479747, + 238.62565044383228, + 227.0778491990613, + 215.85654525048466, + 204.96173859810224, + 194.3934292419141, + 184.15161718192022, + 174.23630241812063, + 164.64748495051526, + 155.3851647791042, + 146.44934190388736, + 137.8400163248648, + 129.55718804203656, + 121.60085705540251, + 113.97102336496279, + 106.66768697071726, + 99.69084787266607, + 93.0405060708091, + 86.7166615651464, + 80.71931435567802, + 75.04846444240384, + 69.70411182532396, + 64.68625650443832, + 59.994898479746986, + 55.63003775124989, + 51.59167431894705, + 47.87980818283848, + 44.49443934292418, + 41.43556779920417, + 38.70319355167841, + 36.2973166003469, + 34.217936945209665, + 32.46505458626672, + 31.038669523518017, + 29.938781756963575, + 29.16539128660341, + 28.71849811243751, + 28.59810223446587, + 28.8042036526885, + 29.336802367105403, + 30.195898377716556, + 31.381491684521983, + 32.89358228752168, + 34.73217018671564, + 36.89725538210388, + 39.38883787368634, + 42.206917661463116, + 45.35149474543414, + 48.822569125599436, + 52.62014080195897, + 56.7442097745128, + 61.194776043260894, + 65.97183960820325, + 71.07540046933983, + 76.50545862667073, + 82.2620140801959, + 88.34506682991534, + 94.75461687582896, + 101.49066421793697, + 108.55320885623914, + 115.94225079073557, + 123.6577900214264, + 131.69982654831136, + 140.0683603713907, + 148.7633914906642, + 157.78491990613196, + 167.13294561779412, + 176.80746862565042, + 186.80848892970093, + 197.13600652994592, + 207.79002142638498, + 218.77053361901852, + 230.07754310784608, + 241.71104989286795, + 253.67105397408432, + 265.9575553514947, + 278.5705540250995, + 291.5100499948985 + ], + [ + 581.1111111111111, + 562.2171207019692, + 543.6496275890214, + 525.4086317722682, + 507.494133251709, + 489.90613202734414, + 472.6446280991735, + 455.7096214671972, + 439.10111213141516, + 422.8191000918273, + 406.86358534843373, + 391.2345679012345, + 375.9320477502296, + 360.9560248954188, + 346.30649933680235, + 331.9834710743802, + 317.9869401081522, + 304.31690643811856, + 290.9733700642791, + 277.956330986634, + 265.2657892051831, + 252.90174471992654, + 240.86419753086415, + 229.1531476379961, + 217.76859504132233, + 206.71053974084276, + 195.97898173655747, + 185.5739210284665, + 175.49535761656972, + 165.7432915008673, + 156.31772268135904, + 147.2186511580451, + 138.4460769309254, + 129.99999999999997, + 121.88042036526885, + 114.08733802673194, + 106.62075298438936, + 99.48066523824097, + 92.66707478828691, + 86.17998163452707, + 80.01938577696151, + 74.18528721559026, + 68.67768595041322, + 63.49658198143047, + 58.64197530864196, + 54.113865932047766, + 49.9122538516478, + 46.0371390674421, + 42.48852157943065, + 39.26640138761349, + 36.37077849199061, + 33.801652892561975, + 31.559024589327613, + 29.642893582287517, + 28.053259871441686, + 26.79012345679012, + 25.85348433833282, + 25.24334251606978, + 24.95969799000102, + 25.002550760126514, + 25.37190082644627, + 26.06774818896031, + 27.090092847668593, + 28.438934802571154, + 30.114274053667987, + 32.11611060095908, + 34.44444444444444, + 37.09927558412405, + 40.08060401999795, + 43.388429752066116, + 47.02275278032854, + 50.9835731047852, + 55.27089072543617, + 59.8847056422814, + 64.8250178553209, + 70.09182736455462, + 75.68513416998263, + 81.60493827160494, + 87.8512396694215, + 94.42403836343227, + 101.32333435363743, + 108.54912764003673, + 116.1014182226303, + 123.98020610141823, + 132.18549127640034, + 140.71727374757685, + 149.57555351494747, + 158.76033057851234, + 168.27160493827165, + 178.10937659422507, + 188.27364554637273, + 198.76441179471485, + 209.58167533925103, + 220.7254361799817, + 232.1956943169064, + 243.99244975002546, + 256.1157024793389, + 268.5654525048464, + 281.3416998265484, + 294.44444444444446 + ], + [ + 568.2103866952352, + 549.4796449341904, + 531.0754004693398, + 512.9976533006836, + 495.2464034282217, + 477.8216508519539, + 460.7233955718804, + 443.9516375880013, + 427.50637690031635, + 411.3876135088256, + 395.59534741352917, + 380.1295786144271, + 364.9903071115192, + 350.1775329048056, + 335.69125599428634, + 321.5314763799613, + 307.6981940618305, + 294.1914090398939, + 281.0111213141516, + 268.15733088460365, + 255.63003775124986, + 243.42924191409043, + 231.55494337312518, + 220.00714212835427, + 208.78583817977758, + 197.8910315273952, + 187.32272217120703, + 177.0809101112132, + 167.16559534741356, + 157.57677787980822, + 148.3144577083971, + 139.3786348331803, + 130.76930925415778, + 122.48648097132946, + 114.53014998469546, + 106.90031629425569, + 99.59697990001021, + 92.62014080195898, + 85.96979900010206, + 79.64595449443934, + 73.64860728497092, + 67.9777573716968, + 62.6334047546169, + 57.61554943373126, + 52.92419140903989, + 48.55933068054283, + 44.52096724823999, + 40.80910111213142, + 37.42373227221712, + 34.36486072849709, + 31.63248648097134, + 29.226609529639838, + 27.147229874502607, + 25.394347515559637, + 23.967962452810944, + 22.86807468625651, + 22.094684215896343, + 21.64779104173044, + 21.5273951637588, + 21.733496581981434, + 22.26609529639833, + 23.125191307009494, + 24.31078461381491, + 25.82287521681461, + 27.66146311600857, + 29.826548311396802, + 32.3181308029793, + 35.13621059075603, + 38.280787674727065, + 41.751862054892364, + 45.54943373125192, + 49.67350270380571, + 54.12406897255381, + 58.90113253749618, + 64.00469339863281, + 69.43475155596364, + 75.19130700948881, + 81.27435975920825, + 87.68390980512194, + 94.41995714722984, + 101.48250178553212, + 108.87154372002855, + 116.58708295071926, + 124.62911947760435, + 132.99765330068357, + 141.6926844199572, + 150.71421283542495, + 160.06223854708696, + 169.7367615549434, + 179.73778185899394, + 190.06529945923876, + 200.71931435567802, + 211.69982654831134, + 223.00683603713912, + 234.640342822161, + 246.6003469033771, + 258.8868482807877, + 271.4998469543924, + 284.43934292419146, + 297.70533619018465 + ], + [ + 555.6361595755534, + 537.068666462606, + 518.8276706458524, + 500.91317212529333, + 483.3251709009285, + 466.06366697275774, + 449.12866034078155, + 432.52015100499955, + 416.2381389654117, + 400.28262422201817, + 384.65360677481885, + 369.3510866238139, + 354.3750637690032, + 339.7255382103866, + 325.40250994796446, + 311.4059789817365, + 297.7359453117029, + 284.39240893786354, + 271.3753698602183, + 258.68482807876745, + 246.32078359351084, + 234.28323640444853, + 222.5721865115804, + 211.18763391490666, + 200.1295786144271, + 189.39802061014183, + 178.99295990205079, + 168.91439649015408, + 159.16233037445159, + 149.7367615549434, + 140.63769003162943, + 131.86511580450974, + 123.41903887358434, + 115.29945923885315, + 107.5063769003163, + 100.03979185797367, + 92.89970411182532, + 86.08611366187124, + 79.59902050811142, + 73.43842465054584, + 67.60432608917455, + 62.09672482399757, + 56.91562085501481, + 52.061014182226295, + 47.532904805632064, + 43.33129272523213, + 39.45617794102643, + 35.907560453014995, + 32.685440261197826, + 29.789817365574926, + 27.220691766146317, + 24.978063462911948, + 23.061932455871844, + 21.47229874502601, + 20.209162330374454, + 19.27252321191715, + 18.662381389654115, + 18.378736863585345, + 18.42158963371084, + 18.790939700030606, + 19.486787062544636, + 20.509131721252935, + 21.85797367615548, + 23.533312927252314, + 25.53514947454341, + 27.86348331802877, + 30.518314457708406, + 33.499642893582276, + 36.80746862565044, + 40.441791653912865, + 44.40261197836956, + 48.68992959902049, + 53.303744515865716, + 58.24405672890521, + 63.51086623813898, + 69.10417304356696, + 75.02397714518926, + 81.27027854300582, + 87.84307723701663, + 94.74237322722168, + 101.96816651362109, + 109.52045709621467, + 117.39924497500247, + 125.60453014998471, + 134.13631262116107, + 142.99459238853186, + 152.1793694520967, + 161.69064381185586, + 171.52841546780948, + 181.69268441995715, + 192.18345066829903, + 203.00071421283545, + 214.14447505356588, + 225.61473319049085, + 237.4114886236098, + 249.53474135292308, + 261.98449137843085, + 274.76073870013266, + 287.8634833180289, + 301.2927252321192 + ], + [ + 543.388429752066, + 524.9841852872155, + 506.90643811855927, + 489.1551882460974, + 471.7304356698296, + 454.6321803897561, + 437.8604224058768, + 421.41516171819205, + 405.29639832670136, + 389.5041322314049, + 374.0383634323028, + 358.89909192939496, + 344.0863177226814, + 329.60004081216204, + 315.4402611978369, + 301.60697887970616, + 288.1001938577696, + 274.91990613202734, + 262.06611570247935, + 249.5388225691256, + 237.33802673196612, + 225.46372819100094, + 213.91592694622994, + 202.69462299765334, + 191.7998163452709, + 181.2315069890828, + 170.98969492908887, + 161.07438016528928, + 151.48556269768392, + 142.22324252627286, + 133.28741965105604, + 124.67809407203349, + 116.39526578920521, + 108.43893480257117, + 100.80910111213143, + 93.50576471788592, + 86.52892561983472, + 79.87858381797776, + 73.55473931231508, + 67.55739210284666, + 61.88654218957248, + 56.54218957249263, + 51.524334251607, + 46.83297622691563, + 42.46811549841853, + 38.429752066115725, + 34.71788593000716, + 31.332517090092857, + 28.273645546372823, + 25.54127129884705, + 23.13539434751557, + 21.056014692378337, + 19.30313233343537, + 17.876747270686668, + 16.776859504132236, + 16.00346903377207, + 15.556575859606166, + 15.43617998163453, + 15.64228139985716, + 16.174880114274057, + 17.03397612488522, + 18.21956943169065, + 19.73166003469033, + 21.570247933884296, + 23.735333129272522, + 26.226915620855017, + 29.044995408631785, + 32.189572492602785, + 35.660646872768076, + 39.45821854912765, + 43.582287521681465, + 48.03285379042953, + 52.80991735537189, + 57.913478216508516, + 63.34353637383941, + 69.10009182736452, + 75.18314457708397, + 81.59269462299766, + 88.32874196510562, + 95.39128660340779, + 102.78032853790435, + 110.49586776859505, + 118.53790429547999, + 126.90643811855935, + 135.60146923783284, + 144.62299765330076, + 153.97102336496275, + 163.64554637281904, + 173.64656667686975, + 183.97408427711454, + 194.62809917355364, + 205.60861136618718, + 216.91562085501477, + 228.54912764003677, + 240.5091317212529, + 252.79563309866333, + 265.40863177226817, + 278.3481277420671, + 291.6141210080606, + 305.206611570248 + ], + [ + 531.4671972247729, + 513.2262014080196, + 495.31170288746046, + 477.72370166309565, + 460.46219773492504, + 443.5271911029487, + 426.91868176716656, + 410.63666972757886, + 394.6811549841853, + 379.052137536986, + 363.749617385981, + 348.77359453117026, + 334.12406897255386, + 319.80104071013164, + 305.8045097439037, + 292.13447607387, + 278.79093970003066, + 265.7739006223855, + 253.08335884093458, + 240.71931435567797, + 228.68176716661563, + 216.97071727374757, + 205.58616467707373, + 194.52810937659422, + 183.79655137230893, + 173.39149066421794, + 163.31292725232117, + 153.56086113661874, + 144.1352923171105, + 135.03622079379656, + 126.26364656667687, + 117.81756963575147, + 109.69799000102029, + 101.9049076624834, + 94.43832262014081, + 87.29823487399244, + 80.48464442403836, + 73.99755127027854, + 67.836955412713, + 62.002856851341704, + 56.49525558616466, + 51.314151617181935, + 46.45954494439343, + 41.931435567799205, + 37.72982348739924, + 33.854708703193566, + 30.306091215182132, + 27.08397102336496, + 24.18834812774206, + 21.61922252831343, + 19.376594225079074, + 17.460463218038974, + 15.870829507193141, + 14.60769309254157, + 13.671053974084277, + 13.06091215182124, + 12.777267625752472, + 12.82012039587797, + 13.18947046219773, + 13.885317824711759, + 14.907662483420056, + 16.25650443832262, + 17.931843689419434, + 19.93368023671053, + 22.262014080195897, + 24.916845219875526, + 27.89817365574942, + 31.20599938781756, + 34.84032241607998, + 38.80114274053668, + 43.08846036118765, + 47.70227527803283, + 52.64258749107232, + 57.90939700030609, + 63.50270380573413, + 69.42250790735636, + 75.66880930517291, + 82.24160799918374, + 89.14090398938885, + 96.36669727578813, + 103.91898785838181, + 111.79777573716966, + 120.00306091215172, + 128.53484338332825, + 137.39312315069887, + 146.5779002142639, + 156.08917457402305, + 165.92694622997647, + 176.09121518212433, + 186.58198143046624, + 197.39924497500243, + 208.5430058157331, + 220.01326395265784, + 231.81001938577705, + 243.93327211509023, + 256.3830221405978, + 269.15926946229973, + 282.2620140801958, + 295.69125599428634, + 309.44699520457095 + ], + [ + 519.8724619936742, + 501.79471482501776, + 484.04346495255584, + 466.6187123762882, + 449.52045709621467, + 432.74869911233554, + 416.3034384246505, + 400.1846750331599, + 384.39240893786354, + 368.92664013876134, + 353.78736863585345, + 338.97459442913987, + 324.4883175186206, + 310.32853790429556, + 296.49525558616466, + 282.9884705642282, + 269.8081828384859, + 256.9543924089379, + 244.4270992755841, + 232.22630343842468, + 220.35200489745944, + 208.80420365268853, + 197.58289970411184, + 186.68809305172942, + 176.11978369554126, + 165.87797163554742, + 155.96265687174778, + 146.37383940414247, + 137.11151923273135, + 128.1756963575146, + 119.566370778492, + 111.28354249566374, + 103.3272115090297, + 95.69737781858994, + 88.39404142434448, + 81.41720232629324, + 74.7668605244363, + 68.44301601877359, + 62.44566880930518, + 56.77481889603102, + 51.43046627895112, + 46.41261095806553, + 41.72125293337416, + 37.35639220487706, + 33.31802877257422, + 29.60616263646569, + 26.220793796551384, + 23.16192225283135, + 20.429548005305584, + 18.02367105397408, + 15.944291398836864, + 14.191409039893896, + 12.765023977145194, + 11.665136210590758, + 10.891745740230595, + 10.444852566064693, + 10.324456688093056, + 10.530558106315684, + 11.063156820732576, + 11.922252831343739, + 13.10784613814917, + 14.619936741148868, + 16.458524640342816, + 18.623609835731042, + 21.115192327313537, + 23.9332721150903, + 27.077849199061333, + 30.548923579226603, + 34.34649525558616, + 38.470564228139985, + 42.92113049688808, + 47.6981940618304, + 52.80175492296703, + 58.231813080297925, + 63.98836853382309, + 70.07142128354246, + 76.48097132945615, + 83.21701867156412, + 90.27956330986635, + 97.66860524436278, + 105.3841444750536, + 113.42618100193856, + 121.79471482501779, + 130.48974594429143, + 139.51127435975917, + 148.85930007142136, + 158.53382307927762, + 168.53484338332814, + 178.86236098357313, + 189.51637588001222, + 200.49688807264553, + 211.80389756147335, + 223.43740434649519, + 235.3974084277115, + 247.6839098051219, + 260.2969084787265, + 273.23640444852566, + 286.5023977145188, + 300.09488827670646, + 314.01387613508814 + ], + [ + 508.60422405876955, + 490.6897255382104, + 473.10172431384547, + 455.84022038567497, + 438.9052137536986, + 422.29670441791654, + 406.0146923783287, + 390.0591776349353, + 374.43016018773596, + 359.12764003673095, + 344.1516171819202, + 329.50209162330367, + 315.1790633608815, + 301.1825323946536, + 287.51249872461995, + 274.1689623507806, + 261.1519232731354, + 248.46138149168453, + 236.0973370064279, + 224.05978981736558, + 212.34873992449747, + 200.9641873278237, + 189.90613202734414, + 179.17457402305888, + 168.76951331496784, + 158.69094990307113, + 148.93888378736864, + 139.51331496786045, + 130.41424344454646, + 121.64166921742681, + 113.19559228650137, + 105.07601265177026, + 97.28293031323334, + 89.81634527089071, + 82.67625752474237, + 75.86266707478828, + 69.37557392102848, + 63.214978063462915, + 57.38087950209163, + 51.8732782369146, + 46.692174267931826, + 41.83756759514337, + 37.30945821854913, + 33.10784613814917, + 29.232731353943468, + 25.684113865932062, + 22.461993674114893, + 19.56637077849199, + 16.997245179063356, + 14.754616875828987, + 12.838485868788904, + 11.248852157943066, + 9.985715743291498, + 9.049076624834196, + 8.438934802571167, + 8.155290276502397, + 8.198143046627894, + 8.567493112947659, + 9.263340475461682, + 10.285685134169979, + 11.634527089072542, + 13.309866340169373, + 15.31170288746045, + 17.640036730945816, + 20.294867870625446, + 23.27619630649934, + 26.584022038567504, + 30.218345066829897, + 34.179165391286595, + 38.46648301193756, + 43.080297928782784, + 48.020610141822246, + 53.287419651056, + 58.88072645648404, + 64.80053055810632, + 71.04683195592284, + 77.61963064993367, + 84.51892664013876, + 91.74471992653812, + 99.2970105091317, + 107.17579838791966, + 115.38108356290172, + 123.91286603407809, + 132.77114580144885, + 141.95592286501372, + 151.46719722477303, + 161.30496888072648, + 171.46923783287411, + 181.96000408121623, + 192.77726762575244, + 203.92102846648288, + 215.39128660340782, + 227.1880420365268, + 239.3112947658403, + 251.7610447913478, + 264.5372921130496, + 277.64003673094584, + 291.0692786450362, + 304.825017855321, + 318.9072543617998 + ], + [ + 497.6624834200591, + 479.91123354759713, + 462.4864809713293, + 445.38822569125597, + 428.6164677073768, + 412.17120701969174, + 396.05244362820116, + 380.2601775329049, + 364.79440873380264, + 349.6551372308948, + 334.8423630241811, + 320.35608611366183, + 306.19630649933686, + 292.36302418120596, + 278.8562391592694, + 265.67595143352713, + 252.8221610039792, + 240.2948678706254, + 228.09407203346592, + 216.21977349250076, + 204.6719722477298, + 193.45066829915314, + 182.55586164677072, + 171.9875522905826, + 161.7457402305887, + 151.8304254667891, + 142.24160799918374, + 132.97928782777265, + 124.04346495255585, + 115.43413937353333, + 107.15131109070502, + 99.19498010407102, + 91.56514641363125, + 84.26181001938575, + 77.28497092133455, + 70.63462911947758, + 64.3107846138149, + 58.31343740434647, + 52.642587491072334, + 47.298234873992435, + 42.280379553106805, + 37.58902152841548, + 33.22416079991838, + 29.185797367615542, + 25.473931231506974, + 22.088562391592703, + 19.029690847872665, + 16.2973166003469, + 13.891439649015398, + 11.812059993878163, + 10.059177634935208, + 8.632792572186506, + 7.5329048056320715, + 6.759514335271904, + 6.312621161106005, + 6.19222528313437, + 6.398326701357, + 6.930925415773899, + 7.790021426385055, + 8.975614733190485, + 10.487705336190182, + 12.326293235384144, + 14.491378430772356, + 16.982960922354852, + 19.801040710131616, + 22.945617794102645, + 26.416692174267943, + 30.214263850627475, + 34.338332823181304, + 38.788899091929395, + 43.56596265687176, + 48.66952351800835, + 54.09958167533924, + 59.856137128864404, + 65.93918987858383, + 72.34873992449747, + 79.08478726660542, + 86.14733190490766, + 93.53637383940415, + 101.25191307009486, + 109.29394959697993, + 117.66248342005917, + 126.35751453933266, + 135.37904295480058, + 144.72706866646257, + 154.40159167431904, + 164.40261197836955, + 174.73012957861437, + 185.38414447505363, + 196.36465666768697, + 207.67166615651453, + 219.3051729415366, + 231.2651770227527, + 243.5516784001633, + 256.164677073768, + 269.10417304356696, + 282.3701663095604, + 295.96265687174775, + 309.8816447301297, + 324.1271298847057 + ], + [ + 487.0472400775431, + 469.4592388531783, + 452.1977349250076, + 435.2627282930314, + 418.6542189572493, + 402.3722069176614, + 386.41669217426795, + 370.78767472706875, + 355.4851545760637, + 340.509131721253, + 325.85960616263645, + 311.5365779002143, + 297.54004693398645, + 283.87001326395267, + 270.52647689011326, + 257.50943781246815, + 244.81889603101732, + 232.4548515457607, + 220.4173043566983, + 208.70625446383028, + 197.3217018671564, + 186.26364656667693, + 175.5320885623916, + 165.12702785430062, + 155.04846444240385, + 145.2963983267014, + 135.87082950719318, + 126.77175798387924, + 117.99918375675955, + 109.55310682583413, + 101.43352719110297, + 93.64044485256609, + 86.17385981022348, + 79.03377206407511, + 72.22018161412103, + 65.7330884603612, + 59.57249260279566, + 53.73839404142435, + 48.23079277624734, + 43.04968880726458, + 38.19508213447608, + 33.66697275788189, + 29.465360677481915, + 25.59024589327621, + 22.041628405264774, + 18.819508213447634, + 15.923885317824732, + 13.354759718396096, + 11.112131415161727, + 9.196000408121625, + 7.606366697275803, + 6.3432302826242335, + 5.4065911641669295, + 4.7964493419038945, + 4.512804815835127, + 4.555657585960622, + 4.925007652280385, + 5.620855014794415, + 6.6431996735027035, + 7.992041628405262, + 9.667380879502094, + 11.669217426793187, + 13.99755127027853, + 16.65238240995816, + 19.633710845832056, + 22.941536577900216, + 26.575859606162645, + 30.536679930619307, + 34.82399755127027, + 39.437812468115496, + 44.378124681154986, + 49.6449341903887, + 55.23824099581673, + 61.158045097439015, + 67.4043464952556, + 73.97714518926635, + 80.87644117947144, + 88.10223446587082, + 95.65452504846444, + 103.53331292725227, + 111.7385981022345, + 120.27038057341085, + 129.12866034078147, + 138.3134374043465, + 147.82471176410564, + 157.66248342005923, + 167.8267523722069, + 178.31751862054884, + 189.1347821650852, + 200.27854300581566, + 211.7488011427404, + 223.5455565758596, + 235.66880930517286, + 248.11855933068063, + 260.8948066523824, + 273.99755127027845, + 287.426793184369, + 301.18253239465355, + 315.26476890113264, + 329.6735027038058 + ], + [ + 476.7584940312213, + 459.3337414549536, + 442.23548617488007, + 425.463728191001, + 409.01846750331606, + 392.8997041118253, + 377.10743801652893, + 361.64166921742685, + 346.5023977145189, + 331.6896235078053, + 317.203346597286, + 303.04356698296095, + 289.21028466483017, + 275.70349964289363, + 262.5232119171513, + 249.66942148760333, + 237.14212835424962, + 224.9413325170901, + 213.0670339761249, + 201.51923273135395, + 190.29792878277726, + 179.40312213039488, + 168.8348127742067, + 158.59300071421285, + 148.67768595041323, + 139.0888684828079, + 129.8265483113968, + 120.89072543618, + 112.28139985715744, + 103.99857157432918, + 96.04224058769515, + 88.41240689725542, + 81.1090705030099, + 74.13223140495867, + 67.48188960310175, + 61.15804509743904, + 55.160697887970635, + 49.48984797469646, + 44.14549535761659, + 39.12764003673095, + 34.436282012039584, + 30.07142128354252, + 26.033057851239686, + 22.321191715131114, + 18.935822875216815, + 15.876951331496805, + 13.144577083971035, + 10.738700132639533, + 8.659320477502298, + 6.906438118559329, + 5.4800530558106395, + 4.380165289256204, + 3.6067748188960334, + 3.159881644730132, + 3.0394857667584967, + 3.245587184981126, + 3.7781858993980233, + 4.637281910009186, + 5.822875216814605, + 7.334965819814302, + 9.173553719008265, + 11.338638914396492, + 13.83022140597897, + 16.64830119375573, + 19.792878277726757, + 23.263952657892055, + 27.061524334251615, + 31.18559330680541, + 35.636159575553506, + 40.41322314049587, + 45.51678400163249, + 50.946842158963335, + 56.7033976124885, + 62.78645036220794, + 69.19600040812163, + 75.93204775022953, + 82.99459238853176, + 90.38363432302825, + 98.099173553719, + 106.14121008060397, + 114.50974390368333, + 123.20477502295681, + 132.22630343842457, + 141.57432915008675, + 151.24885215794302, + 161.24987246199373, + 171.57739006223852, + 182.23140495867762, + 193.21191715131116, + 204.51892664013872, + 216.15243342516055, + 228.1124375063769, + 240.39893888378728, + 253.01193755739217, + 265.95143352719106, + 279.21742679318425, + 292.8099173553719, + 306.7289052137536, + 320.97439036832986, + 335.54637281910004 + ], + [ + 466.79624528109383, + 449.53474135292305, + 432.5997347209468, + 415.99122538516485, + 399.709213345577, + 383.7536986021835, + 368.12468115498416, + 352.8221610039792, + 337.8461381491685, + 323.1966125905519, + 308.8735843281297, + 294.8770533619018, + 281.2070196918682, + 267.8634833180288, + 254.8464442403836, + 242.1559024589328, + 229.7918579736762, + 217.75431078461384, + 206.04326089174572, + 194.65870829507193, + 183.60065299459237, + 172.8690949903071, + 162.4640342822161, + 152.38547087031935, + 142.63340475461686, + 133.20783593510868, + 124.10876441179471, + 115.33619018467505, + 106.89011325374962, + 98.77053361901848, + 90.97745128048157, + 83.51086623813899, + 76.37077849199062, + 69.55718804203653, + 63.070094888276714, + 56.909499030711146, + 51.075400469339876, + 45.56779920416284, + 40.38669523518009, + 35.53208856239159, + 31.003979185797355, + 26.80236710539743, + 22.927252321191723, + 19.378634833180286, + 16.15651464136312, + 13.260891745740244, + 10.691766146311608, + 8.449137843077239, + 6.533006836037137, + 4.943373125191303, + 3.680236710539744, + 2.743597592082442, + 2.133455769819406, + 1.8498112437506373, + 1.8926640138761348, + 2.262014080195897, + 2.9578614427099277, + 3.9802061014182257, + 5.329048056320778, + 7.0043873074176055, + 9.006223854708702, + 11.334557698194066, + 13.98938883787367, + 16.970717273747564, + 20.278543005815727, + 23.91286603407816, + 27.873686358534854, + 32.161003979185786, + 36.77481889603101, + 41.715131109070505, + 46.98194061830427, + 52.57524742373224, + 58.49505152535453, + 64.7413529231711, + 71.31415161718193, + 78.21344760738697, + 85.43924089378633, + 92.99153147637995, + 100.87031935516787, + 109.07560453014993, + 117.60738700132643, + 126.46566676869708, + 135.65044383226194, + 145.16171819202125, + 154.99948984797467, + 165.1637588001225, + 175.65452504846442, + 186.4717885930006, + 197.61554943373127, + 209.08580757065602, + 220.882563003775, + 233.0058157330885, + 245.455565758596, + 258.23181308029797, + 271.33455769819403, + 284.7637996122843, + 298.5195388225691, + 312.60177532904794, + 327.0105091317213, + 341.74574023058864 + ], + [ + 457.1604938271605, + 440.06223854708696, + 423.2904805632078, + 406.8452198755229, + 390.72645648403227, + 374.93419038873583, + 359.46842158963364, + 344.3291500867259, + 329.5163758800122, + 315.0300989694929, + 300.8703193551678, + 287.037037037037, + 273.5302520151005, + 260.3499642893582, + 247.4961738598102, + 234.96888072645646, + 222.76808488929703, + 210.8937863483318, + 199.34598510356082, + 188.12468115498416, + 177.22987450260172, + 166.66156514641364, + 156.41975308641975, + 146.50443832262013, + 136.9156208550148, + 127.65330068360372, + 118.71747780838687, + 110.10815222936435, + 101.82532394653606, + 93.86899295990204, + 86.23915926946229, + 78.93582287521683, + 71.95898377716559, + 65.30864197530863, + 58.984797469645954, + 52.98745026017752, + 47.31660034690338, + 41.97224772982348, + 36.95439240893786, + 32.263034384246495, + 27.898173655749396, + 23.859810223446594, + 20.14794408733803, + 16.762575247423726, + 13.703703703703694, + 10.971329456177948, + 8.565452504846446, + 6.4860728497092115, + 4.733190490766243, + 3.306805428017542, + 2.206917661463117, + 1.4335271911029475, + 0.9866340169370451, + 0.8662381389654104, + 1.0723395571880392, + 1.6049382716049356, + 2.464034282216099, + 3.649627589021531, + 5.161718192021214, + 7.000306091215178, + 9.165391286603407, + 11.656973778185906, + 14.475053565962645, + 17.61963064993367, + 21.090705030098967, + 24.88827670645853, + 29.012345679012356, + 33.46291194776042, + 38.239975512702784, + 43.34353637383941, + 48.7735945311703, + 54.53014998469541, + 60.61320273441485, + 67.02275278032855, + 73.7588001224365, + 80.82134476073868, + 88.21038669523516, + 95.92592592592594, + 103.96796245281095, + 112.33649627589017, + 121.03152739516382, + 130.05305581063158, + 139.40108152229357, + 149.07560453015, + 159.07662483420054, + 169.40414243444553, + 180.05815733088463, + 191.03866952351794, + 202.34567901234576, + 213.9791857973676, + 225.9391898785837, + 238.22569125599432, + 250.83868992959893, + 263.77818589939807, + 277.0441791653913, + 290.63666972757875, + 304.55565758596066, + 318.80114274053665, + 333.3731251913071, + 348.2716049382716 + ], + [ + 447.85123966942155, + 430.9162330374452, + 414.30772370166306, + 398.0257116620754, + 382.0701969186818, + 366.4411794714825, + 351.1386593204774, + 336.1626364656669, + 321.5131109070504, + 307.1900826446281, + 293.1935516784002, + 279.5235180083665, + 266.17998163452717, + 253.16294255688197, + 240.4724007754311, + 228.1083562901745, + 216.0708091011122, + 204.3597592082441, + 192.97520661157026, + 181.91715131109075, + 171.18559330680546, + 160.78053259871447, + 150.70196918681768, + 140.94990307111522, + 131.524334251607, + 122.42526272829308, + 113.65268850117337, + 105.20661157024797, + 97.0870319355168, + 89.29394959697994, + 81.8273645546373, + 74.68727680848896, + 67.87368635853485, + 61.38659320477504, + 55.225997347209486, + 49.39189878583819, + 43.88429752066118, + 38.70319355167841, + 33.84858687888993, + 29.320477502295695, + 25.118865421895727, + 21.243750637690056, + 17.69513314967862, + 14.473012957861453, + 11.57739006223855, + 9.008264462809937, + 6.765636159575568, + 4.849505152535464, + 3.2598714416896275, + 1.996735027038059, + 1.0600959085807644, + 0.44995408631772715, + 0.16630956024895704, + 0.20916233037445453, + 0.5785123966942143, + 1.2743597592082434, + 2.2967044179165397, + 3.645546372819103, + 5.320885623915917, + 7.322722171207012, + 9.651056014692374, + 12.305887154372003, + 15.287215590245873, + 18.595041322314035, + 22.22936435057646, + 26.190184675033155, + 30.47750229568412, + 35.091317212529304, + 40.0316294255688, + 45.29843893480257, + 50.89174574023059, + 56.81154984185284, + 63.05785123966938, + 69.63064993368022, + 76.52994592388531, + 83.75573921028462, + 91.30802979287824, + 99.18681767166613, + 107.39210284664829, + 115.92388531782464, + 124.7821650851954, + 133.9669421487603, + 143.47821650851944, + 153.31598816447303, + 163.4802571166207, + 173.9710233649628, + 184.788286909499, + 195.93204775022946, + 207.4023058871544, + 219.1990613202734, + 231.32231404958662, + 243.77206407509436, + 256.5483113967961, + 269.6510560146924, + 283.0802979287827, + 296.83603713906734, + 310.9182736455464, + 325.3270074482195, + 340.0622385470871, + 355.12396694214874 + ], + [ + 438.8684828078767, + 422.0967248239976, + 405.6514641363126, + 389.53270074482197, + 373.74043464952564, + 358.2746658504234, + 343.1353943475155, + 328.32262014080203, + 313.83634323028264, + 299.67656361595766, + 285.8432812978267, + 272.3364962758902, + 259.156208550148, + 246.30241812059995, + 233.7751249872462, + 221.57432915008675, + 209.70003060912157, + 198.1522293643506, + 186.93092541577388, + 176.0361187633915, + 165.46780940720333, + 155.2259973472095, + 145.31068258340989, + 135.72186511580455, + 126.45954494439343, + 117.52372206917664, + 108.91439649015408, + 100.63156820732581, + 92.67523722069178, + 85.04540353025206, + 77.74206713600654, + 70.76522803795534, + 64.11488623609837, + 57.79104173043567, + 51.793694520967264, + 46.1228446076931, + 40.77849199061322, + 35.76063666972758, + 31.069278645036235, + 26.704417916539132, + 22.666054484236298, + 18.954188348127765, + 15.568819508213458, + 12.509947964493424, + 9.777573716967655, + 7.371696765636175, + 5.292317110498938, + 3.5394347515559677, + 2.1130496888072656, + 1.0131619222528303, + 0.2397714518926679, + -0.20712172227323555, + -0.3275176002448721, + -0.12141618202224125, + 0.4111825323946512, + 1.2702785430058134, + 2.455871849811243, + 3.96796245281094, + 5.806550352004887, + 7.971635547393115, + 10.46321803897561, + 13.281297826752374, + 16.425874910723373, + 19.89694929088867, + 23.69452096724823, + 27.81858993980206, + 32.26915620855016, + 37.046219773492474, + 42.14978063462911, + 47.57983879196, + 53.33639424548516, + 59.419446995204545, + 65.82899704111823, + 72.56504438322618, + 79.62758902152842, + 87.01663095602484, + 94.73217018671562, + 102.77420671360063, + 111.14274053667994, + 119.83777165595342, + 128.85930007142133, + 138.20732578308335, + 147.8818487909396, + 157.88286909499033, + 168.2103866952351, + 178.86440159167438, + 189.84491378430772, + 201.1519232731353, + 212.78543005815735, + 224.7454341393735, + 237.03193551678388, + 249.64493419038877, + 262.5844301601877, + 275.8504234261811, + 289.4429139883685, + 303.3619018467502, + 317.60738700132646, + 332.1793694520967, + 347.07784919906146, + 362.30282624222025 + ], + [ + 430.2122232425263, + 413.6037139067442, + 397.3217018671564, + 381.3661871237629, + 365.7371696765636, + 350.4346495255586, + 335.45862667074783, + 320.8091011121315, + 306.4860728497092, + 292.48954188348125, + 278.81950821344753, + 265.47597183960823, + 252.45893276196307, + 239.7683909805122, + 227.40434649525557, + 215.36679930619326, + 203.6557494133252, + 192.27119681665135, + 181.21314151617182, + 170.48158351188656, + 160.0765228037955, + 149.9979593918988, + 140.24589327619628, + 130.82032445668813, + 121.72125293337415, + 112.94867870625448, + 104.50260177532905, + 96.38302214059792, + 88.58993980206101, + 81.12335475971842, + 73.98326701357004, + 67.16967656361598, + 60.68258340985614, + 54.52198755229058, + 48.687888990919305, + 43.18028772574226, + 37.99918375675952, + 33.14457708397102, + 28.616467707376806, + 24.414855626976838, + 20.53974084277114, + 16.991123354759736, + 13.769003162942564, + 10.873380267319662, + 8.304254667891028, + 6.061626364656679, + 4.145495357616575, + 2.5558616467707393, + 1.2927252321191705, + 0.35608611366186915, + -0.25405570860116145, + -0.5377002346699313, + -0.49484746454443407, + -0.12549739822466965, + 0.5703499642893544, + 1.5926946229976506, + 2.941536577900214, + 4.616875828997044, + 6.618712376288123, + 8.947046219773485, + 11.601877359453114, + 14.583205795327013, + 17.891031527395143, + 21.52535455565757, + 25.48617488011427, + 29.773492500765233, + 34.38730741761046, + 39.32761963064991, + 44.59442913988367, + 50.18773594531171, + 56.107540046934005, + 62.353841444750515, + 68.92664013876133, + 75.82593612896642, + 83.05172941536578, + 90.60401999795934, + 98.48280787674724, + 106.68809305172941, + 115.21987552290582, + 124.07815529027644, + 133.2629323538415, + 142.77420671360062, + 152.61197836955407, + 162.77624732170187, + 173.26701357004382, + 184.08427711458023, + 195.22803795531067, + 206.6982960922354, + 218.4950515253546, + 230.61830425466786, + 243.06805428017535, + 255.8443016018774, + 268.9470462197734, + 282.37628813386397, + 296.1320273441485, + 310.2142638506274, + 324.62299765330073, + 339.35822875216803, + 354.4199571472299, + 369.8081828384859 + ], + [ + 421.8824609733701, + 405.43720028568504, + 389.3184368941944, + 373.5261707988982, + 358.06040199979594, + 342.9211304968881, + 328.1083562901744, + 313.62207937965513, + 299.4622997653301, + 285.6290174471992, + 272.12223242526267, + 258.94194469952043, + 246.08815426997248, + 233.56086113661868, + 221.3600652994592, + 209.48576675849404, + 197.93796551372313, + 186.7166615651464, + 175.82185491276397, + 165.25354555657586, + 155.01173349658197, + 145.09641873278235, + 135.50760126517702, + 126.24528109376595, + 117.30945821854912, + 108.70013263952659, + 100.4173043566983, + 92.46097337006428, + 84.83113967962454, + 77.52780328537905, + 70.55096418732782, + 63.90062238547088, + 57.576777879808176, + 51.57943067033975, + 45.90858075706561, + 40.56422813998571, + 35.5463728191001, + 30.855014794408728, + 26.490154065911646, + 22.45179063360881, + 18.739924497500247, + 15.354555657585973, + 12.295684113865937, + 9.563309866340168, + 7.157432915008667, + 5.078053259871449, + 3.3251709009284802, + 1.8987858381797778, + 0.7988980716253427, + 0.025507601265174706, + -0.4213855729007235, + -0.5417814508723597, + -0.3356800326497289, + 0.1969186817671693, + 1.0560146923783256, + 2.2416079991837554, + 3.7536986021834524, + 5.592286501377417, + 7.757371696765627, + 10.248954188348122, + 13.067033976124884, + 16.21161106009592, + 19.68268544026118, + 23.48025711662074, + 27.60432608917457, + 32.05489235792267, + 36.831955922865035, + 41.935516784001614, + 47.36557494133251, + 53.12213039485767, + 59.205183144577106, + 65.61473319049074, + 72.3507805325987, + 79.41332517090093, + 86.80236710539742, + 94.51790633608812, + 102.55994286297314, + 110.92847668605243, + 119.62350780532601, + 128.64503622079377, + 137.99306193245593, + 147.6675849403122, + 157.66860524436274, + 167.99612284460773, + 178.65013774104682, + 189.63064993368033, + 200.93765942250792, + 212.57116620752976, + 224.5311702887461, + 236.81767166615649, + 249.43067033976112, + 262.3701663095602, + 275.63615957555345, + 289.2286501377411, + 303.1476379961228, + 317.3931231506988, + 331.96510560146925, + 346.86358534843373, + 362.0885623915928, + 377.6400367309457 + ], + [ + 413.8791960004081, + 397.59718396082025, + 381.6416692174267, + 366.01265177022754, + 350.7101316192226, + 335.7341087644118, + 321.0845832057953, + 306.7615549433732, + 292.7650239771452, + 279.09499030711146, + 265.75145393327205, + 252.73441485562694, + 240.04387307417613, + 227.6798285889195, + 215.64228139985713, + 203.93123150698906, + 192.54667891031528, + 181.4886236098357, + 170.75706560555042, + 160.35200489745944, + 150.27344148556267, + 140.5213753698602, + 131.095806550352, + 121.99673502703806, + 113.22416079991835, + 104.77808386899297, + 96.65850423426178, + 88.86542189572492, + 81.39883685338229, + 74.25874910723395, + 67.44515865727986, + 60.958065503520054, + 54.797469645954486, + 48.963371084583194, + 43.455769819406186, + 38.27466585042341, + 33.42005917763493, + 28.891949801040703, + 24.69033772064075, + 20.81522293643505, + 17.26660544842362, + 14.044485256606478, + 11.148862360983575, + 8.57973676155494, + 6.337108458320573, + 4.420977451280488, + 2.831343740434652, + 1.5682073257830837, + 0.631568207325782, + 0.02142638506274773, + -0.2622181410060183, + -0.21936537088052105, + 0.14998469543924342, + 0.8458320579532752, + 1.868176716661564, + 3.2170186715641274, + 4.892357922660957, + 6.894194469952055, + 9.222528313437397, + 11.877359453117027, + 14.858687888990925, + 18.16651362105909, + 21.800836649321482, + 25.76165697377818, + 30.048974594429147, + 34.66278951127437, + 39.60310172431387, + 44.86991123354758, + 50.46321803897562, + 56.383022140597916, + 62.62932353841447, + 69.20212223242524, + 76.10141822263034, + 83.32721150902971, + 90.87950209162334, + 98.75828997041117, + 106.9635751453933, + 115.49535761656975, + 124.35363738394045, + 133.53841444750532, + 143.04968880726463, + 152.88746046321805, + 163.0517294153657, + 173.54249566370785, + 184.35975920824404, + 195.50352004897468, + 206.97377818589942, + 218.7705336190184, + 230.89378634833187, + 243.34353637383938, + 256.1197836955412, + 269.22252831343746, + 282.6517702275278, + 296.40750943781256, + 310.48974594429137, + 324.8984797469645, + 339.6337108458321, + 354.69543924089373, + 370.0836649321499, + 385.79838791960003 + ], + [ + 406.20242832364045, + 390.08366493214976, + 374.2913988368533, + 358.8256300377513, + 343.68635853484335, + 328.8735843281297, + 314.3873074176104, + 300.2275278032855, + 286.39424548515467, + 272.8874604632181, + 259.70717273747573, + 246.85338230792777, + 234.32608917457404, + 222.12529333741455, + 210.25099479644936, + 198.70319355167842, + 187.4818896031018, + 176.58708295071935, + 166.01877359453115, + 155.77696153453732, + 145.86164677073768, + 136.27282930313237, + 127.01050913172125, + 118.07468625650446, + 109.4653606774819, + 101.18253239465365, + 93.2262014080196, + 85.59636771757985, + 78.29303132333436, + 71.31619222528315, + 64.66585042342619, + 58.342005917763515, + 52.34465870829508, + 46.67380879502092, + 41.32945617794104, + 36.3116008570554, + 31.620242832364056, + 27.255382103866953, + 23.217018671564134, + 19.50515253545557, + 16.119783695541265, + 13.060912151821258, + 10.328537904295487, + 7.922660952963985, + 5.84328129782675, + 4.090398938883796, + 2.6640138761350918, + 1.5641261095806551, + 0.7907356392204858, + 0.34384246505458366, + 0.2234465870829484, + 0.4295480053055778, + 0.9621467197224747, + 1.8212427303336383, + 3.006836037139058, + 4.518926640138753, + 6.357514539332716, + 8.522599734720945, + 11.014182226303419, + 13.832262014080182, + 16.976839098051208, + 20.447913478216506, + 24.24548515457603, + 28.369554127129863, + 32.82012039587796, + 37.59718396082032, + 42.700744821956945, + 48.13080297928779, + 53.88735843281295, + 59.97041118253239, + 66.37996122844608, + 73.11600857055397, + 80.17855320885621, + 87.56759514335269, + 95.28313437404346, + 103.32517090092843, + 111.69370472400772, + 120.38873584328128, + 129.41026425874912, + 138.7582899704111, + 148.43281297826755, + 158.4338332823181, + 168.76135088256288, + 179.41536577900212, + 190.39587797163549, + 201.70288746046327, + 213.33639424548514, + 225.29639832670125, + 237.58289970411187, + 250.1958983777165, + 263.1353943475154, + 276.4013876135088, + 289.9938781756963, + 303.9128660340782, + 318.1583511886542, + 332.73033363942443, + 347.6288133863892, + 362.8537904295479, + 378.40526476890125, + 394.28323640444853 + ], + [ + 398.85215794306697, + 382.8966431996736, + 367.26762575247415, + 351.96510560146925, + 336.98908274665854, + 322.33955718804197, + 308.0165289256198, + 294.01999795939196, + 280.34996428935824, + 267.0064279155189, + 253.98938883787363, + 241.29884705642283, + 228.93480257116624, + 216.89725538210388, + 205.18620548923576, + 193.801652892562, + 182.7435975920825, + 172.01203958779718, + 161.60697887970613, + 151.5284154678094, + 141.7763493521069, + 132.35078053259875, + 123.25170900928477, + 114.4791347821651, + 106.03305785123966, + 97.91347821650854, + 90.12039587797163, + 82.65381083562905, + 75.51372308948066, + 68.7001326395266, + 62.213039485766764, + 56.052443628201225, + 50.21834506682992, + 44.71074380165288, + 39.52963983267014, + 34.67503315988164, + 30.146923783287427, + 25.94531170288746, + 22.070196918681773, + 18.521579430670336, + 15.29945923885317, + 12.403836343230296, + 9.834710743801658, + 7.59208244056729, + 5.675951433527188, + 4.086317722681366, + 2.8231813080297954, + 1.8865421895724925, + 1.2764003673094568, + 0.9927558412406883, + 1.035608611366185, + 1.4049586776859482, + 2.1008060401999784, + 3.123150698908276, + 4.471992653810828, + 6.147331904907657, + 8.149168452198753, + 10.477502295684117, + 13.132333435363723, + 16.113661871237618, + 19.421487603305778, + 23.055810631568214, + 27.01663095602487, + 31.303948576675833, + 35.91776349352106, + 40.858075706560555, + 46.124885215794315, + 51.71819202122229, + 57.637996122844584, + 63.88429752066116, + 70.45709621467198, + 77.35639220487701, + 84.58218549127638, + 92.13447607387, + 100.01326395265791, + 108.21854912763997, + 116.75033159881642, + 125.60861136618712, + 134.79338842975204, + 144.3046627895112, + 154.1424344454648, + 164.30670339761247, + 174.79746964595438, + 185.6147331904908, + 196.75849403122123, + 208.22875216814617, + 220.02550760126516, + 232.14876033057843, + 244.59851035608617, + 257.37475767778795, + 270.477502295684, + 283.90674420977456, + 297.6624834200591, + 311.7447199265382, + 326.1534537292113, + 340.8886848280787, + 355.9504132231406, + 371.3386389143965, + 387.0533619018469, + 403.09458218549133 + ], + [ + 391.82838485868785, + 376.03611876339147, + 360.5703499642893, + 345.43107846138156, + 330.6183042546679, + 316.1320273441485, + 301.97224772982344, + 288.1389654116927, + 274.6321803897562, + 261.4518926640138, + 248.59810223446584, + 236.0708091011121, + 223.87001326395267, + 211.99571472298746, + 200.4479134782165, + 189.22660952963983, + 178.33180287725742, + 167.76349352106928, + 157.5216814610754, + 147.6063666972758, + 138.01754922967044, + 128.75522905825937, + 119.81940618304255, + 111.21008060402, + 102.9272523211917, + 94.9709213345577, + 87.34108764411795, + 80.03775124987247, + 73.06091215182124, + 66.4105703499643, + 60.086725844301604, + 54.089378634833196, + 48.41852872155903, + 43.07417610447913, + 38.05632078359352, + 33.364962758902145, + 29.000102030405067, + 24.961738598102233, + 21.249872461993682, + 17.864503622079376, + 14.805632078359343, + 12.0732578308336, + 9.667380879502096, + 7.588001224364861, + 5.835118865421893, + 4.408733802673202, + 3.3088460361187666, + 2.535455565758597, + 2.0885623915926947, + 1.96816651362106, + 2.1742679318436893, + 2.7068666462605857, + 3.5659626568717497, + 4.7515559636771805, + 6.263646566676864, + 8.102234465870827, + 10.267319661259057, + 12.758902152841554, + 15.576981940618293, + 18.721559024589325, + 22.192633404754616, + 25.990205081114176, + 30.11427405366797, + 34.56484032241607, + 39.34190388735843, + 44.445464748495056, + 49.87552290582595, + 55.63207835935106, + 61.715131109070505, + 68.12468115498419, + 74.86072849709215, + 81.92327313539431, + 89.31231506989081, + 97.02785430058157, + 105.06989082746661, + 113.43842465054583, + 122.13345576981938, + 131.15498418528722, + 140.50300989694932, + 150.1775329048056, + 160.17855320885627, + 170.5060708091011, + 181.16008570554018, + 192.1405978981737, + 203.44760738700128, + 215.08111417202332, + 227.04111825323946, + 239.32761963064985, + 251.94061830425474, + 264.88011427405365, + 278.14610754004684, + 291.7385981022345, + 305.65758596061625, + 319.9030711151924, + 334.47505356596264, + 349.3735333129271, + 364.59851035608614, + 380.1499846954392, + 396.02795633098674, + 412.23242526272827 + ], + [ + 385.13110907050304, + 369.5020916233036, + 354.19957147229877, + 339.2235486174881, + 324.5740230588715, + 310.25099479644933, + 296.2544638302213, + 282.58443016018776, + 269.24089378634835, + 256.2238547087032, + 243.5333129272523, + 231.1692684419957, + 219.1317212529334, + 207.42067136006528, + 196.03611876339144, + 184.97806346291193, + 174.2465054586267, + 163.84144475053563, + 153.7628813386389, + 144.01081522293643, + 134.58524640342821, + 125.48617488011429, + 116.71360065299457, + 108.26752372206919, + 100.14794408733802, + 92.35486174880114, + 84.88827670645851, + 77.74818896031017, + 70.9345985103561, + 64.44750535659628, + 58.28690949903071, + 52.452810937659436, + 46.94520967248239, + 41.76410570349964, + 36.90949903071115, + 32.381389654116916, + 28.179777573716972, + 24.30466278951127, + 20.756045301499853, + 17.533925109682684, + 14.638302214059783, + 12.069176614631171, + 9.826548311396802, + 7.9104173043567, + 6.320783593510866, + 5.057647178859307, + 4.121008060402005, + 3.510866238138969, + 3.2272217120702003, + 3.270074482195699, + 3.63942454851546, + 4.335271911029491, + 5.357616569737788, + 6.706458524640353, + 8.38179777573717, + 10.383634323028264, + 12.711968166513628, + 15.366799306193258, + 18.348127742067128, + 21.655953474135288, + 25.29027650239772, + 29.251096826854415, + 33.538414447505346, + 38.152229364350575, + 43.092541577390065, + 48.35935108662383, + 53.95265789205186, + 59.87246199367411, + 66.11876339149067, + 72.69156208550149, + 79.59085807570659, + 86.81665136210589, + 94.36894194469951, + 102.24772982348742, + 110.45301499846957, + 118.98479746964593, + 127.84307723701662, + 137.0278543005816, + 146.5391286603408, + 156.37690031629424, + 166.54116926844208, + 177.031935516784, + 187.8491990613202, + 198.99295990205084, + 210.4632180389756, + 222.25997347209477, + 234.38322620140804, + 246.83297622691555, + 259.60922354861754, + 272.71196816651354, + 286.1412100806039, + 299.89694929088876, + 313.97918579736756, + 328.38791960004085, + 343.12315069890826, + 358.18487909396987, + 373.573104785226, + 389.2878277726762, + 405.32904805632086, + 421.6967656361595 + ], + [ + 378.7603305785125, + 363.29456177941023, + 348.15529027650234, + 333.34251606978887, + 318.8562391592694, + 304.69645954494445, + 290.86317722681355, + 277.3563922048771, + 264.1761044791348, + 251.3223140495868, + 238.795020916233, + 226.59422507907357, + 214.7199265381084, + 203.17212529333742, + 191.95082134476073, + 181.05601469237834, + 170.4877053361902, + 160.24589327619634, + 150.3305785123967, + 140.7417610447914, + 131.47944087338027, + 122.54361799816348, + 113.9342924191409, + 105.65146413631265, + 97.69513314967861, + 90.06529945923887, + 82.76196306499338, + 75.78512396694218, + 69.13478216508521, + 62.81093765942253, + 56.8135904499541, + 51.14274053667995, + 45.798387919600046, + 40.78053259871441, + 36.08917457402306, + 31.724313845525963, + 27.685950413223143, + 23.974084277114578, + 20.588715437200293, + 17.529843893480255, + 14.797469645954486, + 12.391592694623005, + 10.31221303948577, + 8.5593306805428, + 7.132945617794096, + 