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{
"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-v0_8-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": [
{
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"config": {
"linkText": "Export to plot.ly",
"plotlyServerURL": "https://plot.ly",
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{
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"shape": "100, 100"
},
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"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. 0.001] La valeur de J en ce point est 2.0000003976868665\n"
]
}
],
"source": [
"# Algo du gradient pour trouver le minimum\n",
"\n",
"x = np.array([34,78]) # 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": [
"[<matplotlib.lines.Line2D at 0x28e1825fb10>]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
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/1RUxdd66+PnTi9P3o/t0jImjesZ1bx+TlfkCAAAAAPAmwQ20QL/5xElpeJNU3iRLrK3btjtOGpq52mZPSVm8uHjjfm2zV22Nzm0LsjhbAAAAAAAqCG6gBS6tNqxnh/T4wImHpRU4C9Zuj8K83IzXvrZsU+wsLq3T3ji7iktjd3FZdG4n5AEAAAAAqCvBDbSCIGd4rw416lvdEms1DW6enLcuPn7nizGmT6e0f1Lhc+KQ7oIcAAAAAIBaENwA++nRoTDWbdtT+b4wPzfGD+qS8bpnFq6P8vKImSu3pMdPn1oUOTkRj3x+YgztWbPgCAAAAACgtRPcAJU+87YRccUZw2PB2m3p3jjJHjnlUR5tCvLqVK3TpW1BDO7ePkuzBQAAAABoeQQ3QDVLq3VMjw+dPLhG12zeUZxW2bxVslRabm5OxutvenhuHNGvcxw/pFt0bmtpNQAAAACg9RLcAPX2/OIN6TJpb5Xsc5PJ0g074qaH56XnScYztl/n9Lp3jx8Qh/frlI3pAgAAAAA0WbmNPQGg+Tuif6f45gVj4x3j+kS39oWV7ScN616jvXEqlJVHTF++Of5v6qKYt2Zr1uYLAAAAANBUqbgB6q1v57bx4ZMHp0dZWXnMW7MtrcIZ2atjnfbGSZw0NHPok9yrJkuxAQAAAAA0F4IboEElQcqoPh3TI5Py8vJ4buGGKu1De7SP3p3aZLz+k3e9FGu27EpDnuQ4bnDX6NjGHjkAAAAAQPMluAEazcYdxbFjT0mV9hNrUG1TWlYezy5YH1t3l8SryzbH7U8sTPfIufjYgXHDe4/M0owBAAAAALJLcAM0mmQ/nJe+enbMXbM1DWGS/W6eW7QhThraLeO1M1ZsTkObfSV75HTv8OYeOwAAAAAAzY3gBmj0pdVG9+mUHh85dUi6b01peXlW98ZZsHZbLNmwI44f3C06FHkMAgAAAABNh3+xBJpckJMbORn7PVvN3jj5uTlx7GFdM177h5eWxf9OWRB5uTkxrn/nf+6R0y0mDO8R+Xm5dZ47AAAAAEB9+RdKoFk6+/Decc7hvaNz24LKtiMHdI72NaigSZZkq9gnZ9rSTXHb4wvis79+JXJyMgdGAAAAAADZpOIGaJbef8Kg9EiWVpu9amsaxnRr/2aIcyDbd5fEa8s2V2k/YUi3tAIHAAAAAKAxCW6AZr+02uH9OqVHTbz4xsa00qYue+Os2rwrPv2rl/65tFr3dFm2mlT4AAAAAADUlH9xBFqVFxdX3RunpsHNc4vWx8tLNqVHskdOsqdOsjzbN951RIwb0DkLswUAAAAAWhvBDdCqXH3WyDh3bJ94duH69Hhu0d4gpyYVO0n/fZWUlachTpd2mZdoAwAAAACoCcEN0Kok+9gc0b9zenzstKHpsmnLNu6o0f42zy6sWq3Tv0vbGNitXcZrZ63cEod1bxftCj12AQAAAIAD8y+IQKuWBDaHdW9fo/1tFq3bXqcl1srKyuOy/3s2tu0uiaMGdKncI+eYw7oIcgAAAACA/eTu/xaA6iShy5mje0XHov2DlpOGdst47dw1W2PjjuIoLi2PF9/YGD98bH588I7n4n/+MTeLMwYAAAAAmiNf9QaogeG9OsQdHzk+XVptxorN/9wjZ0OcPCxzxc2zC/bfG6c21ToAAAAAQOsiuAGo5dJqRw7okh6fOH1Yja6pbm+cnJyI44dkrtb5/UvLYsn67WnIM35Q12hbmFeneQMAAAAAzYPgBiCLkv1tnltUteJmbL9O0bltQcbrf/fi0nhu0Yb4waPzozAvN44e2CUmjuoZV5wxPEszBgAAAAAakz1uALLs5/96Qlz39tExaVTPaP/PipmThmReJm1XcWm8snRT5fs9pWXx/OIN6TJtAAAAAEDLpOIGIItyc3PiqIFd0uOTE4dFSWlZvL5iS42qbV5Zsin2lJTVaW+c3SWlUV4e0abA0moAAAAA0JwIbgAOofx/LndWEweqrDlpaOa9cR6dtSauumdajB/YJQ169u6R00WQAwAAAABNnOAGoInaXVIW7QrzYsee0sq2tgV5Ma5/5uDnmYXr02qdZH+c5Lj5kXlRmJ8bj31hUvTv0jbLMwcAAAAA6kpwA9BEffnto+Oac0bG9OWb0+qbZxduiLYFuWkAU5dqnWR5tn6d22RptgAAAABAQxDcADRhBXm5ccygrunx6Uk1u2bdtt0xd/W2Ku3Jcmk5OTkHvba8vDxuf2JhusRasi+PpdUAAAAA4NAS3AC0MM8v2lDnvXEWrdse3/377PS8KH9vaJQEPucd1TeG9ewQ2fLC4g1x/OBuTXY8AAAAADhUMq+3A0CzcnjfTvHFc0fFaSN6pHviVEgCmJrsjbPvHjvJ+xsfnhtzVm3N2nxvfGhuXHzbM3HrlAUNMl4yTjJeMi4AAAAANDcqbgBamME92scVZwxPjz0lZTF9+aZ4+Y1NMbRH+4zXJvvoVOeEIZmrV5Jl1jItxVZdZczNj8xLz294YG+lz+WThkV9QpuKcZJxJ4zoofIGAAAAgGZFcAPQghXm58axh3VLj5oEL8/uU3FTYWTvDtGjQ1HG6z9550uxfU9JnDSke5w0rHscOaBzFOUffI+cJFS5dvLoyrClPuHNvqFNIhlXaAMAAABAcyO4ASC1asuu2LqruEp7TZZYKy4ti6nz1sXO4tJ4av76iIci2hTkxgdPPCy+et7hB722IqSpT3hTXWhTn8odAAAAAGgsghsAUn07t43Xrj83Xl22KZ5dsD6eXbQ+Xly8MU6uQXDz2rJNaWizr13FZdG+qGb/N1Of8EZoAwAAAEBLIrgBYL+l1ZLlxZLjszEidpfsH8bUdm+cmlTrLFy7LTbu2BMfnTCk1uGN0AYAAACAlkZwA8ABZdqjpkJ1e+MkIdD4QV0yXnv380vi/6YuirYFeXHc4K5x+oge8cS8delnFaHMR08ZWOU6oQ0AAAAALZHgBoB6O21EjygtK4+X3tgYu0vK0rbxA7tEm4LMwc8z/wx9kqXWkn1yEm0LcmNn8d5xknCmtLQkTt4nAxLaAAAAANBSCW4AqLdPnD4sPXYVl8arSzelS6cN6No243WbdxbHjBVbqrRPHNkrjhrYpTKc+f5D8+OD4zrEu0d3iB9PXZS+ryC0AQAAAKAlEdwA0GCSCpsTh3ZPj5p4YdGGKC+v2n7S0G7xkVP33/Pmrunb4r4522PbnlWV/ZKqnuG9OsS23SXRocj/pQEAAADQ/PlXLgAazXOLqu6Nkzhp2N7gp6KSpiK82bbnzZTngqP7xZ+mrYiP//LFKMjLieMO6xYTR/WMi47pH706tjkk8wcAAACAhpbb4CMCQA1dc86ouPvjJ8VVZ46IE4d0i8K83OjariBG9upY2ScJb7q0Ldjvui7tCqIo/83/CysuLU/3yvnu32fHlp3Fh/RnAAAAAICGpOIGgEZdWu3kYd3TI5HskfPG+h2Rm5tT2efWKQti01vCmE07iuNv01dWGa9/l7YxrGeHQzBzAAAAAMgOFTcANKkgZ1SfjvuFNhXLpCU6FL4Z6GzbXVrl+tNH9oycnDf7VKe8vDyu/9Pr8cdXlsW6bbsbbO4AAAAA0BBU3ADQJL01tPnguA7x7tEd4plNHeL7D82v9ppJo3pmHHfB2m3xi2feSI8k4xnXv3NMHNkzLhzfX7UOAAAAAI1OcANAkw9tvnD28Di5y7b0/BOnDYm8vPz9Ph/YtW2s3bY7TvnnkmsHM2XO2srz8vKI15ZtTo/RfToJbgAAAABodJZKA6BJhzbXTh6dhjX7unzSsLS9wtKNO+OKScOjY5uCjOM/PvfN4KZCsqXOhOE96j13AAAAAKgvwQ0ATTq0SUKa6rw1vPnvh+am1x/Mzj2l8dyiDVXajxnUNTq3yxz63PzwvLjz2Tdi6YYdGfsCAAAAQF1YKg2AZhfaVKj4vOK6itcDXbd8047o36VtLFq3fb/2ZI+bTHYVl8atj8+PXcVl6fuhPdrH6SN7xvlH9YtjD+ua8XoAAAAAqAnBDQDNMrSpS3gzvFfHeOwLk+KN9dvjiblr0/1unl6wPiaOyhzcJJU6FaFNYuG67enRpV2B4AYAAACABiO4AaDZhjZ1rbw5rHv7+NDJyTE4dpeURkFu5pVDH59TdW+cmlbrAAAAAEBN2eMGgEbzwuIN9Q5tDrTnTTJuMn4mRfl5kZubk7Hf43PXVGlLqm2OHNAl47W/fm5JGlDNXLElysvLM/YHAAAAoPVScQNAozl+cLe46swRcfMj8+oV2lRXeZOMm4zfELbvLol2hVX/L/O0ET0jrwahzy+eXhxzVm9N59WrY1G6N865Y/vE2Yf3bpD5AQAAANByCG4AaFSfO3tkTBjRo8FCliS8OW5w1wYbL9G+KD/u/+yEWLdtd0ydtzZdNu2JeetiUg2WSVu5eWca2lRYs3V3/P6lZbFjT4ngBgAAAIAqBDcANLqGDFmyMV6FHh2K4t3jB6RHWVl5lJRlXvbsibn2xgEAAACg5gQ3AFAHyb44hTVYJm3KnOqDm2S5tEwenb06XnpjY0wa1SvGD+wS+Xm2pgMAAABo6QQ3AJBFpWXlUZCXE8Wlb1bnjO7TMfp2bpvx2ntfXh5/eW1l/OixBdGxTX6cOqxHTBzVMy49fmDk5GQOjQAAAABofgQ3AJBFP/7wcbFtd0k8PX9dPD53bVqBU5Nl0kpKy2LqvHWV77fuKokHZqyKBWu3xftPGJTlWQMAAADQWAQ3AJBlHYry45yxfdKjvLw89pSWZbzm1WWbY/PO4irt9sYBAAAAaNkslg8Ah1CyxFlRfl7Gfkl1TnWSpdIymbVyS1z/p9fTPXJ27imt0zwBAAAAaBwqbgCgCdpTUhbtC/Ni+z7BS5uC3Dh+cLeM1z40c3X84pk30qMwPzdOHNItrdS59IRBafUPAAAAAE2Xf70BgCboy28fHZ8/e2S8+MaGtPrm8Tlro1+XttGmoHbVOkkAlOyV89yiDfGBEw/L8qwBAAAAqC/BDQA0UUm1zCnDeqTHdW8fk4YwmWzeURyvLNlYpT2pumlbmDn0AQAAAKBx2eMGAJpRkJPJk/PXRVl51fZkqbRMtuwqjmt++2r8+dUVsXH7nrpOEwAAAIB6UHEDAC3I1l3F0b19Yax/S/AyaVSvjNc+PX9d/OHlZemRmxNx1MAuaeBzyfEDo2/ntlmcNQAAAAAVBDcA0IJcesKgeN9xA2PGii3x+Nw1MWXO2li7bXcM69m+VnvjJFU7ryzZlB5vP6Jv9O2c5YkDAAAAkBLcAEALk5ubE+MGdE6Pz7xtRLo3Tk5OzkGvKS8vj8fnvBncVOjbuU2M7N0hi7MFAAAAYF/2uAGAFq4me+PMW7MtVmzeVaU9WSqtJqHPdfe+Fr9+bkks37SzXnMFAAAAaO1U3AAAsWbL7hjQtW0s27izSnCTycJ12+Pu55fG3bE0fT+8V4f0uvceOyDG9O2UtTkDAAAAtESCGwAgJozoEVO/dEYsWrc93esmOV5cvDFOGd4j47VvXWJt/ppt6XH0wC6CGwAAAIBaEtwAAKlkSbShPTukx7+eOiSKS8uiIC/zMmtJyPNWuTkRE2oQ+gAAAACwP8ENAFCtmoQ2u4pL49mF66u0HzWwS3RtX5jx+v/5x5zo2KYgJo7qGSN6dci4nw4AAABASye4AQDqbNXmXWmFzqyVW2q9N04S+vzf1EWxs7g0vv23WdG3c5v0uncd3S9OGaZaBwAAAGidBDcAQJ0N7tE+/n7VabF6y6544p9740ydty4mjeqV8dpkD50ktKmwcvOu+M0LS6NXxyLBDQAAANBqCW4AgHrr3alNXHzcwPQoLSuPmix49vjcNdW2J8umAQAAALRWghsAoEHl5dZsn5qkOuetOrXJj6MGdMl47Z3PvhFrt+xKQ56kf34N9uMBAAAAaA4ENwDAIZfsb9OlbWEa8iQVOhVOG9mzRiHMr559I2av2ho/eHR+dG5bEBNG9Ihzx/aJdx3VL8szBwAAAMguwQ0AcMi1KciL337q5Ni8szienr8urb5JjokjMy+Tluynk4Q2FZIx/vrayigtLRfcAAAAAM2e4AYAaDRJtczbx/VNj/Ly8v2qb2qzxFrC3jgAAABASyC4AQCahJycnMjPy6lzcHN6Dap1Hpm1Op6avz4NeU4c0i2t/AEAAABoSgQ3AECzUpiXG20KcmNXcVll24heHaJ/l7YZr/3zqyviT9NWxE+fWpSOcdLQ7unybP9y8uDIzc0cGgEAAABkm+AGAGhWbrzk6PjPi8bFi4s3xpQ5a2q8N06yDNsT+1TrJMHPlDlrY8mGHfGvpw7J8qwBAAAAakZwAwA0O8kSZxNG9EiPr0ZESemb1TcH8vryzbFxR3GV9pqEPgAAAACHSu4huxMAQJbk5+XWeW+cmgQ3s1dtiS/9/tX462srY3M14Q8AAABAQ1FxAwC0CuXlEV3aFcSmfYKXovy9+9xk8sisNfHbF5elR7IVzvhBXWPSyJ7x4VMGR+e2BVmeOQAAANCaCG4AgFbhqrNGxGfeNjxeW7Yprb5Jji5tC9Jl1zJJ9tKpUFYe8dIbG2P6ss3x0dPsjQMAAAA0LMENANBq5OXmpNUyyXH1WSOjNElhMti8szheXrKpSvsJQ7pFu0K/SgEAAAANyx43AECrDnIyeXr+umoDnprsjbNtd0lc8euX47cvLI1Vm3fVeZ4AAABA6+FrogAAB7GrpDT6d2kbyzft3K994qieNQp9/vrayvRIjO7TMQ18PnjSYTGwW7uszRkAAABovgQ3AAAH8e7xA+LCo/vHgrXbYsqcvXvjLN2wI0b06pDx2qTvvmav2poeF47vn8UZAwAAAM2Z4AYAIIOcnJwY3qtjenzstKHp0mlJ28GUl5dXCW4SvToWpZU3AAAAANWxxw0AQBb2xlm4bnss27j/8mqJZKm0TKFP4prfvho/mbow5q/ZloZAAAAAQOug4gYAIAvWb9sTo3p3jDmrt9Z6b5zF67bHH15elp5/66+z0j12kusuPX5gHDmgS4PP9YXFG+L4wd2a7HgAAADQmqi4AQDIghOGdIsHP3d6PP3lt8V3LxoXbz+iT3RpVxCnDc8c3Lx1ibXlm3bGr59bEovWbW/wed740Ny4+LZn4tYpCxpkvGScZLxkXAAAAKD2VNwAAGRRvy5t49ITBqVHsjdOTZZZmzJnTZW2ZHW100ZkDn1qWxlz8yPz0vMbHpidvl4+aVi9QpuKcZJxJ4zoofIGAAAAaknFDQDAIVKT0GZXcWk8s3B9lfZkibRu7QszXv+9B2bHzQ/Pi2lLN0VZ2cH3xklClWsnj658n4Quda282Te0SSTjCm0AAACg9lTcAAA0IWu37o6x/TrHK0s2xr65y8SRmatt9pSUxS+eXhzb95TGjQ/PTYOe00b0iAvH948zRvWq9pqKCpuK0KUulTfVhTb1qdwBAACA1kxwAwDQhAzs1i7+cPkpsXlHcUydvzYen7M23fOmJsHNi29sSEObChu274k/TVsRA7u2O2BwU9/wRmgDAAAADUtwAwDQBHVuVxDnHdkvPcrLD77kWYUk4KnOxFGZQ5+6hDdCGwAAAGh49rgBAGjicnJy0iOTpDrnrTq2yY/xA7tkvPaXzyyOjTv2xKXHD6zRnjdCGwAAAGjGFTerV6+Ou+66K5544olYsmRJlJWVRe/evePYY4+Niy++OI455pgGu9fMmTPj7rvvjueffz7WrFkTJSUl0b179zjyyCPjXe96V7ztbW+L3Fx5FQDQsiT72/Tu1CYWrtuenleYMLxH5Odl/t3nnheWxowVW9Lz/NycKPnnBjvVVd4IbQAAAKAZBzcPP/xwXHvttbFt27b92t944430uPfee+Oyyy6Lr371q5GXl1fn+yRLiHzve9+Ln/70p1U+W7lyZXo8+OCDccIJJ8SNN94YPXr0qPO9AACamsL83PjFv50QO/eUxnOL1qfLptV0b5w1W3dVhjaJitCmwr7hjdAGAAAAmnFw88wzz8SVV14ZpaV7N8kdOXJkTJo0KYqKimLatGnx5JNPpoHLr3/96/Tz66+/vs73+q//+q/9Qpvx48fH0Ucfnd5rzpw5MWXKlPReSSXOv/3bv8Vvf/vbaNOmTQP8lAAATUfbwryYNKpXeiTK3hLCVGfq3HXVtp9zeO/4x8zV6XkS1tz+xILYtKO48nOhDQAAADSj4GbXrl1x3XXXVYY2l19+eVx11VX7rc/+9NNPxxVXXBE7duxIw5tzzz03TjrppFrfa/bs2fGzn/0sPS8sLExDnMmTJ+/XZ/r06ekc1q5dmwY5d9xxR3pvAICWLDc38944U+ZW3Rsn8bXzDo/xg7pWVthUF9pMX7Y5pi/fHGcf3jt6dixqwJkDAABA65S1zV5+97vfpcuTJU499dS4+uqrq2yqe8opp8R//Md/VL6/6aab6nSvP/3pT+m+OYmkmuatoU1i3Lhx8fWvf73y/V/+8pc63QsAoKXp2CY/OrXZ//s8w3q2j4Hd2qXhTJd2Bft9lryvqLS558Ul8f/+OD1O+M7DcfFtT8dPpi6MpRt2HNL5AwAAQEuSteDmj3/8Y+X5pz71qQP2e+c73xnDhu39i/8rr7wSS5curfW95s2bV3l+/PHHH7DfhAkTKs/rch8AgJboO+8eFy9/7ez4w+Unx5VvGx5HDegcZ/xzqbVkT5t9K20SyfukPVmG7R8z9i6lVl4e8cLijfGtv86KC370VJTWYIk2AAAA4BAtlbZhw4aYOXNmet6pU6c49thjD9g3qcKZOHFiLFiwIH3/0EMPpVUztZGXl1d5vnr13n88qM6mTZsqz7t06VKrewAAtGT5eblx7GHd0uPz54xKQ5kknKlYJq2i0qYixEnal2/aEWu27q4y1lljekVeDZZoAwAAAA5Rxc2MGTOiPPna5T+XKNs3WKnOUUcdVXn+6quv1vp+FRU7iV/+8pfp/jrVuf322yvPTz/99FrfBwCgtbj9iYX7hTbJnjbT/v2c9LXCXc8uqfbayUf0yTj+ruLS2FOyd6lbAAAAIMvBzeLFiyvPBwwYkLF/v379qr22pi699NLIz99bPDR79ux473vfGw8//HCsXbs2tm3bFtOmTYsrrrgifv3rX1fe78orr6z1fQAAWoO3VtokYU3FnjbJ677hzVu1L8yLU4b1yHiP3720LI791kNx9W9eib9PXxk79pQ00OwBAACgecvKUmlJYFKhb9++Gfv37t278nz9+vW1vt+gQYPiP//zP+PLX/5ylJaWpnveJEFNdcuynXPOOfH//t//iz59Mn8TFACgtTlYaFOh4v2+/QZ0bRsrNu2MSaN7RZuCg1dbJ/4xY1Vs3VUS901bkR5F+blx+sie8b8fOCYK8rK2DSMAAAC0zuBm69atledt27bN2L9NmzbVXlsb73rXu2LEiBFxww03xDPPPFNtn549e8ZJJ50UPXpk/hbowSTLwO3Zs6deY7QkxcXF1Z4DNBTPGTg0fjx1UXz/ofmV779w9vD46CkDq/29J2kvLS2p7L9s48749MQhcdH4fhl/T9q8szieWbD/l3V2l5TF6s07o7y0JPaUxiHlGQNkm+cMkG2eM0C2ec4cWMW2MU0+uNn3L+tFRUW1Cm7qGoisXr06XQotWRYtNzc3JkyYkO6vk5zPnTs3HnvssVizZk184xvfiPvuuy9uu+226NatW53uVVJSEtOnT6/TtS1dslQdQDZ5zkB2/HH2trhr+rbK9x8c1yFO7rLtoL/znNxlb7+K6/738UWxZcPaePfoDge91+Nv7IySsqq/2I7rVtbov2N5xgDZ5jkDZJvnDJBtnjPZl5XgJglL6ipZzqy2FixYEB/96Edj5cqV6bJrP/rRj9LQZl/Lli1L97WZMWNGvPrqq+lSar/61a/qNVcAgJYa2mQKXypU9Ku4vuL1YNc/t3xXte0n9n/zyzwHsnBjcTy7fFfad2iX/Dr97ggAAACtLrhp165d5fnu3bsz9t+1a1etKnT2lYz/yU9+Mg1tCgoK4sc//nGMHl11w9wBAwbEHXfcERdeeGGsWrUqXn755bj//vvjggsuiNrKz8+PMWPG1Pq6liopjatIWZM/++Q/B4CG5DkD2V0e7a7pq/ZbHu0Tpw2p1RjJ92X69HlzmbUkvEn2EzzQOJ/vvCn+PmN1PDRrTSzftPf3wGE928fkU8ZnvNdfHpgTf5i1Pv4wa3v069wmzhrTM84e0yuOO6xr5OXWLcTxjAGyzXMGyDbPGSDbPGcObNasWekqXc0quNk3lDmQfft06FCzb3dW+Pvf/x5Lly5Nz88777xqQ5sKXbt2TUOeZLm0xJ///Oc6BTfJNzsLCwtrfV1rkPwP1p8NkE2eM9BwXli8Yb89ba6dPDounzSsTmN95sxRkZeXHzc8sPcX+WTcE4f1jOMHV12a9sThvdLj+neVx4wVW+IfM1ZFz45FGf+3nawb/PDstZXvV2zeFb98dmn88ZWV8dLXzo7C/PpXUnvGANnmOQNkm+cMkG2eM/vLxkoQWQluevXqVXme7CtTk/1pKvTs2bNW93r22Wcrz0855ZSM/U877bTK82TZNACA1ioJVa46c0Tc/Mi8eoU2FSquT8KbZNzqQpu3/nJ7RP/O6VETM1duiaUbdlZpf9uYXg0S2gAAAEBTkJXgZsSIEZXny5cvz9h/3z5DhtRuaY59g6HOnTP/pX/fYGjbtjfXcgcAaI0+d/bImDCiR8aQpTbhzXGDuzbYePt6cMabX/bZ17lj+2S8dvvuktixpzSt7AEAAIBWF9yMHDky/QZlspzF9OnT09eDlQtNmzat8nzs2LG1ulebNm2qrdw5kE2bNtUq6AEAaOkaOmTJRmiT2FVcGm0KcmNXcVllW1JpM3Fk5ortv01fGV/6w2vpXjhJ0JMcA7u9ubwvAAAANBVZWVOiU6dOceyxx6bn69evT8ObA0lCnccff7zapcxqYvDgwZXn+45zIE8//XTl+cH2wwEAoGn5f+8YE6987Zy4/UPHxkXH9I/ObQvi9BE9on1Rfo2qdcrLk319Nsa3/jorTvveY/GOm6fGtt0Nu4EkAAAA1FfWFgM/77zzKs9vueWWA/a7//77Y9GiRen5EUccsd8yazVx1llnVZ4/9thj+1XvvNX27dvj9ttvr3w/efLkWt0LAIDG1bYwL62W+Z/3HR0vfvWs+M5F4zJes2NPSUydt7ZKe2lZeXSoQegDAAAALSK4ueiii2LQoEHp+RNPPBHf+ta3oqSkpEr1y/XXX1/5/sorr6z1fY455pjKKp3S0tK44oor4vnnn6/SL6n8+dSnPhWLFy+u3EvnwgsvrPX9AABoGgrycqNXxzeXzT2Qx+esjd0lby6vVuHcsb2zNDMAAACou6x9xbCoqCi++c1vxsc//vEoLi6OO++8M6ZOnRpnnnlmtGvXLl577bU00EmWSku8733vi4kTJ1YZ5957743rrruu8v2cOXOq9Pnud78bl1xySSxbtizWrVsXH/rQh9JAJzk6dOgQCxYsiEceeSR27NiR9u/YsWP88Ic/jIKCgmz9+AAANBEPzFhVbfs5Y/tkvHbmii3x4ycWxOQj+sTpI3tGu0IVOgAAAGRXVv/mefLJJ8dNN90UX/7yl2Pr1q1ptcsdd9xRpV8SuuxbeVNbPXr0iN/85jdxzTXXxHPPPZe2vfzyy+nxVsOHD48f/OAHMWzYsDrfDwCA5uOL546KowZ0iQdnrIoXFm+IsvKIAV3bxth+nTJe+/fXV8Z901akR1F+bhreJEu1nXdk32hTkHdI5g8AAEDrkvWvDCZ70DzwwANx1113xZQpU9KqmF27dqVhy/jx4+PSSy+NE088sd736dmzZ/zyl7+MJ598Mv785z+ne92sXbs2XZ6tW7duMW7cuDjnnHPine98Z+Tl+Us2AEBrMaBru/i3CUPSY/223fHIrDVpe05OTsZrH3j9zWqdZLm1h2auTvfLeee4vlmdMwAAAK3XIVnrIQlprr766vSoy145yVFTEyZMSA8AAHir7h2K4n3HD6xR34Vrt8W8NduqtE8c2TPaFvoiEAAAANmR29gTAACApujBGaurbU+WSstk++6SmL5sc+V+jgAAAFBTdlcFAIBqtCvMi/5d2sbyTTsr2/Jzc+LM0b0zXvvo7DXx2btfSa8/+/Deadhz/OCukZ/ne1MAAAAcnOAGAACq8S+nDI4Pn3xYzFixJR6csSo9enVsE53bFWS8NumbSEKfnz+9OD26tiuIB68+PXp1anMIZg8AAEBzJbgBAIADyMnJiSP6d06Pa84ZFTv2lGS8ZndJaUyZs7ZKe6e2BdGzY1GWZgoAAEBLYa0GAACooXaFmb/39PT89bFtd9WAJ1kuLQmCAAAA4GAENwAA0ID+MXN1te3njs28N878NVvjfbc9Ez+ZujCWbtiRhdkBAADQ1FkqDQAAGtC/n3d4TBrVMx58fVU8PGt1bNlVki6RNn5g14zXPjhjdTy/eEN6fOuvs+Lwvp1i8hF90r12urQrPCTzBwAAoHEJbgAAoAG1LcxLl0VLjuLSsnhu4YbYsGNP5OZmXibtgddX7fd+5sotMW/N1vjIqYOzOGMAAACaEsENAABkSUFebkwY0aNGfZdv2hnTl2+u0n7KsB7RqU1BFmYHAABAU2SPGwAAaAL+MWP/apsKSeVOJruKS+OB11fGjj0lWZgZAAAAh5KKGwAAaAL6dm4TJwzpFi8u3hBl5XvbcnIizj68d8Zrp85bF5+66+VoU5Abp4/omYY9Z47pZV8cAACAZkhwAwAATcDkI/qmx/ptu+PhWavjwRmrY3dJafTsWJTx2gf/Wa2zq7gs/jFzdXrk5ebEg1efHsN7dTgEswcAAKChCG4AAKAJ6d6hKC45flB6lFWU3hxESWlZPDJrdZX2nh2KYmiP9lmaJQAAANlijxsAAGiicnNzMvZ5fvGG2LijuEr7OWN71+j68vLM4RAAAACHjuAGAACasafmr6u2ffLYPhmvXbphR0y44bH4xv0z4tmF66O0BhU+AAAAZJel0gAAoBn7wjmj4u1H9E33uUmOuau3RZd2BXHCkG4Zr036L9+0M3721OL06Na+MM4a0yuuOmtk9O/S9pDMHwAAgP0JbgAAoBnLycmJI/p3To9rzhkVi9Ztj0XrtkV+Xm6Ngpt9bdi+J37/0rK4dvLoLM4YAACAgxHcAABACzKkR/v0yGTt1t3x4hsbq7QfN7hbdO9QlKXZAQAAkIk9bgAAoBV6eNbqKK9mS5tza7A3TnFpWfz0yUXpHjkAAAA0LMENAAC0QiN7d4iLxvePTm32L8I/5/DeGa99duH6+OZfZsZp33ss3nHz1Lj54XkxZ9XWKK8uCQIAAKBWLJUGAACt0LGHdUuPpHomCWKS/W5WbNoVA7u1q9XeODNXbkmPGx+eG3+4/OR0TAAAAOpOcAMAAK1YQV5unDaiZ3rURFlZefxjxuoq7d3aF8bRA7tmYYYAAACti6XSAACAGntl6aZYs3V3lfazxvSKvNycjNfvLinN0swAAABaBhU3AABAjc1csTlyciLeup3N5CP6ZLx2zZZdMen7U2LC8B5x7tg+ceaYXtGlXWH2JgsAANAMCW4AAIAa+9DJg+Pt4/rGwzNXp3vdPDV/fRTk5cQpw3pkvPbBmatjx57S+MfM1emRVOicPLR7fPW8MTG6T6dDMn8AAICmTnADAADUSo8ORXHpCYPSY+uu4pi7emu0KcjLeN0/Zqza731pWXk8OX9ddGpT0GBze2Hxhjh+cLcmOx4AAEAm9rgBAADqrGObgjj2sMzBxuYdxfHMgvVV2o8a0Dn6dWnbIHO58aG5cfFtz8StUxY0yHjJOMl4ybgAAACHiuAGAADIukfnrI6SsrdsjBMR54zNvDdOUplzwwOz49mF69PzA1XG3PzIvPQ86Vvf8Ca5PhknkYybjA8AAHAoCG4AAICsO2pAl/js24bHyN4d9ms/twbBzStLNqZByqU/fjZO+PbDce3vX4tHZ6+O3SWllX2S5cyunTy68n19wpt9Q5tEMq7l0gAAgEPFHjcAAEDWDe3ZIa45Z1R6LFq3PR6csSpmrNgSw3vtH+RUJ+lbYf32PXHPi0vT4+f/enxMGtWr8rPLJw1LXytCl4rXiva6hja1uR4AAKC+BDcAAMAhNaRH+/jUxJqFIeXl5fHgjNVV2jsW5ccpw3pUaa9PeCO0AQAAmgJLpQEAAE3WrJVbY8mGHVXazxjdKwrzq//rTBK21HbZNKENAADQVAhuAACAJmvJhu3RqU3VhQImH3HwvXGS0OXKtw2vfJ+EMt+8f2ZawfNWQhsAAKApsVQaAADQZE0+om+cOaZ3PLtwfTzw+qr4x8zVsXlncUwc2TPjtQO7tdvv/U+fWhR/fGVZ3PrBY+Okod3TNqENAADQ1AhuAACAJq0gLzdOG9EzPf7jgiNi4brt0b4o819lqtsbZ+OO4nh01po0uBHaAAAATZHgBgAAaDZyc3NieK8OGfvt2FMSU+etrfazH09dGL99aWls2lFc2Sa0AQAAmgp73AAAAC3O43PWxu6SsgN+nim0eeD1lbF5nz4AAACHioobAACgxTlxaPf47kXj4oEZq+Lp+etjT+neEKdjm/zYuquksl+XdgVVQpvF67bHp+56OQrzcuOM0T3jwqP7xxmje0WbgrxD/nMAAACtj+AGAABocbq1L4xLTxiUHlt3Fcdjc9bGz55cFK8s3VSl8ibZ62bf8Oa+acvT1yTsSfbJSY4k8Pnxh46Lk4d1P+Q/CwAA0LpYKg0AAGjROrYpiOUbd+4X2iSVNhVueGB2Gt4kysvL40/TVlQZY+ee0hjdp+MhmjEAANCaqbgBAABatCSUScKZt+5ps297xespw7rHonXbq4wxaVTP6Nq+8BDOGgAAaK1U3AAAAK0utEkkr8n7Ckm/Gx+aW+04F47vn/FexaVlcc8LS2LzjuIGmTsAANA6qbgBAABaXWhToeJ9Rb8pc9fGx04bEu0K8uK+aStiyYYd0aEoP84a0zvj/Z6cty6u/cP0+Np9M9IKnSTsedvoXtGmIK/BfzYAAKDlEtwAAACtMrQ5UHjzk6mL0v6Pf3FSvLxkU7yxfnuNwpc/vrI8fd1TWhb/mLk6PTq2yY/7rjg1hvXs0EA/GQAA0NIJbgAAgFYb2hwovKl4TdqPPaxrxntu310SD81cXaW9fWF+DOnevrY/AgAA0IrZ4wYAAGjVoU2F6va8ScariX/MXBU7i0urtF9wdL/Izc2p0RgAAAAJwQ0AABCtPbSpb3jz2rLN1bZfcHT/jNeu2bor7nr2jdi4fU+t5goAALRMghsAAKDZe2HxhnqHNgcLb5LxD+b688fGo9dMjKvOHBGHdW+Xto3s3SHG9O2Y8X5/nrYivnrf63HCdx6Oj/3ixfjraytjVzXVOwAAQOtgjxsAAKDZO35wtzQ0ufmRefUKbarb8yYZNxk/k6E9O8Tnzh4ZV581IqYt3RTbdpdETk7mZdL+NG1F+lpcWh4Pz1qdHp3a5MdTX35bdGxTUK+fAwAAaH4ENwAAQIuQhCYTRvSoUchS0/DmuMFdaz1eEtaMH9S1Rn3nr9kW05dXXWZtbL/OQhsAAGilLJUGAAC0GA0V2mRrvLf607Tl1bZfOL5fVu8LAAA0XYIbAACARrJw3fYqbYV5uTH5iL4Zr319+ea489k3YsP2PVmaHQAA0BgslQYAANBIfnTZMfGFc7anlTfJXjeL1m2PM8f0is5tMy+T9qvnlsTdzy+Jb/x5Rkwc2TMuHN8/zhrTO9oW5h2SuQMAANkhuAEAAGhEQ3q0j6vPGhlXnTkiXl22OQrycjJes6ekLP42fWV6XlJWHo/MXpMe/bu0jalfOiNyczOPAQAANE2CGwAAgCYgJycnjh7YpUZ9p8xZE5t3FldpnzSqp9AGAACaOXvcAAAANDPJsmrVSZZLAwAAmjfBDQAAQDNSXl4eG7bvqdKeLJN27KCuGa9/ZNbquPOZxdWOAQAAND5LpQEAADSzJdXu/sRJsXjd9rTy5k/TlsfCddvjgqP71WiZtB8/sTCeW7QhvnH/zJg4smdcML5/nD2md7QtzDsk8wcAAA5OcAMAANAMDe7RPq46a0RceebweG3Z5ujZsSjjNcs37UxDm0RJWXk8MntNepwwuFv89lMnH4JZAwAAmQhuAAAAmnkFzlEDu9So758PsDfOOWN7N/CsAACAurLHDQAAQCuRLKv2Vsnqau86ql+jzAcAAKhKxQ0AAEArsHVXcbQvqvpXwFOH94hendpkvP7OZ9+IsrLyOO/IvtG9Q+Zl2QAAgLoR3AAAALQCHdsUxB8uPyWWrN+RVt78cdryWLh2e1xwdP+M15aWlccPH50Xq7fsjm/+ZWacPqJHXDi+f5x9eO9oV+ivlQAA0JD8hg0AANCKDOreLj575oj4zNuGx+vLt8SQnu0zXvPcwvVpaFMR4jw2Z216XHRM//if9x19CGYNAACth+AGAACgFcrJyYlxAzrXqO991eyNkzj/SHvjAABAQ8tt8BEBAABoMXYVl8bfp6+q0t6tfWFMGNGjUeYEAAAtmeAGAACAA1q7dXeM6tOxSvv5R/aNgrzMf6W84YHZ8fOnFsW6bXuXWgMAAA7OUmkAAAAc0MBu7eL3l58SSzfsiD9NWx5/fGV5LFi7PS4Y3z/jtRu274n/e2JhlJSVx3/8dVacNqJHvHt8/zj78N7RrtBfRwEAoDp+UwYAAKBGAc5n3jYirjhjeMxauTXG9K1ahfNWf52+Mg1tEqVl5TFlztr0uObskfHZM0ccglkDAEDzI7gBAACgxnJycuLwfp1q1PdPryyvtv1dR/dr4FkBAEDLYY8bAAAAGlyytNqLb2ys0j5+UJc4rHv7RpkTAAA0B4IbAAAAGtzmncVx/OCuVdqTPW4yKS8vjyt+9XL87KlFsXbr7izNEAAAmiZLpQEAANDgjujfOX73qVPSyps/v7oi7ntleSxctz3eOa5vxmtfW7Y53R8nOb7111lx6vAe8e7x/eKcw/tE+yJ/jQUAoGXzGy8AAABZM7Bbu7jijOHx6UnDYumGndG9Q1HGa+6b9ubeOKVl5fHE3LXpccv7c+P8o+yPAwBAy2apNAAAALIuJycnBnVvl7FfSWlZ3P/qyirtHYry46wxvbM0OwAAaDoENwAAADQZTy1YH+u2Vd3X5tyxfaJtYV6jzAkAAA4lwQ0AAABNRkFeTpwwuFuV9gvHZ14ibfvukrj4tqfjjicXxZqtu+p0/xcWb6jTdYdqPAAAWj573AAAANBknDKsR3os27gj/vzqirjvleWxcUdx2pbJP2auihcWb0yPb/91Zpw6vEdceHT/mHxEn2hflPmvvzc+NDdufmReXDt5dFw+aVi9f5ZbpyyIGx6YHZ+ZNDTO6Fnv4QAAaCUENwAAADQ5A7q2i09PGh6XTxwW67btibzcnIzX/PGVFZXnZeURU+etS4/RfTvG2H6dM1bGJKFNIglbEvUJbypCm8QPpyyMPmd0izE9Cus8HgAArYel0gAAAGiycnJyomfHooz91m7dHU/OW1ulfWTvDnF4304Zrz9+cLe00qZCErok4Ut9Q5vEF84eLrQBAKDGBDcAAAA0e395bUVaZfNWFxzdPw1/aiKpsKlvePPW0CYZ7xOnDanVGAAAtG6CGwAAAFrE0monDulWpf2Co/tlvHb+mm1x3i1T4ydTF8Z7julf5/CmutCmIfbKAQCgdbHHDQAAAM3e2Yf3To/lm3bGn6etiD9NWx6d2hSkgU4mSd/Xl29Jj+/8bVacMqxHvGNc3/jb9JU13vNGaAMAQEMR3AAAANBi9O/SNg1MkmPrruKM/cvLy+O+acsr3yfLrT05f10U5uXGVWeOiJsfmZcxvBHaAADQkCyVBgAAQIvUsU1Bxj4vL9kYSzfsrNL+ttG94nNnj8y4bJrQBgCAhia4AQAAoNW675UV1bZfOH7v3jhJCHOg8EZoAwBANlgqDQAAgFbrhCHdYv6abfHsovVRXr63rWOb/Jg0qldln4owpiKkSV5vf2JBbNrx5lJsXzh3pNAGAIAGIbgBAACg1Tr/qH7psXLzzvjztBVx37QVcdSAztGmIG+/fm8Nb/YNbRK/ePqN2LWnLC45fmAM7NbuEP4EAAC0NJZKAwAAoNXr27ltfHLisPj7VafFNy4YW22fJLzp0q76fXPWbt0dP3xsfpx3y5Oxp6Qsy7MFAKAlE9wAAADAPory96+2qZDsafPWSpu3uvDoflGY76/aAADUnd8mAQAAIIMktKlYJi2Rm1N9v8tOPOzQTQoAgBZJcAMAAAC1CG2+cO7I+OK5o6NL2/2XTevfpW2M6tMx43gzV2yJFZt2ZmWuAAA0f4IbAAAAqGFoc+3k0fGZM0ak+928/LWz45LjBlR+tnzTzrR/Jl//84yYcMOj8dGfvxCPzFodpWXlWZs/AADNT35jTwAAAACaS2iTBDYVcnNz4ob3HhWDe3So7Ffxum+/fc1fsy2eX7whPX9k9pr06Nu5TVx55oh4/wmDsvwTAQDQHKi4AQAAgFqGNvtK2pPPKyTXHajy5rcvLa/StnLzrthVXNog8wYAoPkT3AAAAEAdQ5vahDe7S8vjj9NWVLm2KD83Lhr/5pJrAAC0bpZKAwAAgHqENhUq+r112bSPnjIwfZ27fk9s2121sua8I/tF53YFDTJ/AACaPxU3AAAAUM/Q5mCVNz+euig9H9erKB77/IT4/Nkjo3+XtpV9Ljtxb7BzMCWlZfHeW5+OWx6ZF6u37KrVnAAAaF5U3AAAANDqvbB4Q71DmwNV3nz/ofnxrTO6xZgehdGnU5u48swRccUZw+OJuWtjypw1ccygrhnHnDJnbbz4xsb0uOmReXHWmF7x/hMGxekjekZubk6d5gkAQNOk4gYAAIBW7/jB3eKqM0fUO7SprvLmM5OGpqHNvvJyc+KM0b3iGxccETk5mYOXXz+/pPK8tKw8HpyxOj7ysxfiqQXr6jVPAACaHhU3AAAAEBGfO3tkTBjRIw1xGkIS3hw3uGsc1a9DTJ8+vc7jLN+0M63MeatkubVThvWo5ywBAGhqVNwAAADAPzVUaNOQ493z/JIoK6/a/v4TBqaVOwAAtCyCGwAAAGjCThjSPd42ulfsu6JaEthcfNzAjNdu2rEnnpy3LsqqS34AAGiSLJUGAAAATViyfFtyJEumJdU397y4NI4e2CV6d2qT8drfv7QsvvXXWTG4e7u49IRB8d5jB0SPDkWHZN4AANSN4AYAAACagWRPm8+fMyquPHNEbN5ZnLF/eXl5/Pr5Jen54vU74rt/nx3//Y85ce7YPnHjJUdHQZ5FOAAAmiK/pQEAAEAzkp+XG91rUDXz7MINsXDt9v3aikvLY/22PUIbAIAmzG9qAAAA0ALd/c9qm7e67MRBh3wuAADUnOAGAAAAWpg9JWXx0hsbq7R3b1+YLpUGAEDTJbgBAACAFqYwPzemfHFS3PbBY+K0ET0q29977ID0s0y+ef/MuPLuV+LZhevTvXIAADh08g/hvQAAAIBDJNnHZvIRfdNjyfod8ZsXlsT7jhuY8brtu0vity8ujW27S+LPr66IYT3bx/tPGBTvOWZAdG1feEjmDgDQmqm4AQAAgBZuUPd28aXJo2Nwj/YZ+97/6oo0tKmwYO32+NZfZ8X3/zEny7MEACAhuAEAAAAq/fr5JdW2J1U3AABkn+AGAAAASL2+fHO8tmxzlfZx/TvHEf07N8qcAABaG8ENAAAAkOreoTA+efrQ6PaWvWwuO7Fm1TZ/n74yNu8oztLsAABah/zGngAAAADQNPTt3Daue8eY+Pw5I+PBGavj7ueWxPTlm+NdR/XLeO3iddvj8l+9HEX5uXHekf3SsOeYQV0iJyfnkMwdAKClENwAAAAA+ynKz0vDmuTYsH1PtC/K/M8Hd7+wd2+c3SVl8YeXl6XH6D4d4/sXH2WZNQCAphbcrF69Ou6666544oknYsmSJVFWVha9e/eOY489Ni6++OI45phjGuxexcXF8ec//zkefPDBmDNnTqxfvz6KiopiyJAhMXHixLjsssuie/fuDXY/AAAAaMneumxadfaUlMXvX1xWpX3h2u3Rt3ObLM0MAKBlynpw8/DDD8e1114b27Zt26/9jTfeSI977703DVO++tWvRl5eXr3uNXv27Ljmmmti/vz5VcKc6dOnp0cSIH3ve99LQxwAAACg/h6csSrWb99Tpf3cI/pE9w5FjTInAIDmKqvBzTPPPBNXXnlllJaWpu9HjhwZkyZNSitgpk2bFk8++WSUl5fHr3/96/Tz66+/vl6hzYc//OHYvHlz+j6pqjn77LOjT58+sWrVqnjooYfS6ptNmzbFFVdcEb/61a/iqKOOaqCfFAAAAFqvaUs3Vdt+2QmDMl6b/LtAwl44AABZDm527doV1113XWVoc/nll8dVV1213y9iTz/9dBqi7NixIw1vzj333DjppJNqfa+SkpL44he/WBnavOtd74r/+I//iDZt3izH/tKXvhSf//znY8qUKWkFzje+8Y202gcAAACon6+dd3hcevzA+PXzS+IPLy2LLbtKYmiP9nHS0G4Zr506b1189++z47ITB8UFR/eLjm0KDsmcAQCaqtxsDfy73/0uVq5cmZ6feuqpcfXVV1f59swpp5ySBiwVbrrppjrd6+677465c+em50n4kyyFtm9ok2jfvn3a3rnz3g0RZ8yYkVbpAAAAAPU3onfHuP78sfH8V86K/3nfUfH5c0bWqIrm188tiZkrt8RX73s9TvzOI/HlP7wWry2rvoIHAKA1yFpw88c//rHy/FOf+tQB+73zne+MYcOGpeevvPJKLF26tNb3+v3vf18ZznzlK1854C+GSWjznve8J12y7cQTT4yNGzfW+l4AAADAgbUpyIuLjhkQ5x3ZL2PfNVt2xUOzVle+37GnNH7zwtL42C9ejJLSsizPFACgFQU3GzZsiJkzZ6bnnTp1imOPPfaAfZOQZeLEiZXvk71oamPBggWVlTPnn39+9O7d+6D9r7322rj//vvjl7/8ZZx88sm1uhcAAADQcH774tIoLdu7x82+Ljl+YOTn1e+fLF5YvKFe12d7PACAQxrcJMuQVWwuOG7cuMjLyzto/6OOOqry/NVXX63VvaZNm1Z5nizJBgAAADR9SWBz9/NVV91IFtFIgpv6uPGhuXHxbc/ErVMWRENIxknGS8YFAMi2/GwMunjx4srzAQMGZOzfr1+/aq+tiYq9bRLDhw9PX+fMmZPusfPkk0/GqlWrorCwMIYOHRqTJ0+O97///VFUVFSrewAAAAANq6y8PK46a0S6x820pW/uaTNpZM8Y0LVdxuufXbg+OhTlxxH99+5lu29lzM2PzEvPb3hg7wodl0/au0R7XUObinGScSeM6BHHD+5W5/EAABoluFm7dm3led++fTP233d5s/Xr19fqXgsXLqw879mzZ9x8883x4x//OEpKSirbd+7cme6fkxx33nln3Hrrrek+NwAAAEDjKMjLjfcdNzA9Zq7YEnc/vyTue2V5XHbiYRmvTVb5+PqfZ8TsVVvjqAGd47ITB8X5R/WLdoX5aahy7eTRlWFLfcKbfUObRDKu0AYAaJbBzdatWyvP27Ztm7F/mzZtqr22tvdKApk77rgjPT/iiCPilFNOSe+f7IPzyCOPpAHOsmXL4gMf+ED84Q9/iEGDBkVdJL8g7tmzp07XtkTFxcXVngM0FM8ZIJs8Y4Bs85zJbHiPNvG1d4yMa84aFoV5ORn/zp1U6CShTeLVZZvj1WXT4z/+Miuuetuw+JeTB8VHTxkYpaUl8f2H5qd9kvAlef+J04bUeE4/nrqo8vrEF84eno7r3wNoijxngGzznDmwim1jmnxws+8vMTVZlmzf4Ka2vwBt37698jwJbZL7ffvb347zzz9/v34rVqyIT3/60zFr1qzYsmVLXHPNNelyanWRVPNMnz69Tte2dLNnv/lNJIBs8JwBsskzBsg2z5mGcesLm6u0bdtdElvWrYrp0/d+dnKXiA+O6xB3Td+Wvk9CmGQ59XeP7pBx/D/O3lZ5XSIZ5+Qu2/xbAM2C5wyQbZ4z2ZeblUFz6z5sTrILYS3s2rVrv/fXX399ldCmYh+d22+/PTp33rv27WuvvRZPPPFEnecJAAAAHHrb95TFU0t3VmnvUJATJw9884uhiSSkSUKXCkkYk4QytQ1tahL2AAA06Yqbdu3e3ERw9+7dtQpfalKhs699+w8dOjQuuuiig+6lc8kll6R74CSS5dNOP/30qK38/PwYM2ZMra9rqZLSuIqUdfTo0VFQUNDYUwJaGM8ZIJs8Y4Bs85xpWM8u3BAFeetjT2npfu3vOXZgHHf0qCr9x42L6NPnzWXPklCmT58+1S6bliyPdtf0Vfstj1ab5dWgsXjOANnmOXNgySpfySpdzSq4eWtFTHX27dOhQ+2+xdK+ffvK89NOOy1jxU6y701FcDNz5syoi+QehYWFdbq2pUv+B+vPBsgmzxkgmzxjgGzznKm/00f3iee+clb8edqKuPv5JTF9+d6l0T548uAD/tl+5sxRkZeXn+51k0hCnI07S+Nr5x1e2efWKQv229Pm2smj4/JJw7L+80BD85wBss1zpn6riDVacNOrV6/K8zVr1mTsv3r16srznj171upeXbp0qfa+B6u6qbBp06Za3QsAAABofB2K8uOyEwelx/Rlm+PJ+etiRO+OB70mCWFeX745/jp9Zfr+jicXxQOvr4rPnz0yVmzaGf/90NzKvkIbAKAxZSW4GTFiROX58uXLM/bft8+QIbUrQR42bFhMmTIlPd+6dWvG/qX7lFLvW60DAAAAND/jBnROj5pYvWX/VUGWb9oZ1/zu1f3ahDYAQGPLzcagI0eOrCwPmj59epSXlx+0/7Rp0yrPx44dW6t77bvXzJw5czL2X7ZsWeV5sqYtAAAA0PLNXb01Xnxj40H7CG0AgBYb3HTq1CmOPfbY9Hz9+vVpeHMgSajz+OOP77dPTW1MmDChciOkp556KuPyZxXVOYnjjz++VvcCAAAAmqdfP7fkoJ93aVcgtAEAWm5wkzjvvPMqz2+55ZYD9rv//vtj0aJF6fkRRxyx3zJrNdG1a9eYNGlSer5nz574r//6rwP2Te5z3333pee5ubn7zREAAABoud5zzIB433EDom1BXrWfb9pRHLdOWVDtZ3tKyqKktCzLMwQAyHJwc9FFF8WgQYPS8yeeeCK+9a1vRUlJyX59nn766bj++usr31955ZV1utc111wTRUVF6fnvf//7+P73vx/FxcX79Vm8eHF88pOfjF279q5ne9lll0Xv3r3rdD8AAACgeUn2wfnee4+KT04cWqXSpsIND8yuNry5+/klMfG/psRPn1wU23bv/28bAAANLT+yJAlSvvnNb8bHP/7xNES58847Y+rUqXHmmWdGu3bt4rXXXksDnYr9b973vvfFxIkTq4xz7733xnXXXXfQfWyGDBmSBkBf/epXo6ysLP7v//4v/vKXv6T36tGjR8yfPz8eeuih2L17d9p/6NChadgDAAAAtB5JKHPTw/Mq33/hnJHxmbeNSNuT0CZR8VqxbFppWXn85MmFsXzTzvjmX2bGjQ/PjQ+ceFh85JTB0adzm0b6SQCAlixrwU3i5JNPjptuuim+/OUvx9atW9OqlzvuuKNKv0suuWS/ypu6eM973pMGQl//+tfTfW5WrlwZd911V5V+J554YvzgBz9I+wIAAACtw77hTOLayaMrw5mK1+rCmwdnrIqlG3ZWXrd1V0nc9viCeGXJxrjnkycf4p8CAGgNshrcJM4666x44IEH0hBlypQpsWzZsnS5sqQSZvz48XHppZemYUpDePvb3x6nnHJK3HPPPfHoo4/GG2+8EVu2bIlOnTrFuHHj4oILLkj7JPvbAAAAAK3DwUKbCtWHN+Xx4IzV1Y75r6cOzuqcAYDWK+vBTSIJaa6++ur0qMteOclRU507d45PfOIT6QEAAAC0bjUJbQ4c3lRdrj1xWPd2cfbhfbIyXwAApScAAABAtPbQpkLyedJvXwO6tt3v/UcnDIm83JyM9y8pLav1nAEABDcAAABAi1OX0OZA4c2yjTvjQycNineO6xvd2xfGe48dkHGM7btL4rTvPRbfuH9GLN2wo44/BQDQGgluAAAAgBalPqHNgcKbO59dEkf07xxPfOmMaFeYeeX53764NFZu3hU/e2pxTPyvx+KKX78c05ZuquVPAgC0RoIbAAAAoMV4YfGGeoc2BwpvknFnrtxSoyXS7nhyUeX7svKIv762Mi780VMxe1Xm6wGA1k1wAwAAALQYxw/uFledOaLeoU114U0ybjJ+Jg/OWJ0ur1Z1bl1jdJ9O9ZoPANDyZa7tBQAAAGhGPnf2yJgwokeNQpaahjfHDe5a4/H+b+rCats/dtrQBpkPANCyqbgBAAAAWpyGCm3qMt533j0uLjqmf+Tn5lS2DenRPs4a0zvjteXl5XWeIwDQMghuAAAAABrQ4f06xf+87+iYeu0Z8cmJQ6Njm/z4twlDIm+fIOdAvvfgnPjYL16I5xauF+IAQCtlqTQAAACALOjbuW1c9/Yx8dm3jdiv+uZAtu0uibuefSO27iqJh2etiSMHdI6PnzY03n5En8jP891bAGgt/L8+AAAAQBZ1KMqPNgV5Gfvd88LSNLSp8NqyzfHZu1+Jr98/I8szBACaEsENAAAAQCMrKS2Lnz65qNrPLj524CGfDwDQeAQ3AAAAAI3s76+viuWbdlZpP2FwtzhqYJdGmRMA0DgENwAAAACN7ORh3eOqM0dEt/aF+7V//PShjTYnAKBxCG4AAAAAGlmPDkXxubNHxtNfflt8+91HxJAe7WNoj/Zx5uheGa9dsWlnnHfL1Pjdi0tjd0npIZkvAJA9+VkcGwAAAIBaaFOQFx848bB4//GDYuWWXZGbm5Pxmp8/vTheX74lvvj71+K/HpwTHzl1cHzghMOic7uCQzJnAKBhqbgBAAAAaGKSwKZ/l7YZ+23dVRx3P7ek8v2arbvjew/MiQnfezS27S7J8iwBgGwQ3AAAAAA0U/e8sDS2VhPQTBrVKzoUWWgFAJojwQ0AAABAM1RcWhY/e2pxtZ99/LQhh3w+AEDDENwAAAAANEPJ7jefP3tkjO7Tcb/2E4d0iyMHdGm0eQEA9aNmFgAAAKAZys/LjfccOyAuOqZ/TJ23Lv5v6sL09ROnD63R9V//84zo1LYgPnzyYdGjQ1HW5wsA1IzgBgAAAKAZy8nJidNH9kyPOau2xoheHTJes3zTzrjz2TeitKw8bnt8QbznmP7x0QlDY3gNrgUAsstSaQAAAAAtxKg+HSM3N1lE7eB+/tSiNLRJ7Ckpi7ufXxpn/c/jcc8LSw7BLAGAgxHcAAAAALQiW3YVp0HNW+Xl5sSEET0bZU4AwJsENwAAAACtyG+eXxLbdpdUaT/vyL7Rv0vbOo35wuINDTCz7I0HAM2J4AYAAACgFTlucLc4a0zvKu0fP21onca78aG5cfFtz8StUxY0wOwiHScZLxkXAFojwQ0AAABAK3LMoK7xk385Lh65ZmJcduKgKMrPjZOHdo8j+nfOeO30ZZvj8/dMi5krtlRWxtz8yLz0/IYHZtc7vEmuT8ZJJOOqvAGgNcpv7AkAAAAAcOgN69khvvPucfH5s0fGph3FNbrmx1MXxv2vroh7X1keE4b3iI+dNiSunTwqbnhgTvp5Rehy+aRh9QptEtdOHh3HD+5W63EAoLlTcQMAAADQivXoUBTDe3XI2G/Zxh3xt+krK98/OX9dfORnL8Qjs9ak4U2FulTeVBfa1CX8AYCWQHADAAAAQEY/e2pxlJaVV2k/9rCucfmk4WnYUpfwRmgDAPsT3AAAAABwUJt3Fsdvnl9SpT0/Nyc+curg9DwJW2ob3ghtAKAqwQ0AAAAAB5VU2lxy/KBoV5i3X/v5R/WLvp3bVr6vTXgjtAGA6gluAAAAADiobu0L49/PPzye+fKZacDSq2NR2v6x04ZU6VtdePOe/306HpyxqnKpNaENABxY/kE+AwAAAIBKndsVpAHLRycMiacWrIux/TpX268ihKkIZ15asjE+eedLMaRH+xjRq0P8Y+bqyr5CGwDYn+AGAAAAgFopzM+NM0b1Omift4Y3iUXrtqdHBaENAFRlqTQAAAAAsuK8I/tGzgE++/SkYUIbAKiG4AYAAACArPjpU4ti7642+yvKz40v7bMPDgDwJsENAAAAAFkxsnfH6NS26kr9u0vK4tYpCxplTgDQ1AluAAAAAMiKTTuKY8vOkmo/S/a+OVh4s3lncZSVVVevAwAtW9WvPAAAAABAPSWhTBLOVLh28qgY1rNDvLZ8c/zw0flpW8Xn1e1186XfvxqL1+2Iz509Is45vE/k5h5otxwAaFkENwAAAABkObQZXRnOnDO2T7QvzK/8vLrw5vXlm+PBGavT80/d9XIc3rdTfO7skXHWmF6RkyPAAaBls1QaAAAAAIcktKmQvE/aD7Rs2k0Pz92v/8yVW+Ljv3wx7nhyUVbnDgBNgYobAAAAAA5ZaFOhov2tlTenDOseD89aU6V/+8K8uOiYAVmaOQA0HYIbAAAAAA5paHOw8GZc/07V9v3IqYOjW/vCBp0zADRFlkoDAAAA4JCHNgdaNm368i0xeWyf6N+lbWVbh6L8+PhpQxt41gDQNKm4AQAAAKBRQpsDVd48MGNVfOGckdGlXWH86LH5cfFxA9PzTGav2hLbd5fEsYd1q/XPAQBNheAGAAAAgDp5YfGGeoc2Bwpvvv+PufG7T50cU744KUrLyms0xnf+NjuemLs2Jo7sGZ87e2QcPbBLneYCAI3JUmkAAAAA1Mnxg7vFVWeOqHdoU92yacm4yfhF+XnRrjDzd49fXLwhDW0Sj89dGxf+6Kn46M9fiNeXb67XnADgUFNxAwAAAECdJZUtE0b0SEOWhpCEN8cN7lrr8W58eG6Vtkdmr4lxAzrHEf07N8jcAOBQUHEDAAAAQL00VGhT1/GeXbg+npq/vkp7pzb58W8ThjTgzAAg+wQ3AAAAADRrq7fsSkOat/rE6UOjU5uCRpkTANSV4AYAAACAZu2Co/vH1Gvflu6L07Fob4DTpV1BfORU1TYAND/2uAEAAACg2evctiDdb+dfTx0cP5m6KHp0KIwO/wxxDubpBevi3peXx5VvGxGDurc7JHMFgIMR3AAAAADQYnRpVxhfOHdUjfqWl5fHjQ/NjRcWb4z7XlkeFx83IK44Y3gM6CrAAaDxWCoNAAAAgFbpyfnr0tAmUVJWHnc/vzTO+P6U+P6Dcxp7agC0YoIbAAAAAFqdpNrmfx6aW6W9uLQ8OrW1SA0AjUdwAwAAAECrM2Xu2nhlyaYq7T06FMWHThrcKHMCgITgBgAAAIBWZ1TvjnHZiYMiPzdnv/bLJw2LtoV5jTYvABDcAAAAANDq9OvSNr7z7nHx2BcmxSXHDYy83Jzo1bEoPnDioBots7Z5R/EhmScArY8FOwEAAABotQZ2axc3vPfItNJm2cad0aYgc7XNo7PXxFW/mRb/durg+OiEodG5XcEhmSsArYOKGwAAAABavcE92seEET1qVG3zPw/NjW27S+IHj86PCd97NG5+eF5s2aUCB4CGIbgBAAAAgBp6cMbqmLFiS+X7rbtK4saH58b7bnsmDXUAoL4ENwAAAABQA2Vl5XHTw3Or/ewDJx0WOTk5B73+hcUbGnQ+DT0eAE2D4AYAAAAAauDFNzbG7FVbq7T379I23nfcgINee+NDc+Pi256JW6csaJC5JOMk4yXjAtCyCG4AAAAAoAZOGNIt/nTFqXHGqJ77tX/mbcOjKD/voJUxNz8yLz2/4YHZ9Q5vkuuTcRLJuEmgBEDLIbgBAAAAgBo6amCX+Nm/nhD3fvqUOG1EjxjYrW2899iDV9scP7hbfOncUZXv6xPe7BvaJK6dPDqOO6xrncYCoGnKb+wJAAAAAEBzc8ygrnHnR0+MTTv2REFe5u9GD+jWbr/3FeHL5ZOG1Su0Sa7fs2dPreYOQNOm4gYAAAAA6qhLu8KMfUrLyuOmh6vuRZOEMD96bO8SanUNbQBoeQQ3AAAAAJBFf351eSxcu73az/7rwbkZl00T2gC0LoIbAAAAAMiSktKyuPnhg1fVHGzPG6ENQOsjuAEAAACALFmzdXd0aFN1m+mhPdvHF88dedDwRmgD0DoJbgAAAAAgS/p1aRv3f2ZC3P6hY2N0n46V7VedOSKuOGNEGsZUF94IbQBar6pxPwAAAADQYHJycuLcsX3i7DG944EZq+L+V1fEeUf2Sz+rCGMqQprk9fYnFsSmHcWV13/itKFCG4BWRHADAAAAAIdAbm5OvGNc3/TY11vDm31Dm8TPnl4UZeXl8dkzR0TntgWHcMYANAZLpQEAAABAI0vCmy7t9g9lcnP2vhaXlsdPnlwUZ3x/Stz17BtRUlrWOJME4JAQ3AAAAABAI0v2tHlrpU1Z+f59NmzfEz94ZF7sLhHcALRkghsAAAAAaOTQpmKZtMTBlkP70uTR0b7I7gcALZngBgAAAACaSGhz7eTR8cSXzohjB3Wt0vfIAZ3jovH9D/EMATjUBDcAAAAA0ERCm2Svm6Ti5g+fPiU+NmHIfv3H9e8cuRUb3wDQYgluAAAAAKCJhDb7+up5h6ftFX713JL0uoMpKyuPl97YmIUZA3CoCG4AAAAAoImFNhWS9n3Dm+S6g4U3f5m+Kt5z69PxsV+8GIvWbW/gmQNwKAhuAAAAAKAJhja1DW92lZTFfz00Lz1