6.033057851239669, + 5.259667380879499, + 4.812774206713595, + 4.692378328741959, + 4.89847974696459, + 5.431078461381482, + 6.2901744719926445, + 7.475767778798073, + 8.987858381797771, + 10.826446280991718, + 12.991531476379945, + 15.483113967962442, + 18.301193755739202, + 21.445770839710203, + 24.916845219875498, + 28.71441689623506, + 32.838485868788894, + 37.28905213753695, + 42.06611570247931, + 47.16967656361594, + 52.599734720946834, + 58.356290174471994, + 64.43934292419137, + 70.84889297010506, + 77.584940312213, + 84.64748495051526, + 92.03652688501168, + 99.75206611570243, + 107.79410264258746, + 116.16263646566676, + 124.85766758494024, + 133.87919600040806, + 143.22722171207016, + 152.90174471992654, + 162.90276502397705, + 173.23028262422204, + 183.8842975206611, + 194.86480971329445, + 206.17181920212224, + 217.8053259871441, + 229.7653300683604, + 242.0518314457708, + 254.66483011937544, + 267.60432608917455, + 280.87031935516774, + 294.4628099173551, + 308.3817977757371, + 322.6272829303131, + 337.1992653810836, + 352.0977451280481, + 367.3227221712068, + 382.8741965105601, + 398.7521681461074, + 414.9566370778492, + 431.48760330578506 + ], + [ + 372.71604938271605, + 357.41352923171104, + 342.4375063769003, + 327.78798081828387, + 313.46495255586166, + 299.4684215896337, + 285.7983879196, + 272.45485154576073, + 259.4378124681155, + 246.74727068666465, + 234.383226201408, + 222.3456790123457, + 210.63462911947764, + 199.2500765228038, + 188.19202122232423, + 177.460463218039, + 167.05540250994798, + 156.97683909805122, + 147.22477298234872, + 137.79920416284057, + 128.70013263952657, + 119.92755841240691, + 111.48148148148148, + 103.36190184675036, + 95.56881950821344, + 88.10223446587085, + 80.96214671972248, + 74.1485562697684, + 67.66146311600858, + 61.50086725844304, + 55.66676869707173, + 50.159167431894716, + 44.978063462911955, + 40.123456790123456, + 35.59534741352924, + 31.39373533312927, + 27.518620548923582, + 23.97000306091215, + 20.747882869094994, + 17.852259973472094, + 15.283134374043458, + 13.040506070809109, + 11.124375063769005, + 9.534741352923168, + 8.2716049382716, + 7.334965819814306, + 6.724823997551269, + 6.441179471482498, + 6.484032241607996, + 6.8533823079277605, + 7.549229670441784, + 8.571574329150081, + 9.920416284052644, + 11.595755535149474, + 13.597592082440553, + 15.925925925925915, + 18.580757065605546, + 21.56208550147944, + 24.869911233547576, + 28.504234261810005, + 32.4650545862667, + 36.752372206917656, + 41.36618712376285, + 46.30649933680235, + 51.573308846036106, + 57.16661565146413, + 63.08641975308643, + 69.33272115090294, + 75.90551984491377, + 82.80481583511884, + 90.03060912151821, + 97.58289970411178, + 105.46168758289969, + 113.66697275788182, + 122.19875522905825, + 131.05703499642888, + 140.24181205999383, + 149.75308641975306, + 159.5908580757066, + 169.75512702785426, + 180.24589327619634, + 191.06315682073253, + 202.206917661463, + 213.6771757983879, + 225.47393123150692, + 237.5971839608204, + 250.0469339863279, + 262.8231813080297, + 275.925925925926, + 289.3551678400163, + 303.11090705030085, + 317.1931435567799, + 331.601877359453, + 346.33710845832064, + 361.39883685338225, + 376.78706254463816, + 392.5017855320886, + 408.54300581573307, + 424.91072339557195, + 441.60493827160496 + ], + [ + 366.9982654831139, + 351.8589939802061, + 337.0462197734924, + 322.5599428629731, + 308.40016324864814, + 294.56688093051724, + 281.0600959085807, + 267.87980818283853, + 255.02601775329052, + 242.49872461993672, + 230.2979287827772, + 218.42363024181205, + 206.87582899704114, + 195.65452504846442, + 184.759718396082, + 174.19140903989387, + 163.94959697990006, + 154.03428221610042, + 144.44546474849506, + 135.183144577084, + 126.24732170186714, + 117.63799612284463, + 109.35516784001632, + 101.39883685338232, + 93.76900316294255, + 86.46566676869709, + 79.48882767064585, + 72.83848586878892, + 66.5146413631262, + 60.51729415365781, + 54.84644424038364, + 49.50209162330376, + 44.48423630241812, + 39.79287827772676, + 35.42801754922968, + 31.38965411692684, + 27.677787980818287, + 24.292419140903988, + 21.233547597183964, + 18.501173349658195, + 16.095296398326695, + 14.015916743189479, + 12.26303438424651, + 10.836649321497806, + 9.73676155494337, + 8.963371084583208, + 8.516477910417304, + 8.396082032445669, + 8.6021834506683, + 9.134782165085198, + 9.993878175696356, + 11.179471482501784, + 12.69156208550148, + 14.530149984695445, + 16.695235180083657, + 19.18681767166615, + 22.004897459442915, + 25.149474543413945, + 28.62054892357921, + 32.418120599938774, + 36.5421895724926, + 40.9927558412407, + 45.76981940618302, + 50.87338026731965, + 56.30343842465054, + 62.0599938781757, + 68.14304662789513, + 74.55259667380878, + 81.28864401591673, + 88.35118865421896, + 95.74023058871545, + 103.45576981940616, + 111.49780634629117, + 119.86634016937046, + 128.561371288644, + 137.58289970411178, + 146.93092541577388, + 156.60544842363024, + 166.60646872768083, + 176.93398632792565, + 187.58800122436492, + 198.56851341699826, + 209.87552290582582, + 221.5090296908479, + 233.46903377206402, + 245.7555351494746, + 258.36853382307925, + 271.3080297928782, + 284.57402305887166, + 298.16651362105904, + 312.0855014794408, + 326.330986634017, + 340.90296908478723, + 355.801448831752, + 371.02642587491073, + 386.57790021426376, + 402.4558718498113, + 418.6603407815529, + 435.191307009489, + 452.0487705336191 + ], + [ + 361.60697887970616, + 346.6309560248954, + 331.9814304662789, + 317.6584022038568, + 303.6618712376288, + 289.9918375675951, + 276.6483011937557, + 263.63126211611063, + 250.94072033465974, + 238.5766758494031, + 226.53912866034074, + 214.8280787674727, + 203.44352617079892, + 192.38547087031935, + 181.65391286603403, + 171.24885215794305, + 161.17028874604634, + 151.41822263034382, + 141.9926538108356, + 132.89358228752167, + 124.12100806040198, + 115.67493112947659, + 107.55535149474542, + 99.76226915620855, + 92.29568411386593, + 85.15559636771759, + 78.34200591776349, + 71.85491276400369, + 65.69431690643812, + 59.86021834506684, + 54.35261707988981, + 49.171513110907064, + 44.316906438118565, + 39.78879706152433, + 35.58718498112438, + 31.71207019691868, + 28.163452708907258, + 24.941332517090093, + 22.045709621467203, + 19.47658402203857, + 17.233955718804204, + 15.317824711764116, + 13.72819100091828, + 12.465054586266712, + 11.52841546780941, + 10.91827364554638, + 10.634629119477609, + 10.677481889603106, + 11.046831955922872, + 11.742679318436902, + 12.76502397714519, + 14.113865932047755, + 15.789205183144585, + 17.79104173043568, + 20.119375573921026, + 22.774206713600655, + 25.755535149474554, + 29.063360881542717, + 32.697683909805114, + 36.65850423426181, + 40.945821854912765, + 45.559636771758, + 50.49994898479745, + 55.766758494031215, + 61.36006529945925, + 67.27986940108154, + 73.52617079889811, + 80.09896949290886, + 86.99826548311395, + 94.22405876951333, + 101.77634935210695, + 109.6551372308948, + 117.86042240587695, + 126.39220487705339, + 135.25048464442406, + 144.43526170798896, + 153.94653606774816, + 163.7843077237017, + 173.94857667584944, + 184.43934292419138, + 195.25660646872774, + 206.4003673094582, + 217.87062544638297, + 229.66738087950216, + 241.7906336088154, + 254.2403836343231, + 267.0166309560249, + 280.11937557392093, + 293.54861748801153, + 307.30435669829603, + 321.38659320477495, + 335.79532700744824, + 350.53055810631565, + 365.59228650137754, + 380.9805121926334, + 396.69523518008356, + 412.73645546372825, + 429.1041730435669, + 445.7983879196002, + 462.8191000918274 + ], + [ + 356.54218957249265, + 341.729415365779, + 327.2431384552596, + 313.0833588409347, + 299.25007652280385, + 285.74329150086726, + 272.56300377512497, + 259.709213345577, + 247.18192021222328, + 234.98112437506376, + 223.10682583409852, + 211.55902458932763, + 200.33772064075097, + 189.44291398836853, + 178.87460463218036, + 168.63279257218653, + 158.71747780838692, + 149.12866034078158, + 139.86634016937046, + 130.93051729415367, + 122.3211917151311, + 114.03836343230284, + 106.0820324456688, + 98.45219875522908, + 91.14886236098359, + 84.17202326293237, + 77.52168146107539, + 71.19783695541273, + 65.2004897459443, + 59.529639832670156, + 54.18528721559025, + 49.167431894704634, + 44.476073870013266, + 40.11121314151617, + 36.072849709213344, + 32.360983573104775, + 28.97561473319049, + 25.916743189470456, + 23.184368941944697, + 20.778491990613194, + 18.69911233547596, + 16.946229976533004, + 15.5198449137843, + 14.419957147229866, + 13.646566676869694, + 13.199673502703796, + 13.079277624732159, + 13.285379042954787, + 13.817977757371684, + 14.677073767982847, + 15.862667074788266, + 17.37475767778796, + 19.213345576981926, + 21.37843077237015, + 23.87001326395263, + 26.688093051729393, + 29.83267013570042, + 33.303744515865716, + 37.10131619222524, + 41.22538516477907, + 45.67595143352716, + 50.45301499846953, + 55.55657585960611, + 60.986634016937, + 66.74318947046217, + 72.82624222018158, + 79.2357922660953, + 85.97183960820318, + 93.0343842465054, + 100.4234261810019, + 108.13896541169267, + 116.18100193857762, + 124.54953576165691, + 133.24456688093048, + 142.26609529639828, + 151.61412100806032, + 161.2886440159167, + 171.2896643199673, + 181.61718192021218, + 192.27119681665124, + 203.25170900928478, + 214.55871849811237, + 226.1922252831342, + 238.15222936435055, + 250.438730741761, + 263.05172941536586, + 275.99122538516474, + 289.2572186511579, + 302.84970921334553, + 316.7686970717273, + 331.01418222630326, + 345.58616467707367, + 360.48464442403827, + 375.7096214671973, + 391.2610958065503, + 407.13906744209754, + 423.3435363738394, + 439.87450260177525, + 456.73196612590556, + 473.9159269462299 + ], + [ + 351.8038975614734, + 337.1543720028568, + 322.8313437404346, + 308.8348127742068, + 295.164779104173, + 281.8212427303337, + 268.80420365268844, + 256.1136618712377, + 243.74961738598105, + 231.7120701969187, + 220.0010203040506, + 208.61646770737678, + 197.5584124068973, + 186.82685440261199, + 176.42179369452094, + 166.3432302826242, + 156.59116416692177, + 147.16559534741353, + 138.0665238240996, + 129.29394959697993, + 120.84787266605447, + 112.72829303132335, + 104.93521069278644, + 97.46862565044384, + 90.32853790429547, + 83.5149474543414, + 77.02785430058158, + 70.86725844301603, + 65.03315988164474, + 59.52555861646772, + 54.34445464748495, + 49.489847974696474, + 44.96173859810223, + 40.76012651770227, + 36.88501173349658, + 33.336394245485145, + 30.114274053667994, + 27.21865115804509, + 24.649525558616467, + 22.4068972553821, + 20.490766248342, + 18.901132537496174, + 17.637996122844605, + 16.7013570043873, + 16.091215182124266, + 15.807570656055498, + 15.850423426180994, + 16.219773492500757, + 16.915620855014787, + 17.937965513723086, + 19.28680746862564, + 20.96214671972247, + 22.963983267013564, + 25.29231711049892, + 27.94714825017853, + 30.928476686052427, + 34.23630241812059, + 37.870625446383016, + 41.83144577083968, + 46.11876339149064, + 50.73257830833587, + 55.672890521375365, + 60.93970003060908, + 66.5330068360371, + 72.4528109376594, + 78.69911233547597, + 85.27191102948679, + 92.17120701969182, + 99.3970003060912, + 106.94929088868481, + 114.8280787674727, + 123.03336394245478, + 131.56514641363125, + 140.42342618100193, + 149.60820324456688, + 159.11947760432602, + 168.95724926027953, + 179.1215182124273, + 189.6122844607693, + 200.4295480053055, + 211.57330884603613, + 223.04356698296084, + 234.84032241607989, + 246.96357514539335, + 259.41332517090086, + 272.18957249260285, + 285.2923171104989, + 298.7215590245892, + 312.477298234874, + 326.5595347413528, + 340.96826854402593, + 355.7034996428935, + 370.7652280379552, + 386.1534537292113, + 401.8681767166615, + 417.90939700030594, + 434.2771145801449, + 450.9713294561778, + 467.9920416284053, + 485.3392510968268 + ], + [ + 347.3921028466483, + 332.90582593612896, + 318.7460463218039, + 304.9127640036731, + 291.40597898173655, + 278.22569125599426, + 265.3719008264462, + 252.84460769309257, + 240.64381185593305, + 228.76951331496787, + 217.2217120701969, + 206.00040812162024, + 195.10560146923785, + 184.5372921130497, + 174.29548005305583, + 164.3801652892562, + 154.79134782165087, + 145.52902765023978, + 136.59320477502294, + 127.98387919600042, + 119.70105091317211, + 111.74471992653812, + 104.11488623609834, + 96.81154984185288, + 89.83471074380165, + 83.18436894194471, + 76.86052443628202, + 70.8631772268136, + 65.19232731353944, + 59.84797469645956, + 54.83011937557392, + 50.13876135088257, + 45.77390062238547, + 41.73553719008264, + 38.023671053974084, + 34.638302214059784, + 31.579430670339764, + 28.847056422813996, + 26.441179471482506, + 24.36179981634527, + 22.6089174574023, + 21.182532394653613, + 20.082644628099175, + 19.309254157739005, + 18.862360983573105, + 18.741965105601466, + 18.948066523824096, + 19.480665238240995, + 20.339761248852156, + 21.52535455565759, + 23.03744515865727, + 24.87603305785123, + 27.041118253239464, + 29.53270074482196, + 32.3507805325987, + 35.495357616569734, + 38.966431996735025, + 42.764003673094585, + 46.88807264564838, + 51.338638914396476, + 56.115702479338836, + 61.219263340475464, + 66.64932149780633, + 72.40587695133148, + 78.48892970105089, + 84.8984797469646, + 91.63452708907255, + 98.69707172737473, + 106.08611366187122, + 113.80165289256196, + 121.84368941944702, + 130.21222324252622, + 138.90725436179977, + 147.9287827772676, + 157.27680848892973, + 166.95133149678597, + 176.95235180083662, + 187.2798694010815, + 197.9338842975207, + 208.91439649015402, + 220.2214059789818, + 231.85491276400364, + 243.81491684521976, + 256.10141822263034, + 268.714416896235, + 281.65391286603415, + 294.9199061320274, + 308.5123966942148, + 322.43138455259674, + 336.6768697071727, + 351.24885215794296, + 366.1473319049077, + 381.3723089480664, + 396.92378328741967, + 412.801754922967, + 429.00622385470854, + 445.5371900826447, + 462.3946536067748, + 479.5786144270994, + 497.08907254361804 + ], + [ + 343.30680542801747, + 328.9837771655953, + 314.9872461993673, + 301.31721252933374, + 287.97367615549433, + 274.95663707784917, + 262.26609529639825, + 249.90205081114178, + 237.8645036220794, + 226.1534537292113, + 214.76890113253745, + 203.71084583205794, + 192.97928782777268, + 182.57422711968167, + 172.4956637077849, + 162.74359759208244, + 153.31802877257428, + 144.21895724926028, + 135.4463830221406, + 127.00030609121518, + 118.88072645648403, + 111.08764411794715, + 103.62105907560453, + 96.48097132945618, + 89.66738087950208, + 83.18028772574229, + 77.01969186817671, + 71.18559330680544, + 65.67799204162841, + 60.49688807264566, + 55.64228139985716, + 51.11417202326294, + 46.912559942862984, + 43.03744515865728, + 39.48882767064586, + 36.26670747882869, + 33.37108458320581, + 30.801958983777165, + 28.559330680542807, + 26.643199673502707, + 25.05356596265687, + 23.790429548005314, + 22.85379042954801, + 22.243648607284975, + 21.96000408121621, + 22.002856851341704, + 22.372206917661465, + 23.0680542801755, + 24.090398938883794, + 25.43924089378636, + 27.114580144883174, + 29.116416692174276, + 31.444750535659633, + 34.099581675339266, + 37.080910111213136, + 40.388735843281296, + 44.02305887154373, + 47.98387919600043, + 52.271196816651354, + 56.885011733496576, + 61.82532394653607, + 67.09213345576983, + 72.68544026119781, + 78.60524436282012, + 84.85154576063668, + 91.42434445464751, + 98.32364044485259, + 105.5494337312519, + 113.10172431384552, + 120.98051219263343, + 129.18579736761558, + 137.71757983879195, + 146.57585960616262, + 155.76063666972757, + 165.2719110294868, + 175.10968268544025, + 185.273951637588, + 195.76471788593003, + 206.5819814304663, + 217.72574227119674, + 229.19600040812173, + 240.9927558412407, + 253.11600857055396, + 265.56575859606164, + 278.34200591776346, + 291.44475053565975, + 304.87399244975006, + 318.6297316600346, + 332.7119681665137, + 347.1207019691868, + 361.8559330680542, + 376.9176614631161, + 392.305887154372, + 408.02061014182243, + 424.06183042546684, + 440.42954800530543, + 457.1237628813387, + 474.1444750535659, + 491.49168452198774, + 509.1653912866035 + ], + [ + 339.548005305581, + 325.388225691256, + 311.5549433731251, + 298.04815835118865, + 284.8678706254464, + 272.0140801958984, + 259.48678706254464, + 247.28599122538523, + 235.41169268442002, + 223.86389143964902, + 212.64258749107233, + 201.74778083868995, + 191.1794714825018, + 180.93765942250792, + 171.0223446587083, + 161.43352719110297, + 152.1712070196919, + 143.23538414447506, + 134.6260585654525, + 126.34323028262423, + 118.38689929599019, + 110.75706560555045, + 103.45372921130496, + 96.47689011325376, + 89.82654831139678, + 83.50270380573411, + 77.50535659626567, + 71.83450668299153, + 66.49015406591164, + 61.47229874502602, + 56.780940720334655, + 52.41607999183756, + 48.37771655953473, + 44.665850423426164, + 41.28048158351188, + 38.22161003979184, + 35.489235792266086, + 33.08335884093458, + 31.003979185797355, + 29.251096826854386, + 27.824711764105686, + 26.724823997551255, + 25.95143352719109, + 25.504540353025185, + 25.38414447505355, + 25.590245893276176, + 26.122844607693068, + 26.981940618304233, + 28.16753392510966, + 29.679624528109358, + 31.518212427303304, + 33.68329762269153, + 36.17488011427403, + 38.99295990205079, + 42.13753698602179, + 45.60861136618709, + 49.40618304254665, + 53.53025201510047, + 57.980818283848535, + 62.757881848790895, + 67.86144270992753, + 73.2915008672584, + 79.04805632078353, + 85.13110907050294, + 91.54065911641666, + 98.27670645852461, + 105.33925109682684, + 112.72829303132328, + 120.44383226201403, + 128.48586878889907, + 136.85440261197834, + 145.54943373125184, + 154.57096214671964, + 163.91898785838177, + 173.59351086623812, + 183.59453117028863, + 193.92204877053354, + 204.5760636669727, + 215.5565758596061, + 226.86358534843373, + 238.49709213345577, + 250.45709621467188, + 262.7435975920823, + 275.3565962656872, + 288.2960922354861, + 301.5620855014795, + 315.1545760636669, + 329.0735639220486, + 343.3190490766248, + 357.89103152739506, + 372.7895112743596, + 388.0144883175186, + 403.56596265687165, + 419.4439342924192, + 435.64840322416075, + 452.1793694520966, + 469.0368329762269, + 486.2207937965513, + 503.73125191307014, + 521.5682073257831 + ], + [ + 336.1157024793389, + 322.11917151311087, + 308.44913784307715, + 295.1056014692379, + 282.08856239159275, + 269.3980206101418, + 257.03397612488516, + 244.9964289358229, + 233.28537904295482, + 221.900826446281, + 210.8427711458014, + 200.11121314151617, + 189.7061524334252, + 179.6275890215284, + 169.8755229058259, + 160.44995408631775, + 151.3508825630038, + 142.57830833588412, + 134.13223140495867, + 126.01265177022754, + 118.21956943169063, + 110.75298438934803, + 103.61289664319966, + 96.7993061932456, + 90.31221303948577, + 84.15161718192022, + 78.31751862054892, + 72.80991735537191, + 67.62881338638914, + 62.77420671360066, + 58.246097337006425, + 54.04448525660647, + 50.16937047240077, + 46.62075298438933, + 43.39863279257219, + 40.50300989694928, + 37.933884297520656, + 35.69125599428629, + 33.775124987246194, + 32.185491276400356, + 30.922354861748786, + 29.985715743291493, + 29.375573921028458, + 29.091929394959685, + 29.13478216508518, + 29.504132231404945, + 30.199979593918975, + 31.222324252627267, + 32.57116620752983, + 34.24650545862666, + 36.24834200591774, + 38.5766758494031, + 41.23150698908273, + 44.21283542495663, + 47.52066115702476, + 51.15498418528719, + 55.11580450974389, + 59.40312213039485, + 64.01693704724003, + 68.95724926027953, + 74.22405876951329, + 79.81736557494133, + 85.73716967656355, + 91.98347107438013, + 98.55626976839095, + 105.45556575859605, + 112.68135904499542, + 120.23364962758896, + 128.11243750637686, + 136.31772268135902, + 144.84950515253544, + 153.70778491990606, + 162.892561983471, + 172.40383634323027, + 182.24160799918374, + 192.40587695133144, + 202.89664319967343, + 213.71390674420974, + 224.8576675849403, + 236.32792572186503, + 248.12468115498422, + 260.2479338842974, + 272.69768390980505, + 285.473931231507, + 298.57667584940305, + 312.0059177634936, + 325.76165697377814, + 339.84389348025695, + 354.25262728293035, + 368.9878583817977, + 384.0495867768593, + 399.43781246811545, + 415.15253545556567, + 431.19375573921036, + 447.561473319049, + 464.255688195082, + 481.27640036730946, + 498.6236098357309, + 516.297316600347, + 534.297520661157 + ], + [ + 333.0098969492909, + 319.17661463116, + 305.66982960922354, + 292.4895418834813, + 279.63575145393327, + 267.10845832057953, + 254.90766248342, + 243.03336394245488, + 231.48556269768395, + 220.26425874910723, + 209.3694520967248, + 198.80114274053668, + 188.55933068054284, + 178.64401591674317, + 169.05519844913783, + 159.79287827772677, + 150.85705540250996, + 142.24772982348742, + 133.9649015406591, + 126.00857055402511, + 118.37873686358535, + 111.07540046933987, + 104.09856137128864, + 97.4482195694317, + 91.124375063769, + 85.1270278543006, + 79.45617794102643, + 74.11182532394655, + 69.09397000306092, + 64.40261197836956, + 60.037751249872464, + 55.99938781756964, + 52.28752168146107, + 48.90215284154677, + 45.84328129782675, + 43.11090705030099, + 40.70503009896949, + 38.62565044383226, + 36.872768084889294, + 35.446383022140594, + 34.346495255586156, + 33.57310478522599, + 33.12621161106009, + 33.005815733088454, + 33.211917151311084, + 33.744515865727976, + 34.60361187633914, + 35.789205183144574, + 37.301295786144266, + 39.13988368533823, + 41.30496888072644, + 43.79655137230894, + 46.61463116008569, + 49.75920824405673, + 53.230282624222, + 57.02785430058156, + 61.15192327313539, + 65.60248954188349, + 70.37955310682581, + 75.48311396796242, + 80.91317212529333, + 86.6697275788185, + 92.75278032853787, + 99.16233037445156, + 105.89837771655952, + 112.96092235486174, + 120.34996428935825, + 128.06550352004894, + 136.10754004693396, + 144.47607387001327, + 153.17110498928682, + 162.1926334047546, + 171.54065911641666, + 181.215182124273, + 191.21620242832364, + 201.54372002856846, + 212.19773492500758, + 223.17824711764104, + 234.48525660646874, + 246.11876339149057, + 258.0787674727069, + 270.3652688501173, + 282.9782675237219, + 295.917763493521, + 309.18375675951427, + 322.77624732170193, + 336.6952351800836, + 350.9407203346596, + 365.51270278543006, + 380.4111825323946, + 395.63615957555334, + 411.1876339149066, + 427.0656055504539, + 443.2700744821957, + 459.80104071013153, + 476.65850423426167, + 493.8424650545863, + 511.3529231711049, + 529.189878583818, + 547.3533312927252 + ], + [ + 330.2305887154372, + 316.5605550454035, + 303.2170186715641, + 290.199979593919, + 277.5094378124681, + 265.1453933272115, + 253.1078461381491, + 241.3967962452811, + 230.0122436486073, + 218.95418834812773, + 208.22263034384244, + 197.81756963575143, + 187.73900622385472, + 177.9869401081522, + 168.561371288644, + 159.46229976533007, + 150.6897255382104, + 142.24364860728497, + 134.1240689725538, + 126.33098663401695, + 118.86440159167432, + 111.72431384552598, + 104.91072339557188, + 98.42363024181206, + 92.26303438424651, + 86.42893582287525, + 80.9213345576982, + 75.74023058871543, + 70.88562391592694, + 66.35751453933274, + 62.155902458932765, + 58.28078767472708, + 54.73217018671564, + 51.51004999489848, + 48.61442709927559, + 46.04530149984695, + 43.802673196612595, + 41.886542189572495, + 40.296908478726664, + 39.033772064075094, + 38.097132945617794, + 37.48699112335476, + 37.203346597286, + 37.24619936741149, + 37.61554943373126, + 38.311396796245276, + 39.333741454953575, + 40.68258340985614, + 42.35792266095297, + 44.35975920824407, + 46.68809305172941, + 49.34292419140904, + 52.32425262728294, + 55.632078359351105, + 59.266401387613506, + 63.22722171207019, + 67.51453933272116, + 72.1283542495664, + 77.06866646260583, + 82.3354759718396, + 