/eNbqOOfGx+Nbf5kZm3cWN+jPAEB2CW4AAAAAoImGNrUJb/40Z3us3rK78n1xaXn85MlF8eE7novy8vIG+RkAyL78Q3APAAAAAGjV6hPaVKjoXzFOxetHTxkY63aUxn1zql8a7ZMTh0VOTk49Zg/AoSS4AQAAAIAsemHxhnqHNgcLb47q3yGWbSmJwtyc2FO6f2XNCYO7xduP6FOv+QNwaFkqDQAAAACy6PjB3eKqM0fUO7Spbtm0ZNzjDusaR/cpih++o2d8+KSBkZe7t7omKbL59/MPV20D0MyouAEAAACALPvc2SNjwogeaYjTEJLw5rjBXdPx9uzZk7Z1LMyNr75jdHz4lCHx7b/Oip4di+KI/p0zjlVaVp7ugZOf5zveAE2B4AYAAAAADoGGCm0yjTe8V8f42b+eEHtKymo0zm9eWBJ3PvNGfO28w+PU4T0adI4A1J4YHQAAAABaoML8zP/0t2VXcfz3P+bG7FVb4wM/eS4+9osXY9G67YdkfgBUT3ADAAAAAK3ULY/Miw3b9y61lnh41uo458bH4ydTFzbqvABaM8ENAAAAALRCSWXNz59eXKW9uLQ8hvfq0ChzAkBwAwAAAACt0s+fWpSGNG81aVTPmDSqV6PMCQDBDQAAAAC0Sl897/D4+vmHR+e2BZVtebk58dV3jmnUeQG0doIbAAAAAGiFCvJy4yOnDonHvzgpPnLK4DS0+dBJh8XwXh0be2oArVp+Y08AAAAAAGg8XdoVxtffNTY+eNKg6NGhqEbX3P38kigrL49LjhsY+Xm+Gw7QkDxVAQAAAIC00iYJcTJZv213fOdvs+Irf3w9zrvlyXhq/roqfV5YvKFB59bQ4wE0ZYIbAAAAAKDGbnx4bmzdVZKez161NT7wk+fiY794Md5Yv33v5w/NjYtveyZunbKgQe6XjJOMl4wL0BoIbgAAAACAGpm9akv8+rklVdofnrU6Vm3elVbG3PzIvLTthgdm1zu8Sa5Pxkkk46q8AVoDwQ0AAAAAkFF5eXl86y+zoqy86mfvGNcnThzaPY4f3C2unTy6sr0+4c2+oU0iGTcZH6ClE9wAAAAAABnl5OTER08bEsN6tt+vvTAvN657+5jK95dPGlbv8Ka60CYZF6A1ENwAAAAAADVyxqhe8cDVp8c33jU2urQrSNuSMGdgt3b79atPeCO0AVq7/MaeAAAAAADQfBTk5ca/nDI4Lji6X9z+xML49AFClYqwpSKESV53FZfG584eecCxhTYAKm4AAAAAgDro0q4wDVY6ttlbeVOdt1be3PzIvPjknS9GSWlZlb5CG4C9BDcAAAAAQNYk4cvYfp0q3z84Y3Wc/J+PxFPz11W2CW0A3iS4AQAAAACyZtrSTTFjxZb92tZu2xMf+MlzsWjddqENwFvY4wYAAAAAyIry8vL45v0zDvj5u//3qdi0o7jyvdAGQMUNAAAAAJAlW3eXROe2B94DR2gDUJXgBgAAAADIik5tCuJn/3pC/Pxfj4/hvTpUtrcp2P+fJbu0KxDaAPyT4AYAAAAAyKpJo3rF3686Lb7xrrHRq2NR7Couq1J5k+x1A4DgBgAAAAA4BArycmPHntJYs3X3fpU2FW54YPZ+4c3mHcXxtftej/Xb3uwP0BoIbgAAAACArEtCmSSc2XdPm2n/fk76Wl148+2/zYw7n30jzvqfx+OPryyL8vLyRpk3wKGWf8jvCAAAAABEaw9tKva0qXit+Dx5fWP99vjti8vS9xt3FMfn7nk1/jRtRXzrwiNiQNd2jfIzABwqKm4AAAAAgEYJbSok7/etvPnNC0urjDNlztr4zt9mZXm2AI1PcAMAAAAANFpoc6Dw5q3aF+bFV955eFbmCdCUCG4AAAAAgEYNbSokn19xRvV9vjR5dPTv0rbB5wnQ1AhuAAAAAIBGD20qfPHc0VUqb/p1aRMfOumwBp8nQFMkuAEAAAAAmkRoc6Bl01Zs2hW3P7GwQecJ0FQJbgAAAACABvHC4g31Dm0OFN4k4ybjH8z3H5wTj81ZU6f7AbSq4Gb16tXx3//933HBBRfE+PHj46ijjopzzjknrrvuunj55Zezfv/XXnstxo4dG6NGjYpbbrkl6/cDAAAAgNbo+MHd4qozR9Q7tKkuvEnGTcY/kKfmr4sfPjY//vVnL8RVv3kl1m/bXa97AzSW/Gzf4OGHH45rr702tm3btl/7G2+8kR733ntvXHbZZfHVr3418vLyGvz+O3bsiC9+8YtRUlLS4GMDAAAAAPv73NkjY8KIHgcNWWob3hw3uOtBx9u5pzSuu3d65fs/TVsRT8xdG/9+/uFx4dH9Iycnp0HmAtDsg5tnnnkmrrzyyigtLU3fjxw5MiZNmhRFRUUxbdq0ePLJJ6O8vDx+/etfp59ff/31DT6H7373u7F48eIGHxcAAAAAqF5DhTY1He+mh+fGkg079mvbuKM4vvrH1+PU4T2iV8c2DTofgGYZ3OzatStdCq0itLn88svjqquu2i/dfvrpp+OKK65Iq2KS8Obcc8+Nk046qcHm8Oijj8Y999zTYOMBAAAAAE3LvNVb4/+mLqz2sy9NHi20AZqdrO1x87vf/S5WrlyZnp966qlx9dVXVylJPOWUU+I//uM/Kt/fdNNNDXb/9evXp8uvJQoKChpsXAAAAACg6Rjeq0N8593jomOb/b+jfsygLvGhkw5rtHkBNLng5o9//GPl+ac+9akD9nvnO98Zw4bt3aTslVdeiaVLlzbI/b/yla+k4U27du3iYx/7WIOMCQAAAAA0LcmXxS89YVA8/PmJce7Y3mlbYV5u3PCeIyM31942QPOTleBmw4YNMXPmzPS8U6dOceyxxx70wTpx4sTK9w899FC973/33XfHY489lp5/+ctfjkGDBtV7TAAAAACg6erdqU3c/qHj4rYPHhPXvWN0jOjdsbGnBNB0gpsZM2ZEeXl5ej5u3LjIy8s7aP+jjjqq8vzVV1+t170XLVoUN9xwQ3qeBEKXXHJJvcYDAAAAAJqPyUf0jX89dUiN+j49f118/c8zYtvukqzPC6BRg5vFixdXng8YMCBj/379+lV7bW2VlJTEF7/4xdi5c2d06dIlvv3tb9d5LAAAAACg5dq5pzS+fO/0+PnTi+PcG5+Ix+asqfzshcUbGvReDT0e0LLtv2NXA1m7dm3led++fTP2791779qTiWRfmrr60Y9+FNOnT0/Pv/nNb0bPnj0jG5Jqoj179mRl7OaouLi42nOAhuI5A2STZwyQbZ4zQLZ5ztTNfz84N5Zs2JGeL9+0M/71Zy/Eu47sEz07FsUdT70RXzh7eHzitJpV7hzMj6cuiu8/ND8+M2loXPm2vXt9Q3PjOXNgFauPNfngZuvWrZXnbdu2zdi/TZs21V5bG6+88krcfvvt6fmFF14Y5557bmRLUtlTERCxv9mzZzf2FIAWznMGyCbPGCDbPGeAbPOcqZkFG4vjp09V/QL5n19bVXmehC2rVq2Kd4/uUOf7/HH2trhr+rb0/IdTFkafnE0xpkdhnceDpsBzppkulbZvNUpRUVGtgpu6VLJs3749XSKttLQ0XXbtq1/9aq3HAAAAAABax7fj73hlS5RV89mo7gVx2RFvBjVJ6JKEL/UNbRIfHNdBaAM0XsVNbm7d86CcnJxaX5PsZbN06dL02v/8z/+Mjh07Rjbl5+fHmDFjsnqP5iQpjatIWUePHh0FBQWNPSWghfGcAbLJMwbINs8ZINs8Z2rvlv7b42t/mhXPLd5Y2VaQlxM3vv+4GN6rQ/Tru3d5s0QSvvTp06dWy6Yly6PdNf3N6p2GWnYNGovnzIHNmjUrXaWryQc37dq1qzzfvXt3xv67du2qVYXOvh566KH4wx/+kJ7/y7/8S5x00kmRbUlAVFgoHa9O8j9YfzZANnnOANnkGQNkm+cMkG2eMzUzsm9h/OaTJ8c9LyyNb/9tVmzdVRKfOWNEHD6gW/r5Z84cFXl5+XHDA3v/oToJcZL3l0/KvEfNrVMWVIY+iWsnj67RddBceM7Uvxil0YObfUOZA9m3T4cONV8zcu3atfG1r30tPR8xYkR8/vOfr/VcAQAAAIDW+Y+tl54wKM4Y3Stuf3xhlXCl4n1FeFPxerAQJgltKvolhDZAkwluevXqVXm+Zs2ajP1Xr15ded6zZ88a3+e73/1ubNy4t5xx7Nixcdddd1Xb7/XXX688f+WVV+KOO+5Iz/v27RvveMc7anw/AAAAAKBl6d2pTfz7+YdX+1l14c0fXloaN7z3qDj2sK779RXaAE06uEmqXyosX748Y/99+wwZUvO1HvcNhe67774aXfPUU0+lR+KEE04Q3AAAAAAAB/TW8Gb+2u3xnlufjo+cMji+cO6o6FCUL7QBmn5wM3LkyLTUsLy8PKZPn56+Hmydt2nTplWeJ5UzAAAAAABNRRLCrNq8K37xzOLKtp8/vTgemrk6JgzvHve8uKyyXWgDNMngplOnTnHsscfGiy++GOvXr0/DmyOPPLLavkmo8/jjj1e+P+2002p8nzvvvLNG/e6999647rrr0vPPfOYz8dnPfrbG9wAAAAAAWrfi0rJ4YfGGKu3LN+0U2gANLjey5Lzzzqs8v+WWWw7Y7/77749Fixal50ccccR+y6wBAAAAADS237+0LGau3HLQPkIboMkHNxdddFEMGjQoPX/iiSfiW9/6VpSUlOzX5+mnn47rr7++8v2VV16ZrekAAAAAANTJe48dkAYzRfnV/3Nql3YFQhugaS+VligqKopvfvOb8fGPfzyKi4vTZc2mTp0aZ555ZrRr1y5ee+21NNBJlkpLvO9974uJEycedJmzxJw5c7I1ZQAAAACAKgryctNgZvIRfeLDdzwXSzfu3O/zTTuK49YpC4Q3QNMObhInn3xy3HTTTfHlL385tm7dGosXL4477rijSr9LLrlkv8obAAAAAICm5oHXV+0X2iSVNklok7jhgdnpq/AGaNLBTeKss86KBx54IO66666YMmVKLFu2LHbt2hU9evSI8ePHx6WXXhonnnhitqcBAAAAAFBnSUVNRTiz7542+7ZXF97MWrklRvbuGHm5OY0wa6A5ynpwk0hCmquvvjo96rJXTnLUR0OMAQAAAAC0TgcKbRIVr9WFN4vXbY/33Pp0HDmgc9x4ydHRt3PbRpk/0LwckuAGAAAAAKClhTYVqgtvSsvK4h8zV8eOPaXx7MIN8fabp8YN7zkyzh3b5xD/BEBzk9vYEwAAAAAAaK6hTYWkPfm8wvf/MTdeW7a58n2yF84n73wpvvLH6VFWVp7lmQPNmeAGAAAAAKAeoc2BwpvqlJWXR679boCDENwAAAAAANQztKmQ9PvgSYOq/Wx4rw7x7+eNbbB5Ai2T4AYAAAAAoAFCmwrfunBcXHXmiP3a8nJy4geXjo+2hXkNNlegZRLcAAAAAABExAuLN9Q7tKnwubNHxrWTR1W+Ly0vj+17ShpknkDLJrgBAAAAAIiI4wd3q6yUqU9oU+HyScMr97y56szh6fgAmeRn7AEAAAAA0EoklTITRvRosJAlCX+OG9y1RuOVl5fHDQ/MictOGBSDurdrkPsDzY+KGwAAAACAfTR0ZUxNx/v504vjtscXxDt+MDXue2V5g84BaD4ENwAAAAAAjWzmii3xn3/bu7/Ott0lcfU90+Lz90xLz4HWRXADAAAAANCIduwpic/e/XLsKS3br/3eV5bHv/7s+XQJtcQLizc06H0bejygYQhuAAAAAAAa0W1TFsSCtdur/ezKM0dETk5O3PjQ3Lj4tmfi1ikLGuSeyTjJeMm4QNMiuAEAAAAAaESfmjQsLjluYJX2T04cGqeN6JlWxtz8yLy07YYHZtc7vEmuT8ZJJOOqvIGmRXADAAAAANCI2hXmxw3vPTJ+eNn46NgmP207ckDnuObsUen58YO7xbWTR1f2r094s29ok0jGTcYHmo69TwEAAAAAABrVeUf2i6MGdImv3Pd6fPNdY6Mw/83v3V8+aVj6WhG6VLxWtNc1tKnN9cChIbgBAAAAAGgiBnZrF7/8txOq/ay68KaktCw+e+aIjOMKbaD5sFQaAAAAAEAzkYQt+y6b9t8PzY1P3vlSlJeXH/AaoQ00L4IbAAAAAIBmJAldvnTu3v1vEg/OWBXn3vhEbNqxp0pfoQ00P4IbAAAAAIBmprh0/wqbuWu2xWnfeyyeW7i+sk1oA82T4AYAAAAAoBl5cfGGuPmRuVXat+4qiW/+ZWZ6LrSB5iu/sScAAAAAAEDNPbdoQ5QdYEubGSu2xNHf/Eds2lFc2Sa0geZFxQ0AAAAAQDNyxRnD445/OS66tS+sbMvNefNzoQ00b4IbAAAAAIBm5swxveOBq06LCcN7pO+vOWdUdGlXsF+f5L3QBpofwQ0AAAAAQDPUq1Ob+OW/nRA3XXJ05Lyl0ib++T7Z6wZoXgQ3AAAAAADNVG5uTqzcvCu+9+CcyrZ9K29ueGD2fuFN6YE2xwGaDMENAAAAAEAzlYQySTiz75420/79nPT1reHNE3PXxnm3PBlL1u9opNkCNZFfo14AAAAAADT50KZiT5uK14rPk9ei/NzYXVIW7/rRk/Gjy46JU/+5Pw7QtKi4AQAAAABoQaFNheT9vpU3SWhTsffNh3/6fPz0yUVRXm7pNGhqBDcAAAAAAC0stKnwydOHxvCe7au0J3vdfPMvM+OxOWuyOleg9gQ3AAAAAAAtMLRJbN5ZHAX5edV+9q6j+sUZo3plZZ5A3QluAAAAAABaYGiT6Nq+MP5w+cnxziP7VvlseK8OkZOTk5W5AnUnuAEAAAAAaIGhTYV2hfnxw/ePjy+eO2q/9v95aG46LtC0CG4AAAAAAJqwFxZvqHNoUyGprLnijOFxx78cFx84cVBlezJuMj7QdAhuAAAAAACasOMHd4urzhxR59BmX2eO6R3ffve4dJxEMm4yPtB05Df2BAAAAAAAOLjPnT0yJozo0WAhSxL+HDe46wHHKy8vj5senhfnHdk3RvTu2CD3BGpGxQ0AAAAAQDPQ0JUxBxvvzmffiJsfmRcX/uip+N/H5jfofS3NBgcnuAEAAAAAoNIzC9bHN+6fmZ5v31Ma33twTnzojufSKpz6unXKgrj4tmfixofmNsBMoWUS3AAAAAAAkFq6YUd8+lcvRWnZ/iHN1Hnr4l0/fLLeoc0ND8xOz5NqHpU3UD3BDQAAAAAAqR8+Oj827iiu9rPpy7ek4Ut9Q5vEtZNHN/jSb9BSCG4AAAAAAEh988Kx8b7jBhzw8yR8qW14U11oc/mkYfWaJ7RkghsAAAAAAFJF+Xlxw3uOjK+ff3jk5eakbW8/ok986dxRdQpvhDZQe/l1uAYAAAAAgBYqJycnPnLqkBjZu2Pc8uj8+P7FR0X7ovy0vSKEqXg9WAgjtIG6EdwAAAAAAFDFKcN7xMnDuqeBTaIidKlJeCO0gboT3AAAAAAAUK2K0KbCgcKbS44fGCs27Ywj+ncW2kA9CW4AAAAAAKix6sKbXz//RqzZsjvOGds77n91ZWVfoQ3UnuAGAAAAAIB6hTdLN+xMX4U2UH+5DTAGAAAAAACtTBLKTB7bp9rPThraLT41ceghnxO0BIIbAAAAAABqbcaKzfHI7NXVfvb68i2xbOPeKhygdgQ3AAAAAADU2qjeHePIAV2q/ey8I/vGwG7tDvmcoCUQ3AAAAAAAUGv/N3VRvPTGxmo/+80LS+PWKQsO+ZygJRDcAAAAAABQK0koc8MDs/ersMnPzdlvz5vkc+EN1F5+Ha4BAAAAAKCVemtoc+3k0XH5pGGxZP2OGNS93X6fV7wmnwM1o+IGAAAAAIB6hTaJJLRJJO+T9goqb6B2BDcAAAAAANQrtHmrg4U367ftjpfe2HAIZgzNk6XSAAAAAABosNCmQsXn+y6btqekNB6etSbmrt4aP7zsmDj78N5Znjk0PypuAAAAAABo0NDmQJU3Nz48L6Yv3xy7S8riU3e9FL97cWlW5gzNmeAGAAAAAIAGD20qJP2/dO6oKu2lZeXxxd+/Frc/bv8b2JfgBv5/e3cCbmVV7w98AYdRVAQUESUQz1EScsAJBTERLc0ybw6ZN7OcLdCsR71ZlnZtvkpaUmm3HFLzOpR1r0WU4oBTipKAIIMTCMigIDKf/7Ne/+927zNwpr3P2Wfvz+d5znPe/e6113qxWOy9v+9vLQAAAACglqcXrmhxaJPq07NLvc/9+rEFYc36TSGf1w3tmeAGAAAAAIBaDhzUO0wYW9ni0Cb6zIjdwumHDKx1vkeXTmHJO+vDrdNeCfmqEDpp0rRw7eQ5eekP2kJFm4wKAAAAAEDRu3hcVRhV2TcJcVqiU8cO4epPDQt9tukaJk6Zm5zr3qVTWLthc3KcVva0JBzKXtYtjpGP64a2oOIGAAAAAIB65Sv86NChQxIEfeeTe4funTuF3555UFLJk4qhSwxf8rUXj9CG9krFDQAAAAAAreaMQweFjw/fOey0bbdw0OD3w5U0dGlO5U1doU1LKnegram4AQAAAACgVcXQJhVDluZW3ghtKEUqbgAAAAAAaFNp2FKz8mZM1Y5hS3V1GDZg+1qvEdpQqgQ3AAAAAAAUZXhz/d/nho4dOoRfff6AMHJIn0xboQ2lzFJpAAAAAAAUhZrLpq3dsDmsWb8pnPHfT4UH//Vmck5oQ6lTcQMAAAAAQNE47eCB4dePLQjLVq/PnNuwaUu44PZ/hqM/vHN48MX3A5xIaEMpUnEDAAAAAEDR+MXD83JCm9SW6iC0oSwIbgAAAAAAKBoXHVUVPrnPLlttI7ShlAluAAAAAAAoGl0qOobrTtk3fOHQQXU+36tHZ6ENJU1wAwAAAABAUenYsUO48vgPh9GVfWs9t2rtxnDjQ/Pa5LqgNQhuAAAAAAAoOpMenh8emftWTqVN6gcPzhbeULIENwAAAAAAFJUYysRwJntPm+nfOjr5nRLeUKoENwAAAAAAFHVok+5pE3/XF96s37S5Da4W8q+iAH0CAAAAAEBeQ5tU+jhtF38veWdd+OuLb4b/OmXfcMjufVr5qiG/VNwAAAAAANAuQptUzcqb3zy+MCx6e1344m+eDv98ZUWrXC8UiuAGAAAAAIB2E9qk4vOfO3hgzrm1GzaHL/z66fD8a6sKdq1QaIIbAAAAAADaVWgTzVmyOtz33Bu1zq9evyn8+81PhpeXrm7xtT29UPUOrU9wAwAAAABAuwptoiE79gxHDe1X53N9enYNu+7Qo8XXdtKkaeHayXNa1A80leAGAAAAAIBWF6tZmhvaRJ06dgj/dfI+4ePDdq713IK33g0z3ng7L4HSxClzVd7QqgQ3AAAAAAC0ugMH9Q4TxlY2K7RJVXTqGCaeul84auhOtZ57ZuHKvFUBxWuF1lLRaiMBAAAAAECWi8dVhVGVfVsUjHSp6Bh+9rn9wy2PvxI2bN4cfvSX95c2S8OXpgRCLVm6DfJFcAMAAAAAQJvJRzVL14pO4ezDd0+OO3bomAlfmhLeCG0oFpZKAwAAAACgZMSwJYYuqRjGxFBma4Q2FBPBDQAAAAAAZRPeTJ2zLLy1Zn3mOaENxcZSaQAAAAAAlJw0fMleNu2lN98Jf3phcdhjp57hjrMPCXc+/ZrQhqIjuAEAAAAAoCzCm/unL0p+z35zdfjYxKlhyTsfVN4IbSgWlkoDAAAAAKBkxTDm2GE71zovtKFYCW4AAAAAAChZ6zdtDrOXrK73+cMr+wptKCqCGwAAAAAASlbXik7h9rMODrv17l7ruc6dOoRfnXFAm1wX1EdwAwAAAABASeu/ffdw3PD+tc5v3Fwdfv3owja5JqiP4AYAAAAAgJJ240PzwqSH52ce9+jSKXP8gwdnJ89DsRDcAAAAAABQsmIoE8OZ1MVHVYaZV30sXPqxvTLnhDcUk4q2vgAAAAAAAGiN0CaGNecfMSQ5Tn+nz6e/0/PQVlTcAAAAAABQVqFNKj5WeUOxEdwAAAAAAFB2oU1D4c2zr64Mm7dUt+g6nl64okWvpzwJbgAAAAAAKMvQJhWfP2xIn8zj+PoTf/54+N7/zmrRdZw0aVq4dvKcZvdBeRLcAAAAAABQtqFNWhnz2Lzltc7f9OiCcOu0hS26jolT5qq8oUkENwAAAAAAlG1oEx04qHf46rjKOp/71h9eDH+fvaRF1xH7h8YS3AAAAAAA0K7FipbmhjapMVU7hU4dO9Q6H3e5Of+2Z8PrK9cWNDyClOAGAAAAAIB2LVa0TBhb2aKwZJ/deoXrTtm3zucuHlcVBvTqvtXXC23Il4q89QQAAAAAAG0khiujKvu2aFmy4/fZJby6Ym340V9eyjlfXR1Chw61q3FSQhvyScUNAAAAAAAlIR97yVxwxJBwygG7hR6dO2XOxVAmhjN1EdqQb4IbAAAAAAD4/2JlzXc/PSxMvmRMEsJsLbwR2lAIghsAAAAAAMjSuVPHZE+bGMLUF94IbSgUe9wAAAAAAEA90jAmDWni719MnRdWrd2YaSO0IZ9U3AAAAAAAwFbUrLzJDm2+dkyV0Ia8EtwAAAAAAEADYjjTq0fnnHPdOncMk2cuDes3bW6z66L0CG4AAAAAAKABcU+b7EqbaN3GLeH511aFq/80s82ui9IjuAEAAAAAgAZCm3SPm6hDh9znb3vi1XD/c2+0/oVRkgQ3AAAAAADQyNBmx227hurq2u2+dvfzYe6S1a17cZQkwQ0AAAAAADQitLn0Y3uF3511cOjRpVOttpu2VIdr/za3ReM9vXBFi15PaRDcAAAAAABAI0Kb848YEir7bRu+d+LwOl/zvzMWJ69r7ngnTZoWrp08p9nXTGkQ3AAAAAAAQCNCm9QuvbrntB+5e5/McXxdU8Ob7PEmTpmr8qbMCW4AAAAAAKCRoU104KDe4ZKjqzKPp81fHsZU7dis8Kau8WL/lC/BDQAAAAAANDK0SX3lyMrk+dTDc5Y1ObxpyniUj4rWGGTJkiXhtttuC1OnTg2vvvpq2LJlS+jXr18YMWJEOOmkk8L++++ft7Eef/zx8Ic//CFMnz49LF26NGzcuDH06tUrDB06NBx11FHh05/+dOjSpUvexgMAAAAAoP1rToiSPp++Lg1v4u/s83X1I7ShzYKbv/3tb+HSSy8Na9asyTn/yiuvJD/33ntvOO2008IVV1wROnXq1OxxVqxYEb7+9a+HRx99tNZzy5YtS35icPSLX/wi/PSnPw3Dhg1r9lgAAAAAAJSOuKdMc0OUxoQ3BwzaIWf5M6ENbRbcTJs2LYwfPz5s3rw5eVxVVRWOOOKI0LVr16QiJoYs1dXV4Xe/+13y/JVXXtmscd59993wxS9+McyaNSt5HAOg0aNHh7333jtUVFSE+fPnhylTpoS1a9eGN954I5xxxhnhjjvuSK4HAAAAAIDyFkOVCWMrw8Qpc5sVomwtvLnwo0NCz64ffBUvtKHNgpt169aFyy+/PBPanH/++WHChAmhQ4cOOcuaXXjhhUmgEsObY445JhxyyCFNHuvnP/95JrQZMGBAuPHGG8Oee+6Z0+att94KX/nKV8Kzzz6bVP9cdtll4Z577sm5HgAAAAAAytPF46rCqMq+OZUxLQ1vPrlP//DQS8vC7558Nfx5/Ojwh+mLhDY0qGMokLvvvjssXrw4OT7ssMPCRRddVCskOfTQQ8PVV1+deXzdddc1eZwYEKUVOx07dkxCnJqhTdS3b99kmbT4O3rxxRfDU0891eTxAAAAAAAoTc0NbVIxhIlhTOqPzy8OLy56J6xcuzF8ZtLjQhvaNri57777MsfnnXdeve2OO+64MGTI+//nfO6558Jrr73WpHGeeOKJpGInDYL22uuDvxQ1bbfdduGEE07IWcoNAAAAAADy5ZzDdw8HD64dAC1atS5zLLSh1YObFStWhJkzZ2bCkhEjRtTbNlbhjBkzJvN48uTJTRprzpw5meNhw4Y12H7gwIGZ42XL3t8cCgAAAAAA8qFjhxB6b9Ol3uc/e9BuQhtaf4+buAxZdXV1cjx8+PDQqVOnrbbfZ599MsfPP/98k8b6whe+EI499tiwZMmSzDJoW7N06dLMcY8ePZo0FgAAAAAAbE0sVvjhZz4SZr+5Oix4690az4Vw/Ed2abNro4wrbhYuXJg53nXXXRtsv8suu9T52sbo0qVLMkas6vnQhz7UYPu//vWvmePKysomjQUAAAAAAA3ZtlvncMSeO9Y6H+sdnn/97Ta5Jsq84iZ7CbL+/fs32L5fv36Z4+XLl4dCeeCBBzJLq3Xu3DkceeSRzeonVhNt2LAhz1fXfm3cuLHOY4B8Mc8AhWSOAQrNPAMUmnkGis8vH1kQ/vuxD4oUenTpFNZu2Jwc/+DB2WHz5k3hnNGDQ3thnqlfuvpY0Qc3q1evzhx37969wfbdunWr87X59Morr4Srr7468/iUU05p1NJqddm0aVOYMWNGHq+udMyePbutLwEoceYZoJDMMUChmWeAQjPPQNu7b/aacNuMNZnHnxm6Tdh3565h9lsbMud/PPnl8Oabb4ZP79WzWWPMemtDGNq3/n10Csk8006XSsuuRunatWuTgptCVLLEfW3OPvvs8Pbb75egDRgwIIwfPz7v4wAAAAAAUL5qhjanD+8ZOnYI4Yp/rMg8TsV2sX1zxoj93fViYYogaHsFqbjp2LFjizZuyqfFixeHM888M6m4SSuAJk6cGLbffvtm91lRURGGDh2ax6ts32JpXJqy7rXXXskydAD5ZJ4BCskcAxSaeQYoNPMMFM/yaLfNeDPz+Gvj9gj7D+wVTrv5mUxQE899bef3K27SczvvvHOjl03LHuP3M98NJ4wcGg740A6h0Mwz9Zs1a1aySlfRBzc9evTIHK9fv77B9uvWrWtShU5jvfzyy+Gss85KwpuoS5cu4frrrw/Dhw9vUb8xXIp9UVv8C+u/DVBI5hmgkMwxQKGZZ4BCM89A27jxoXmZMCa69GN7hfOPGJI5jvvaRLFNfFzzXKdOFZn2TRnj0MoP9o9vLeaZwhajFGyptOzgJjuUqU92m549m7emX02PPfZYOPXUUzOhTbymSZMmhdGjR+elfwAAAAAAiIFKGsLUDG2ieBzPpdK2Nc/d+NDLzR6D0lKQ4GannXbK2V+mIUuWLMkc77jjji0e/8477wznnHNOWL36/TX+evXqFX7zm9+Eww47rMV9AwAAAABAUwKV+sObPbPOvZT019wxKB0FWSqtsrIyc/zGG2802D67zeDBjVvLrz4//vGPw69+9avM41133TXcdNNNLe4XAAAAAACaG6ikz6Wvib+rdspdgSp9Lm0rtClPBQluqqqqknXdqqurw4wZM5LfW1vnbfr06Znjvffeu1ljxjGuvPLKcNddd2XOfeQjH0mWR+vTp0+z+gQAAAAAgJqeXriiWYFKzfBmztI1tdrE5w4YtEN4ZuFKoU2ZKshSadttt10YMWJEcrx8+fIkvNla4PLwww9nHjd3D5rvf//7OaHNRz/60XDLLbcIbQAAAAAAyKsDB/UOE8ZWNitQiW1P3H9Avc8fseeOQpsyV5DgJvrEJz6ROb7++uvrbffAAw+EBQsWJMfDhg3LWWatsf785z8ne9hkj33DDTeE7t27N7kvAAAAAABoyMXjqsLd541sVqDyXyfvG4btsl2dz618d4PQpswVLLg58cQTw8CBA5PjqVOnhu9+97th06ZNOW0ef/zxZHmz1Pjx45s8zooVK8K3vvWtzONRo0aFH/7wh6GioiCrwAEAAAAAQKbyprl+d84hYdtuud9jb9OlU3j+9bczj4U25alg6UbXrl3DVVddFc4+++ywcePGcOutt4ZHHnkkjB07NvTo0SO88MILSaATl0qLTj755DBmzJha/dx7773h8ssvzzx+6aWXcp7/7//+77BmzQfrAO6555451Tdbs8cee9Q5JgAAAAAAFNJ23TqHGz83Ipx+85OZc+9u2Jw5FtqUr4KWpYwcOTJcd9114bLLLgurV68OCxcuDDfffHOtdqecckpO5U1T3HfffTmP6+q/Pscff7zgBgAAAACANjGqsm+474JDw5n//XRY9d7GzPlePToLbcpYwZZKSx111FHhwQcfDOeff34YOnRo2HbbbUPnzp1D//79w7HHHhtuueWWpDKnU6dOzVombdmyZQW5bgAAAAAAKLQn5q/ICW2iVWs3hhsfmtfsPp9euCIPV0ZbaZWNYPr27Rsuuuii5Kc5e+XEn7r07t271tJpAAAAAADQHsRw5gcPzs6ptImhTZSeb2rlTdrnhLGV4eJxVXm+Ykqi4gYAAAAAANh6aBOde/iQZG+bVHy+KZU32X1OnDJX5U07JbgBAAAAAIA2Dm2i9FxzwpuafcY+DhzUO2/XTOsR3AAAAAAAQCupK2CpGdSk57PP/ddfX2pSn01dYo3iIbgBAAAAAIBWUF/AEn9qhzfV4YR9d8mc++nfX66z8kZoU3oq2voCAAAAAACg1DUUsKTHaZsfPFi7wiZ9Lm0rtClNghsAAAAAACigxgYsNcObumQ/J7QpTYIbAAAAAAAokKZWxcTn3n5vQ5j08Px629QMdoQ2pcUeNwAAAAAAUABPL1zRrKqYyz4+NBxe2bfW+d16d691TmhTegQ3AAAAAABQAAcO6h0mjK1sVsBy0xkHht7bdM45t/q9TTmPhTalSXADAAAAAAAFcvG4qnD3eSObHLB0qegYvvzRyjBi4A6Zc6ve29ii0CZWAFH8BDcAAAAAAFDgypumunbynHDVn2aGoz7cL/TqkVt5Ex83NbSJe+2cNGla0i/FTXADAAAAAABFJFbGTJwyNzmOe+SsWvtBpU0UH8cgprFi23SvndivypviJrgBAAAAAIAiq9CJS6HVlF15E4OYxoQ32aFNFPttTgUQrUdwAwAAAAAA7cC5hw/JCXQaCm/qCm2ausQarU9wAwAAAAAARaRm4JJKzzUmvBHatF+CGwAAAAAAKBJ1BS41g5r0fH3hjdCmfato6wsAAAAAAAAaDlzS5+Lvjw/bOWzbrSKsXrcp57max0Kb9kdwAwAAAAAARR7apMdpm//715u1+qi5vJrQpn2yVBoAAAAAALShxi5tFs+duP+ARvUptGm/BDcAAAAAANBGmrofzU9O2icM6NW9la6OtiC4AQAAAACANvD0whVN3o+mQ4cO4bwxuzfYd+w39t/Y66B4CG4AAAAAAKANHDiod5gwtrJJS5tdO3lO+OYfXgx77NSz1nO9enRO+oliv7H/xlT8nDRpWtIvxaGirS8AAAAAAADK1cXjqsKoyr6NClliZczEKXOT45eXrqn1/Kq1G5Pfd583stGhTVrxE/tt7HVQWCpuAAAAAACgDTU2LInt0oqampU2qRjEPLNwZbP21hHaFAfBDQAAAAAAtGPnHj4kJ9CJgUwMZpoS2jRmmTZah+AGAAAAAADagZqBSyo915jwRmhT/AQ3AAAAAABQ5OoKXGoGNen5+sIboU37UNHWFwAAAAAAANSvocAlfS7+TgOd7HM129XVB8VDxQ0AAAAAALTT0CYe11V5c8nRVTnnhDbth4obAAAAAAAoQo1d2iw9l11l07Nr3V//C22Kn4obAAAAAAAoMk3Zj+bphSvCl0YNDodX9s2cW7N+U7PHjv3RdgQ3AAAAAABQRGJw0tjQ5trJc8JJk6aFmx6ZH5auXt9g37HfrQUzMTCK/cV+aRuCGwAAAAAAKCIHDuodJoytbFSlzcQpc5PjH/7lpVDZr2ed7So6dsjsgxP7jf03VOUT+1V50zbscQMAAAAAAEXm4nFVYVRl33pDlig+FwOZNGx54PnFoWtFx7B+05acdpu2VIf1mzaHu88b2ajQJor9bm1sCkfFDQAAAAAAFKHGBCexGietpomyQ5tOHTtkjq/729zwzMKVLd5Ph8IT3AAAAAAAQDsWQ5YxVTvmnBsxcIcw75pjc0KdGM7EkCab0Kb4CG4AAAAAAKAdi+HLw3OW5Zz756srk/M1K3KywxuhTXGyxw0AAAAAALRTNcOXWHmThjjp+TSMSR/H30/MX54T9ghtiofgBgAAAAAA2qG6KmYOGLRDOGT3PjkhTV3hTWNDm6cXrgj77NKzoH8OclkqDQAAAAAASiC0Wbdxczhp0rTM45rLo9W1F058XF9oE18T+/vp33P3xaGwBDcAAAAAAFAClTYTp8xNHqfP1Qxv9r3qr7X2womP0z1v6hvjhofmh1lvbSjYn4dcghsAAAAAAGjHoU2smDlwUO9aQU36fGrV2o2Z4+zKm7Qip74xvjZujzC0b5cC/YmoSXADAAAAAADtQNxvpq7QJhWP6wpvevXonNNP504dwq+/cGCttrH/uoKhc0YPLtifidoENwAAAAAA0A7EqpoJYyvrDG22Ft5kV9pEGzdXh8vvfSGnbez3mYUrtxoM0ToqWmkcAAAAAACghS4eVxVGVfZNQpz6pGFLdghT0++feT0M7tszaRv3xxHaFA/BDQAAAAAAtCNbC22aIjuoEdoUD8ENAAAAAACUkJr71GxNzXb1hTaz3toQhvbtkrdrpH72uAEAAAAAgBINbWIQc9aowbXa9dmmdghTX2jzy0cWhCv+sSLc9eLqAlwxNQluAAAAAACghCttrvjEh8MuvbrlnNu8pbrRff548svJ8e9nvhueeWVlnq6W+lgqDQAAAAAASjS0Sc/dcfYh4Y/TF4WfTJ6TPF713sZ626ZVNzX7PH14z3DAh3Yo2J+B9wluAAAAAACgxJZHi9Jz6e+vjK0MNz+2IKxa+0Fo06tH53Du4UNqta15HEObT+/VsxX+NAhuAAAAAACghEKb7H1qsgOZJ+YvzwltovRxfF1d4U30tXF7hJG91hT0z8EH7HEDAAAAAADt0NMLV2w1tInHafVN9PCcZTmVNqm0j+y22X2eM3pwQa6fugluAAAAAACgHTpwUO8wYWxlnaFNKp7bd7deOefGVO0Ypn/r6JygJq3IyVZfnzEwonAslQYAAAAAAO3UxeOqwqjKvkmIU5fP/eqJMP21VTnnYuVNXGItDWXSipvsipz6QptfPrIg/Hjyy0lgFMcm/1TcAAAAAABAO1ZfaPON+2aEx+Z9UEUzuO82meMY1qThTazAyRYf1xXa3Dd7TRLaRBOnzFV5UyCCGwAAAAAAKDExlLn9yVdzzi14692ckCaGNx/59l9yKm2yK3Jqhja3zViTU5FTX2BEywhuAAAAAACghMTQJV3+LMoOa2IoM3L3DwKXd9ZtyhzvP7BXrYqcdHm0mqFNXRU55IfgBgAAAAAASjS0iSHLb794UPI7NW1+3Uucjdqjb0672M8Zv34qszxa9LVxewhtCkxwAwAAAAAAJRrapCHLAYN2yAll6nLn068l7bPbZS+jdvrwnuGc0YOTY/vbFI7gBgAAAAAA2rkYpNQX2lw7eU44adK0Wsum1bR09fqkj/i6mu2O3r17+PRePTMBUewv9kv+CW4AAAAAAKCdO3BQ7zBhbGWt0CYGOhOnzE2OYyiTXUFTlxjKxOXRstvFPXHOHbF9Zr+bNCCK/aq8yT/BDQAAAAAAlICLx1WFu88bmbMHTQx06loiLYYx2Q7Jepwd2nzu4IHht18YkRzfN3tNzn43sd/YP/kluAEAAAAAgBLR2CDl8KqdwiXjqjKPn5i/InTrnBsZxOXS/vPTwzOhzW0z1mSey67qIb8ENwAAAAAAUKLi0mfZe9+k4rmKTh1zqnHWbdyS0yZW3sTXx+XRhDatR3ADAAAAAABlENrEwCUufZZKn+vVo3PO67Irb2Kb7OXRvjZuj5zQxh43+Se4AQAAAACAMght1m3cHG5/8tVkCbRUbLNq7cac18bKm+w2qdOH9wznjB6cM8ZJk6aFayfPKdifoxwJbgAAAAAAoMRDmwMG7RAmTpmbWQKtrmAmu/ImtmnsGLFflTf5I7gBAAAAAIASEQOUmqFNXNrswEG9c/azqSuYOffwITltaor73Dzzyso6g6HYP/khuAEAAAAAgBIRA5QJYytzQptUPN5aMBPDmF9MnVfr/Og9+iS/T/7wNuHZV1fVGQyRPxV57AsAAAAAAGhjF4+rCqMq+za6CiYum5ZW4NTc7yZ65OXl4ejdu4cunTqEH09+uVZoE6t8VNzkj4obAAAAAAAoMXUFKTWXOEvF0KaiY4da588bs3vm+K/z30uWSqsZ2sQ+T5o0LVw7eU5er7+cCW4AAAAAAKDE1RXaxEqb1KYt1bVe8/rK9+pcWi07tEn7nDhlblJ5Q8tZKg0AAAAAAErY1iptBvfdJix46906X/enFxaH1es2NarPGOZYLi0/BDcAAAAAAFCi6gpYXl+5Ntz+5KvJ4/pCm1S69022miHQ5w4emFTgkB+WSgMAAAAAgBIUly6rGdqs27g5CW1ipU22bbp02mpf++3cJZw+vGet83G5tdifPW7yR3ADAAAAAAAlKC5dNmFsZSa0OWDQDsleNHVV2ry7YfNW+3ruzQ3hxWUbaoU2aUWOPW7yx1JpAAAAAABQoi4eVxVGVfbN7D+THbZENfe46da5Y1i3cUudj2N4k6rZjz1u8kfFDQAAAAAAlLA0UIn73dTcsyaGNjGESWWHNunjQX165JyLYU/N0CZW85AfghsAAAAAAChxMbTJ3u8mWwxhau55EyttUguXr815LrtCJ4Y20UmTptnnJk8ENwAAAAAAUKahTarmnjex0iY7vIm27dIh53FaqZP2bZ+b/LDHDQAAAAAAlKgYpGSHNmmFTH1BTvaeNzWXTVu9obpWpY59bvJPxQ0AAAAAAJSoGKRMGFuZCVbOP2JI8pMGODXF0KZmpU1Fx9xKm5rLqqV92+cmP1TcAAAAAABACbt4XFUYVdk3pxrm0bkfVMrUVLPSZtOW6q0uq5a9z00MieJ4NJ+KGwAAAAAAKHHZoc037psRHpu3vMHX5NbZhLBLz0612tRces0+Ny2n4gYAAAAAAMrEjQ/NC7c/+Wqj2ubW2YSwaM3mWm2emL/cPjd5puIGAAAAAADKJLRJK2OifXfr1eI+s0Obzx08MNk/h5YR3AAAAAAAQImLy5dlhzaHDekTpr+2Kgzuu02z+qv5uhgCxUqeayfPafG1ljvBDQAAAAAAlLi4fNmEsZWZyph0j5sFb73brP6yX/eh3j2SECiyx03L2eMGAAAAAADKwMXjqsKoyr5JiPPo3LfCKyvWZp7boUfnsHLtxgb7GNSnR1i4/IPX9d++W04/sZLHHjcto+IGAAAAAADKRAxVvnHfjJywJWpMaBNlhzbR4rfX5TyOlTwqblpGcAMAAAAAAGXixofmJXvR1Kexe97ECp26xGXYVNy0jOAGAAAAAADKQKyE+cGDszOPe3WvHb40ds+buip09t2tVxIKXTt5TguvtLwJbgAAAAAAoAzESpgJYyszIcuq9xq3PFpjfKh3jzD9tVXJ8cQpcy2X1gIVLXkxAAAAAADQflw8riq8tWb9VpdLS3Xr3DGs27ilwXb9t++Ws2fOpR/by3JpLaDiBgAAAAAAykRDe9xka0xoEy1+e12N121u1rXxPsENAAAAAACU4R43jdWhie0tldYyghsAAAAAACizPW7icmZxX5rGqG7iOIcN6WOptBYQ3AAAAAAAQBntcXP3eSPD6yvX5uxLk0+PzVuu4qYFBDcAAAAAAFBGnlm4stH73NTUq3tFg21U3LSM4AYAAAAAAMpEc/e5Sa16b1ODbVTctIzgBgAAAAAAynCfm8bucdNUKm5aRnADAAAAAABlts/NVZ/a2x43RUpwAwAAAAAAZealN1e39SVQD8ENAAAAAACUkVgNc/uTrxZ0jEfnvlXQ/kuZ4AYAAAAAAMp0n5tCmThlruXSmklwAwAAAAAAZbjPzbgP79TWl0EdBDcAAAAAAFBmbnxoXpg8c2lbXwZ1ENwAAAAAAEAZiUuY/eDB2W19GdRDcAMAAAAAAGW2x81hQ/q09WVQD8ENAAAAAACUWcXNY/OWt/VlUA/BDQAAAAAAlFnFzYSxlQUfZ9bidwo+RikS3AAAAAAAQJm5eFxV+NzBAwvW/5iqHcPnRw4qWP+lTHADAAAAAABluFza7U++WrD+v3zkHgXru9QJbgAAAAAAoMwUcrm02G/sn+YR3AAAAAAAQBnq1rlTu+q3XFS0xiBLliwJt912W5g6dWp49dVXw5YtW0K/fv3CiBEjwkknnRT233//vI21cOHCZKzHH388LFq0KHTo0CEZ67DDDgsnn3xy2HPPPfM2FgAAAAAAtNel0n7w4OyC9B37PWDQDqpuijW4+dvf/hYuvfTSsGbNmpzzr7zySvJz7733htNOOy1cccUVoVOnlqVwd9xxR7jmmmvChg0bcs4vWLAg+bnzzjvDhRdeGC644IIWjQMAAAAAAO1ZDFUOG9InPDZved77jv0KbYo0uJk2bVoYP3582Lx5c/K4qqoqHHHEEaFr165h+vTp4dFHHw3V1dXhd7/7XfL8lVde2eyx7r///vDtb38783i//fYLhxxySHL81FNPhX/+859h06ZNYeLEiaFLly7hrLPOavGfDwAAAAAA2mvFTSFCmyj2G/sX3hRZcLNu3bpw+eWXZ0Kb888/P0yYMCFZuiwVlzOLFTBr165NwptjjjkmE7Y0xbJly8J3vvOd5Dj2HwOcU089NafNH/7wh8z1XHvttWHs2LFh8ODBLf5zAgAAAABAe6Pipnh1LFTHd999d1i8eHFyHPeXueiii3JCm+jQQw8NV199debxdddd16yxbr755iT8ieKeOTVDm+hTn/pUEhxFsfLmhhtuaNZYAAAAAADQ3rVGxQ1FFtzcd999mePzzjuv3nbHHXdcGDJkSHL83HPPhddee61J42zZsiWppmnMWGeccUbYfvvtM3vvpGEPAAAAAACUY8VNIai4KcLgZsWKFWHmzJnJ8XbbbRdGjBhRb9tYhTNmzJjM48mTJzdprBdffDEZL91DZ8CAAfW27datW2YptriU2yOPPNKksQAAAAAAoBSouCmz4CaGKdXV1cnx8OHDQ6dOnbbafp999skcP//8800eK7Xvvvs22L4lYwEAAAAAALS74GbhwoWZ41133bXB9rvsskudr23qWLvttltBxwIAAAAAgFIQlzKbMLay0e3327lLuOekncPoPRq3vNozC1e24OrKW0UhOl22bFnmuH///g2279evX+Z4+fLlzR5r5513brD9Tjvt1OyxUrG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"text/plain": [