87.92878277726763, + 93.84858687888993, + 100.09488827670644, + 106.66768697071727, + 113.56698296092235, + 120.79277624732173, + 128.34506682991534, + 136.22385470870316, + 144.42913988368537, + 152.96092235486176, + 161.81920212223247, + 171.00397918579733, + 180.51525354555656, + 190.35302520151004, + 200.51729415365784, + 211.00806040199976, + 221.82532394653603, + 232.96908478726658, + 244.43934292419146, + 256.2360983573104, + 268.35935108662386, + 280.8091011121314, + 293.5853484338332, + 306.6880930517295, + 320.11733496581974, + 333.8730741761046, + 347.95531068258344, + 362.3640444852565, + 377.09927558412414, + 392.16100397918575, + 407.54922967044166, + 423.2639526578921, + 439.3051729415365, + 455.67289052137545, + 472.3671053974084, + 489.38781756963556, + 506.7350270380574, + 524.408733802673, + 542.4089378634834, + 560.7356392204877 + ], + [ + 327.7777777777777, + 314.2709927558413, + 301.09070503009895, + 288.23691460055096, + 275.7096214671972, + 263.50882563003773, + 251.63452708907252, + 240.08672584430164, + 228.86542189572495, + 217.97061524334248, + 207.4023058871543, + 197.1604938271605, + 187.2451790633609, + 177.65636159575553, + 168.39404142434444, + 159.45821854912762, + 150.84889297010514, + 142.56606468727682, + 134.60973370064278, + 126.97990001020304, + 119.67656361595755, + 112.69972451790633, + 106.0493827160494, + 99.7255382103867, + 93.72819100091826, + 88.05734108764413, + 82.71298847056423, + 77.69513314967863, + 73.00377512498726, + 68.63891439649018, + 64.60055096418733, + 60.88868482807878, + 57.50331598816449, + 54.44444444444444, + 51.712070196918695, + 49.306193245587195, + 47.226813590449964, + 45.473931231506995, + 44.0475461687583, + 42.94765840220387, + 42.1742679318437, + 41.7273747576778, + 41.60697887970616, + 41.81308029792879, + 42.34567901234569, + 43.20477502295685, + 44.39036832976228, + 45.902458932761974, + 47.74104683195594, + 49.90613202734418, + 52.39771451892665, + 55.21579430670341, + 58.360371390674445, + 61.831445770839736, + 65.62901744719927, + 69.7530864197531, + 74.2036526885012, + 78.98071625344356, + 84.08427711458015, + 89.51433527191104, + 95.27089072543619, + 101.35394347515562, + 107.76349352106928, + 114.49954086317723, + 121.56208550147947, + 128.95112743597593, + 136.6666666666667, + 144.70870319355166, + 153.07723701663096, + 161.7722681359045, + 170.7937965513724, + 180.14182226303438, + 189.81634527089074, + 199.81736557494133, + 210.14488317518624, + 220.7988980716253, + 231.77941026425876, + 243.08641975308646, + 254.71992653810838, + 266.6799306193245, + 278.96643199673514, + 291.57943067033983, + 304.5189266401387, + 317.78491990613213, + 331.37741046831957, + 345.29639832670154, + 359.54188348127747, + 374.1138659320477, + 389.01234567901247, + 404.23732272217126, + 419.7887970615243, + 435.6667686970718, + 451.87123762881333, + 468.40220385674945, + 485.25966738087953, + 502.44362820120386, + 519.9540863177228, + 537.7910417304356, + 555.9544944393431, + 574.4444444444445 + ], + [ + 325.6514641363126, + 312.30792776247324, + 299.290888684828, + 286.6003469033773, + 274.2363024181206, + 262.19875522905824, + 250.48770533619015, + 239.1031527395164, + 228.04509743903685, + 217.31353943475156, + 206.90847872666052, + 196.8299153147638, + 187.07784919906135, + 177.65228037955308, + 168.55320885623914, + 159.78063462911948, + 151.3345576981941, + 143.2149780634629, + 135.421895724926, + 127.95531068258342, + 120.81522293643505, + 114.00163248648097, + 107.51453933272114, + 101.3539434751556, + 95.51984491378431, + 90.01224364860728, + 84.83113967962451, + 79.97653300683605, + 75.4484236302418, + 71.24681154984185, + 67.37169676563614, + 63.82307927762473, + 60.60095908580756, + 57.70533619018465, + 55.13621059075603, + 52.89358228752167, + 50.977451280481574, + 49.38781756963574, + 48.124681154984174, + 47.188042036526866, + 46.577900214263835, + 46.294255688195065, + 46.33710845832056, + 46.706458524640325, + 47.402305887154355, + 48.42465054586264, + 49.7734925007652, + 51.44883175186203, + 53.45066829915312, + 55.77900214263849, + 58.4338332823181, + 61.41516171819199, + 64.72298745026015, + 68.35731047852259, + 72.31813080297925, + 76.60544842363021, + 81.21926334047544, + 86.15957555351493, + 91.42638506274864, + 97.01969186817668, + 102.93949596979897, + 109.18579736761552, + 115.7585960616263, + 122.65789205183138, + 129.88368533823075, + 137.43597592082438, + 145.31476379961225, + 153.52004897459435, + 162.0518314457708, + 170.9101112131415, + 180.09488827670646, + 189.6061626364656, + 199.44393429241907, + 209.60820324456685, + 220.09896949290885, + 230.91623303744507, + 242.05999387817562, + 253.53025201510044, + 265.32700744821955, + 277.45026017753275, + 289.90001020304055, + 302.67625752474237, + 315.7790021426384, + 329.2082440567289, + 342.9639832670135, + 357.04621977349257, + 371.4549535761657, + 386.190184675033, + 401.25191307009493, + 416.6401387613508, + 432.354861748801, + 448.3960820324457, + 464.76379961228434, + 481.4580144883176, + 498.4787266605448, + 515.8259361289663, + 533.4996428935823, + 551.4998469543923, + 569.8265483113969, + 588.4797469645954 + ], + [ + 323.8516477910417, + 310.67136006529944, + 297.81756963575134, + 285.2902765023978, + 273.0894806652382, + 261.21518212427304, + 249.66738087950208, + 238.44607693092544, + 227.551270278543, + 216.98296092235483, + 206.74114886236094, + 196.82583409856136, + 187.23701663095605, + 177.97469645954493, + 169.0388735843281, + 160.42954800530555, + 152.14671972247731, + 144.1903887358433, + 136.5605550454035, + 129.25721865115804, + 122.28037955310681, + 115.63003775124989, + 109.30619324558718, + 103.30884603611877, + 97.6379961228446, + 92.29364350576472, + 87.27578818487908, + 82.58443016018774, + 78.21956943169063, + 74.18120599938783, + 70.46933986327926, + 67.08397102336497, + 64.02509947964494, + 61.29272523211915, + 58.886848280787675, + 56.807468625650436, + 55.05458626670747, + 53.62820120395877, + 52.52831343740434, + 51.754922967044166, + 51.308029792878266, + 51.187633914906634, + 51.393735333129264, + 51.92633404754616, + 52.78543005815733, + 53.97102336496275, + 55.48311396796244, + 57.3217018671564, + 59.48678706254463, + 61.97836955412713, + 64.79644934190387, + 67.9410264258749, + 71.4121008060402, + 75.20967248239975, + 79.33374145495354, + 83.78430772370164, + 88.56137128864401, + 93.66493214978063, + 99.09499030711146, + 104.85154576063665, + 110.93459851035607, + 117.34414855626977, + 124.08019589837767, + 131.1427405366799, + 138.53178247117637, + 146.24732170186718, + 154.28935822875218, + 162.6578920518314, + 171.35292317110495, + 180.37445158657277, + 189.72247729823488, + 199.39700030609114, + 209.3980206101418, + 219.72553821038667, + 230.3795531068258, + 241.36006529945917, + 252.66707478828684, + 264.3005815733088, + 276.260585654525, + 288.5470870319354, + 301.16008570554027, + 314.0995816753392, + 327.36557494133245, + 340.95806550352006, + 354.8770533619018, + 369.122538516478, + 383.6945209672482, + 398.5930007142127, + 413.8179777573717, + 429.36945209672473, + 445.247423732272, + 461.4518926640139, + 477.9828588919497, + 494.8403224160801, + 512.0242832364045, + 529.534741352923, + 547.3716967656362, + 565.5351494745433, + 584.025099479645, + 602.8415467809407 + ], + [ + 322.37832874196516, + 309.36128966431994, + 296.670747882869, + 284.30670339761247, + 272.26915620855016, + 260.5581063156821, + 249.17355371900823, + 238.11549841852877, + 227.38394041424345, + 216.9788797061524, + 206.90031629425567, + 197.1482501785532, + 187.72268135904503, + 178.62360983573106, + 169.85103560861134, + 161.40495867768595, + 153.28537904295482, + 145.49229670441792, + 138.02571166207528, + 130.88562391592694, + 124.07203346597285, + 117.58494031221305, + 111.42434445464747, + 105.5902458932762, + 100.08264462809917, + 94.90154065911642, + 90.04693398632793, + 85.51882460973371, + 81.31721252933374, + 77.44209774512805, + 73.89348025711662, + 70.67136006529947, + 67.77573716967656, + 65.20661157024793, + 62.963983267013575, + 61.047852259973475, + 59.45821854912765, + 58.19508213447608, + 57.258443016018774, + 56.64830119375574, + 56.36465666768697, + 56.40750943781247, + 56.77685950413223, + 57.47270686664626, + 58.49505152535456, + 59.843893480257115, + 61.519232731353945, + 63.521069278645044, + 65.8494031221304, + 68.50423426181004, + 71.4855626976839, + 74.79338842975207, + 78.42771145801449, + 82.38853178247119, + 86.6758494031221, + 91.28966431996733, + 96.22997653300683, + 101.4967860422406, + 107.09009284766857, + 113.00989694929088, + 119.25619834710741, + 125.82899704111827, + 132.72829303132332, + 139.95408631772267, + 147.5063769003163, + 155.38516477910417, + 163.59044995408632, + 172.12223242526272, + 180.9805121926334, + 190.16528925619835, + 199.67656361595758, + 209.51433527191097, + 219.67860422405877, + 230.16937047240077, + 240.98663401693707, + 252.1303948576675, + 263.6006529945924, + 275.39740842771147, + 287.52066115702485, + 299.9704111825323, + 312.7466585042343, + 325.8494031221303, + 339.2786450362206, + 353.03438424650545, + 367.1166207529843, + 381.52535455565766, + 396.2605856545251, + 411.3223140495867, + 426.7105397408428, + 442.425262728293, + 458.4664830119373, + 474.8342005917763, + 491.5284154678092, + 508.5491276400367, + 525.8963371084583, + 543.570043873074, + 561.5702479338843, + 579.8969492908885, + 598.5501479440875, + 617.5298438934802 + ], + [ + 321.23150698908273, + 308.37771655953475, + 295.85042342618095, + 283.6496275890216, + 271.77532904805634, + 260.22752780328534, + 249.00622385470865, + 238.11141720232632, + 227.54310784613816, + 217.30129578614424, + 207.38598102234462, + 197.7971635547393, + 188.53484338332825, + 179.5990205081114, + 170.98969492908887, + 162.7068666462606, + 154.7505356596266, + 147.12070196918683, + 139.8173655749413, + 132.84052647689012, + 126.19018467503315, + 119.86634016937049, + 113.86899295990204, + 108.1981430466279, + 102.853790429548, + 97.8359351086624, + 93.14457708397103, + 88.77971635547394, + 84.74135292317112, + 81.02948678706255, + 77.64411794714826, + 74.58524640342824, + 71.85287215590247, + 69.44699520457097, + 67.36761554943375, + 65.61473319049078, + 64.18834812774207, + 63.08846036118765, + 62.31506989082748, + 61.86817671666158, + 61.74778083868994, + 61.953882256912564, + 62.48648097132946, + 63.34557698194064, + 64.53117028874607, + 66.04326089174575, + 67.88184879093971, + 70.04693398632794, + 72.53851647791043, + 75.35659626568719, + 78.5011733496582, + 81.9722477298235, + 85.76981940618307, + 89.8938883787369, + 94.34445464748495, + 99.1215182124273, + 104.22507907356393, + 109.65513723089484, + 115.41169268441995, + 121.49474543413938, + 127.90429548005308, + 134.64034282216105, + 141.7028874604632, + 149.09192939495966, + 156.80746862565047, + 164.8495051525355, + 173.2180389756148, + 181.91307009488827, + 190.93459851035607, + 200.2826242220182, + 209.95714722987455, + 219.9581675339251, + 230.28568513416997, + 240.93970003060912, + 251.9202122232426, + 263.22722171207016, + 274.86072849709217, + 286.82073257830837, + 299.10723395571887, + 311.7202326293235, + 324.6597285991226, + 337.9257218651158, + 351.51821242730324, + 365.4372002856852, + 379.68268544026114, + 394.25466789103166, + 409.15314763799614, + 424.37812468115493, + 439.9295990205082, + 455.8075706560555, + 472.012039587797, + 488.5430058157331, + 505.4004693398632, + 522.5844301601879, + 540.0948882767066, + 557.9318436894195, + 576.0952963983268, + 594.5852464034282, + 613.4016937047242, + 632.5446383022141 + ], + [ + 320.4111825323947, + 307.72064075094374, + 295.35659626568713, + 283.3190490766249, + 271.60799918375676, + 260.22344658708295, + 249.16539128660338, + 238.43383328231818, + 228.02877257422713, + 217.95020916233037, + 208.19814304662788, + 198.77257422711966, + 189.67350270380575, + 180.90092847668606, + 172.4548515457606, + 164.33527191102948, + 156.5421895724926, + 149.07560453015, + 141.9355167840016, + 135.12192633404754, + 128.6348331802877, + 122.47423732272217, + 116.64013876135085, + 111.13253749617385, + 105.95143352719109, + 101.09682685440261, + 96.56871747780836, + 92.36710539740844, + 88.49199061320272, + 84.9433731251913, + 81.72125293337413, + 78.82563003775124, + 76.2565044383226, + 74.01387613508822, + 72.09774512804813, + 70.5081114172023, + 69.24497500255075, + 68.30833588409342, + 67.69819406183039, + 67.41454953576164, + 67.45740230588713, + 67.82675237220688, + 68.52259973472091, + 69.5449443934292, + 70.89378634833177, + 72.5691255994286, + 74.5709621467197, + 76.89929599020505, + 79.55412712988468, + 82.53545556575857, + 85.8432812978267, + 89.47760432608914, + 93.43842465054581, + 97.7257422711968, + 102.33955718804198, + 107.27986940108148, + 112.54667891031524, + 118.13998571574328, + 124.0597898173655, + 130.30609121518205, + 136.87888990919288, + 143.778185899398, + 151.0039791857973, + 158.5562697683909, + 166.4350576471788, + 174.64034282216096, + 183.17212529333742, + 192.03040506070803, + 201.21518212427296, + 210.72645648403218, + 220.5642281399857, + 230.72849709213338, + 241.21926334047538, + 252.03652688501165, + 263.18028772574223, + 274.65054586266695, + 286.447301295786, + 298.5705540250994, + 311.020304050607, + 323.79655137230884, + 336.89929599020513, + 350.32853790429544, + 364.08427711458, + 378.16651362105904, + 392.57524742373215, + 407.31047852259974, + 422.3722069176614, + 437.76043260891726, + 453.4751555963677, + 469.51637588001216, + 485.8840934598508, + 502.57830833588406, + 519.5990205081113, + 536.946229976533, + 554.6199367411489, + 572.6201408019589, + 590.9468421589634, + 609.6000408121619, + 628.5797367615551, + 647.8859300071421 + ], + [ + 319.91735537190084, + 307.3900622385471, + 295.18926640138756, + 283.3149678604224, + 271.7671666156515, + 260.5458626670748, + 249.65105601469233, + 239.08274665850428, + 228.8409345985104, + 218.92561983471074, + 209.33680236710538, + 200.0744821956943, + 191.13865932047753, + 182.52933374145493, + 174.24650545862664, + 166.29017447199266, + 158.66034078155292, + 151.3570043873074, + 144.38016528925618, + 137.72982348739924, + 131.40597898173655, + 125.40863177226814, + 119.73778185899397, + 114.39342924191409, + 109.37557392102846, + 104.68421589633711, + 100.31935516784, + 96.2809917355372, + 92.56912559942862, + 89.18375675951432, + 86.1248852157943, + 83.39251096826854, + 80.98663401693705, + 78.9072543617998, + 77.15437200285683, + 75.72798694010814, + 74.62809917355371, + 73.85470870319354, + 73.40781552902763, + 73.287419651056, + 73.49352106927863, + 74.02611978369552, + 74.88521579430669, + 76.0708091011121, + 77.58289970411181, + 79.42148760330575, + 81.58657279869398, + 84.07815529027648, + 86.89623507805325, + 90.04081216202428, + 93.51188654218954, + 97.3094582185491, + 101.43352719110294, + 105.88409345985103, + 110.66115702479335, + 115.76471788592998, + 121.19477604326086, + 126.95133149678604, + 133.0343842465054, + 139.44393429241913, + 146.17998163452705, + 153.24252627282928, + 160.6315682073257, + 168.34710743801648, + 176.3891439649015, + 184.7576777879808, + 193.45270890725436, + 202.4742373227221, + 211.82226303438424, + 221.4967860422406, + 231.49780634629118, + 241.82532394653597, + 252.47933884297515, + 263.45985103560855, + 274.76686052443625, + 286.4003673094581, + 298.36037139067435, + 310.64687276808485, + 323.2598714416896, + 336.1993674114885, + 349.46536067748195, + 363.0578512396694, + 376.9768390980511, + 391.22232425262735, + 405.7943067033975, + 420.6927864503623, + 435.9177634935211, + 451.4692378328741, + 467.3472094684216, + 483.55167840016315, + 500.08264462809905, + 516.9401081522294, + 534.1240689725537, + 551.6345270890727, + 569.4714825017854, + 587.6349352106927, + 606.1248852157944, + 624.94133251709, + 644.0842771145803, + 663.5537190082645 + ], + [ + 319.75002550760126, + 307.3859810223446, + 295.34843383328223, + 283.6373839404143, + 272.25283134374047, + 261.1947760432609, + 250.46321803897558, + 240.05815733088465, + 229.9795939189879, + 220.22752780328537, + 210.80195898377713, + 201.70288746046322, + 192.93031323334355, + 184.4842363024181, + 176.36465666768694, + 168.57157432915005, + 161.1049892868075, + 153.96490154065913, + 147.151311090705, + 140.6642179369452, + 134.50362207937962, + 128.6695235180084, + 123.16192225283135, + 117.98081828384858, + 113.1262116110601, + 108.59810223446587, + 104.3964901540659, + 100.52137536986022, + 96.97275788184879, + 93.75063769003164, + 90.85501479440873, + 88.28588919498011, + 86.04326089174575, + 84.12712988470564, + 82.53749617385982, + 81.27435975920824, + 80.33772064075094, + 79.72757881848791, + 79.44393429241913, + 79.48678706254465, + 79.8561371288644, + 80.55198449137842, + 81.57432915008673, + 82.92317110498928, + 84.59851035608612, + 86.60034690337719, + 88.92868074686255, + 91.58351188654218, + 94.56484032241607, + 97.87266605448426, + 101.50698908274663, + 105.46780940720335, + 109.7551270278543, + 114.36894194469953, + 119.30925415773898, + 124.57606366697273, + 130.16937047240077, + 136.08917457402308, + 142.33547597183957, + 148.9082746658504, + 155.8075706560555, + 163.03336394245486, + 170.58565452504843, + 178.46444240383633, + 186.66972757881845, + 195.2015100499949, + 204.05978981736558, + 213.24456688093048, + 222.7558412406897, + 232.59361289664318, + 242.75788184879096, + 253.24864809713287, + 264.0659116416692, + 275.20967248239975, + 286.6799306193246, + 298.47668605244354, + 310.5999387817569, + 323.04968880726454, + 335.8259361289664, + 348.9286807468625, + 362.357922660953, + 376.1136618712375, + 390.1958983777165, + 404.6046321803898, + 419.3398632792572, + 434.40159167431904, + 449.7898173655749, + 465.50454035302505, + 481.5457606366698, + 497.91347821650845, + 514.6076930925414, + 531.6284052647688, + 548.9756147331904, + 566.6493214978063, + 584.6495255586163, + 602.9762269156206, + 621.6294255688194, + 640.6091215182124, + 659.9153147637998, + 679.5480053055811 + ], + [ + 319.90919293949594, + 307.70839710233645, + 295.8340985613712, + 284.2862973166004, + 273.0649933680237, + 262.17018671564125, + 251.60187735945306, + 241.36006529945928, + 231.44475053565967, + 221.85593306805427, + 212.59361289664318, + 203.6577900214264, + 195.04846444240383, + 186.76563615957556, + 178.80930517294155, + 171.17947148250178, + 163.87613508825632, + 156.89929599020508, + 150.24895418834814, + 143.92510968268545, + 137.927762473217, + 132.25691255994286, + 126.91255994286297, + 121.89470462197738, + 117.203346597286, + 112.83848586878891, + 108.80012243648608, + 105.08825630037752, + 101.70288746046322, + 98.6440159167432, + 95.91164166921743, + 93.50576471788595, + 91.42638506274871, + 89.67350270380575, + 88.24711764105706, + 87.14722987450261, + 86.37383940414244, + 85.92694622997655, + 85.80655035200492, + 86.01265177022754, + 86.54525048464443, + 87.4043464952556, + 88.58993980206102, + 90.10203040506073, + 91.94061830425468, + 94.10570349964289, + 96.59728599122539, + 99.41536577900214, + 102.55994286297319, + 106.03101724313849, + 109.828588919498, + 113.95265789205185, + 118.40322416079994, + 123.1802877257423, + 128.2838485868789, + 133.71390674420977, + 139.47046219773492, + 145.55351494745437, + 151.963064993368, + 158.69911233547597, + 165.7616569737782, + 173.15069890827468, + 180.8662381389654, + 188.90827466585043, + 197.2768084889297, + 205.97183960820328, + 214.99336802367108, + 224.3413937353331, + 234.01591674318945, + 244.0169370472401, + 254.344454647485, + 264.99846954392405, + 275.97898173655744, + 287.28599122538515, + 298.91949801040715, + 310.8795020916233, + 323.1660034690338, + 335.77900214263855, + 348.71849811243754, + 361.9844913784307, + 375.5769819406184, + 389.4959697990001, + 403.741454953576, + 418.31343740434653, + 433.211917151311, + 448.4368941944701, + 463.98836853382306, + 479.86634016937035, + 496.0708091011122, + 512.601775329048, + 529.4592388531781, + 546.6431996735027, + 564.1536577900213, + 581.9906132027345, + 600.1540659116416, + 618.644015916743, + 637.460463218039, + 656.603407815529, + 676.0728497092134, + 695.868788899092 + ], + [ + 320.394857667585, + 308.3573104785226, + 296.6462605856545, + 285.26170798898073, + 274.20365268850117, + 263.47209468421585, + 253.06703397612483, + 242.98847056422818, + 233.23640444852566, + 223.81083562901745, + 214.71176410570348, + 205.9391898785838, + 197.4931129476584, + 189.37353331292724, + 181.58045097439037, + 174.11386593204776, + 166.97377818589942, + 160.1601877359453, + 153.67309458218546, + 147.51249872461995, + 141.67840016324863, + 136.1707988980716, + 130.98969492908884, + 126.13508825630035, + 121.60697887970612, + 117.40536679930618, + 113.53025201510047, + 109.98163452708906, + 106.75951433527189, + 103.863891439649, + 101.29476584022035, + 99.05213753698601, + 97.13600652994589, + 95.54637281910007, + 94.28323640444849, + 93.3465972859912, + 92.73645546372816, + 92.45281093765938, + 92.49566370778489, + 92.86501377410465, + 93.56086113661867, + 94.58320579532696, + 95.93204775022953, + 97.60738700132636, + 99.60922354861746, + 101.9375573921028, + 104.59238853178242, + 107.57371696765631, + 110.88154269972448, + 114.51586572798692, + 118.47668605244357, + 122.76400367309452, + 127.37781858993976, + 132.31813080297925, + 137.58494031221298, + 143.178247117641, + 149.09805121926328, + 155.34435261707986, + 161.9171513110906, + 168.81644730129574, + 176.04224058769506, + 183.59453117028872, + 191.4733190490765, + 199.6786042240587, + 208.21038669523514, + 217.06866646260582, + 226.25344352617074, + 235.7647178859299, + 245.6024895418834, + 255.76675849403117, + 266.2575247423732, + 277.0747882869094, + 288.2185491276399, + 299.68880726456473, + 311.48556269768386, + 323.60881542699707, + 336.0585654525047, + 348.8348127742067, + 361.93755739210275, + 375.36679930619306, + 389.1225385164779, + 403.2047750229567, + 417.6135088256298, + 432.34873992449747, + 447.410468319559, + 462.79869401081515, + 478.51341699826537, + 494.55463728190983, + 510.9223548617488, + 527.6165697377817, + 544.6372819100089, + 561.9844913784307, + 579.6581981430464, + 597.6584022038567, + 615.9851035608609, + 634.6383022140595, + 653.6179981634526, + 672.9241914090396, + 692.5568819508213, + 712.5160697887969 + ], + [ + 321.2070196918682, + 309.33272115090296, + 297.784919906132, + 286.5636159575554, + 275.66880930517294, + 265.1004999489848, + 254.85868788899086, + 244.94337312519136, + 235.35455565758596, + 226.09223548617487, + 217.15641261095803, + 208.54708703193552, + 200.26425874910723, + 192.3079277624732, + 184.67809407203345, + 177.37475767778795, + 170.39791857973677, + 163.7475767778798, + 157.4237322722171, + 151.4263850627487, + 145.75553514947453, + 140.41118253239466, + 135.39332721150902, + 130.70196918681768, + 126.33710845832056, + 122.29874502601776, + 118.58687888990917, + 115.20151004999488, + 112.14263850627486, + 109.4102642587491, + 107.0043873074176, + 104.92500765228037, + 103.17212529333739, + 101.7457402305887, + 100.64585246403426, + 99.87246199367411, + 99.4255688195082, + 99.30517294153654, + 99.51127435975918, + 100.04387307417609, + 100.90296908478724, + 102.08856239159266, + 103.60065299459237, + 105.43924089378633, + 107.60432608917455, + 110.09590858075704, + 112.9139883685338, + 116.05856545250481, + 119.52963983267011, + 123.32721150902967, + 127.45128048158348, + 131.90184675033157, + 136.67891031527392, + 141.78247117641055, + 147.2125293337414, + 152.96908478726655, + 159.052137536986, + 165.46168758289969, + 172.1977349250076, + 179.2602795633098, + 186.6493214978063, + 194.3648607284971, + 202.40689725538203, + 210.7754310784613, + 219.47046219773486, + 228.4919906132027, + 237.84001632486482, + 247.51453933272109, + 257.5155596367717, + 267.84307723701664, + 278.4970921334558, + 289.4776043260891, + 300.7846138149168, + 312.41812059993873, + 324.378124681155, + 336.6646260585653, + 349.27762473217007, + 362.2171207019691, + 375.48311396796237, + 389.07560453014986, + 402.9945923885318, + 417.2400775431078, + 431.812059993878, + 446.71053974084276, + 461.93551678400155, + 477.4869911233548, + 493.3649627589021, + 509.5694316906436, + 526.1003979185798, + 542.9578614427098, + 560.1418222630342, + 577.6522803795531, + 595.489235792266, + 613.6526885011733, + 632.1426385062748, + 650.9590858075704, + 670.1020304050606, + 689.5714722987449, + 709.3674114886237, + 729.4898479746963 + ], + [ + 322.34567901234567, + 310.6346291194776, + 299.2500765228038, + 288.1920212223243, + 277.46046321803897, + 267.05540250994795, + 256.9768390980512, + 247.22477298234875, + 237.7992041628405, + 228.70013263952657, + 219.92755841240685, + 211.48148148148147, + 203.36190184675033, + 195.56881950821344, + 188.10223446587082, + 180.96214671972248, + 174.1485562697684, + 167.66146311600855, + 161.500867258443, + 155.66676869707172, + 150.1591674318947, + 144.97806346291193, + 140.12345679012344, + 135.59534741352923, + 131.39373533312929, + 127.51862054892358, + 123.97000306091215, + 120.747882869095, + 117.85225997347209, + 115.28313437404347, + 113.04050607080909, + 111.124375063769, + 109.53474135292318, + 108.2716049382716, + 107.3349658198143, + 106.72482399755127, + 106.4411794714825, + 106.48403224160799, + 106.85338230792776, + 107.54922967044178, + 108.57157432915008, + 109.92041628405264, + 111.59575553514946, + 113.59759208244056, + 115.92592592592592, + 118.58075706560552, + 121.56208550147942, + 124.8699112335476, + 128.50423426181, + 132.46505458626672, + 136.75237220691764, + 141.36618712376287, + 146.30649933680235, + 151.57330884603616, + 157.1666156514641, + 163.0864197530864, + 169.33272115090296, + 175.90551984491378, + 182.80481583511883, + 190.0306091215182, + 197.5828997041118, + 205.4616875828997, + 213.66697275788178, + 222.19875522905824, + 231.0570349964289, + 240.24181205999386, + 249.75308641975312, + 259.59085807570654, + 269.75512702785426, + 280.2458932761963, + 291.0631568207326, + 302.2069176614631, + 313.6771757983879, + 325.473931231507, + 337.59718396082036, + 350.0469339863279, + 362.82318130802975, + 375.92592592592587, + 389.3551678400163, + 403.1109070503009, + 417.19314355678, + 431.6018773594531, + 446.3371084583205, + 461.3988368533823, + 476.7870625446382, + 492.50178553208866, + 508.54300581573307, + 524.9107233955718, + 541.6049382716051, + 558.6256504438322, + 575.9728599122537, + 593.6465666768697, + 611.6467707376797, + 629.9734720946843, + 648.6266707478828, + 667.6063666972757, + 686.912559942863, + 706.5452504846444, + 726.5044383226203, + 746.7901234567901 + ], + [ + 323.81083562901745, + 312.2630343842465, + 301.04173043566976, + 290.1469237832875, + 279.5786144270993, + 269.3368023671054, + 259.42148760330576, + 249.83267013570048, + 240.57034996428936, + 231.63452708907252, + 223.02520151005, + 214.74237322722172, + 206.7860422405877, + 199.15620855014794, + 191.85287215590245, + 184.87603305785126, + 178.22569125599432, + 171.90184675033163, + 165.90449954086316, + 160.23364962758902, + 154.88929701050915, + 149.87144168962354, + 145.18008366493214, + 140.81522293643508, + 136.77685950413223, + 133.0649933680237, + 129.6796245281094, + 126.62075298438936, + 123.88837873686359, + 121.48250178553211, + 119.40312213039486, + 117.65023977145191, + 116.22385470870321, + 115.12396694214877, + 114.35057647178861, + 113.90368329762269, + 113.78328741965109, + 113.98938883787369, + 114.52198755229058, + 115.38108356290176, + 116.56667686970718, + 118.07876747270687, + 119.91735537190083, + 122.08244056728907, + 124.57402305887156, + 127.39210284664829, + 130.53667993061933, + 134.0077543107846, + 137.8053259871442, + 141.92939495969802, + 146.3799612284461, + 151.15702479338842, + 156.26058565452507, + 161.69064381185595, + 167.44719926538107, + 173.53025201510053, + 179.93980206101418, + 186.67584940312216, + 193.7383940414243, + 201.1274359759208, + 208.8429752066116, + 216.8850117334966, + 225.2535455565758, + 233.94857667584938, + 242.9701050913172, + 252.31813080297934, + 261.99265381083563, + 271.99367411488623, + 282.3211917151311, + 292.9752066115703, + 303.9557188042037, + 315.2627282930313, + 326.8962350780533, + 338.8562391592695, + 351.14274053668, + 363.75573921028456, + 376.6952351800836, + 389.9612284460769, + 403.55371900826447, + 417.47270686664615, + 431.7181920212224, + 446.2901744719926, + 461.1886542189572, + 476.4136312621162, + 491.96510560146913, + 507.84307723701676, + 524.0475461687582, + 540.5785123966941, + 557.4359759208245, + 574.6199367411489, + 592.1303948576675, + 609.9673502703806, + 628.1308029792878, + 646.6207529843895, + 665.4372002856852, + 684.5801448831751, + 704.0495867768595, + 723.845525966738, + 743.9679624528111, + 764.4168962350781 + ], + [ + 325.6024895418835, + 314.2179369452096, + 303.15988164473004, + 292.42832364044483, + 282.0232629323538, + 271.9446995204571, + 262.1926334047546, + 252.76706458524643, + 243.66799306193246, + 234.89541883481274, + 226.44934190388733, + 218.3297622691562, + 210.5366799306193, + 203.0700948882767, + 195.93000714212832, + 189.11641669217423, + 182.62932353841444, + 176.46872768084887, + 170.63462911947758, + 165.12702785430054, + 159.94592388531777, + 155.0913172125293, + 150.5632078359351, + 146.36159575553512, + 142.48648097132943, + 138.93786348331798, + 135.71574329150084, + 132.82012039587795, + 130.2509947964493, + 128.00836649321494, + 126.09223548617483, + 124.50260177532903, + 123.23946536067744, + 122.30282624222015, + 121.6926844199571, + 121.40903989388833, + 121.45189266401385, + 121.82124273033358, + 122.51709009284762, + 123.53943475155593, + 124.88827670645848, + 126.5636159575553, + 128.5654525048464, + 130.89378634833176, + 133.5486174880114, + 136.52994592388524, + 139.83777165595342, + 143.47209468421585, + 147.43291500867255, + 151.7202326293235, + 156.33404754616868, + 161.27435975920818, + 166.54116926844193, + 172.13447607387, + 178.0542801754922, + 184.3005815733088, + 190.8733802673196, + 197.77267625752472, + 204.998469543924, + 212.55076012651762, + 220.42954800530552, + 228.63483318028764, + 237.16661565146404, + 246.02489541883472, + 255.20967248239967, + 264.7209468421589, + 274.5587184981124, + 284.72298745026006, + 295.2137536986021, + 306.03101724313836, + 317.17477808386894, + 328.64503622079366, + 340.44179165391273, + 352.5650443832261, + 365.0147944087337, + 377.7910417304355, + 390.8937863483317, + 404.32302826242216, + 418.0787674727068, + 432.16100397918564, + 446.569737781859, + 461.30496888072634, + 476.36669727578794, + 491.7549229670441, + 507.46964595449424, + 523.5108662381389, + 539.8785838179776, + 556.5727986940105, + 573.593510866238, + 590.9407203346595, + 608.6144270992754, + 626.6146311600857, + 644.9413325170899, + 663.5945311702887, + 682.5742271196815, + 701.8804203652686, + 721.5131109070502, + 741.4722987450259, + 761.7579838791961, + 782.3701663095601 + ], + [ + 327.7206407509438, + 316.49933680236705, + 305.60453014998467, + 295.0362207937966, + 284.7944087338027, + 274.87909397000305, + 265.29027650239766, + 256.0279563309867, + 247.09213345576984, + 238.4828078767473, + 230.19997959391898, + 222.243648607285, + 214.61381491684523, + 207.31047852259974, + 200.3336394245485, + 193.68329762269158, + 187.35945311702892, + 181.36210590756048, + 175.6912559942863, + 170.34690337720644, + 165.3290480563208, + 160.63769003162946, + 156.27282930313237, + 152.23446587082952, + 148.52259973472098, + 145.1372308948067, + 142.07835935108665, + 139.3459851035609, + 136.94010815222939, + 134.86072849709217, + 133.1078461381492, + 131.68146107540053, + 130.58157330884606, + 129.80818283848592, + 129.36128966432, + 129.24089378634835, + 129.446995204571, + 129.9795939189879, + 130.83868992959907, + 132.0242832364045, + 133.53637383940418, + 135.37496173859816, + 137.54004693398636, + 140.03162942556887, + 142.84970921334565, + 145.99428629731662, + 149.46536067748195, + 153.2629323538415, + 157.3870013263953, + 161.83756759514344, + 166.61463116008574, + 171.71819202122236, + 177.14825017855324, + 182.90480563207842, + 188.98785838179782, + 195.3974084277115, + 202.13345576981948, + 209.19600040812168, + 216.58504234261812, + 224.30058157330888, + 232.34261810019393, + 240.71115192327323, + 249.40618304254667, + 258.4277114580145, + 267.7757371696766, + 277.4502601775329, + 287.45128048158364, + 297.7787980818284, + 308.4328129782676, + 319.413325170901, + 330.7203346597287, + 342.35384144475057, + 354.31384552596677, + 366.6003469033773, + 379.213345576982, + 392.1528415467809, + 405.41883481277426, + 419.01132537496187, + 432.93031323334367, + 447.1757983879196, + 461.74778083869006, + 476.64626058565455, + 491.87123762881333, + 507.4227119681666, + 523.3006836037139, + 539.5051525354557, + 556.0361187633915, + 572.8935822875217, + 590.0775431078463, + 607.5880012243648, + 625.4249566370777, + 643.5884093459853, + 662.0783593510866, + 680.8948066523826, + 700.0377512498725, + 719.5071931435567, + 739.3031323334355, + 759.4255688195083, + 779.8745026017756, + 800.6499336802367 + ], + [ + 330.1652892561984, + 319.1072339557188, + 308.3756759514335, + 297.97061524334254, + 287.89205183144577, + 278.13998571574325, + 268.71441689623504, + 259.6153453729211, + 250.84277114580144, + 242.39669421487602, + 234.27711458014485, + 226.48403224160802, + 219.0174471992654, + 211.87735945311704, + 205.06376900316292, + 198.5766758494031, + 192.4160799918376, + 186.5819814304663, + 181.07438016528926, + 175.8932761963065, + 171.038669523518, + 166.51056014692375, + 162.3089480665238, + 158.43383328231812, + 154.8852157943067, + 151.66309560248953, + 148.7674727068666, + 146.198347107438, + 143.95571880420366, + 142.03958779716353, + 140.44995408631772, + 139.18681767166618, + 138.25017855320883, + 137.6400367309458, + 137.35639220487704, + 137.39924497500255, + 137.76859504132233, + 138.46444240383633, + 139.4867870625446, + 140.8356290174472, + 142.51096826854402, + 144.5128048158351, + 146.84113865932045, + 149.4959697990001, + 152.47729823487398, + 155.7851239669421, + 159.41944699520457, + 163.38026731966124, + 167.6675849403122, + 172.28139985715742, + 177.22171207019687, + 182.48852157943065, + 188.08182838485868, + 194.00163248648096, + 200.24793388429748, + 206.82073257830828, + 213.7200285685134, + 220.94582185491277, + 228.4981124375063, + 236.37690031629418, + 244.58218549127636, + 253.11396796245282, + 261.9722477298234, + 271.15702479338836, + 280.6682991531476, + 290.50607080910106, + 300.6703397612489, + 311.1611060095908, + 321.9783695541271, + 333.1221303948576, + 344.5923885317825, + 356.3891439649015, + 368.51239669421483, + 380.9621467197224, + 393.7383940414243, + 406.84113865932034, + 420.2703805734108, + 434.0261197836955, + 448.10835629017447, + 462.5170900928476, + 477.25232119171517, + 492.31404958677683, + 507.7022752780327, + 523.4169982654831, + 539.4582185491275, + 555.8259361289665, + 572.5201510049994, + 589.5408631772267, + 606.8880726456484, + 624.5617794102642, + 642.5619834710742, + 660.8886848280787, + 679.5418834812772, + 698.5215794306705, + 717.8277726762575, + 737.4604632180389, + 757.4196510560147, + 777.7053361901847, + 798.3175186205491, + 819.2561983471074 + ], + [ + 332.9364350576471, + 322.04162840526476, + 311.47331904907657, + 301.2315069890828, + 291.3161922252831, + 281.72737475767775, + 272.46505458626666, + 263.5292317110499, + 254.91990613202728, + 246.63707784919904, + 238.68074686256497, + 231.05091317212523, + 223.7475767778798, + 216.77073767982853, + 210.1203958779716, + 203.7965513723089, + 197.7992041628405, + 192.1283542495663, + 186.78400163248642, + 181.7661463116008, + 177.07478828690944, + 172.70992755841235, + 168.67156412610953, + 164.95969799000096, + 161.57432915008667, + 158.51545760636665, + 155.78308335884088, + 153.37720640750936, + 151.29782675237215, + 149.54494439342918, + 148.11855933068048, + 147.01867156412607, + 146.24528109376587, + 145.79838791959997, + 145.67799204162836, + 145.88409345985096, + 146.41669217426787, + 147.275788184879, + 148.46138149168445, + 149.97347209468415, + 151.8120599938781, + 153.9771451892663, + 156.4687276808488, + 159.28680746862557, + 162.4313845525966, + 165.90245893276187, + 169.70003060912143, + 173.82409958167526, + 178.27466585042333, + 183.0517294153657, + 188.15529027650228, + 193.58534843383316, + 199.34190388735834, + 205.42495663707777, + 211.83450668299142, + 218.57055402509937, + 225.63309866340157, + 233.0221405978981, + 240.73767982858874, + 248.77971635547382, + 257.1482501785531, + 265.8432812978267, + 274.86480971329445, + 284.21283542495655, + 293.88735843281285, + 303.8883787368635, + 314.2158963371084, + 324.86991123354744, + 335.8504234261809, + 347.1574329150085, + 358.7909397000305, + 370.7509437812467, + 383.03744515865714, + 395.65044383226194, + 408.5899398020609, + 421.85593306805407, + 435.4484236302416, + 449.3674114886235, + 463.6128966431996, + 478.18487909396976, + 493.0833588409345, + 508.3083358840933, + 523.8598102234463, + 539.7377818589939, + 555.9422507907354, + 572.4732170186716, + 589.3306805428016, + 606.514641363126, + 624.025099479645, + 641.8620548923577, + 660.0255076012647, + 678.5154576063666, + 697.3319049076622, + 716.4748495051525, + 735.9442913988366, + 755.7402305887151, + 775.8626670747882, + 796.3116008570553, + 817.0870319355168, + 838.1889603101723 + ], + [ + 336.0340781552903, + 325.30252015100496, + 314.89745944291394, + 304.8188960310173, + 295.0668299153148, + 285.64126109580656, + 276.5421895724926, + 267.769615345373, + 259.3235384144475, + 251.20395877971634, + 243.41087644117948, + 235.9442913988369, + 228.80420365268853, + 221.9906132027344, + 215.5035200489746, + 209.34292419140905, + 203.5088256300378, + 198.00122436486075, + 192.82012039587798, + 187.9655137230895, + 183.43740434649527, + 179.23579226609533, + 175.3606774818896, + 171.8120599938782, + 168.58993980206102, + 165.69431690643813, + 163.12519130700952, + 160.88256300377515, + 158.96643199673505, + 157.3767982858892, + 156.11366187123764, + 155.17702275278037, + 154.5668809305173, + 154.28323640444853, + 154.32608917457404, + 154.6954392408938, + 155.39128660340785, + 156.41363126211613, + 157.7624732170187, + 159.4378124681155, + 161.43964901540664, + 163.76798285889197, + 166.4228139985716, + 169.4041424344455, + 172.71196816651363, + 176.34629119477606, + 180.30711151923276, + 184.5944291398837, + 189.20824405672894, + 194.14855626976845, + 199.41536577900214, + 205.0086725844302, + 210.92847668605248, + 217.17477808386903, + 223.7475767778798, + 230.6468727680849, + 237.87266605448428, + 245.4249566370779, + 253.3037445158657, + 261.5090296908479, + 270.0408121620243, + 278.89909192939496, + 288.08386899295994, + 297.5951433527191, + 307.4329150086726, + 317.5971839608204, + 328.08795020916244, + 338.9052137536986, + 350.0489745944291, + 361.51923273135395, + 373.3159881644731, + 385.4392408937863, + 397.88899091929403, + 410.66523824099585, + 423.767982858892, + 437.19722477298234, + 450.952963983267, + 465.03520048974593, + 479.4439342924192, + 494.1791653912865, + 509.2408937863484, + 524.6291194776044, + 540.3438424650545, + 556.3850627486992, + 572.7527803285379, + 589.4469952045712, + 606.4677073767983, + 623.8149168452197, + 641.4886236098358, + 659.4888276706458, + 677.8155290276501, + 696.4687276808489, + 715.4484236302417, + 734.7546168758291, + 754.3873074176104, + 774.346495255586, + 794.6321803897562, + 815.2443628201204, + 836.1830425466791, + 857.4482195694318 + ], + [ + 339.4582185491276, + 328.88990919293946, + 318.64809713294557, + 308.732782369146, + 299.14396490154064, + 289.88164473012955, + 280.9458218549127, + 272.3364962758902, + 264.05366799306194, + 256.0973370064279, + 248.4675033159881, + 241.16416692174263, + 234.18732782369148, + 227.5369860218345, + 221.2131415161718, + 215.21579430670337, + 209.54494439342923, + 204.2005917763493, + 199.18273645546373, + 194.49137843077233, + 190.12651770227524, + 186.08815426997242, + 182.37628813386385, + 178.9909192939496, + 175.93204775022951, + 173.19967350270377, + 170.79379655137225, + 168.71441689623504, + 166.96153453729212, + 165.53514947454337, + 164.43526170798893, + 163.6618712376288, + 163.21497806346287, + 163.09458218549125, + 163.30068360371388, + 163.83328231813076, + 164.69237832874194, + 165.87797163554734, + 167.39006223854705, + 169.228650137741, + 171.39373533312923, + 173.8853178247117, + 176.70339761248846, + 179.84797469645952, + 183.3190490766248, + 187.11662075298432, + 191.24068972553812, + 195.69125599428622, + 200.46831955922863, + 205.57188042036526, + 211.00193857769608, + 216.75849403122123, + 222.8415467809407, + 229.2510968268544, + 235.9871441689623, + 243.0496888072645, + 250.438730741761, + 258.15426997245174, + 266.19630649933674, + 274.564840322416, + 283.25987144168954, + 292.2813998571574, + 301.62942556881944, + 311.30394857667574, + 321.30496888072634, + 331.6324864809713, + 342.2865013774105, + 353.2670135700438, + 364.5740230588715, + 376.2075298438934, + 388.16753392510964, + 400.45403530252, + 413.0670339761248, + 426.00652994592383, + 439.272523211917, + 452.8650137741045, + 466.7840016324864, + 481.02948678706247, + 495.60146923783276, + 510.4999489847973, + 525.7249260279564, + 541.2764003673094, + 557.1543720028567, + 573.3588409345986, + 589.8898071625343, + 606.7472706866647, + 623.931231506989, + 641.4416896235076, + 659.2786450362207, + 677.4420977451279, + 695.9320477502292, + 714.7484950515253, + 733.8914396490152, + 753.3608815426998, + 773.1568207325781, + 793.2792572186509, + 813.7281910009182, + 834.5036220793794, + 855.6055504540353, + 877.0339761248852 + ], + [ + 343.2088562391593, + 332.80379553106826, + 322.7252321191715, + 312.9731660034691, + 303.5475971839608, + 294.44852566064685, + 285.6759514335272, + 277.22987450260183, + 269.11029486787066, + 261.31721252933374, + 253.85062748699116, + 246.71053974084282, + 239.89694929088873, + 233.40985613712888, + 227.24926027956332, + 221.41516171819208, + 215.90756045301507, + 210.7264564840323, + 205.87184981124378, + 201.3437404346496, + 197.14212835424962, + 193.26701357004393, + 189.71839608203248, + 186.49627589021534, + 183.60065299459245, + 181.0315273951638, + 178.78889909192944, + 176.87276808488932, + 175.2831343740435, + 174.01999795939196, + 173.08335884093466, + 172.47321701867162, + 172.18957249260282, + 172.23242526272836, + 172.60177532904814, + 173.29762269156217, + 174.31996735027045, + 175.668809305173, + 177.34414855626983, + 179.34598510356093, + 181.67431894704632, + 184.32915008672592, + 187.3104785225998, + 190.61830425466795, + 194.2526272829304, + 198.21344760738705, + 202.50076522803803, + 207.11458014488326, + 212.05489235792274, + 217.32170186715652, + 222.9150086725845, + 228.83481277420677, + 235.08111417202332, + 241.65391286603415, + 248.55320885623922, + 255.77900214263857, + 263.33129272523223, + 271.2100806040201, + 279.41536577900223, + 287.9471482501786, + 296.80542801754933, + 305.9902050811143, + 315.5014794408734, + 325.3392510968269, + 335.5035200489746, + 345.9942862973167, + 356.8115498418531, + 367.9553106825835, + 379.4255688195083, + 391.22232425262735, + 403.3455769819408, + 415.79532700744824, + 428.57157432915017, + 441.6743189470463, + 455.1035608611367, + 468.8593000714212, + 482.9415365779003, + 497.35027038057353, + 512.085501479441, + 527.1472298745025, + 542.5354555657588, + 558.250178553209, + 574.2913988368534, + 590.6591164166924, + 607.3533312927253, + 624.3740434649528, + 641.7212529333743, + 659.39495969799, + 677.3951637588003, + 695.7218651158046, + 714.3750637690031, + 733.3547597183962, + 752.6609529639833, + 772.2936435057649, + 792.2528313437405, + 812.5385164779103, + 833.1506989082748, + 854.0893786348332, + 875.3545556575862, + 896.9462299765331 + ], + [ + 347.2859912253852, + 337.0441791653913, + 327.12886440159167, + 317.5400469339864, + 308.27772676257524, + 299.3419038873584, + 290.73257830833586, + 282.4497500255076, + 274.4934190388736, + 266.86358534843384, + 259.56024895418835, + 252.5834098561371, + 245.9330680542802, + 239.60922354861748, + 233.61187633914906, + 227.9410264258749, + 222.596673808795, + 217.5788184879094, + 212.88746046321805, + 208.52259973472093, + 204.4842363024181, + 200.77237016630954, + 197.38700132639525, + 194.32812978267526, + 191.59575553514944, + 189.18987858381797, + 187.11049892868073, + 185.3576165697378, + 183.93123150698912, + 182.83134374043465, + 182.05795327007448, + 181.6110600959086, + 181.49066421793694, + 181.6967656361596, + 182.22936435057645, + 183.0884603611876, + 184.27405366799303, + 185.78614427099276, + 187.62473217018672, + 189.78981736557495, + 192.28139985715742, + 195.09947964493415, + 198.2440567289052, + 201.71513110907048, + 205.51270278543006, + 209.63677175798384, + 214.08733802673197, + 218.86440159167432, + 223.96796245281095, + 229.39802061014183, + 235.15457606366695, + 241.23762881338638, + 247.64717885930008, + 254.38322620140804, + 261.4457708397102, + 268.8348127742067, + 276.55035200489743, + 284.5923885317825, + 292.96092235486174, + 301.6559534741353, + 310.67748188960314, + 320.02550760126525, + 329.7000306091215, + 339.7010509131721, + 350.02856851341693, + 360.68258340985614, + 371.6630956024896, + 382.9701050913172, + 394.6036118763391, + 406.5636159575554, + 418.85011733496583, + 431.4631160085705, + 444.4026119783696, + 457.66860524436277, + 471.2610958065503, + 485.180083664932, + 499.42556881950816, + 513.9975512702786, + 528.8960310172431, + 544.1210080604019, + 559.6724823997552, + 575.5504540353024, + 591.754922967044, + 608.2858891949802, + 625.1433527191102, + 642.327313539435, + 659.8377716559535, + 677.6747270686664, + 695.8381797775737, + 714.3281297826752, + 733.144577083971, + 752.287521681461, + 771.7569635751454, + 791.5529027650241, + 811.6753392510968, + 832.1242730333637, + 852.8997041118254, + 874.0016324864808, + 895.430058157331, + 917.184981124375 + ], + [ + 351.68962350780527, + 341.61106009590856, + 331.85899398020604, + 322.4334251606979, + 313.3343536373839, + 304.56177941026425, + 296.1157024793388, + 287.99612284460767, + 280.20304050607075, + 272.73645546372813, + 265.59636771757977, + 258.7827772676257, + 252.2956841138659, + 246.13508825630032, + 240.30098969492906, + 234.79338842975204, + 229.61228446076927, + 224.75767778798075, + 220.22956841138654, + 216.02795633098657, + 212.1528415467809, + 208.60422405876946, + 205.3821038669523, + 202.4864809713294, + 199.91735537190078, + 197.6747270686664, + 195.7585960616263, + 194.16896235078045, + 192.9058259361289, + 191.9691868176716, + 191.35904499540857, + 191.0754004693398, + 191.11825323946528, + 191.48760330578506, + 192.1834506682991, + 193.20579532700737, + 194.55463728190995, + 196.22997653300675, + 198.23181308029785, + 200.5601469237832, + 203.21497806346284, + 206.1963064993367, + 209.50413223140487, + 213.1384552596673, + 217.099275584124, + 221.38659320477493, + 226.00040812162015, + 230.94072033465963, + 236.20752984389338, + 241.80083664932144, + 247.7206407509437, + 253.96694214876024, + 260.53974084277104, + 267.43903683297617, + 274.66483011937544, + 282.21712070196907, + 290.095908580757, + 298.3011937557391, + 306.8329762269155, + 315.69125599428617, + 324.8760330578511, + 334.38730741761043, + 344.2250790735638, + 354.3893480257115, + 364.88011427405354, + 375.6973778185898, + 386.84113865932045, + 398.3113967962451, + 410.1081522293642, + 422.23140495867756, + 434.6811549841852, + 447.457402305887, + 460.56014692378324, + 473.98938883787355, + 487.7451280481582, + 501.8273645546371, + 516.2360983573103, + 530.9713294561778, + 546.0330578512395, + 561.4212835424954, + 577.1360065299459, + 593.1772268135903, + 609.544944393429, + 626.2391592694621, + 643.2598714416894, + 660.6070809101111, + 678.280787674727, + 696.280991735537, + 