"<Figure size 1000x500 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 425,
"width": 823
}
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x[:,0], x[:,1], 'x:')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "Mime type rendering requires nbformat>=4.2.0 but it is not installed",
"output_type": "error",
"traceback": [
"\u001b[31m---------------------------------------------------------------------------\u001b[39m",
"\u001b[31mValueError\u001b[39m Traceback (most recent call last)",
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[12]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m fig = go.Figure(data=[go.Scatter3d(x=x[:,\u001b[32m0\u001b[39m], y=x[:,\u001b[32m1\u001b[39m], z=J(x[:,\u001b[32m0\u001b[39m], x[:,\u001b[32m1\u001b[39m]), marker={\u001b[33m'\u001b[39m\u001b[33msize\u001b[39m\u001b[33m'\u001b[39m:\u001b[32m3\u001b[39m})])\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m \u001b[43mfig\u001b[49m\u001b[43m.\u001b[49m\u001b[43mshow\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
"\u001b[36mFile \u001b[39m\u001b[32mc:\\Users\\Martial\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\plotly\\basedatatypes.py:3436\u001b[39m, in \u001b[36mBaseFigure.show\u001b[39m\u001b[34m(self, *args, **kwargs)\u001b[39m\n\u001b[32m 3403\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m 3404\u001b[39m \u001b[33;03mShow a figure using either the default renderer(s) or the renderer(s)\u001b[39;00m\n\u001b[32m 3405\u001b[39m \u001b[33;03mspecified by the renderer argument\u001b[39;00m\n\u001b[32m (...)\u001b[39m\u001b[32m 3432\u001b[39m \u001b[33;03mNone\u001b[39;00m\n\u001b[32m 3433\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m 3434\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplotly\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mio\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mpio\u001b[39;00m\n\u001b[32m-> \u001b[39m\u001b[32m3436\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mpio\u001b[49m\u001b[43m.\u001b[49m\u001b[43mshow\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
"\u001b[36mFile \u001b[39m\u001b[32mc:\\Users\\Martial\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\plotly\\io\\_renderers.py:425\u001b[39m, in \u001b[36mshow\u001b[39m\u001b[34m(fig, renderer, validate, **kwargs)\u001b[39m\n\u001b[32m 420\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m 421\u001b[39m \u001b[33m\"\u001b[39m\u001b[33mMime type rendering requires ipython but it is not installed\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m 422\u001b[39m )\n\u001b[32m 424\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m nbformat \u001b[38;5;129;01mor\u001b[39;00m Version(nbformat.__version__) < Version(\u001b[33m\"\u001b[39m\u001b[33m4.2.0\u001b[39m\u001b[33m\"\u001b[39m):\n\u001b[32m--> \u001b[39m\u001b[32m425\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m 426\u001b[39m \u001b[33m\"\u001b[39m\u001b[33mMime type rendering requires nbformat>=4.2.0 but it is not installed\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m 427\u001b[39m )\n\u001b[32m 429\u001b[39m display_jupyter_version_warnings()\n\u001b[32m 431\u001b[39m ipython_display.display(bundle, raw=\u001b[38;5;28;01mTrue\u001b[39;00m)\n",
"\u001b[31mValueError\u001b[39m: Mime type rendering requires nbformat>=4.2.0 but it is not installed"
]
}
],
"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": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"DIVERGE\n"
]
},
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11f452c6990>]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<Figure size 1000x500 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 425,
"width": 842
}
},
"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": 17,
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "Mime type rendering requires nbformat>=4.2.0 but it is not installed",
"output_type": "error",
"traceback": [
"\u001b[31m---------------------------------------------------------------------------\u001b[39m",
"\u001b[31mValueError\u001b[39m Traceback (most recent call last)",
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[17]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m fig = go.Figure(data=[go.Scatter3d(x=x[:,\u001b[32m0\u001b[39m], y=x[:,\u001b[32m1\u001b[39m], z=J(x[:,\u001b[32m0\u001b[39m], x[:,\u001b[32m1\u001b[39m]), marker={\u001b[33m'\u001b[39m\u001b[33msize\u001b[39m\u001b[33m'\u001b[39m:\u001b[32m3\u001b[39m})])\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m \u001b[43mfig\u001b[49m\u001b[43m.\u001b[49m\u001b[43mshow\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
"\u001b[36mFile \u001b[39m\u001b[32mc:\\Users\\Martial\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\plotly\\basedatatypes.py:3436\u001b[39m, in \u001b[36mBaseFigure.show\u001b[39m\u001b[34m(self, *args, **kwargs)\u001b[39m\n\u001b[32m 3403\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m 3404\u001b[39m \u001b[33;03mShow a figure using either the default renderer(s) or the renderer(s)\u001b[39;00m\n\u001b[32m 3405\u001b[39m \u001b[33;03mspecified by the renderer argument\u001b[39;00m\n\u001b[32m (...)\u001b[39m\u001b[32m 3432\u001b[39m \u001b[33;03mNone\u001b[39;00m\n\u001b[32m 3433\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m 3434\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplotly\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mio\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mpio\u001b[39;00m\n\u001b[32m-> \u001b[39m\u001b[32m3436\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mpio\u001b[49m\u001b[43m.\u001b[49m\u001b[43mshow\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
"\u001b[36mFile \u001b[39m\u001b[32mc:\\Users\\Martial\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\plotly\\io\\_renderers.py:425\u001b[39m, in \u001b[36mshow\u001b[39m\u001b[34m(fig, renderer, validate, **kwargs)\u001b[39m\n\u001b[32m 420\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m 421\u001b[39m \u001b[33m\"\u001b[39m\u001b[33mMime type rendering requires ipython but it is not installed\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m 422\u001b[39m )\n\u001b[32m 424\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m nbformat \u001b[38;5;129;01mor\u001b[39;00m Version(nbformat.__version__) < Version(\u001b[33m\"\u001b[39m\u001b[33m4.2.0\u001b[39m\u001b[33m\"\u001b[39m):\n\u001b[32m--> \u001b[39m\u001b[32m425\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[32m 426\u001b[39m \u001b[33m\"\u001b[39m\u001b[33mMime type rendering requires nbformat>=4.2.0 but it is not installed\u001b[39m\u001b[33m\"\u001b[39m\n\u001b[32m 427\u001b[39m )\n\u001b[32m 429\u001b[39m display_jupyter_version_warnings()\n\u001b[32m 431\u001b[39m ipython_display.display(bundle, raw=\u001b[38;5;28;01mTrue\u001b[39;00m)\n",
"\u001b[31mValueError\u001b[39m: Mime type rendering requires nbformat>=4.2.0 but it is not installed"
]
}
],
"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": [
"[<matplotlib.lines.Line2D at 0x7fbc5c54e080>]"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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aHSivjnBUAAAgGpCIA23E6/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/7l9ydwz3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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"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": [
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],
"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": [
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]
},
"execution_count": 15,
"metadata": {},