714.6076930925416, + 733.2608917457401, + 752.240587695133, + 771.5467809407202, + 791.1794714825016, + 811.1386593204776, + 831.4243444546473, + 852.0365268850114, + 872.9752066115702, + 894.2403836343228, + 915.8320579532701, + 937.7502295684112 + ], + [ + 356.41975308641975, + 346.5044383226201, + 336.91562085501477, + 327.6533006836038, + 318.71747780838695, + 310.10815222936435, + 301.82532394653606, + 293.86899295990213, + 286.23915926946233, + 278.93582287521684, + 271.9589837771656, + 265.30864197530866, + 258.98479746964597, + 252.98745026017755, + 247.31660034690336, + 241.97224772982355, + 236.9543924089379, + 232.26303438424654, + 227.89817365574942, + 223.8598102234466, + 220.14794408733803, + 216.7625752474238, + 213.70370370370372, + 210.97132945617798, + 208.56545250484646, + 206.48607284970922, + 204.7331904907663, + 203.30680542801758, + 202.20691766146317, + 201.43352719110297, + 200.98663401693705, + 200.86623813896549, + 201.07233955718806, + 201.604938271605, + 202.46403428221612, + 203.64962758902158, + 205.16171819202128, + 207.00030609121524, + 209.16539128660344, + 211.65697377818591, + 214.4750535659627, + 217.6196306499337, + 221.09070503009903, + 224.88827670645856, + 229.0123456790124, + 233.46291194776046, + 238.2399755127028, + 243.34353637383944, + 248.77359453117035, + 254.5301499846955, + 260.61320273441487, + 267.0227527803286, + 273.7588001224366, + 280.8213447607388, + 288.2103866952352, + 295.925925925926, + 303.96796245281104, + 312.33649627589034, + 321.0315273951637, + 330.0530558106316, + 339.4010815222937, + 349.07560453015003, + 359.07662483420063, + 369.40414243444553, + 380.0581573308846, + 391.0386695235181, + 402.3456790123458, + 413.9791857973677, + 425.9391898785838, + 438.2256912559943, + 450.83868992959907, + 463.778185899398, + 477.04417916539137, + 490.6366697275789, + 504.5556575859607, + 518.8011427405366, + 533.373125191307, + 548.2716049382717, + 563.4965819814305, + 579.0480563207835, + 594.9260279563312, + 611.1304968880727, + 627.6614631160086, + 644.5189266401388, + 661.7028874604631, + 679.2133455769821, + 697.0503009896948, + 715.2137536986022, + 733.7037037037039, + 752.5201510049995, + 771.6630956024894, + 791.132537496174, + 810.9284766860525, + 831.0509131721254, + 851.4998469543925, + 872.2752780328536, + 893.3772064075097, + 914.8056320783593, + 936.5605550454038, + 958.641975308642 + ], + [ + 361.4763799612284, + 351.7243138455259, + 342.2987450260177, + 333.19967350270383, + 324.42709927558406, + 315.98102234465864, + 307.86144270992753, + 300.0683603713907, + 292.60177532904805, + 285.4616875828997, + 278.64809713294557, + 272.16100397918575, + 266.00040812162024, + 260.1663095602489, + 254.65870829507193, + 249.47760432608916, + 244.62299765330067, + 240.09488827670646, + 235.8932761963065, + 232.01816141210077, + 228.46954392408935, + 225.2474237322722, + 222.35180083664926, + 219.7826752372207, + 217.54004693398628, + 215.6239159269462, + 214.03428221610037, + 212.77114580144877, + 211.83450668299153, + 211.22436486072846, + 210.94072033465972, + 210.9835731047852, + 211.35292317110498, + 212.048770533619, + 213.07111519232728, + 214.41995714722987, + 216.09529639832667, + 218.09713294561777, + 220.42546678910313, + 223.08029792878276, + 226.06162636465666, + 229.36945209672476, + 233.00377512498721, + 236.9645954494439, + 241.25191307009487, + 245.86572798694004, + 250.80604019997955, + 256.0728497092133, + 261.66615651464133, + 267.5859606162636, + 273.83226201408013, + 280.40506070809096, + 287.30435669829603, + 294.53014998469536, + 302.0824405672889, + 309.9612284460769, + 318.16651362105904, + 326.69829609223547, + 335.5565758596061, + 344.741352923171, + 354.2526272829303, + 364.09039893888377, + 374.25466789103143, + 384.74543413937346, + 395.56269768390973, + 406.7064585246403, + 418.1767166615652, + 429.97347209468415, + 442.0967248239975, + 454.5464748495051, + 467.322722171207, + 480.42546678910304, + 493.85470870319347, + 507.61044791347814, + 521.6926844199571, + 536.1014182226302, + 550.8366493214977, + 565.8983777165595, + 581.2866034078155, + 597.0013263952656, + 613.0425466789103, + 629.4102642587491, + 646.104479134782, + 663.1251913070095, + 680.4724007754309, + 698.146107540047, + 716.146311600857, + 734.4730129578612, + 753.1262116110601, + 772.1059075604528, + 791.4121008060399, + 811.0447913478216, + 831.0039791857973, + 851.2896643199675, + 871.9018467503315, + 892.84052647689, + 914.1057034996429, + 935.6973778185899, + 957.6155494337313, + 979.8602183450668 + ], + [ + 366.85950413223134, + 357.270686664626, + 348.0083664932149, + 339.0725436179981, + 330.4632180389756, + 322.18038975614724, + 314.2240587695132, + 306.59422507907357, + 299.2908886848281, + 292.3140495867768, + 285.66370778491984, + 279.33986327925714, + 273.34251606978876, + 267.67166615651456, + 262.32731353943467, + 257.3094582185491, + 252.6181001938577, + 248.2532394653606, + 244.21487603305778, + 240.50300989694918, + 237.11764105703492, + 234.0587695133149, + 231.32639526578913, + 228.92051831445764, + 226.84113865932036, + 225.0882563003774, + 223.66187123762873, + 222.56198347107426, + 221.78859300071412, + 221.3416998265482, + 221.22130394857658, + 221.4274053667992, + 221.96000408121608, + 222.81910009182727, + 224.00469339863267, + 225.51678400163235, + 227.35537190082636, + 229.52045709621456, + 232.01203958779703, + 234.8301193755738, + 237.97469645954482, + 241.4457708397101, + 245.24334251606965, + 249.36741148862347, + 253.81797775737158, + 258.5950413223139, + 263.69860218345053, + 269.1286603407814, + 274.8852157943066, + 280.96826854402605, + 287.37781858993964, + 294.11386593204764, + 301.17641057034984, + 308.56545250484635, + 316.28099173553693, + 324.32302826242204, + 332.69156208550135, + 341.38659320477495, + 350.4081216202427, + 359.75614733190474, + 369.43067033976115, + 379.43169064381175, + 389.75920824405654, + 400.4132231404957, + 411.3937353331291, + 422.7007448219568, + 434.3342516069788, + 446.29425568819494, + 458.5807570656054, + 471.1937557392101, + 484.13325170900913, + 497.3992449750023, + 510.9917355371899, + 524.9107233955717, + 539.1562085501479, + 553.7281910009181, + 568.6266707478827, + 583.8516477910416, + 599.4031221303948, + 615.281093765942, + 631.4855626976838, + 648.0165289256197, + 664.8739924497496, + 682.0579532700743, + 699.5684113865929, + 717.4053667993061, + 735.5688195082133, + 754.0587695133147, + 772.8752168146106, + 792.0181614121004, + 811.4876033057847, + 831.2835424956635, + 851.4059789817363, + 871.8549127640036, + 892.6303438424649, + 913.7322722171203, + 935.1606978879704, + 956.9156208550145, + 978.9970411182532, + 1001.4049586776858 + ], + [ + 372.5691255994287, + 363.14355677992046, + 354.04448525660644, + 345.27191102948683, + 336.82583409856136, + 328.7062544638302, + 320.9131721252933, + 313.4465870829507, + 306.30649933680235, + 299.4929088868482, + 293.00581573308847, + 286.8452198755229, + 281.01112131415164, + 275.5035200489746, + 270.32241607999185, + 265.4678094072034, + 260.9397000306091, + 256.73808795020915, + 252.86297316600346, + 249.31435567799204, + 246.09223548617487, + 243.19661259055198, + 240.62748699112336, + 238.38485868788902, + 236.4687276808489, + 234.87909397000308, + 233.61595755535154, + 232.6793184368942, + 232.06917661463117, + 231.7855320885624, + 231.82838485868788, + 232.1977349250077, + 232.8935822875217, + 233.91592694623, + 235.26476890113256, + 236.94010815222939, + 238.9419446995205, + 241.27027854300584, + 243.92510968268547, + 246.90643811855932, + 250.2142638506275, + 253.84858687888988, + 257.8094072033466, + 262.0967248239976, + 266.7105397408428, + 271.65085195388224, + 276.917661463116, + 282.51096826854405, + 288.4307723701663, + 294.67707376798296, + 301.2498724619937, + 308.1491684521988, + 315.37496173859813, + 322.92725232119176, + 330.8060401999795, + 339.0113253749617, + 347.5431078461382, + 356.4013876135088, + 365.5861646770737, + 375.09743903683295, + 384.9352106927865, + 395.09947964493426, + 405.5902458932762, + 416.40750943781245, + 427.551270278543, + 439.02152841546786, + 450.81828384858693, + 462.9415365779002, + 475.3912866034078, + 488.1675339251097, + 501.2702785430059, + 514.6995204570961, + 528.4552596673809, + 542.5374961738598, + 556.9462299765331, + 571.6814610754004, + 586.7431894704622, + 602.1314151617182, + 617.8461381491685, + 633.8873584328129, + 650.2550760126519, + 666.9492908886848, + 683.9700030609121, + 701.3172125293338, + 718.9909192939496, + 736.9911233547598, + 755.317824711764, + 773.9710233649625, + 792.9507193143558, + 812.2569125599427, + 831.8896031017241, + 851.8487909397, + 872.1344760738699, + 892.7466585042343, + 913.6853382307929, + 934.9505152535454, + 956.5421895724928, + 978.460361187634, + 1000.7050300989697, + 1023.2761963064994 + ], + [ + 378.60524436282003, + 369.342924191409, + 360.4071013161922, + 351.7977757371697, + 343.5149474543414, + 335.55861646770734, + 327.92878277726754, + 320.6254463830221, + 313.64860728497086, + 306.99826548311387, + 300.6744209774512, + 294.67707376798273, + 289.0062238547087, + 283.66187123762876, + 278.6440159167431, + 273.9526578920518, + 269.5877971635547, + 265.5494337312519, + 261.8375675951433, + 258.452198755229, + 255.393327211509, + 252.66095296398322, + 250.2550760126517, + 248.17569635751448, + 246.4228139985715, + 244.99642893582282, + 243.89654116926837, + 243.1231506989082, + 242.6762575247423, + 242.5558616467707, + 242.7619630649933, + 243.2945617794102, + 244.15365779002133, + 245.33925109682679, + 246.8513416998265, + 248.68992959902045, + 250.8550147944087, + 253.34659728599115, + 256.1646770737679, + 259.3092541577389, + 262.7803285379042, + 266.57790021426376, + 270.70196918681756, + 275.1525354555657, + 279.929599020508, + 285.0331598816446, + 290.4632180389756, + 296.2197734925007, + 302.3028262422201, + 308.71237628813384, + 315.44842363024173, + 322.51096826854393, + 329.9000102030405, + 337.6155494337312, + 345.65758596061613, + 354.02611978369544, + 362.72115090296904, + 371.74267931843684, + 381.09070503009883, + 390.7652280379552, + 400.7662483420058, + 411.0937659422508, + 421.74778083868983, + 432.72829303132323, + 444.0353025201509, + 455.6688093051729, + 467.6288133863891, + 479.9153147637995, + 492.5283134374042, + 505.46780940720316, + 518.7338026731966, + 532.326293235384, + 546.2452810937658, + 560.4907662483419, + 575.0627486991121, + 589.9612284460767, + 605.1862054892357, + 620.7376798285889, + 636.6156514641362, + 652.8201203958778, + 669.3510866238139, + 686.2085501479439, + 703.3925109682683, + 720.9029690847872, + 738.7399244975, + 756.9033772064075, + 775.393327211509, + 794.2097745128046, + 813.3527191102949, + 832.8221610039791, + 852.6181001938575, + 872.7405366799305, + 893.1894704621975, + 913.9649015406591, + 935.0668299153145, + 956.4952555861644, + 978.2501785532088, + 1000.3315988164471, + 1022.73951637588, + 1045.4739312315069 + ], + [ + 384.96786042240586, + 375.86878889909195, + 367.09621467197223, + 358.65013774104693, + 350.53055810631577, + 342.73747576777885, + 335.2708907254362, + 328.13080297928786, + 321.3172125293338, + 314.83011937557393, + 308.6695235180084, + 302.8354249566371, + 297.32782369146014, + 292.14671972247737, + 287.2921130496889, + 282.7640036730947, + 278.56239159269467, + 274.68727680848895, + 271.1386593204776, + 267.91653912866036, + 265.0209162330375, + 262.4517906336089, + 260.2091623303745, + 258.29303132333445, + 256.7033976124886, + 255.440261197837, + 254.50362207937974, + 253.89348025711666, + 253.60983573104792, + 253.6526885011734, + 254.02203856749315, + 254.71788593000724, + 255.7402305887155, + 257.0890725436181, + 258.7644117947149, + 260.766248342006, + 263.09458218549133, + 265.74941332517096, + 268.73074176104484, + 272.038567493113, + 275.6728905213754, + 279.6337108458321, + 283.9210284664831, + 288.5348433833283, + 293.4751555963678, + 298.74196510560154, + 304.3352719110296, + 310.25507601265184, + 316.50137741046836, + 323.0741761044792, + 329.97347209468427, + 337.19926538108365, + 344.7515559636772, + 352.6303438424651, + 360.8356290174473, + 369.3674114886237, + 378.22569125599443, + 387.41046831955936, + 396.92174267931847, + 406.75951433527194, + 416.92378328741967, + 427.4145495357618, + 438.231813080298, + 449.37557392102855, + 460.8458320579533, + 472.64258749107245, + 484.7658402203858, + 497.21559024589334, + 509.9918375675952, + 523.0945821854913, + 536.5238240995818, + 550.2795633098664, + 564.3617998163454, + 578.7705336190185, + 593.505764717886, + 608.5674931129475, + 623.9557188042036, + 639.6704417916541, + 655.7116620752986, + 672.0793796551372, + 688.7735945311705, + 705.7943067033978, + 723.1415161718193, + 740.8152229364352, + 758.8154269972453, + 777.1421283542497, + 795.7953270074483, + 814.7750229568412, + 834.0812162024284, + 853.7139067442099, + 873.6730945821854, + 893.9587797163556, + 914.5709621467197, + 935.5096418732784, + 956.774818896031, + 978.3664932149779, + 1000.2846648301195, + 1022.5293337414549, + 1045.100499948985, + 1067.998163452709 + ], + [ + 391.6569737781859, + 382.7211509029691, + 374.11182532394645, + 365.82899704111827, + 357.8726660544842, + 350.2428323640445, + 342.93949596979894, + 335.9626568717478, + 329.3123150698908, + 322.9884705642281, + 316.9911233547597, + 311.3202734414855, + 305.97592082440565, + 300.95806550352, + 296.26670747882866, + 291.90184675033163, + 287.8634833180288, + 284.15161718192024, + 280.7662483420059, + 277.70737679828585, + 274.9750025507601, + 272.5691255994286, + 270.48974594429137, + 268.73686358534843, + 267.3104785225997, + 266.2105907560453, + 265.43720028568515, + 264.9903071115192, + 264.8699112335476, + 265.0760126517702, + 265.6086113661871, + 266.4677073767983, + 267.6533006836037, + 269.1653912866034, + 271.00397918579733, + 273.16906438118554, + 275.6606468727681, + 278.4787266605448, + 281.62330374451585, + 285.09437812468116, + 288.89194980104077, + 293.0160187735945, + 297.46658504234256, + 302.2436486072849, + 307.34720946842157, + 312.7772676257525, + 318.5338230792776, + 324.616875828997, + 331.0264258749107, + 337.7624732170186, + 344.8250178553209, + 352.2140597898174, + 359.9295990205081, + 367.9716355473931, + 376.34016937047227, + 385.03520048974593, + 394.0567289052138, + 403.40475461687583, + 413.07927762473213, + 423.08029792878267, + 433.40781552902763, + 444.06183042546684, + 455.0423426181001, + 466.34935210692777, + 477.98285889194966, + 489.94286297316603, + 502.22936435057653, + 514.8423630241812, + 527.7818589939802, + 541.0478522599734, + 554.6403428221611, + 568.5593306805428, + 582.8048158351188, + 597.3767982858891, + 612.2752780328537, + 627.5002550760124, + 643.0517294153657, + 658.9297010509131, + 675.1341699826548, + 691.6651362105906, + 708.522599734721, + 725.7065605550454, + 743.217018671564, + 761.0539740842771, + 779.2174267931842, + 797.707376798286, + 816.5238240995817, + 835.6667686970716, + 855.1362105907561, + 874.9321497806345, + 895.0545862667072, + 915.5035200489747, + 936.2789511274358, + 957.3808795020916, + 978.8093051729414, + 1000.5642281399855, + 1022.6456484032242, + 1045.0535659626566, + 1067.787980818284, + 1090.848892970105 + ], + [ + 398.67258443016016, + 389.90001020304044, + 381.453933272115, + 373.3343536373839, + 365.541271298847, + 358.0746862565043, + 350.934598510356, + 344.121008060402, + 337.63391490664213, + 331.47331904907657, + 325.6392204877053, + 320.13161922252823, + 314.9505152535455, + 310.09590858075694, + 305.5677992041627, + 301.36618712376276, + 297.4910723395571, + 293.9424548515457, + 290.7203346597285, + 287.82471176410564, + 285.255586164677, + 283.01295786144266, + 281.09682685440254, + 279.5071931435567, + 278.2440567289051, + 277.3074176104478, + 276.69727578818475, + 276.41363126211604, + 276.4564840322416, + 276.8258340985613, + 277.52168146107533, + 278.5440261197836, + 279.89286807468613, + 281.568207325783, + 283.57004387307404, + 285.8983777165594, + 288.55320885623905, + 291.534537292113, + 294.84236302418105, + 298.47668605244354, + 302.4375063769003, + 306.7248239975512, + 311.33863891439637, + 316.2789511274358, + 321.5457606366696, + 327.1390674420976, + 333.0588715437199, + 339.3051729415365, + 345.8779716355473, + 352.77726762575236, + 360.0030609121517, + 367.55535149474537, + 375.4341393735332, + 383.6394245485153, + 392.1712070196916, + 401.0294867870624, + 410.2142638506274, + 419.7255382103866, + 429.56330986634, + 439.72757881848776, + 450.2183450668298, + 461.03560861136606, + 472.1793694520966, + 483.64962758902135, + 495.4463830221404, + 507.56963575145375, + 520.0193857769615, + 532.7956330986633, + 545.8983777165594, + 559.3276196306498, + 573.0833588409346, + 587.1655953474134, + 601.5743291500866, + 616.309560248954, + 631.3712886440157, + 646.7595143352717, + 662.4742373227219, + 678.5154576063666, + 694.8831751862053, + 711.5773900622382, + 728.5981022344657, + 745.9453117028872, + 763.619018467503, + 781.6192225283133, + 799.9459238853176, + 818.5991225385164, + 837.5788184879092, + 856.8850117334963, + 876.5177022752779, + 896.4768901132536, + 916.7625752474233, + 937.3747576777878, + 958.3134374043462, + 979.5786144270992, + 1001.1702887460461, + 1023.0884603611872, + 1045.3331292725231, + 1067.9042954800527, + 1090.8019589837772, + 1114.0261197836953 + ], + [ + 406.0146923783288, + 397.40536679930625, + 389.1225385164779, + 381.1662075298439, + 373.5363738394041, + 366.2330374451587, + 359.25619834710744, + 352.6058565452505, + 346.2820120395878, + 340.28466483011937, + 334.6138149168453, + 329.26946229976534, + 324.25160697887975, + 319.5602489541884, + 315.19538822569126, + 311.1570247933885, + 307.4451586572799, + 304.0597898173656, + 301.00091827364554, + 298.26854402611986, + 295.86266707478836, + 293.7832874196511, + 292.0304050607081, + 290.6040199979594, + 289.504132231405, + 288.73074176104484, + 288.2838485868789, + 288.16345270890724, + 288.3695541271299, + 288.90215284154687, + 289.76124885215796, + 290.9468421589634, + 292.4589327619631, + 294.2975206611571, + 296.4626058565453, + 298.9541883481278, + 301.77226813590454, + 304.9168452198755, + 308.38791960004085, + 312.1854912764004, + 316.3095602489543, + 320.76012651770236, + 325.53719008264466, + 330.6407509437812, + 336.07080910111216, + 341.82736455463726, + 347.91041730435677, + 354.3199673502704, + 361.0560146923783, + 368.1185593306806, + 375.5076012651771, + 383.2231404958679, + 391.2651770227528, + 399.63371084583207, + 408.32874196510556, + 417.3502703805734, + 426.6982960922355, + 436.3728191000919, + 446.3738394041425, + 456.7013570043873, + 467.3553719008265, + 478.3358840934599, + 489.6428935822875, + 501.27640036730946, + 513.2364044485257, + 525.5229058259362, + 538.1359044995411, + 551.0754004693399, + 564.3413937353332, + 577.9338842975206, + 591.8528721559026, + 606.0983573104785, + 620.6703397612489, + 635.5688195082134, + 650.7937965513723, + 666.3452708907254, + 682.2232425262728, + 698.4277114580145, + 714.9586776859504, + 731.8161412100804, + 749.0001020304052, + 766.5105601469237, + 784.3475155596366, + 802.510968268544, + 821.0009182736455, + 839.8173655749415, + 858.9603101724315, + 878.4297520661157, + 898.2256912559945, + 918.3481277420672, + 938.797061524334, + 959.5724926027958, + 980.6744209774512, + 1002.1028466483014, + 1023.8577696153454, + 1045.9391898785836, + 1068.3471074380168, + 1091.0815222936435, + 1114.1424344454651, + 1137.5298438934803 + ], + [ + 413.6832976226915, + 405.2372206917661, + 397.117641057035, + 389.3245587184981, + 381.8579736761555, + 374.71788593000707, + 367.904295480053, + 361.4172023262932, + 355.2566064687276, + 349.42250790735636, + 343.9149066421793, + 338.7338026731966, + 333.8791960004081, + 329.3510866238139, + 325.14947454341393, + 321.2743597592082, + 317.7257422711968, + 314.5036220793796, + 311.6079991837567, + 309.03887358432803, + 306.7962452810937, + 304.88011427405365, + 303.29048056320784, + 302.02734414855627, + 301.0907050300989, + 300.48056320783587, + 300.1969186817671, + 300.2397714518926, + 300.60912151821236, + 301.3049688807264, + 302.32731353943467, + 303.6761554943373, + 305.35149474543414, + 307.3533312927252, + 309.6816651362106, + 312.3364962758902, + 315.31782471176405, + 318.62565044383217, + 322.25997347209454, + 326.22079379655133, + 330.50811141720226, + 335.12192633404754, + 340.06223854708696, + 345.3290480563207, + 350.9223548617488, + 356.842158963371, + 363.08846036118763, + 369.66125905519834, + 376.5605550454034, + 383.7863483318028, + 391.33863891439637, + 399.21742679318436, + 407.4227119681665, + 415.9544944393429, + 424.81277420671347, + 433.9975512702785, + 443.50882563003773, + 453.34659728599115, + 463.5108662381389, + 474.0016324864808, + 484.8188960310172, + 495.96265687174775, + 507.4329150086725, + 519.2296704417915, + 531.3529231711049, + 543.8026731966124, + 556.5789205183145, + 569.6816651362105, + 583.110907050301, + 596.8666462605855, + 610.9488827670646, + 625.3576165697376, + 640.0928476686051, + 655.1545760636669, + 670.542801754923, + 686.257524742373, + 702.2987450260176, + 718.6664626058565, + 735.3606774818895, + 752.3813896541168, + 769.7285991225385, + 787.4023058871543, + 805.4025099479643, + 823.7292113049688, + 842.3824099581673, + 861.3621059075605, + 880.6682991531476, + 900.300989694929, + 920.2601775329048, + 940.5458626670747, + 961.1580450974387, + 982.0967248239976, + 1003.3619018467501, + 1024.9535761656973, + 1046.8717477808384, + 1069.116416692174, + 1091.6875828997042, + 1114.585246403428, + 1137.8094072033468, + 1161.3600652994592 + ], + [ + 421.6784001632487, + 413.39557188042033, + 405.43924089378635, + 397.80940720334667, + 390.5060708091012, + 383.52923171104993, + 376.878889909193, + 370.55504540353036, + 364.5576981940619, + 358.8868482807877, + 353.5424956637078, + 348.5246403428222, + 343.83328231813084, + 339.4684215896338, + 335.43005815733096, + 331.7181920212224, + 328.33282318130813, + 325.2739516375881, + 322.5415773900623, + 320.1357004387308, + 318.0563207835936, + 316.3034384246506, + 314.877053361902, + 313.7771655953475, + 313.0037751249873, + 312.55688195082143, + 312.4364860728498, + 312.64258749107245, + 313.1751862054893, + 314.0342822161005, + 315.2198755229059, + 316.7319661259056, + 318.57055402509957, + 320.7356392204878, + 323.2272217120703, + 326.0453014998471, + 329.18987858381814, + 332.66095296398333, + 336.45852464034283, + 340.58259361289674, + 345.03315988164485, + 349.81022344658714, + 354.91378430772386, + 360.34384246505465, + 366.10039791857986, + 372.1834506682992, + 378.59300071421296, + 385.32904805632086, + 392.3915926946231, + 399.78063462911956, + 407.4961738598103, + 415.53821038669537, + 423.9067442097746, + 432.60177532904817, + 441.6233037445159, + 450.971329456178, + 460.6458524640344, + 470.6468727680851, + 480.9743903683298, + 491.6284052647689, + 502.6089174574024, + 513.9159269462301, + 525.549433731252, + 537.5094378124681, + 549.7959391898786, + 562.4089378634834, + 575.3484338332825, + 588.6144270992756, + 602.2069176614632, + 616.1259055198451, + 630.3713906744211, + 644.9433731251914, + 659.8418528721561, + 675.0668299153149, + 690.618304254668, + 706.4962758902153, + 722.7007448219571, + 739.2317110498931, + 756.0891745740232, + 773.2731353943476, + 790.7835935108665, + 808.6205489235793, + 826.7840016324865, + 845.2739516375881, + 864.0903989388838, + 883.233343536374, + 902.7027854300583, + 922.4987246199369, + 942.6211611060099, + 963.0700948882768, + 983.845525966738, + 1004.947454341394, + 1026.3758800122437, + 1048.130802979288, + 1070.2122232425263, + 1092.620140801959, + 1115.3545556575862, + 1138.4154678094073, + 1161.8028772574232, + 1185.5167840016327 + ], + [ + 430, + 421.88042036526883, + 414.0873380267319, + 406.62075298438936, + 399.480665238241, + 392.66707478828687, + 386.1799816345271, + 380.01938577696154, + 374.1852872155903, + 368.67768595041326, + 363.49658198143044, + 358.641975308642, + 354.11386593204776, + 349.9122538516478, + 346.03713906744207, + 342.48852157943065, + 339.26640138761354, + 336.3707784919907, + 333.801652892562, + 331.5590245893276, + 329.6428935822875, + 328.0532598714417, + 326.7901234567901, + 325.85348433833286, + 325.24334251606973, + 324.959697990001, + 325.00255076012655, + 325.3719008264463, + 326.06774818896037, + 327.0900928476686, + 328.4389348025712, + 330.114274053668, + 332.1161106009591, + 334.44444444444446, + 337.09927558412403, + 340.08060401999796, + 343.3884297520662, + 347.0227527803285, + 350.98357310478514, + 355.2708907254362, + 359.88470564228146, + 364.82501785532094, + 370.0918273645546, + 375.6851341699826, + 381.6049382716049, + 387.8512396694215, + 394.4240383634324, + 401.3233343536374, + 408.54912764003666, + 416.10141822263034, + 423.9802061014182, + 432.1854912764004, + 440.71727374757677, + 449.5755535149474, + 458.76033057851237, + 468.27160493827165, + 478.1093765942252, + 488.27364554637285, + 498.76441179471476, + 509.58167533925103, + 520.7254361799817, + 532.1956943169065, + 543.9924497500255, + 556.1157024793388, + 568.5654525048463, + 581.3416998265483, + 594.4444444444445, + 607.8736863585348, + 621.6294255688194, + 635.7116620752984, + 650.1203958779718, + 664.8556269768391, + 679.9173553719008, + 695.3055810631569, + 711.0203040506071, + 727.0615243342515, + 743.4292419140903, + 760.1234567901234, + 777.1441689623508, + 794.4913784307722, + 812.1650851953882, + 830.1652892561983, + 848.4919906132026, + 867.1451892664014, + 886.1248852157942, + 905.4310784613816, + 925.0637690031629, + 945.0229568411385, + 965.3086419753087, + 985.9208244056729, + 1006.8595041322313, + 1028.1246811549843, + 1049.7163554739311, + 1071.6345270890727, + 1093.879196000408, + 1116.4503622079378, + 1139.348025711662, + 1162.5721865115804, + 1186.1228446076932, + 1210 + ] + ] + } + ], + "layout": { + "template": { + "data": { + "bar": [ + { + "error_x": { + "color": "#2a3f5f" + }, + "error_y": { + "color": "#2a3f5f" + }, + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + }, + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "bar" + } + ], + "barpolar": [ + { + "marker": { + "line": { + "color": "#E5ECF6", + "width": 0.5 + }, + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "barpolar" + } + ], + "carpet": [ + { + "aaxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "baxis": { + "endlinecolor": "#2a3f5f", + "gridcolor": "white", + "linecolor": "white", + "minorgridcolor": "white", + "startlinecolor": "#2a3f5f" + }, + "type": "carpet" + } + ], + "choropleth": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "choropleth" + } + ], + "contour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "contour" + } + ], + "contourcarpet": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "contourcarpet" + } + ], + "heatmap": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmap" + } + ], + "heatmapgl": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "heatmapgl" + } + ], + "histogram": [ + { + "marker": { + "pattern": { + "fillmode": "overlay", + "size": 10, + "solidity": 0.2 + } + }, + "type": "histogram" + } + ], + "histogram2d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2d" + } + ], + "histogram2dcontour": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "histogram2dcontour" + } + ], + "mesh3d": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "type": "mesh3d" + } + ], + "parcoords": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "parcoords" + } + ], + "pie": [ + { + "automargin": true, + "type": "pie" + } + ], + "scatter": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter" + } + ], + "scatter3d": [ + { + "line": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatter3d" + } + ], + "scattercarpet": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattercarpet" + } + ], + "scattergeo": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergeo" + } + ], + "scattergl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattergl" + } + ], + "scattermapbox": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scattermapbox" + } + ], + "scatterpolar": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolar" + } + ], + "scatterpolargl": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterpolargl" + } + ], + "scatterternary": [ + { + "marker": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "type": "scatterternary" + } + ], + "surface": [ + { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + }, + "colorscale": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "type": "surface" + } + ], + "table": [ + { + "cells": { + "fill": { + "color": "#EBF0F8" + }, + "line": { + "color": "white" + } + }, + "header": { + "fill": { + "color": "#C8D4E3" + }, + "line": { + "color": "white" + } + }, + "type": "table" + } + ] + }, + "layout": { + "annotationdefaults": { + "arrowcolor": "#2a3f5f", + "arrowhead": 0, + "arrowwidth": 1 + }, + "autotypenumbers": "strict", + "coloraxis": { + "colorbar": { + "outlinewidth": 0, + "ticks": "" + } + }, + "colorscale": { + "diverging": [ + [ + 0, + "#8e0152" + ], + [ + 0.1, + "#c51b7d" + ], + [ + 0.2, + "#de77ae" + ], + [ + 0.3, + "#f1b6da" + ], + [ + 0.4, + "#fde0ef" + ], + [ + 0.5, + "#f7f7f7" + ], + [ + 0.6, + "#e6f5d0" + ], + [ + 0.7, + "#b8e186" + ], + [ + 0.8, + "#7fbc41" + ], + [ + 0.9, + "#4d9221" + ], + [ + 1, + "#276419" + ] + ], + "sequential": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ], + "sequentialminus": [ + [ + 0, + "#0d0887" + ], + [ + 0.1111111111111111, + "#46039f" + ], + [ + 0.2222222222222222, + "#7201a8" + ], + [ + 0.3333333333333333, + "#9c179e" + ], + [ + 0.4444444444444444, + "#bd3786" + ], + [ + 0.5555555555555556, + "#d8576b" + ], + [ + 0.6666666666666666, + "#ed7953" + ], + [ + 0.7777777777777778, + "#fb9f3a" + ], + [ + 0.8888888888888888, + "#fdca26" + ], + [ + 1, + "#f0f921" + ] + ] + }, + "colorway": [ + "#636efa", + "#EF553B", + "#00cc96", + "#ab63fa", + "#FFA15A", + "#19d3f3", + "#FF6692", + "#B6E880", + "#FF97FF", + "#FECB52" + ], + "font": { + "color": "#2a3f5f" + }, + "geo": { + "bgcolor": "white", + "lakecolor": "white", + "landcolor": "#E5ECF6", + "showlakes": true, + "showland": true, + "subunitcolor": "white" + }, + "hoverlabel": { + "align": "left" + }, + "hovermode": "closest", + "mapbox": { + "style": "light" + }, + "paper_bgcolor": "white", + "plot_bgcolor": "#E5ECF6", + "polar": { + "angularaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "radialaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "scene": { + "xaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + }, + "text/html": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = go.Figure(data=[go.Surface(x=mx, y=my, z=mz)])\n", + "py.iplot(fig, show_link=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "\n", + "La contrainte de la propriété peut sembler être une limite trop dure mais il y a de nombreux problèmes qui\n", + "génèrent des matrices A qui respectent ces contraintes. Par exemples les problèmes de simuation numérique\n", + "comme celui de l'avion qu'on a vu génère une telle matrice, qui de plus sera très creuse avec une dizaine\n", + "de valeur non nulle par ligne même pour une matrice de 1 milliard par 1 milliard.\n", + "\n", + "C'est pour ce type de matrice qu'un méthode itérative comme le gradient offre un gain de performance incroyable\n", + "puisqu'on a la solution en quasiment $O(n^2)$ au lieu de $O(n^3)$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/cama/fr/ma53 Notations du produit scalaire.ipynb b/PVCM/cama/fr/ma53 Notations du produit scalaire.ipynb new file mode 100644 index 0000000..32af5ab --- /dev/null +++ b/PVCM/cama/fr/ma53 Notations du produit scalaire.ipynb @@ -0,0 +1,99 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5, + "cells": [ + { + "cell_type": "markdown", + "id": "cfa8acda", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Écritures du produit scalaire\n", + "\n", + "Voici 3 différentes facon d'écrire le produit scalaire. Certaines sont plus claires que d'autres mais on trouve les 3 dans la littérature.\n", + "\n", + "### ${\\bf v} \\,.\\, {\\bf w}$\n", + "\n", + "Dans la feuille d'exercice qui suit et dans la cours par la suite, il y a beaucoup de produits scalaire qui utilise le point. Il est important de noter l'ordre de résolution des opérateurs dans un formule comme \n", + "\n", + "$$A \\, {\\bf v} \\, . \\, {\\bf w}$$\n", + "\n", + "* Si on fait $A ({\\bf v} \\, . \\, {\\bf w})$ alors le résultat est une matrice.\n", + "* Si on fait $(A {\\bf v} )\\, . \\, {\\bf w}$ alors le résultat est un réel.\n", + "\n", + "Dans la majorité des cas et en particulier dans ce cours, c'est la 2e lecture qui est la bonne.\n", + "\n", + "#### Danger\n", + "\n", + "Cette écriture est dangereuse.\n", + "Imaginez qu'on multiplie notre équation par $A^{-1}$. Alors on a envie d'écrire\n", + "\n", + "$$\n", + "A^{-1} \\, A \\, {\\bf v} \\, . \\, {\\bf w} = {\\bf v} \\, . \\, {\\bf w}\n", + "$$\n", + "\n", + "mais c'est faux (dans le second cas) car on oublie sur quoi porte le point du produit scalaire.\n", + "\n", + "### ${\\bf v}^T \\, {\\bf w}$\n", + "\n", + "\n", + "La notation matricielle de l'exemple précédant s'écrit \n", + "\n", + "$${\\bf v}^T A \\, {\\bf w}$$\n", + "\n", + "Dans ce cas on peut faire les calculs dans l'ordre de son choix. Si on commence par les 2 premiers on aura un vecteur horizontal, si on commence par les 2 dernièrs on aura un vecteur verctical. Cette notation est moins risquée lorsqu'on fait des\n", + "calculs plus complexes.\n", + "\n", + "\n", + "Avec la notation matricielle ce risque n'exite pas puisque multiplier par $A^{-1}$ donne\n", + "\n", + "$$\n", + "A^{-1} \\, {\\bf v}^T A \\, {\\bf w}\n", + "$$\n", + "\n", + "et on voit bien que les A ne se simplifient pas. \n", + "\n", + "### $<{\\bf v}, {\\bf w}>$\n", + "\n", + "\n", + "Une autre facon d'ecrire le produit matriciel pour éviter les confusions, est d'utiliser les signes\n", + "< et > ce qui donne **** pour le produit scalaire entre **a** et **b**. Avec cette notation l'erreur\n", + "de lecture du produit scalaire avec le point disparait :\n", + "\n", + "$$\n", + "A^{-1} \\, < A \\, {\\bf v} \\,, \\, {\\bf w}> \n", + "$$\n", + "\n", + "Parfois on utilise les parenthèses à la place de inférieur et supérieur mais je trouve cela moins lisible." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "db3e803c", + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" "b/PVCM/cama/fr/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" new file mode 100644 index 0000000..2a7cf27 --- /dev/null +++ "b/PVCM/cama/fr/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" @@ -0,0 +1,182 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## La méthode du gradient pour résoudre A x = b\n", + "\n", + "Le but de ce TP est de vous laisser avancer tout seul. Reprenez les cours et programmez la méthode du gradient\n", + "pour résoudre le système matriciel $A {\\bf x} = {\\bf b}$ avec A symétrique et à diagonale dominante\n", + "($a_{ii} > \\sum_{k \\ne i} |a_{ik}|$).\n", + "\n", + "* Commencez en 2D avec une matrice 2x2, vérifier que le résultat est bon et tracer la courbe de convergence\n", + "* Passez en nxn (on montrera que cela marche avec une matrice 9x9)\n", + "\n", + "Il peut être intéressant de normaliser la matrice A pour éviter que les calculs explosent." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "def solve_with_gradiant(A, b):\n", + " mu = 0.01\n" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[49, 13],\n", + " [13, 13]])" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "A = np.random.randint(10, size=(2,2))\n", + "A = A + A.T\n", + "A += np.diag(A.sum(axis=1))\n", + "A" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([62, 26])" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b = A.sum(axis=1)\n", + "b" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "solve_with_gradiant(A,b)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Introduire de l'inertie\n", + "\n", + "Introduire de l'inertie dans la méthode du gradient. Que constate-t-on ?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Valeur optimale de µ\n", + "\n", + "On note que deux directions de pente sucessives sont orthogonales si le point suivant est le minumum dans\n", + "la direction donnée ($\\nabla J ({\\bf x}^k$)).\n", + "\n", + "$$\\nabla J ({\\bf x}^{k+1})^T \\; \\nabla J ({\\bf x}^k) = 0$$\n", + "\n", + "#### Démonstration \n", + "\n", + "\n", + "\n", + "
\n", + "On veut régler µ pour arriver au minimum de J lorsqu'on avance dans la direction $- \\nabla J({\\bf x}^{k})$.\n", + "Cela veut dire que la dérivée partielle de $J({\\bf x}^{k+1})$ par rapport à µ doit être\n", + "égale à 0 ou bien en faisant apparaitre µ dans l'équation :\n", + "\n", + "$$\n", + "\\frac{\\partial J ({\\bf x}^k - µ \\; \\nabla J ({\\bf x}^k))}{\\partial µ} = 0\n", + "$$\n", + "\n", + "En développant on a\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{\\partial J ({\\bf x}^{k+1})}{\\partial {\\bf x}^{k+1}} \\; \n", + "\\frac{\\partial {\\bf x}^{k+1}}{\\partial µ} & = 0 \\\\\n", + "J'({\\bf x}^{k+1}) \\, . \\, (- \\nabla J ({\\bf x}^k)) & = 0 \\\\\n", + "(A\\, {\\bf x}^{k+1} - b) \\, . \\, \\nabla J ({\\bf x}^k) & = 0 \\quad \\textrm{puisque A est symétrique}\\\\\n", + "\\nabla J ({\\bf x}^{k+1}) \\, . \\, \\nabla J ({\\bf x}^k) & = 0 \\quad \\textrm{CQFD}\n", + "\\end{align}\n", + "$$\n", + "\n", + "\n", + "\n", + "\n", + "
\n", + "\n", + "En utilisant cette propriété, évaluer la valeur optimale de µ pour atteindre le minimum dans la direction de\n", + "$\\nabla J ({\\bf x}^k)$.\n", + "\n", + "Écrire le méthode du gradient avec le calcul du µ optimal à chaque itération pour résoudre $A {\\bf x} = {\\bf b}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma60 M\303\251thode du gradient conjugu\303\251.ipynb" "b/PVCM/cama/fr/ma60 M\303\251thode du gradient conjugu\303\251.ipynb" new file mode 100644 index 0000000..7b01941 --- /dev/null +++ "b/PVCM/cama/fr/ma60 M\303\251thode du gradient conjugu\303\251.ipynb" @@ -0,0 +1,365 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "Cette leçon a 3 effets positifs :\n", + "\n", + "* manipuler des bases de sous-espaces\n", + "* mélanger les dérivées partielles et les vecteurs\n", + "* trouver un algorithme plus performant que la méthode du gradiant pour résoudre \n", + " $A \\, {\\bf x} = {\\bf b}$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "# Méthode du gradient conjugué\n", + "\n", + "On a vu que dans la méthode du gradiant on peut calculer le µ optimal pour\n", + "aller directement au minimum de la fonctionnelle $J$ dans le long de la ligne\n", + "${\\bf x}^k \\; + µ \\, \\nabla J({\\bf x}^k)$ avec µ qui varie de $- \\infty$\n", + "à $+ \\infty$ (cf ma33).\n", + "\n", + "On a aussi vu que si on a le µ optimal, alors la plus forte pente suivante, \n", + "$\\nabla J ({\\bf x}^{k+1})$, sera orthogonale à la pente qui définie la droite sur laquelle on cherche µ. On a donc\n", + "\n", + "$$\\nabla J ({\\bf x}^{k+1})^T \\, . \\, \\nabla J ({\\bf x}^k) = 0$$\n", + "\n", + "C'est bien car cela veut dire que le minimum suivant, ${\\bf x}^{k+2}$, sera le minimum de l'espace généré par $\\nabla J ({\\bf x}^{k+1})$ et $\\nabla J ({\\bf x}^k)$\n", + "(ce qui est mieux que d'être seulement le minimum le long d'une ligne). \n", + "\n", + "Malheureusement rien me dit que ${\\bf x}^{k+3}$ ne sera pas calulé le long de notre\n", + "première direction, $\\nabla J({\\bf x}^k)$. On a vu dans le cas\n", + "du gradiant sans recherche du µ optimal qu'on peut osciller entre 2 valeurs. Cela\n", + "n'est pas possible avec le µ optimal mais on peut tourner en rond sur quelques valeurs.\n", + "\n", + "Même si on ne tourne pas en rond et qu'on converge est il probable qu'on cherche\n", + "à nouveau un minimum dans une partie de l'espace $ℝ^n$ qu'on a déjà explorée.\n", + "\n", + "Une recherche optimal du minimum d'une fonction convexe dans un espace $ℝ^n$ ne\n", + "devrait pas prendre plus de $n$ itération si on est toujours capable de caluler\n", + "le µ optimal dans la direction choisie. Pour s'en convaincre il suffit de choisir\n", + "comme directions les vecteurs de la base de notre espace $ℝ^n$. Une fois qu'on\n", + "a trouvé le minimum dans toutes les directions de la base, on a le minimum global.\n", + "Il n'y a plus aucune direction possible de recherche qui ne serait pas la combinaison linéaire des vecteurs\n", + "déjà utilisés." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "#### Cas 2D\n", + "\n", + "
\n", + " \n", + "Si on cherche le point ${\\bf x} = (x_1, x_2)$ qui minimise $J({\\bf x})$ (convexe)\n", + "et qu'on sait calculer le µ optimal de notre méthode de gradient,\n", + "alors on trouve le minimum globale en 2 itérations au maximum.\n", + "\n", + "Mais on \n", + "prend un µ trop grand qui nous fasse passer au dessus du minimum\n", + "global, alors à la prochaine itération la plus grande pente sera exactement\n", + "l'opposée de celle qu'on vient d'utiliser et on oscillera.\n", + "\n", + "Sur le dessin on voit bien qu'on trouve le minimum global en 2 itérations\n", + "mais on se dit que c'est un coup de chance et d'ailleurs est-ce vraiment\n", + "en 2 itérations puisqu'il est écrit ${\\bf x}^k$ ? C'est toute la limite\n", + "d'un dessin qui veut expliquer ce qui se passe dans $ℝ^n$ à des humains\n", + "habitués à $ℝ^3$ (cf cette vidéo sur la 4e dimension en dehors\n", + "du cours).\n", + "\n", + "\n", + "\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## Générer une base de $ℝ^n$\n", + "\n", + "Si on veut trouver notre minimum global en $n$ itération au maximum, il faut que\n", + "nos directions ne soit pas redondante et donc que les $n$ premières directions\n", + "génèrent $ℝ^n$ ou forment une base de $ℝ^n$.\n", + "\n", + "Il faut donc que la nouvelle direction ${\\bf d}^k$ soit orthogonales à toutes les directions\n", + "précédentes ou qu'elle permette de trouver une base qui génère un\n", + "espace de dimension $k+1$ (on commence avec ${\\bf d}^0$).\n", + "\n", + "Est-ce possible ?\n", + "\n", + "### Le cas $A {\\bf x} = {\\bf b}$\n", + "\n", + "Dans ce cas la fonctionnelle à minimiser est\n", + "\n", + "$$\n", + "J({\\bf x}) = \\frac{1}{2} \\, {\\bf x}^T \\, A \\, {\\bf x} - {\\bf b}\\, . {\\bf x}\n", + "$$\n", + "\n", + "et son gradient est $\\nabla J({\\bf x}) = A \\; {\\bf x} - {\\bf b}$ si A est \n", + "symétrique.\n", + "\n", + "\n", + "On sait que si on calcule ${\\bf x}^k$ comme avant on a seulement d'orthogonalité\n", + "de deux directions successives. Cela arrive lorsque\n", + "µ est choisi pour minimiser $J$ le long de la droite de direction \n", + " $\\nabla J({\\bf x}^k)$.\n", + " \n", + "Que se passe-t-il si ${\\bf x}^{k+1}$ **minimise $J$ dans l'espace \n", + "${\\bf G_k}$ généré par\n", + "toutes les directions précédentes** ? \n", + "\n", + "$$\n", + "J({\\bf x}^{k+1}) = \\min_{\\bf v \\in G_k} J({\\bf x}^k + {\\bf v})\n", + "$$\n", + "avec ${\\bf G_k} = span\\{{\\bf d}^0, {\\bf d}^1,\\dots, {\\bf d}^k\\} \n", + " = \\left\\{ {\\bf v} = \\sum_{i=0}^{k} \\alpha_i \\, {\\bf d}^i \\quad \\forall \\alpha_i \\in ℝ \\right\\}$.\n", + "\n", + "Alors toutes les dérivées partielles par rapport aux vecteurs de ${\\bf G_k}$ \n", + "sont nulles (tout comme $\\partial J / \\partial x$ et $\\partial J / \\partial y$ \n", + "sont nulles au minumum de J dans le dessin ci-dessus). Vectoriellement\n", + "cela s'écrit ainsi :\n", + "\n", + "$$\n", + "\\nabla J({\\bf x}^{k+1}) \\, . \\, {\\bf w} = 0 \\quad \\forall {\\bf w} \\in {\\bf G_k} \\qquad (0)\n", + "$$\n", + "\n", + "ce qui se vérifie facilement si ${\\bf w}$ est un des vecteurs de la base :\n", + "\n", + "$$\n", + "\\nabla J({\\bf x}^{k+1}) \\, . \\, {\\bf e}_i = \n", + "\\begin{bmatrix}\n", + "\\partial J / \\partial x_{1} \\\\\n", + "\\partial J / \\partial x_{2} \\\\\n", + "\\vdots \\\\\n", + "\\partial J / \\partial x_{i} \\\\\n", + "\\vdots \\\\\n", + "\\partial J / \\partial x_{n} \\\\\n", + "\\end{bmatrix}\n", + "\\, . \\,\n", + "\\begin{bmatrix}\n", + "0 \\\\\n", + "0 \\\\\n", + "\\vdots \\\\\n", + "1 \\\\\n", + "\\vdots \\\\\n", + "0 \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\frac{\\partial J}{\\partial x_i}({\\bf x}^{k+1}) \n", + "$$\n", + "\n", + "On note que dire la dérivée partielle de $J$ dans une direction ${\\bf w}$\n", + "de ${\\bf G_k}$ est nulle,\n", + "revient à dire que $\\nabla J({\\bf x}^{k+1})$ est orthogonal à ${\\bf w}$ \n", + "(ou nul si $\\nabla J({\\bf x}^{k+1})$ la même dimension que ${\\bf G_k}$).\n", + "\n", + "#### Générons les directions ${\\bf d}^i$\n", + "\n", + "Ainsi notre formule itérative devient :\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = {\\bf x}^k + µ^k\\, {\\bf d}^k\n", + "$$\n", + "\n", + "Pour calculer les ${\\bf d}^k$ on utilise la formule qui nous dit que les\n", + "dérivées partielles de $J$ par rapport à un vecteur ${\\bf w \\in G_k}$ sont\n", + "nulles. Et comme les directions ${\\bf d}^i$ génèrent l'espace ${\\bf G_k}$\n", + "il suffit que les dérivées partielles de $J$ par rapport à tous les ${\\bf d}^i$\n", + "soient nulles :\n", + "\n", + "$$\n", + "\\nabla J({\\bf x}^{k+1}) \\, . \\, {\\bf d}^i = 0 \\quad \\forall i \\le k \\qquad (1)\n", + "$$\n", + "\n", + "On déroule les calculs\n", + "\n", + "$$\n", + "\\begin{align}\n", + "(A\\, {\\bf x}^{k+1} - b) \\, . \\, {\\bf d}^i &= 0 \\quad \\forall i \\le k \\\\\n", + "(A\\, ({\\bf x}^{k} + µ^k \\, {\\bf d}^k) - b) \\, . \\, {\\bf d}^i &= 0 \\quad \\forall i \\le k \\\\\n", + "(A\\, {\\bf x}^{k} - b) \\, . \\, {\\bf d}^i + µ^k \\, A \\, {\\bf d}^k \\, . \\, {\\bf d}^i &= 0 \\quad \\forall i \\le k \\\\\n", + "\\nabla J({\\bf x}^{k}) \\, . \\, {\\bf d}^i + µ^k \\, A \\, {\\bf d}^k \\, . \\, {\\bf d}^i &= 0 \\quad \\forall i \\le k \\\\\n", + "\\end{align}\n", + "$$\n", + "\n", + "Si $i < k$ alors le premier terme est nul ce qui donne\n", + "\n", + "$$\n", + "A \\, {\\bf d}^k \\, . \\, {\\bf d}^i = 0 \\quad \\forall i < k \\qquad (2)\n", + "$$\n", + "\n", + "Comme A est symétrique, on a aussi $A \\, {\\bf d}^i \\, . \\, {\\bf d}^k = 0 \\quad \\forall i < k\\quad$ ($\\sum_{m=1}^N \\sum_{n=1}^N a_{m,n}\\, d^i_n\\, d^k_m = \\sum_{n=1}^N \\sum_{m=1}^N a_{n,m}\\, d^k_m\\, d^i_n$). \n", + "\n", + "Ainsi on a des conditions pour construire la nouvelle direction ${\\bf d}^k$.\n", + "\n", + "On suppose que la nouvelle direction est le gradiant + une correction qui est une combinaison linéaire des directions précédantes :\n", + "$$\n", + "{\\bf d}^k = - \\nabla J({\\bf x}^k) + \\sum_{j=0}^{k-1} β_j {\\bf d}^j\n", + "$$\n", + "alors l'équation (2) devient\n", + "$$\n", + "A \\, \\left( - \\nabla J({\\bf x}^k) + \\sum_{j=0}^{k-1} β_j {\\bf d}^j \\right) . {\\bf d}^i = 0 \\quad \\forall i < k\n", + "$$\n", + "La somme va faire apparaître des $A\\, {\\bf d}^j {\\bf d}^i$ qui sont tous nul d'après (2) et sa version symétrique sauf $A\\, {\\bf d}^i {\\bf d}^i$. Donc\n", + "\n", + "$$\n", + "β_i = \\frac{A\\, \\nabla J({\\bf x}^k) \\, . \\, {\\bf d}^i}{A\\, {\\bf d}^i \\, . \\, {\\bf d}^i} \n", + "$$\n", + "\n", + "et ainsi\n", + "$$\n", + "{\\bf d}^k = - \\nabla J({\\bf x}^k) \n", + " + \\sum_{i=0}^{k-1} \\frac{A\\, \\nabla J({\\bf x}^k) \\, . \\, {\\bf d}^i}\n", + " {A\\, {\\bf d}^i \\, . \\, {\\bf d}^i} \\; {\\bf d}^i\n", + "$$ \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "## 2e tentative\n", + "\n", + "La méthode trouvée est bien car elle montre qu'on peut optimiser la descente de gradiant mais le calcul\n", + "de ${\\bf d}^k$ est bien trop lourd. Aussi on va tout recommencer pour trouver une autre facon plus efficace.\n", + "\n", + "### Travaillons dans la base des $\\nabla J({\\bf x}^i)$\n", + "\n", + "On repart de l'équation (0) qui permet de \n", + "montrer que les $\\nabla J({\\bf x}^i), i \\le k$ forment une bases du sous espace $\\bf G_k$. Aussi tout vecteur s'exprime dans cette base et donc\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = {\\bf x}^k + μ^k \\, {\\bf d}^k \\quad \\textrm{avec} \\quad {\\bf d}^k = - \\nabla J({\\bf x}^k) + \\sum_{i=0}^{k-1} γ^i \\, \\nabla J({\\bf x}^i)\n", + "$$\n", + "\n", + "On note que ces ${\\bf d}^i, i \\le k$ forment aussi une base de $\\bf G_k$.