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bJgzTm1eN00M/21/pKQ3/Mq32eOXz+aJcHQAASHRhBXFjzFBJkySVSrrQWrtbkqy1FZIuk382O0/+JSvN6W+YpIMk+SRdYK3dGujPY629TdJ3klIlnRdO3UBdB/btrAP7dg7a/tcPF+uiZ7/V2u2sHwcAAJET7oz4BZJckqZZa7fXbbDWeiQ9F7g9t5n97d1rrthau6GB9u8D176hFgq0xI9rd+r/vlypL5Zu04mPzNLzX62Ux8vsOAAACF+4QfzQwHV2kPY5gesRzexvXeCaY4xpaAPo4YHrmmb2B7RYVY1XN78xT3tzd1mVR09/sVIV1R5nCwMAAAkh3CA+OHBdGaR9744p3YwxWU11Zq0t0k+h/t/GmBxJMsa4jDG3SDpc/mUwL7S8ZKB5dlVUq0u71Hqv3TNpJAf/AACAiAg3iO89/aQ4SHvd5So5zexzoqQZko6VtMYY86OkjZLuk3/N+QnW2nWNvB+IiJysNL1y2RjdM3Gk2qcl66yDeutIDvwBAAAREu7UXkbgWh6kve7rGUGe2Vel/EtaDgu8Z/86bRsC7c1WVFTU9EMRVF5e7sj3jVfxMF4HdpAeP62n0pJdQevcuqdGHdLcSktu3TOy4mG8YgnjFTrGLDSMV2gYr9AwXqGJx/EKNzU0tVi2bv9NfsLNGNNJ0ufyH+bzhaQDJaVJGijp7/LPks8yxoxtSbFAS+W0S1b7tIa3N/R4fbrrs826etp6Ldgc7O+kAAAA9YU7I75H/r3C04O0p9X5ujkJ5WZJB0iaL2mCtbY68PpKSdcbYyol/U7SY/Jvc9ikvLy85jwWMXv/Fhbt7xuvEmG8npq1XEuL/f9Q87sPN+rCMf10x2nDlJwU+dnxRBivaGK8QseYhYbxCg3jFRrGKzROjVdBQUGL3xtuUti7NrxLkPbsOl9vbUZ/ZwWuD9QJ4XXdK/8s/IHGmMENtANRtXLbHv3t4yX1Xtu+p6pVQjgAAEgs4aaFxYFr/yDt/QLXjdba5pyGsvf5xQ01Wmt36KdA36+hZ4BoyslK1dmjetfed8xI0eTThzfyDgAAAL9wg/jcwHVMkPa9r3/TzP52Ba49Gmo0xqRLyt3nWcAx7dNT9JeJI/XqFWPUPztTf5owTF3bpzX9RgAA0OaFG8SnBq5nGmPqLU8xxiRJujhw+1Iz+/s8cL00SPsF8tdcImles6sEWtmYgdn68IbxmnRQQ+dQ+X1ut2jLroooVgUAAGJZWEHcWlso6X1JHSS9YYzJlmpnrp+RlCfJSnqr7vuMMTnGmKHGmEH7dHm/pBpJZxhj/mqMaVfnPWdL+lvg9j5rbVU4tQORlp6SJJfL1WDb+p3luvrl73XsQzP12ndr5fM1uYkQAABIcJH4RNmV8p+gebT8B/DMlX+/74vln7meaK317vOea+Q/nOfTui9aawskXS5/GP+dpE3GmAJjzBZJr8sf+P8tf2AH4oLP59Mf35qvPVUe7a6o0c1vFurKl1r+CWsAAJAYwg7igVMuR8m/z/dWSfnyB+kpkkYHjq0Ppb/nJR0s/3KWEkkj5d9mcYakc6y1F1trmU5E3Pi0aIs+t/U3DTpiCCd0AgDQ1oW7j7gkyVpbLOn6wI/mPD9Z0uRG2udJujAStQFOO3porm6fMEwPfmRVXu3RIQO66PxD+jpdFgAAcBibHQOtLMnt0q8OH6CPbhivY4bm6r5JI+V2N7yWHAAAtB0EcSBK+mZn6tmLR2tg16ygz9z/4WIVrtsZxaoAAIBTCOJAjPhg/kb96/PlOvOxr3Tv9CKVV3mcLgkAALQigjgQA3aWVen2dxZKkrw+6clZK/TbN9gqHwCAREYQB2LAhws2aVtpZe19SpJL1x4z2MGKAABAayOIAzHg54f01XOXjFbPjumSpN8cNVhDu3dwuCoAANCaIrJ9IYDwHW1y9dGN4/Xsl6t05VEDgz7HqZwAACQGZsSBGNI+PUXXHzdEaclJDbaXVXt1/fsb9O68DQRyAADiHEEciCPPF2zX0uJKXTflB13+wlxtLCl3uiQAANBCBHEgTny7crum2V219zOKtuiFr1c7WBEAAAgHQRyIEyu2liq5zv+x/bIzdd0xQ5wrCAAAhIUgDsSJnx/SV4+d1lvDuqZJku6blK+M1IbXkgMAgNjHrilAHOnbKVUPnNxTJam5GjsoO+hz2/dUqUu71ChWBgAAQsWMOBBn3C6Xxg3OCdpeuG6nxt33qR7+ZImqarxRrAwAAISCIA4kkKoar25+o1AV1V49+ulSTfjHFypct9PpsgAAQAMI4kACeXLmci3etLv2fsnmUhWXVjlYEQAACIYgDiSQId3aKycrrfZ+4oG9dPTQXAcrAgAAwRDEgQRy0ojumnHTeJ09qrey26Xq9gnDnC4JAAAEwa4pQILplJmqB8/Zv9GdUzxen75ZUdzohz4BAEDrYkYcSFCNbV/43Fcrdf4z3+jaKT9oW2llFKsCAAB7EcSBNmZNcZke/NhKkqbN26DjH5qpOSuKHa4KAIC2hyAOtDG3vbNAFdU/7S/u8fo0MKedgxUBANA2EcSBNubmE42G9+xQe3/bhGHK7ZDuYEUAALRNfFgTaGNG9Oqot68+TE9/sULfr96hc0b1drokAADaJII40AalJLn1m6MGy+fzyeVyNfjMxpJyvTdvoy45rL+Sk/jHMwAAIo0/XYE2LFgI9/l8+uNbC/SX6UWa+PhsLdqwK8qVAQCQ+AjiAP7Hu/M26L+Lt0iS5q8v0en//FI/rNnhcFUAACQWgjiAejxenx6dsbTeawf06aT9e3dyqCIAABITQRxAPUlul/7z67E6dWQPSVJqslv3n50vt7vhZSwAAKBl+LAmgP/RtX2aHvvFQTptwSZtLa3UoK5ZTpcEAEDCIYgDCOqkEd0bbf944SbNKNqsP546TB0zUqJUFQAAiYGlKQBapKS8Wre9vUCvzV2n4x+aqY8WbnK6JAAA4gpBHECL3Du9SFt2V0qStuyu1NUvf6+128scrgoAgPhBEAcQsrKqGhWsrr+d4ZVHDlKfLpkOVQQAQPwhiAMIWWZqst677nBdd8xgJbtdGtS1na45ZrDTZQEAEFf4sCaAFklLTtJNJxidPLKHajw+packNfhcZY1HKW432x8CALAPZsQBhCWvRweN7N0xaPt9HyzWuU99reVbS6NYFQAAsY8gDqDVFKzerudnr9J3q3bo5Ee/0L8+X64aj9fpsgAAiAkEcQCtoqLao5vfKJTP57+vqvHqlW9Xq4ogDgCAJII4gFZSVuVR3312UblvUr4yU/loCgAAEkEcQCvp0i5Vz148Wo/+/AB1zkzRz0f30WGDc5wuCwCAmMHUFIBW43K5dMYBvXT44BwlJwX/e/+a4jJlZ6WqXRq/JQEA2g5mxAG0uuysNHXMSGmwrdrj1ZUvFeiEh2dp1pKtUa4MAADnEMQBOOqpWSu0aOMurd9Zroue/Va/fX0eO6sAANoEgjgAxyzfWqpHP11a77WqGm+jy1gAAEgU/GkHwDE9OqbrojH9tPfQzS7tUnXHacOcLQoAgCghiANwTGZqsm6bMExvXjVO+3XL0h2nDVN2VprTZQEAEBVsUQDAcQf27az3rztCyXunxhvw8cJNyuvRQX322ZscAIB4RRAHEBNSGlkXvnZ7ma5/9Ue5XNLNJxpdNLa/3I2EdgAA4gFLUwDENJ/Pp1unzld5tUdlVR5NnrZIv/r3d/L5fE6XBgBAWAjiAGLap0Vb9OWybfVeO3F4d7lczIgDAOIbQRxATDtmaK7unTRS7QOnbo4blK1zR/dxuCoAAMLHGnEAMc3tdum8Q/rqaJOru95fpFtOHMpsOAAgITAjDiAudO+YrsfOP0h9sxveNcXn8+nOaYv07crtUa4MAICWIYgDSAjvz9+oZ79aqZ89+bVuf3uBSitrnC4JAIBGsTQFQNzbvqdKd7yzsPb+xTmrta20UteNYs9xAEDsYkYcQNz77+ItKt5TVXufmuTWTcfv52BFAAA0jSAOIO6dPaq3plw+Rv0D68evPWawhnRr73BVAAA0jqUpABLC2EHZ+vCG8Xrh61W6eNyAoM95vT5O5QQAxARmxAEkjPSUJF0xfpBSkxv+rW1XRbVOfvQL/ee7NZzMCQBwXERmxI0xnSXdIWmipB6Stkr6UNKd1trVLejPLekySRdLGi4pVVKRpKclPWGt5U9QACG774PFspt365Y35+vdeRt078T8oNshAgDQ2sKeEQ+E8NmSrpfUWVKhpAxJl0r60RiTH2J/6ZKmS3pS0qGS1knaIulASY9LmmKM4d+VAYTk6+XFeuWbNbX3Xy0r1n/mrmnkHQAAtK5ILE15WtJQ+cNzL2vtwZJ6SnpeUidJrxpjkkLo735JJ0paK+lAa+1wa20/SadJ2iPpXEm/iEDdANqQjSXlykj56beigTntdO0xQxysCADQ1oUVxI0xQyVNklQq6UJr7W5JstZWyL+0pEhSnvxLVprT30BJV0uqkXSytbZwb5u19j1JfwvcXhpO3QDankkH9dbHN47X4YNzJEn3n52v9JRQ5ggAAIiscGfEL5DkkjTNWlvvXGlrrUfSc4Hbc5vZ33mSkiS9ZK1d2ED7c5L+KOnZlpULoC3r0yVTL/7qEL151TiN7t8l6HObSiqiWBUAoK0K98Oahwaus4O0zwlcj2hmf8cGru801GitXSXpnmb2BQD/w+VyaVS/zkHbv1+zQ+c++bUuPWyAbjhuP2WkMmsOAGgd4QbxwYHryiDte3dM6WaMybLWljbR34jAtcgY01HSJZLGS8qStEjSU9baReEUDADBVNZ4dMsbhar2+PTkrBX6aOEmPXjO/jq4kdlzAABaKtylKV0D1+Ig7XWXq+Q01lFgt5S9/fWRtFDSw/KvLz9e/l1Z5hljLm9xtQDQiMc/W66lW36aL1hVXKayKo+DFQEAElm4M+IZgWt5kPa6r2cEeWavuudRT5G0U9LJkj6XP8TfJOlGSU8YY5Zba//bnAKLioqa81jElJeXO/J94xXjFRrGKzShjleOq0xd2yVp6x5/+D5+UJa6erapqGhbq9UYa/g1FhrGKzSMV2gYr9DE43iFG8Q9anxWvW5bU4fwpNf5up2kQ6y1e5e8rJN0kzEmV/6tC++RNCbEWgGgUQf3ytQTZ/TR8wXb9dWaPbp8dLbTJQEAEli4QXyP/HuFpwdpT6vzdbBZ84baX6wTwuu6R/4gfqgxJtdau6WpAvPy8pp6JKL2/i0s2t83XjFeoWG8QtPS8RqVL+2qqFaH9JQG22s8Xs1cslXHDM2Vy5VY54vxayw0jFdoGK/QMF6hcWq8CgoKWvzecNeI710bHuyTTHWnk7Y20dcu/TRrXhjkmSXy7zEuSf2bKg4AWipYCJekZ75cqV/9e64uf2EuWx0CAFos3CC+OHDtH6S9X+C60Vpb1lhH1toqBd99ZS+ffgrr1c0pEAAiacXWUj38yRJJ0oyiLTr+oZn6cmnbWUMOAIiccIP43MA12Hrtva9/08z+vg1cDw7S3k9SiiSvpFXN7BMAIuaOdxeqssZbe5+U5JLp3r6RdwAA0LBwg/jUwPVMY0y95SnGmCRJFwduX2pmf/8JXM82xvRqoP3qwHWmtXZHKIUCQCTccdrwegcC3XHaMHVtn9bIOwAAaFhYQdxaWyjpfUkdJL1hjMmWavcEf0ZSniQr6a267zPG5BhjhhpjBu3T5buSvpb/AJ/36rYbY86VdE3g9i/h1A0ALTU4N0uv/3qs/nz6cJ2a30NnHtDQnAEAAE0Ld0Zckq6U/wTNoyWtMcbMlbRB/tnwEkkTrbXefd5zjaQiSZ/WfTHw3Dnyh/cDJFljTKExZoWkVyWlSrrdWvupAMAhbrdLvxzXX4+df1DQXVPW7SjTozOWqqpm39/+AADwCzuIW2vXSRol6e/y74ySL//OJlMkjbbWhrSrurV2vaSDJP1J/g+DDpb/sJ+PJJ1krb073JoBoDX5fD794a0FenjGEk34xxf6ce1Op0sCAMSgcPcRlyRZa4vlP4L++mY+P1nS5EbayyTdFfgBAHFl6vfrNWuJf8fWJZtLNenxr/T6lePqrS0HACASS1MAAAFer09PzFxe77XR/bvowD6dHKoIABx5TNgAACAASURBVBCrCOIAEEFut0uvXzlWZ4/qLUlKS3brvrPy5XYn1gmcAIDwRWRpCgDgJ50yU/XgOfvr9P17amNJuQbktHO6JABADCKIA0ArGb9f10bbP5i/Ue/P36jJpw9XThZ7kQNAW8PSFABwwM6yKt3+zkK9V7hRxz80U2//sF4+n8/psgAAUUQQBwAH3PVekbaVVkqSdpRV63dvzNPa7eUOVwUAiCaCOABEWXmVR3bzrnqv/eaoweqbnelQRQAAJxDEASDKMlKT9PZvDtMtJw1VarJbplt7XX30YKfLAgBEGR/WBAAHJCe5ddVRg3Ti8G6qqPYqNbnheZHyKo9SklxKTmLeBAASDb+zA4CDBnbN0rCeHYK23zO9SBMfn61FG3YFfQYAEJ8I4gAQo75duV0vzlmt+etLdPo/v9TfPraqrPE4XRYAIEII4gAQgyqqPbrlzcLa+xqvT9PmbRA7HAJA4iCIA0AMqqz2/s+SlfvOyld6SpJDFQEAIo0gDgAxqGNmih47/yA9eeEo5bZP0y8O7asxA7OdLgsAEEHsmgIAMezE4d01ZmC2ktyuoM+s2Fqq7HZp6piZEsXKAADhYkYcAGJcx4wUZaU1PG9SVePVb17+Xsc9PFMfLtgU5coAAOEgiANAHHti5nIt3rRbW3dX6sqXCnT1y9+r2uN1uiwAQDMQxAEgTi3bUqp//HdpvdfSkt1K4fAfAIgL/G4NAHGqT5cMXXXkICUH1o/nZKXq9gnDHK4KANBcBHEAiFNpyUm66QSjd685XCN7ddSfTx+hzu1SnS4LANBM7JoCAHFuWM8Oevvqw9TIxip6r3CD8np00KCuWdErDADQKII4ACSAxrY3XLVtj377+jx5fdINxw3R5UcMZB05AMQAficGgATm9fr0+6mFqqj2qqrGq79+aHXxc9/K5/M5XRoAtHkEcQBIYJ8v2aI5K7bXe+3MA3rJ5WpkHQsAICoI4gCQwI42uXrk3APUOXDq5hFDcnT2qN4OVwUAkFgjDgAJzeVy6cwDe+nwITm6d/pi3XDcEGbDASBGMCMOAG1ATlaa/vaz/dWnS2aD7T6fT7dOna+C9WVRrgwA2i5mxAEAeufHDZry7RpJ0nGDsvRgv0HqlMme5ADQmpgRB4A2bltppf48bWHt/YzlpbrlzUIHKwKAtoEgDgBt3FfLtqmkvLr2PsXt0s0nDXWwIgBoGwjiANDGnXFAL7151Tjt181/6uYFB3TmBE4AiAKCOABAB/btrPeuPUK/OTRbk4Z3DPpcjccbxaoAILERxAEAkqTUZLdOG9pRye6GtzcsKavWcQ/N1HNfrZTHy8mcABAugjgAoFn+Mn2RVhWX6c/TFulnT36tZVt2O10SAMQ1gjgAoElfLt2m1+auq70vWL1D7/64wcGKACD+EcQBAE3aWV6l9mk/HT0xODdLVx8z2MGKACD+EcQBAE2akN9Tn9x0pI7Ly5XLJd1/Vr7SkpOcLgsA4honawIAmqV7x3Q9fdHBWrhhl0b0Cr6zypriMvXNzoxiZQAQn5gRBwA0m8vlajSEf7dqu4568DPd/vYC7a6oDvocAIAgDgCIkIpqj255s1Ben/TinNU68eFZmr1sm9NlAUDMIogDACLiH/9dqhVb99TebyipkBrekhwAIII4ACBCjhjSVf3rrA0/75A+Gjcox8GKACC2EcQBABExZmC2PrxhvH49fqB6dcrQrafkOV0SAMQ0gjgAIGLSU5J06yl5+uSm8eqQntLgM9Uer94r3CCfzxfl6gAgthDEAQARl5kafHfcJ2cu1zWv/KBfPPON1hSXRbEqAIgtBHEAQNQs27Jbf/90mSRp9vJinfjILH1mtzhcFQA4gyAOAIiaP09bpCqPt/Y+IzVJ+Y3sSw4AiYwgDgCImr+cOVKHDc6uvZ98+nBlZ6U5WBEAOIcj7gEAUdM3O1Mv/epQvT53neasKNZp+T2cLgkAHMOMOAAgqlwul342uo8eOvcAuVwNn/izprhM932wWOVVnihXBwDRQxAHAMQUn8+nW98q1BMzl+ukR2fp6+XFTpcEAK2CIA4AiCmvzV2rr5b5w/fq4jKd9/Qcfbdqu8NVAUDkEcQBADHD6/Xpua9W1Xtt3KBsHdyvszMFAUArIogDAGKG2+3SG1eN00Vj+0mSMlKSdN+k/KBryQEgnrFrCgAgpmSlJevOM0ZoQn5PrdtRpr7ZmQ0+5/P5JImQDiBuMSMOAIhJhwzookkH9Q7aPq1woy7791xtLCmPYlUAEDkEcQBA3Nm+p0qT312oTxdv0QkPzdIr36yR1+tzuiwACAlBHAAQd+6ctlDb91RJknZX1mjyuwu1bgcz4wDiC0EcABBXyqs8/xO6rz9uSNC15AAQqwjiAIC4kpGapNd+PVZ/Pn24MlOTlNejg64YP9DpsgAgZBHbNcUY01nSHZImSuohaaukDyXdaa1dHYH+x0n6QtJaa23/cPsDAMQvt9ulX47rr2PzclVe5VFKUsPzSnsqa5Sc5FJaclKUKwSApkVkRjwQwmdLul5SZ0mFkjIkXSrpR2NMfpj9p0v6PzGDDwCoo3fnTA3p1j5o+93vL9Jp//hSP6zZEcWqAKB5IhVsn5Y0VNJ0Sb2stQdL6inpeUmdJL1qjAlnOuKOQP8AADTL7GXbNOXbtVqyuVST/jVbd723SBXVHqfLAoBaYQdxY8xQSZMklUq60Fq7W5KstRWSLpNUJClP/iUrLen/IEm/lcTH4QEAzVJe5dHvp86vvff5pM/sFgcrAoD/FYkZ8QskuSRNs9Zur9tgrfVIei5we26oHRtjUgLv90m6K8w6AQBtRI3Xq0MHdKm9d7mkv56Vr/QU1ooDiB2RCOKHBq6zg7TPCVyPaEHft0rKl3S/pPlNPAsAgCSpfXqKHjhnf71w6SHq1SlDvxzbXwf379L0GwEgiiIRxAcHriuDtO/dMaWbMSaruZ0aY0ZI+qOkxZLubnl5AIC2avx+XfXxjeN180km6DNLNu/WttLKKFYFAH6RCOJdA9fiIO11l6vkNKfDwAc7n5WUIukyay2/QwIAWqRdWrIyUxverbeyxqPfvPy9jntopt76YZ18Pl+UqwPQlkViH/GMwDXYhynrvp4R5Jl93SRptKTHrLVftbQwSSoqKgrn7SErLy935PvGK8YrNIxXaBiv0LW1MXvhh+1atqVUknTjf+bplS+X6E/HdFey29Ws97e18QoX4xUaxis08ThekZgRb2ovqLrfo8mpBmPMEEl/lrRW/jXiAABE3OqdVXpt/s56r3XOSG52CAeAcEViRnyP/HuFpwdpT6vzdaNbEBpjXPIvScmQdOXerRDDkZeXF24XIdn7t7Bof994xXiFhvEKDeMVurY0ZkM8Xv22MksPz1iiqhqvurZP0wPnj1XHzJRm99GWxisSGK/QMF6hcWq8CgoKWvzeSATxYvmDeLCPo2fX+XprE31dLelwSVOstdMjUBsAAA1KTnLrqqMG6YTh3fT7Nwv1q8MHhhTCASBckQjiiyUNktQ/SHu/wHWjtbasib7ODlzPM8acF6w/Y8zeJS4DrLWrmlsoAAD7GtQ1S6/9eqxcruBLUt76YZ1Mtw4a1rNDFCsDkOgiEcTnSjpV0hhJ/2qgfUzg+k0z+prfSE2dJQ2TVBn4npJU0fwyAQBoWGMhfPnWUt3y5nx5vT5deeQgXXPMYA4GAhARkQjiUyXdIelMY0yXuqdrBrYhvDhw+1JTHVlrrw3WZoyZIGmapE3W2sPDqhgAgGbwen36/ZuFqqrxSpL++dkyfbOyuMkZdABojrB3TbHWFkp6X1IHSW8YY7IlyRiTLukZSXmSrKS36r7PGJNjjBlqjBkUbg0AALSGWUu36rtVO+q99otD+xHCAUREJLYvlKQr5T9B82hJa4wxcyVtkH82vETSRGutd5/3XCOpSNKnEaoBAICIOsrk6skLRym3vX8DsKNNV51xQE+HqwKQKCISxK216ySNkvR3+XdGyZdUI2mKpNHW2vjZWR0AgDpOHN5dn9x0pC4c009/mTiS2XAAEROJNeKSJGttsaTrAz+a8/xkSZND6P89SfzuBwCIuo4ZKbrrzBFB230+n/7f6/N0wrBuOmlEjyhWBiCeRWppCgAAbdab36/X1O/X68qXvtdvXi7Qlt1s6gWgaQRxAADCsL28Rne9t6j2fvr8Tbr97QUOVgQgXhDEAQAIw8LNFdpTWVN7n57i1q0ncyQ5gKYRxAEACMMR/bM07drDld+7oyTp/x1v1D+nncNVAYgHEfuwJgAAbVVejw6aetU4Tf1hvSYd2Cvoc5U1HqUlcyonAD9mxAEAiIDkJLd+dnAfJSc1/Efrjj1VOubBmXrss2Wq9ux7tAaAtoggDgBAFNz1/iKt31muBz6yOvOxr7RgfYnTJQFwGEEcAIBW9rndoqnfr6+9X7hhlz4t2uJgRQBiAUEcAIBWVlXjVZd2qbX3Q7u311VHDXKwIgCxgCAOAEArO2F4d31y43idtn9PuV3S/WflKzWZP4KBto7fBQAAiILsrDT947wD9fGN47V/n05Bn1u2ZXcUqwLgJII4AABRNDi3fdC2OSuKddxDs3TTaz9qZ1lVFKsC4ASCOAAAMaC8yqPfv1koSZr6/Xod99BMfWb5QCeQyAjiAADEgEdmLNGq4rLa+22lVcpM4fAfIJERxAEAiAEnj+wh0+2nZSsXjumnQwdmO1gRgNZGEAcAIAYc0KeTpl17uG44boj6ZWfq5pOM0yUBaGUEcQAAYkRqsls3HLefPr5xvNqnpzT4TFWNV6/NXSuP1xfl6gBEGkEcAIAYk5YcfG34458v081vFOqcJ2Zr6Wa2OgTiGUEcAIA4YTft1mOfLZMkfb9mp079+5easWizw1UBaCmCOAAAceLu9xep2vPTkpQOGck6uH9nBysCEA6COAAAceKBs/fXcXndau/vPGOEOmWmOlgRgHAkO10AAABonu4d0/X0RaP0XuFGzV5erFNG9nC6JABhYEYcAIA44nK5dNr+PXXvpJFBn1m5bY/ueGeBdldUR7EyAKEiiAMAkEC8Xp9+/2ah/v31ap3w8Cx9tniL0yUBCIIgDgBAApny3Rp9s3K7JGljSYUuef47fbOi2OGqADSEIA4AQILwen169du19V4bv19XHTKgi0MVAWgMQRwAgAThdrv0+pVj9esjB8rtkjJTk3TPxBFyuVxOlwagAeyaAgBAAklPSdKtJ+fp1JE9tGZ7mXp3zmzwOZ/Pvx85IR1wDjPiAAAkoPzenTQhv2fQ9rd+WK9fPPON1hSXRbEqAHURxAEAaGO27q7Une8t0uzlxTrhkZl65osV8nh9Tb8RQEQRxAEAaGMmT1uonWX+PcYrqr164COr9TvKHa4KaHsI4gAAtCEV1R6VlNU/6OfG4/dT3+yG15IDaD0EcQAA2pD0lCS9+KtD9Nez8tU+PVkje3XUZYcPcLosoE1i1xQAANoYl8uln43uoyNNV+2prFFyUsPzcrsrqpXsdisjNSnKFQJtAzPiAAC0Ud06pGtg16yg7X+etkgnPTpLs5dvi2JVQNtBEAcAAP9j1pKteqNgnVYXl+n8p7/RrVPna09ljdNlAQmFIA4AAOrZU1mjW6fOr/dawertSk7i8B8gkgjiAADgfxybl1v7tcsl3X9WvtKSWSsORBJBHAAA1NMuLVl3njFCr/16rAbmtNOlhw3QgX07O10WkHDYNQUAADTokAFdNP36Ixp9ZtGGXeqUmaKenTKiVBWQOJgRBwAAQaWnJCk9peElKRXVHl3zyvc64eFZevmb1fJ6fVGuDohvBHEAANAij366VCu27VFpZY3++NYCnf/MHFXVeJ0uC4gbBHEAABCyJZt366lZK+q9NiAnS6nJRAugufi/BQAAhGxw1yz9acIwZQZO3ezeIV23njLU4aqA+MKHNQEAQMjcbpd+Oa6/js3L1R/eWqCLxvRTh/QUp8sC4gpBHAAAtFjvzpn69yWj5XIFP+znP9+t0ZBu7cW+KkB9BHEAABCWxkL40s27dfvbC1Xt9eqMoR30ywO7RLEyILaxRhwAALQKj9enm98sVJXHK59Pertol279ZKN8PrY5BCSCOAAAaCVfLdumH9bsrPfaxGEdG51BB9oSgjgAAGgV4/frqhd/dYh6d/avDh/bJ1NH9GvncFVA7GCNOAAAaDVHDOmqj24Yr0c/XaojcmuYDQfqYEYcAAC0qnZpyfrDKXnKadfw/J/P59NvXi7Q1O/XsX4cbQpBHAAAOOo/363V9PmbdNNr83TJ899p/c5yp0sCooIgDgAAHLOppEJ/eb+o9v5zu1V/fnehgxUB0UMQBwAAjpm3bqeqPN7a+4yUJN0+YZiDFQHRQxAHAACOOXF4d31w/RE6pL//oJ/fnWjUp0umw1UB0cGuKQAAwFEDu2bp1SvG6P35G3XKyB5BnyurqlFmKtEFiYMZcQAA4Di326XT9u+pJHfD2xsWl1bqyAc+14MfWVVUe6JcHdA6COIAACDmTZ62SFt3V+qfny3TqX//QgWrtztdEhA2gjgAAIhpnyzarGnzNtTeL9+6R3NWEMQR/yKy0MoY01nSHZImSuohaaukDyXdaa1d3YL+hkq6WdIxgf7KJc2T9Iy19sVI1AwAAOJDSpJLue3TtGV3pSRpWI8OumL8QIerAsIX9ox4IITPlnS9pM6SCiVlSLpU0o/GmPwQ+ztN0g+SLpHUTdJiSRWSxkt6wRjzsjGG83EBAGgjjjK5+uSmI/Xz0X2U7Hbpr2fnKyWJf9RH/IvEr+KnJQ2VNF1SL2vtwZJ6SnpeUidJrxpjkprTkTGmm6SXJaUH+s221u5vre0u/2z7bknnS7o2AnUDAIA40TEjRfedla/PfnuURvTqGPS5BetLolgVEJ6wgnhgCckkSaWSLrTW7pYka22FpMskFUnKkz9EN8dlktpL+l7Sldbasr0N1tq3Jd0auL0xnLoBAEB8amyP8a+WbdOEf3ypq14q0JbdFVGsCmiZcGfEL5DkkjTNWlvvUxPWWo+k5wK35zazv6MC16nWWm8D7e8Frv0DS2IAAABUVlWj308tlCR9sGCTjn9olj5auMnhqoDGhfthzUMD19lB2ucErkc0s7/bJb0kaW6Q9nZ1vmZHfwAAIEl66OMlWru9vPZ+V0W1crJSHawIaFq4YXZw4LoySPveHVO6GWOyrLWljXVmrZ2jn8J7Q84IXLdK2tbsKgEAQEI7++De+nbVdhWu868R/+XY/hrVr4vDVQGNC3dpStfAtThIe93lKjnhfCNjTHf5tzSUpFestb5w+gMAAIljaPcOmnrVOP3xlDwNzs3S7040TpcENMnl87U8zxpjPPKH+QOstfMaaE+SVBO4HWatLWrh92kn6VP5l8JskzTCWru5sfcUFBT4JCkzM/iHOlpDebn/n8UyMjKi+n3jFeMVGsYrNIxX6Biz0DBeoYnWeHm8PiW5G97puMrj00dLd+nk/TooOcgzsYJfX6FxarzKyvx7i4waNSrkX1Dhzoh7Qui/RYnfGJMl/4c0Dw18vwuaCuEAAKDtChbCJWnKvB16/JtiXf/+ei0rroxiVcD/CneN+B759wpPD9KeVufr8iDPBGWM6Sp/CD9EklfSJdbaj0LpIy8vL9RvG5aioiJHvm+8YrxCw3iFhvEKHWMWGsYrNE6P18INJXpjof9jbSu2V+mG6Rv02PkH6qQRPRyppylOj1e8cWq8CgoKWvzecGfE964ND/ZpiOw6X28NpWNjzEBJX8sfwmvknwnneHsAANAi939oVeP96R/os9ulauygsD7CBoQl3CC+OHDtH6S9X+C6se7hPE0xxuRL+krSIEllks6w1k5paZEAAAAP/2x/nXFAz9r7u88coY4ZKQ5WhLYu3CC+d7/vMUHa977+TXM7NMYMkfSJpO6Sdkg6zlo7vcUVAgAASMrOStOjPz9Q//fLg3XxuP46YXh3p0tCGxduEJ8auJ5pjKm3PCWwY8rFgduXmtOZMSZT0jRJufLvjnKUtfbrMGsEAACodWxeN00+fXjQ9uVbS/W71+dpx56qKFaFtiisIG6tLZT0vqQOkt4wxmRLkjEmXdIzkvIkWUlv1X2fMSbHGDPUGDNony7/KMnI/8HMcwL9AwAARIXX69MtbxTq9YJ1Ov7hmXq/cKPC2eoZaEwkjom/UtKXko6WtMYYUyRpoKTOkkokTbTWevd5zzWS7pD/5M3+kmSMSZN0daC9TNLdxjS6Gf/Z1tpNEagfAABAkvTinNWau3qHJGlbaZWufuV7Tbl8jMYOym7inUDowg7i1tp1xphRkv4k/xH0+ZJ2Spoi6Q5r7dJmdjVSUsfA11mSDmvi+WBbJgIAAITM5/PpnR/X13vt2KG5GjMw2OZwQHgiMSMua22xpOsDP5rz/GRJk/d5ba6k2D7iCgAAJCyXy6VXrxirf32+XP/8bKnSkpN098QRcrmIJ2gdEQniAAAAiSA12a3rjxuik0d218pte9SjY8PHpft8Pnl9jZ/iCTQl3F1TAAAAEs5+3drrxEa2N3y9YJ3OeWK2lm7eHcWqkGgI4gAAACHYsqtCd7+3SN+v2alT//6l/vHpUlXV7LsvBdA0gjgAAEAI/vTOQu2qqJEkVXm8euzzZdq8q8LhqhCPCOIAAADNVFHtkWeffcV/e4JRny6ZDlWEeEYQBwAAaKb0lCQ9deEo/fP8A5XdLlX79+mkSw4b4HRZiFPsmgIAABACl8ulCfk9ddigHO2uqAm6c0pJWbXcbql9ekqUK0S8YEYcAACgBTq3S1Xf7OBLUiZPW6gTHp6lzxZviWJViCcEcQAAgAj7bPEWvfXDem0sqdAlz3+nG179Qbsrqp0uCzGGIA4AABBBuyuq9Ye35td7bfGm3UpLTnKoIsQqgjgAAEAEpSS5dcYBvWrXjrtd0l/PzldqMrEL9fFhTQAAgAhKT0nS708eqlNH9tDNbxZq/H45yu/dyemyEIMI4gAAAK1gZO+Oeveaw+Tx+oI+U7hupzpmpKhfdrsoVoZYwb+RAAAAtJKUJLfSUxpeG15e5dG1U37QiY/M0jNfrGg0sCMxEcQBAAAc8PCMJVpdXKaKaq/ufr9IZz8xW5U1HqfLQhQRxAEAAKJs6ebdeuaLFfVeG9mrIzurtDEEcQAAgCgbnJul+8/KV4d0/8f1enZM180nDXW4KkQbH9YEAACIMpfLpXMO7qMj9+uqP72zUOce0kdZacSytoafcQAAAIfkdkjXExeOavSZF79epUG5WRo3KCc6RSFqCOIAAAAxauWOKt35/kpVe3w675C+uvWUoeqQnuJ0WYgQ1ogDAADEII/Xp0e+2qpqj39bwynfrtEvnv5GPh/bHCYKgjgAAEAMmr+5QkuLK+u9dvXRg+RyuRyqCJFGEAcAAIhBB/TI0F9P6qmBXf2nbp48ortOGtHD4aoQSawRBwAAiFEjuqVr+nX5+tfny/WLMX2DPufz+Zgpj0PMiAMAAMSw9JQk3Xj8fsptn95gu9fr0+UvzNXL36yW18v68XhCEAcAAIhjL3+7RjOKtuiPby3QeU/P0cpte5wuCc1EEAcAAIhT63eW677pRbX336zcrnvr3CO2EcQBAADilN20q959u9Qk3XH6cIeqQagI4gAAAHHqmKHd9NGN4zV+v66SpN+fkqdenTIcrgrNxa4pAAAAcax350z9+5LR+u/iLTra5AZ9bldFNadyxhhmxAEAAOKcy+XSsXnd5HY3vIXh1t2VOuqBz3XXe4tUVlUT5eoQDEEcAAAgwd3x7gJt31Ol//typU58ZJa+WrbN6ZIggjgAAEBC+3DBRk2fv6n2fu32ci3cUOJgRdiLIA4AAJDAOmakqnfnnz7Amd+7oy49bICDFWEvgjgAAEACGzsoWx/dMF6XHNZfqclu3X9WvpKTiICxgJ8FAACABNcuLVl3nDZcX9x8tPJ6dAj63NxV2+Xz+aJYWdtGEAcAAGgjunVID9o2c8lWnf3E17r4ue+0fmd5FKtquwjiAAAAbVxpZY3+MHW+JH8gP+GhmZo2b4PDVSU+gjgAAEAb97ePbb1Z8PJqj/p0yXSworaBIA4AANDGXTimnw4Z0KX2/leHD9ABfTo5WFHbQBAHAABo4wZ2zdKrl4/R3WeO0PCeHXTT8cbpktoEgjgAAADkdrt0wZh+mnbN4cpITWrwmYpqj56atVwV1Z4oV5eYCOIAAACo5Xa7grY9MmOp7pm+WKf+/QsVrN4exaoS0/9v786j7CjLPI5/O52GDiSBkJCwCAmB5EkUghpk0cMmyiJKABnFMwgKzIhHlHEckRkccAWcgyIzjisqKgdmxggIBBzRM27sBCEszUM0hDWBAKETQmfrvvNH1e2+3X2r+y5vdd1b9/c5J6dSt956+33feuu5761VA3ERERERGdXDz3bzgz+uAOCvazZwynfvYsmyVRmXqrlpIC4iIiIio/r67U5v38DLfnaZ3Mlhc6dlWKLmp4G4iIiIiIzqylPfwocO3KN//qsn7cukzo4MS9T8xmddABERERFpfDtM6ODSkxfwvgW78YflL/HOeTOyLlLT0xFxEREREanY2/eZxgXHzUtc/sQL6zn32gd4cf3GMSxVc9JAXERERESC6O0rcP7iZdyybBXv/sYf+Pn9z1AoFEZfsUVpIC4iIiIiQVx950oefOZVALp7tvDZxcu4a8XLGZeqcWkgLiIiIiJ1KxQK/OaxFwZ9dsybZnDI7KkZlajxaSAuIiIiInVra2vjmrMP4sL3zKezYxyTOsfz5UX70taW/IKgVqenpoiIiIhIEO3j2vi7w2bz7jfO4MmXNzB9cmfZdIVCga19BTraW/uYcGvXXkRERESCmzVte4606YnLr7v3GRZ96w4eea57DEvVeDQQFxEREZExs6q7h0tv7eKxVetY9J938LVfPc7GLb1ZFysTMh0EfQAAE59JREFUGoiLiIiIyJgoFAp8/oZHWL9pKxA97vAnd67kpdc2ZVyybGggLiIiIiJjYtPWPiZ2Dr5F8fxjjDdM2S6jEmVLA3ERERERGROdHe1ceepb+OEZB7DL5E4OmDmF0w+ZlXWxMqOnpoiIiIjImDpq/gzettdOrN+4lXHjyj/ecO2GzQBM2X6bsSzamNIRcREREREZc5M7O9h9xwmJyy+66VHefcXvWbJsFYVCYQxLNnY0EK/BrAuWMOuCJWO2noiIiEgruf2xF7j5oed56bXNfOLaB/j7ny2lu2dL7sZgQQbiZjbFzL5pZk+Z2WYze87MfmhmMxshv5BKN2I1G7TW9URERERaSXfPFj5/48ODPlvV3cP+X/x1/3xexmB1D8TNbApwJ3AeMAVYBkwAzgQeNLMFWeaXtko2aKNtdBEREZFGNaGjnb89aCYd7dG14+3j2vja+4cP//IwBgtxRPwHwDzgVmB3dz8A2A24GtgR+C8za88wv6BWXnb8sM9G2sjllpXLQ0RERERgm/Hj+NRRc1jyqUN58x47cs7hs3nTbjvkcgxW10DczOYBJwOvAR929/UA7r4ROBvoAuYDJ2WRX1oq7QjN0AFEREREGtHcGZP4xcffznlHze3/LG9jsHqPiJ8GtAE3u/srpQvcvRf4cTz7wYzyS81oHaFZOoCIiIhIo2of18Y24wcPV5PGYFt6C/3/H6pRx2D1Pkf8oHh6Z8Lyu+PpoRnll6qVlx0/bGMf95MVZdN2felYnnhhff985/h29pxa/i1Sq7s3sm7jlv75GZM62WG7jmHpCoUCy198bdBnc2dMKpvnq69v5sX1A6+P3WFCBzMmd5ZNu/KlDWzu7euf33On7ejsGH41UM/mXp5Z+7rqpDo1dJ1e2rB10L6XhzqluZ2eWhs9t3endRtzU6eiNLbTqvVb2HXS8HI2c53yuJ1Up/zV6aGLjmb/L/16UJoTrnmyfHkadBAO9Q/E94mn5WsOT8XTGWY20d1fS0iXVn6pKzcYL5fmgafXcvK3B35fvHmPHbnxE+8om/7yXzuLlz7bP/9vpyzgAwfsMSzd1r4CR1/xh/758ePa+Msl7ymb500PPc9Fv3y0f/7DB8/kyyfuWzbtOdcs5fHVAwOX2847lPm7Th6Wrmv1OtVJdWr4Ov30z69w++Knc1WnMdlOL7bnr04pbCebti3fPH73XNUpj9tJdcpfnT522Gza2mC0x4s38iAc6h+I7xxPX05YXnp5yTSia7/HMj+6urpGS1K3286YnXgk/LYzZtPV1cXKNRsHfd7T05NYtu5XXx00v+r5VXR1Da/q1r7Bva9QKCTmuXp196D5tWvXJqbduGnToPknV6yAV7cdli5EnXp6eoCB7ZSHOg0Vsk6l7ZWXOpUKXaeenh629vYO+qzZ6wT5207QvHXq6+tLrFez1inN7TQ05kPz16mcUHUqba+81KlUPXWasHUdFxw2nW/f8xLdG/vKrlMcgzWyeq8RL74OqSdheennya9OSi8/EREREcmZNto4bNZEvr9o+JH+ZlLvEfFeRh7Mly6r5N2kofNj/vz5lSSry0iXphz3kxWsvOx4CjusY870df2fz911cmLZ5j7dxsqBMzrY7D2ZP3+XYem29PYxZ/qa/vn2cW2JeT6x6TnmPDnwC9X23IX58+eU//v3baCjY8NA2rn7sPfOE4elC1Gn4i/V4np5qNNQIetU2l55qdOgvx+4Tl1dXUyf1MOc6QPXJjZ7nSDd7bQpPpKVpzr155lCnXbbrsCECRPKlqFZ65Tmdhoa8/NQp3JC1am0vfJSp1Ih6lTJGCxtS5curXndtsJoF9eMwMzWEj3b+2B3v6fM8olAsdlmuftTQ9Okld/SpUsLAAsXLqykKjWr9EHxjX6NUlbKBWVJpvaqjtqremqz6qi9qqP2qo7aa2SNMgYrDsQXLlzYVu269V6aUryWe6eE5VNL/r8mIU2a+aWqXAe47YzZ3HbG7IrSioiIiEj18jIGq3cg/ng8nZWwfGY8XeXuryekSTO/1Iz2jMpq3/4kIiIiIqPL0xis3oH4/fH04ITlxc+HXWYyRvmlotIHxTdTRxARERFpdHkbg9U7EL8+np5oZoMuJzGzduAj8ew1GeUXXLVva2qWjiAiIiLSyPI4BqtrIO7uy4AlwGRgsZlNBTCzTuAqYD7gwA2l65nZNDObZ2Z7h8gvS5XcAKAbNUVERETCysMYrN4j4gDnEL3x8kjgaTO7H3ie6Oh1N3CSuw990vq5QBfw20D5jZnRrkEKvZ6IiIiI5HMMVu9zxHH3Z81sIXARsAhYALwKXAdc7O7Ls8wvDbVuxEbb+CIiIiLNJG9jsLoH4gDu/jJwXvyvkvRfAL4QKj8RERERkWYT4tIUERERERGpkgbiIiIiIiIZ0EBcRERERCQDGoiLiIiIiGRAA3ERERERkQxoIC4iIiIikgENxEVEREREMqCBuIiIiIhIBtoKhULWZUjF0qVL81kxEREREWk4CxcubKt2HR0RFxERERHJQG6PiIuIiIiINDIdERcRERERyYAG4iIiIiIiGdBAXEREREQkAxqIi4iIiIhkQANxEREREZEMjM+6AI3AzKYAFwMnAbsCa4BfAV9y96fGKj8zOx04F9gP2AQ8CHzD3W+qtgxpSqG95gHnA++M8+sBHgKucvefJaxzM/DeEbJ9zt3fUG1Z0hCyvcxsKvDSKMm+6u6fH7JeO/BJ4CxgDvAacA9wmbv/sZoypC1Ue5nZSmBmhcmPdPfflazbNP1rKDMbB9wF7O3u02pYP9fxa6gA7ZXr+DVUPe3VCvFrqFrbq5XiVy370Ah5NV38avmBeLzR7gTmAeuBZcBs4EzgZDM73N2XpZ2fmV0GfA4oAI8CncDhwOFmdpG7f7n2WoaTQnu9D/gfovpuBB4HZgCHAYeZ2bH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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"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",
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"y": [
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},
"metadata": {},
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}
],
"source": [
"fig = go.Figure(data=[go.Scatter3d(x=x[:,0], y=x[:,1], z=J(x[:,0], x[:,1]), marker={'size':3})])\n",
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]
},
{
"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."
]
},
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