\n", + "\n", + "L'équation (2) nous dit que $A \\, {\\bf d}^k \\, . \\, {\\bf d}^i = 0 \\quad \\forall i < k$, aussi\n", + "\n", + "$$\n", + "\\begin{align}\n", + "< A \\, {\\bf d}^k, {\\bf x}^{j+1} - {\\bf x}^j > &= 0 \\quad \\forall j < k \\\\ \n", + "< {\\bf d}^k, A \\, ({\\bf x}^{j+1} - {\\bf x}^j) > &= 0 \\quad \\textrm{car A est symétrique} \\\\\n", + "< {\\bf d}^k, A \\, {\\bf x}^{j+1} - {\\bf b} - A {\\bf x}^j + {\\bf b} > &= 0 \\\\\n", + "< {\\bf d}^k, \\nabla J({\\bf x}^{j+1}) - \\nabla J({\\bf x}^j) > &= 0 \\\\\n", + "< - \\nabla J({\\bf x}^k) + \\sum_{i=0}^{k-1} γ^i \\, \\nabla J({\\bf x}^i) , \\nabla J({\\bf x}^{j+1}) - \\nabla J({\\bf x}^j) > &= 0 \\quad (3) \\\\\n", + "\\end{align}\n", + "$$\n", + "\n", + "Si j = k-1 alors\n", + "$$\n", + "\\begin{align}\n", + "< - \\nabla J({\\bf x}^k), \\nabla J({\\bf x}^k) > + \\, γ^{k-1} < \\nabla J({\\bf x}^{k-1}), -\\nabla J({\\bf x}^{k-1}) > &= 0 \\\\\n", + "γ^{k-1} = -\\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >}\n", + "\\end{align}\n", + "$$\n", + "\n", + "Si j = k-2 alors\n", + "$$\n", + "\\begin{align}\n", + "γ^{k-1} \\, < \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) > + \\, γ^{k-2} < \\nabla J({\\bf x}^{k-2}), -\\nabla J({\\bf x}^{k-2}) > &= 0 \\\\\n", + "γ^{k-2} = γ^{k-1} \\frac{< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >} \n", + " {< \\nabla J({\\bf x}^{k-2}), \\nabla J({\\bf x}^{k-2}) >}\n", + " = \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{k-2}), \\nabla J({\\bf x}^{k-2}) >}\n", + "\\end{align}\n", + "$$\n", + "et en continuant les calculs, on a $\\forall j < k-1$\n", + "$$\n", + " γ^j = \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{j}), \\nabla J({\\bf x}^{j}) >}\n", + "$$\n", + "\n", + "La formule générale de ${\\bf d}^k$ est donc\n", + "$$\n", + "\\begin{align}\n", + "{\\bf d}^k &= -\\nabla J({\\bf x}^k) \n", + " - \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >} \\, \\nabla J({\\bf x}^{k-1})\n", + " + \\sum_{i=0}^{k-2} \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{i}), \\nabla J({\\bf x}^{i}) >} \\, \\nabla J({\\bf x}^i) \\\\\n", + " &= -\\nabla J({\\bf x}^k) + β \\left( -\\nabla J({\\bf x}^{k-1}) \n", + " + \\sum_{i=0}^{k-2} \\frac{< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >} \n", + " {< \\nabla J({\\bf x}^{i}), \\nabla J({\\bf x}^{i}) >} \\, \\nabla J({\\bf x}^i) \\right) \\\\\n", + " &= -\\nabla J({\\bf x}^k) + β \\, {\\bf d}^{k-1} \\quad \\textrm{avec} \\quad β = \\frac{< \\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k}) >} \n", + " {< \\nabla J({\\bf x}^{k-1}), \\nabla J({\\bf x}^{k-1}) >} \n", + "\\end{align}\n", + "$$\n", + "\n", + "On a donc réussi à exprimer la nouvelle direction seulement en fonction du gradient courant et de la direction précédente." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "fr" + }, + "source": [ + "### Nouveau calcul de μ\n", + "\n", + "Le calcul précédent de μ reste valable puisque ce calcul ne dépend pas de la facon d'exprimer ${\\bf d}^k$.\n", + "\n", + "$$\n", + "µ^k = -\\frac{\\nabla J({\\bf x}^{k}) \\, . \\, {\\bf d}^k}\n", + " {A \\, {\\bf d}^k \\, . \\, {\\bf d}^k}\n", + "\\, \n", + "$$\n", + "\n", + "Avec notre choix de ${\\bf d}^k$ cela donne\n", + "\n", + "$$\n", + "µ^k = -\\frac{<\\nabla J({\\bf x}^{k}), - \\nabla J({\\bf x}^{k}) + β \\, {\\bf d}^{k-1}>}\n", + " {}\n", + " = \\frac{<\\nabla J({\\bf x}^{k}), \\nabla J({\\bf x}^{k})>}\n", + " {}\n", + "$$\n", + "puisque ${\\bf d}^{k-1} \\perp \\nabla J({\\bf x}^{k})$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma61 Syst\303\250me matriciel non lin\303\251aire.ipynb" "b/PVCM/cama/fr/ma61 Syst\303\250me matriciel non lin\303\251aire.ipynb" new file mode 100644 index 0000000..93e0001 --- /dev/null +++ "b/PVCM/cama/fr/ma61 Syst\303\250me matriciel non lin\303\251aire.ipynb" @@ -0,0 +1,502 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Système matriciel non linéaire\n", + "\n", + "Si la matrice A dépend de ${\\bf x}$, ce qu'on écrit $A({\\bf x})$, alors le système\n", + "matriciel \n", + "\n", + "$$\n", + "A({\\bf x}) \\, {\\bf x} = {\\bf b}\n", + "$$\n", + "\n", + "n'est pas linéaire.\n", + "\n", + "#### Exemple\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "1 & x_1 \\\\\n", + "2x_1 & -x_2 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_{1} \\\\\n", + "x_{2} \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "b_{1} \\\\\n", + "b_{2} \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "donne le système suivant qui n'est clairement pas linéaire puisqu'on a des\n", + "carrés :\n", + "\n", + "$$\n", + "\\begin{align}\n", + "x_1 + x_1 \\, x_2 &= b_1 \\\\\n", + "2 \\, x_1^2 - x_2^2 &= b_2 \n", + "\\end{align}\n", + "$$\n", + "\n", + "Comment résoudre un tel système ? A-t-il une solution ?\n", + "\n", + "On voit bien qu'il y a toujours autant d'équations que d'inconnues donc il y a\n", + "de l'espoir. Par contre on sait que les équations du 2e degré ont plusieurs solutions donc il devrait en être de même dans certains cas." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### La méthode du point fixe\n", + "\n", + "La méthode du point fixe consiste à appliquer l'algorithme itératif suivant :\n", + "\n", + "$$\n", + "{\\bf x}^{k+1} = {\\bf g}({\\bf x}^k)\n", + "$$\n", + "\n", + "dans le but de résoudre l'équation ${\\bf g}({\\bf x}) = {\\bf x}$.\n", + "\n", + "Si vous ne connaissez pas cette méthode voici un exemple d'utilisation en 1D avec\n", + "la courbe $g$ dessinée pour bien comprendre." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "image/jpeg": "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\n", + "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import YouTubeVideo\n", + "YouTubeVideo('ufPZOgrdHK4')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On voit (si on a regardé la vidéo), on sait (sinon) que suivant le point de départ, la méthode converge ou diverge.\n", + "\n", + "\n", + "Regardons comment on peut résoudre notre système non linéaire avec la méthode du point fixe." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### La méthode du point fixe pour résoudre $A({\\bf x}) \\, {\\bf x} = {\\bf b}$\n", + "\n", + "La première chose est de définir la fonction $\\bf g$ telle que la solution de \n", + "${\\bf g}({\\bf x}) = {\\bf x}$ soit aussi la solution du système matriciel non linéaire.\n", + "Cela implique que ${\\bf g}$ est :\n", + "\n", + "$$\n", + "{\\bf g}({\\bf x}) = A^{-1}({\\bf x}) \\, {\\bf b}\n", + "$$\n", + "\n", + "Bien sûr on sait qu'inverser A est trop cher aussi on préfère écrire notre\n", + "algorithme itératif ${\\bf x^{k+1}} = {\\bf g}({\\bf x^k})$ sous forme de problème matriciel linéaire à résoudre :\n", + "\n", + "$$\n", + "A({\\bf x}^k) \\, {\\bf x}^{k+1} = {\\bf b}\n", + "$$\n", + "\n", + "Si on connait ${\\bf x}^k$ alors on peut évaluer $A({\\bf x}^k)$ et donc il\n", + "s'agit d'une matrice de réels. On voit qu'alors le système est bien linéaire\n", + "et qu'il permet de trouver ${\\bf x}^{k+1}$.\n", + "\n", + "Cet algorithme itératif peut donc marcher mais on sent bien que cela va\n", + "dépendre du type de la matrice A (on a l'habitude) et de la valeur initiale\n", + "${\\bf x}^0$ comme souligné dans la vidéo. De plus on voit qu'il va être\n", + "très cher puisqu'on a un système matriciel à résoudre à chaque itération !" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Test\n", + "\n", + "Regardons comment marche cet algorithme pour résoudre\n", + "\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "x_0 - 2 x_1 & x_1 \\\\\n", + "x_0 & 2 x_0 + x_1 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_0 \\\\\n", + "x_1 \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "1 \\\\\n", + "9 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Il y a deux solutions qui sont [1, 2] et [2, 1]." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x^1 = [1.5 2.5] erreur² = 0.48999999999999977\n", + "x^2 = [0.73913043 1.43478261] erreur² = 0.18534274820344412\n", + "x^3 = [1.37617066 2.74037461] erreur² = 0.6387945198307682\n", + "x^4 = [0.72846505 1.45602065] erreur² = 0.18097695808599654\n", + "x^5 = [1.37323934 2.74623359] erreur² = 0.6430523663786714\n", + "x^6 = [0.72824232 1.45646606] erreur² = 0.1808855461166179\n", + "x^7 = [1.37317932 2.74635363] erreur² = 0.6431399506048754\n", + "x^8 = [0.72823777 1.45647516] erreur² = 0.1808836795920618\n", + "x^9 = [1.37317809 2.74635608] erreur² = 0.6431417383272344\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "\n", + "def A(x):\n", + " return np.array([[x[0] - 2*x[1], x[1]] ,\n", + " [x[0] , x[1] + 2*x[0]]]) / 10 \n", + "\n", + "b = np.array([1, 9]) / 10 # avec normalisation grossière\n", + "\n", + "x = np.array([1, 1])\n", + "for i in range(1, 10):\n", + " x = lin.solve(A(x), b)\n", + " print(f'x^{i} = ', x, end=' ')\n", + " print(f'erreur² = ', np.square(A(x) @ x - b).sum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "La solution oscille sans converger. On peut tester d'autre ${\\bf x}^0$ \n", + "mais on obtient souvent le même résultat.\n", + "\n", + "La méthode du point fixe de base a un petit rayon de convergence à savoir il\n", + "faut que la valeur initial soit proche de la solution pour converger.\n", + "\n", + "### Appliquons l'inertie\n", + "\n", + "Ou la méthode de surrelaxation qui consite à avancer moins vite vers le prochain\n", + "point." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x^1 = [1.99601592 1.00199403] erreur² = 2.845730924209918e-06\n", + "x^2 = [1.98435526 1.00784963] erreur² = 4.338186795289511e-05\n", + "x^3 = [1.94167764 1.02955991] erreur² = 0.00057735040271093\n", + "x^4 = [1.81575881 1.09680461] erreur² = 0.005006527863139465\n", + "x^5 = [1.58849624 1.23874527] erreur² = 0.017837680043912996\n", + "x^6 = [1.3654867 1.43296028] erreur² = 0.023567622207356913\n", + "x^7 = [1.21494033 1.62266463] erreur² = 0.015938576382362332\n", + "x^8 = [1.12471347 1.76667765] erreur² = 0.007550226984782101\n", + "x^9 = [1.07194609 1.86111664] erreur² = 0.0030000984268709436\n" + ] + } + ], + "source": [ + "µ = 0.5 # j'avance de moitié vers le prochain x\n", + "\n", + "x = np.array([1.998, 1])\n", + "for i in range(1, 10):\n", + " x_old = x\n", + " x = lin.solve(A(x), b)\n", + " x = µ * x + (1-µ) * x_old\n", + " print(f'x^{i} = ', x, end=' ')\n", + " print(f'erreur² = ', np.square(A(x) @ x - b).sum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Et là la convergence est rapide. L'inertie augmente significativement le rayon\n", + "de convergence de la méthode du point fixe (plus µ est petit et plus le rayon\n", + "de convergence est grand mais moins on avance vite).\n", + "\n", + "Bien sûr l'algorithme converge vers l'une des solutions et y reste. Il ne peut\n", + "pas trouver toutes les solutions. Si on veut trouver au autre solution il y\n", + "faut choisir un autre point initial et avoir de la chance d'être dans le \n", + "rayon de convergence de cette autre solution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## La méthode de Newton-Raphson\n", + "\n", + "Il s'agit d'appliquer la méthode de Newton pour une fonction vectorielle.\n", + "\n", + "Voici une vidéo qui rappelle ce qu'est la méthode de Newton pour une fonction\n", + "en 1D. Vous pouvez vous arrêter à la 4e minute." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/jpeg": "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\n", + "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import YouTubeVideo\n", + "YouTubeVideo('h0XUxE47l00')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dans notre cas on veut toujours résoudre notre système matriciel non linéaire.\n", + "\n", + "On va donc définir la méthode itérative par analogie avec la méthode 1D. En 1D on a :\n", + "\n", + "$$\n", + "x^{k+1} = x^k - \\frac{f(x^k)}{f'(x^k)} \\quad \\textrm{ou bien} \\\\\n", + "f'(x^k) \\; (x^{k+1} - x^k) = - f(x^k)\n", + "$$\n", + " \n", + "Cela donne en $n$ dimensions :\n", + "\n", + "$$\n", + "J_{\\bf f}({\\bf x}^k) \\; ({\\bf x}^{k+1} - {\\bf x}^k) = - {\\bf f}({\\bf x}^k)\n", + "$$\n", + "\n", + "avec $J_{\\bf f}$ la matrice Jacobienne de ${\\bf f}$ :\n", + "\n", + "$$\n", + "J_{\\bf f}\\left({\\bf x}\\right)=\n", + "\\begin{pmatrix} \n", + "\\dfrac{\\partial f_1}{\\partial x_1} & \\cdots & \\dfrac{\\partial f_1}{\\partial x_n} \\\\\n", + "\\vdots & \\ddots & \\vdots \\\\\n", + "\\dfrac{\\partial f_n}{\\partial x_1} & \\cdots & \\dfrac{\\partial f_n}{\\partial x_n}\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "et pour notre système non linéaire\n", + "\n", + "$$\n", + "{\\bf f}({\\bf x}) = A({\\bf x})\\, {\\bf x} - {\\bf b}\n", + "$$\n", + "\n", + "On notera que ${\\bf f}$ est une fonction vectorielle à savoir qu'elle retourne\n", + "un vecteur." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Test\n", + "\n", + "On reprend le même système matriciel :\n", + "\n", + "$$\n", + "\\begin{bmatrix}\n", + "x_0 - 2 x_1 & x_1 \\\\\n", + "x_0 & 2 x_0 + x_1 \\\\\n", + "\\end{bmatrix}\n", + "\\;\n", + "\\begin{bmatrix}\n", + "x_0 \\\\\n", + "x_1 \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "1 \\\\\n", + "9 \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "La matrice Jacobienne de la fonction ${\\bf f}$ définie ci-dessus est : \n", + "\n", + "$$\n", + "J_{\\bf f}({\\bf x}) = \n", + "\\begin{bmatrix}\n", + "2 x_0 - 2 x_1 & 2 x_1 - 2 x_0\\\\\n", + "2 x_0 + 2 x_1 & 2 x_0 + 2 x_1 \\\\\n", + "\\end{bmatrix}\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x^0 = [0.80714286 1.40214286] erreur² = 0.1738391124362817\n", + "x^1 = [0.82661178 1.47589539] erreur² = 0.14013193945500102\n", + "x^2 = [0.84449678 1.53832416] erreur² = 0.11305725653981773\n", + "x^3 = [0.86066582 1.59186587] erreur² = 0.09127299702681221\n", + "x^4 = [0.87518409 1.63820488] erreur² = 0.07372379277598218\n", + "x^5 = [0.88818095 1.67857971] erreur² = 0.0595731611254003\n", + "x^6 = [0.89980142 1.71393945] erreur² = 0.04815469077192336\n", + "x^7 = [0.91018754 1.74503332] erreur² = 0.038935573039892035\n", + "x^8 = [0.91947123 1.77246602] erreur² = 0.03148872349291875\n", + "x^9 = [0.92777209 1.79673415] erreur² = 0.025471148220392294\n", + "x^10 = [0.9351973 1.81825117] erreur² = 0.020606983474307096\n", + "x^11 = [0.94184231 1.83736516] erreur² = 0.01667410290306686\n", + "x^12 = [0.94779187 1.85437189] erreur² = 0.013493486464829903\n", + "x^13 = [0.9531212 1.86952455] erreur² = 0.010920748632859209\n", + "x^14 = [0.95789703 1.88304134] erreur² = 0.00883936731257032\n", + "x^15 = [0.96217855 1.89511126] erreur² = 0.007155259635295223\n", + "x^16 = [0.96601835 1.90589887] erreur² = 0.005792428863449946\n", + "x^17 = [0.96946319 1.91554793] erreur² = 0.0046894658536456735\n", + "x^18 = [0.97255463 1.92418452] erreur² = 0.003796734034536249\n", + "x^19 = [0.97532973 1.93191956] erreur² = 0.0030741021940233564\n", + "x^20 = [0.97782148 1.93885083] erreur² = 0.0024891170269789866\n", + "x^21 = [0.98005934 1.94506477] erreur² = 0.002015529173331623\n", + "x^22 = [0.9820696 1.95063793] erreur² = 0.0016321037099287408\n", + "x^23 = [0.98387574 1.95563824] erreur² = 0.0013216597493956443\n", + "x^24 = [0.98549877 1.96012605] erreur² = 0.0010702947077985679\n", + "x^25 = [0.98695747 1.96415505] erreur² = 0.0008667575172292292\n", + "x^26 = [0.98826867 1.96777309] erreur² = 0.0007019420351895113\n", + "x^27 = [0.98944742 1.97102285] erreur² = 0.0005684774962019743\n", + "x^28 = [0.99050723 1.9739424 ] erreur² = 0.0004603973426083823\n", + "x^29 = [0.99146019 1.9765658 ] erreur² = 0.0003728713824135844\n" + ] + } + ], + "source": [ + "def f(x):\n", + " return A(x) @ x - b\n", + "\n", + "def J_f(x):\n", + " return 2 * np.array([[x[0] - x[1], x[1] - x[0]],\n", + " [x[0] + x[1], x[0] + x[1]]])\n", + "\n", + "x = np.array([1, 1.1])\n", + "for i in range(30):\n", + " delta = lin.solve(J_f(x), -f(x))\n", + " x = x + delta\n", + " print(f'x^{i} = ', x, end=' ')\n", + " print(f'erreur² = ', np.square(A(x) @ x - b).sum())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On converge alors que la méthode du point fixe oscille \n", + "sans convreger pour cette valeur initiale.\n", + "\n", + "On converge néanmoins moins vite qu'avec la méthode du point fixe sur-relaxée.\n", + "\n", + "**Remarques** sur la méthode de Newton-Raphson\n", + "\n", + "* Le coût de construction de la matrice Jacobienne peut être très lourd\n", + "* Une technique pour aller plus vite consiste à dire que d'une itération à une\n", + " autre on n'a pas beaucoup bougé et donc la matrice Jacobienne n'a pas du trop \n", + " changer. Aussi on recalcule cette matrice que toutes les 3 ou plus itérations\n", + "* Il s'agit d'une matrice pleine qu'il rend plus compliqué la résolution du système\n", + " lors de l'iteration (une méthode de gradiant ne marchera pas en général)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git "a/PVCM/cama/fr/ma62 Gradient conjugu\303\251 -- Exercice.ipynb" "b/PVCM/cama/fr/ma62 Gradient conjugu\303\251 -- Exercice.ipynb" new file mode 100644 index 0000000..0bca368 --- /dev/null +++ "b/PVCM/cama/fr/ma62 Gradient conjugu\303\251 -- Exercice.ipynb" @@ -0,0 +1,409 @@ +{ + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Programmer le gradient conjugué\n", + "\n", + "A partir de ce [cours sur le gradient conjugué](http://perso.unifr.ch/ales.janka/numeroptim/07_conjgrad.pdf) programmez en Python + Numpy le gradient conjugué en exploitant les astuces mathématiques indiquées pour optimiser\n", + "votre code.\n", + "\n", + "* Effectuez des tests pour valider votre code. \n", + "* Comparez la vitesse de convergence à celle du gradient avec μ optimal. Tracez des courbes de convergence (cf la feuille qui en parle)\n", + "* Comparez les temps de calcul.\n", + "\n", + "\n", + "Note : Veuillez écrire des fonctions les plus propres possibles, en particulier qui n'utilisent pas des variables globales comme c'est le cas dans ma correction du gradient (ma33)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.linalg as lin\n", + "import matplotlib.pylab as plt\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def make_system(N):\n", + " A = 1.0 * np.random.randint(-10, 10, size=(N,N))\n", + " A[np.diag_indices(N)] = 0.1 + np.abs(A).sum(axis=0) # diag dominante\n", + " A = A + A.T # symétrique\n", + " A = A / np.abs(A).sum(axis=0).mean()\n", + " b = 1.0 * np.random.randint(-10,10,size=(N))\n", + " return A, b\n", + "\n", + "A, b = make_system(2)\n", + "print(A, \"\\n\\n\", b)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def gradient_conjugué(A, x0, b, error=1E-9, convergence=False):\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# vérfions que ca marche\n", + "\n", + "# combien faut-il d'itérations\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_error(N, method=gradient_conjugué):\n", + " A, b = make_system(N)\n", + " x = method(A, np.zeros(N), b)\n", + " err = A @ x - b\n", + " return np.sqrt(err @ err)\n", + "\n", + "compute_error(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparons avec le gradient simple" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def gradient(A, x0, b, e = 1E-9, convergence=False, max_iterations=1000):\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# vérifions que ca marche\n", + "\n", + "compute_error(10, method=gradient)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Perfs" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# comparons les performances\n", + "\n", + "seed = 123\n", + "np.random.seed(seed)\n", + "\n", + "%timeit compute_error(1000, method=gradient)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "seed = 123\n", + "np.random.seed(seed)\n", + "\n", + "%timeit compute_error(1000, method=gradient_conjugué)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Nombre d'iteration dans les 2 cas\n", + "\n", + "On teste avec N=1000 puis N=10000." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "N = 1000\n", + "A,b = make_system(N)\n", + "x0 = np.zeros(N)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Pour le gradient simple" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "err = gradient(A, x0, b, convergence=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#plot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Pour le gradient conjugué" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "err = gradient_conjugué(A, x0, b, convergence=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#plot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Un cas réel\n", + "\n", + "Logiquement vous devriez être décu aussi on va tester avec un problème réel qui correspond à cet exemple\n", + "de l'[équation de Poisson](https://doc.freefem.org/tutorials/poisson.html). Le système matriciel de ce problème est téléchargeable \n", + "[ici](https://www.lrde.epita.fr/~ricou/cama/data/Ab.npz). Une fois le fichier sauvé, pour récupérer\n", + "A et b faites :\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "npz = np.load('/tmp/Ab.npz',allow_pickle=True)\n", + "A = npz['A']\n", + "b = npz['b']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Faites une étude rapide de A, indiquez quel pourcentage des valeurs de A est différent de 0. Afficher l'image de la matrice avec `plt.imshow(A)` (faire une grande image pour voir quelque chose).\n", + "* Refaites la comparaison entre les deux méthodes avec ce système matriciel.\n", + "* Regardez la documentation de `lin.solve` (en particulier les options) et comparer `lin.solve` à vos deux algorithmes." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparaison gradient simple et conjugué" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%time err = gradient_conjugué(A, np.zeros(len(A)), b, convergence=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#plot" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# le gradient simple\n", + "\n", + "%time err = gradient(A, np.zeros(len(A)), b, convergence=True, max_iterations=10000)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On voit la supériorité du gradient conjugué tant en nombre d'itérations (175 contre 7800) qu'en temps de calcul (environ 40 fois plus rapide)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparaison avec `lin.solve` de Scipy\n", + "\n", + "Le solveur de Scipy a des option que celui de Numpy n'a pas." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# regarder la doc pour avoir les options optimales\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# calculer le résidu\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On note aussi `lin.solve` est plus rapide et sa solution est nettement meilleure... `lin.solve` utilise une méthode directe ici. Cela est dû au fait que Scipy utilise la bibliothèque Lapack (qui est imbatable)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Le gradient conjugué de Scipy (avec Lapack)\n", + "\n", + "Le gradient conjugué à tout son sens pour les matrices creuses aussi il est dans la partie \"sparse\" de Scipy.\n", + "On a vu que notre matrice à plus de 99 % de valeur nulles ce qui en fait bien une matrice creuse. Aussi je\n", + "la charge dans le format COO (téléchargez __[Acoo.npz](https://www.lrde.epita.fr/~ricou/cama/data/Acoo.npz)__) qui ne stocke que les valeurs non nulles et" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import scipy.sparse as sparse\n", + "from scipy.sparse.linalg import cg\n", + "\n", + "Ac = sparse.load_npz('/tmp/Acoo.npz')\n", + "%time x = cg(Ac, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On gagne un ordre de grandeur." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ] +} \ No newline at end of file diff --git a/PVCM/notebooks_cama.tgz b/PVCM/notebooks_cama.tgz new file mode 100755 index 0000000..79741a2 Binary files /dev/null and b/PVCM/notebooks_cama.tgz differ -- cgit v1.2.3