{ "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 2, "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import numpy.linalg as lin\n", "import matplotlib.pylab as plt\n", "\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'\n", "\n", "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "In this course we look at 2 points:\n", " \n", "* how to improve Jacobi\n", "* the convergence of iterative algorithms (how to understand it and exploit it well)" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "## Add inertia to Jacobi\n", "\n", "Jacobi's method leads to the following iterative system\n", "\n", "$$\n", "{\\bf x}^{k+1} = M^{-1} \\, ( N\\; {\\bf x}^k + {\\bf b})\n", "$$\n", "\n", "We have seen that this method only converges if the matrix B has its spectral radius less than 1, $\\rho(M^{-1}\\,N) < 1$.\n", "\n", "We can modify this method so that it has a greater radius of convergence\n", "and therefore converges for more matrices. For this we add inertia:\n", "\n", "$$\n", "{\\bf x}^{k+1} = w \\, M^{-1} \\, (N\\; {\\bf x}^k + {\\bf b}) + (1-w) \\, {\\bf x}^k\n", "$$\n", "\n", "with $0 < w \\le 1$.\n", "\n", "If $w = 1$ then we have classic Jacobi and if $w = 0$ then we don't move, ${\\bf x}^{k+1} = {\\bf x}^k$.\n", "\n", "We talk about inertia because we see that we are moving more slowly since the new value of ${\\bf x}^{k+1}$\n", "is between the old value of ${\\bf x}^{k+1}$ and ${\\bf x}^k$.\n", "\n", "\n", "Note: $w \\, {\\bf a} + (1-w) \\, {\\bf b}$ represents segment $[{\\bf b}, {\\bf a}]$ when $w$ varies between 0 and 1.\n", "\n", "The idea is that with inertia we may enter the convergence zone whereas without it we would have jumped\n", "Above.\n", "\n", "This method is called *over-relaxation*, I don't know why." ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "### Let's program inertia for Jacobi\n", "\n", "We start with a simple Jacobi to check that we diverge." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A:\n", " [[5 7 6 0]\n", " [1 7 2 5]\n", " [5 6 5 1]\n", " [0 6 3 7]] \n", "b:\n", " [18 15 17 16] \n", "\n", "M:\n", " [[5 0 0 0]\n", " [0 7 0 0]\n", " [0 0 5 0]\n", " [0 0 0 7]]\n", "N:\n", " [[ 0 -7 -6 0]\n", " [-1 0 -2 -5]\n", " [-5 -6 0 -1]\n", " [ 0 -6 -3 0]]\n", "\n", "x_0 = [0.062 0.652 0.185 0.852]\n", "x_1 = [2.465 1.472 2.384 1.647]\n", "x_2 = [-1.322 -0.067 -1.161 0.002]\n", "x_3 = [5.088 2.662 4.803 2.841]\n", "x_4 = [-5.89 -1.986 -5.451 -2.055]\n", "x_5 = [12.921 6.009 12.084 6.324]\n", "x_6 = [-19.314 -7.672 -17.997 -8.044]\n", "x_7 = [35.937 15.79 33.53 16.575]\n", "x_8 = [-58.741 -24.41 -54.8 -25.618]\n", "x_9 = [103.534 44.49 96.557 46.694]\n", "x_10 = [-174.554 -73.588 -162.861 -77.23 ]\n", "x_11 = [302.056 128.775 281.706 135.159]\n", "x_12 = [-514.732 -218.038 -480.218 -228.824]\n", "x_13 = [885.114 376.327 825.542 394.983]\n", "x_14 = [-1513.908 -642.302 -1412.303 -674.084]\n", "x_15 = [2597.587 1103.419 2422.887 1158.103]\n", "x_16 = [-4448.651 -1888.411 -4149.91 -1981.882]\n", "x_17 = [7627.267 3238.983 7114.521 3399.456]\n", "x_18 = [-13068.402 -5548.37 -12190.539 -5823.066]\n", "x_19 = [22399.965 9511.401 20894.459 9982.548]\n" ] } ], "source": [ "np.random.seed(799)\n", "\n", "A = np.random.randint(10, size=(4,4))\n", "b = A.sum(axis=1) # ainsi la solution est [1,1,1,1]\n", "print('A:\\n', A, \"\\nb:\\n\", b, \"\\n\")\n", "\n", "M = np.diag(A) # attention, c'est un vecteur\n", "N = np.diag(M) - A # np.diag d'une matrice donne un vecteur, np.diag d'un vecteur donne une matrice\n", "print(f\"M:\\n {np.diag(M)}\\nN:\\n {N}\\n\")\n", "\n", "x0 = np.random.random(4)\n", "x = x0\n", "for i in range(20):\n", " print(f\"x_{i} = {x}\")\n", " x = (N @ x + b) / M" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "Now let's add inertia to Jacobi:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x_0 = [0.062 0.652 0.185 0.852]\n", "x_1 = [1.264 1.062 1.284 1.25 ]\n", "x_2 = [0.918 0.882 0.948 1.037]\n", "x_3 = [1.072 0.941 1.082 1.08 ]\n", "x_4 = [1.028 0.925 1.032 1.048]\n", "x_5 = [1.047 0.939 1.042 1.049]\n", "x_6 = [1.041 0.943 1.029 1.042]\n", "x_7 = [1.043 0.949 1.024 1.039]\n", "x_8 = [1.042 0.954 1.017 1.036]\n", "x_9 = [1.043 0.959 1.011 1.034]\n", "x_10 = [1.044 0.962 1.005 1.032]\n", "x_11 = [1.045 0.966 1. 1.031]\n", "x_12 = [1.046 0.969 0.995 1.03 ]\n", "x_13 = [1.048 0.971 0.99 1.03 ]\n", "x_14 = [1.05 0.973 0.986 1.029]\n", "x_15 = [1.053 0.974 0.981 1.029]\n", "x_16 = [1.056 0.976 0.977 1.03 ]\n", "x_17 = [1.059 0.977 0.972 1.03 ]\n", "x_18 = [1.063 0.977 0.968 1.031]\n", "x_19 = [1.067 0.978 0.963 1.032]\n" ] } ], "source": [ "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", "w = 0.5 # on choisit w \n", "for i in range(20):\n", " print(f\"x_{i} = {x}\")\n", " x = w * (N @ x + b) / M + (1-w) * x" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "The sought solution being [1,1,1,1] it seems to work well!" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "### Let's study convergence\n", "\n", "To fully understand an iterative method, it is necessary to study its convergence and therefore draw a curve\n", "absolute error (when the solution is known), or relative error (between 2 successive ${\\bf x}^i$)\n", "or the residual ($||A \\, {\\bf x}^i - {\\bf b}||$) or any other measure that makes sense.\n", "\n", "Let's look:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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hTT2SJElSOy1JAA9cBTwbGG62Ygjh5cCXgBXAQeAe4Ajg+cDzQwjnABfFGItVVU9Nj7cCk7M0/VizfekEA8t76e/rYXRiCoDRiSn2jU6wZsWyNvdMkiRJ7dDSAD6EUACuAN69wPpHAP9MErx/CvijGOOB9N4rgX8Cfhe4DfhYWb21wLHA3hjjcxfzGTpNoVBgaHU/Dz8xMn1teN+YAbwkSVKXalkOfAjhSOAGkgB+oS4F1gA/At5UCt4BYoxfZuaLwVur6pVm3+9exLM71mxpNJIkSepOLQngQwhnA/cC5wHbWeAMPPCC9Hh9jHFqlvtfTY/HhRDWl10vBfB3LfC5HW1ooHoveBeySpIkdatWzcA/FVgNfBY4hSQPfSH+DLgY+HKd+wNlP5en/5yWHvMZwK92Bl6SJEmJVuXA/wB4RozxDoAQwoIaiTHeytzB/3npcQews+x6aQb+wRDCHwAvBtYDD5HM5t+4oA51iMHVvo1VkiRJiUKxWL2Zy+KFEF4AfBsYXsg2knXaPBLYBqwD/ibG+Edl9x5Pr+8j+ZeAav8GvCbGuG+uZ2zZsqUIsGrVqlZ0uSkjI8ki1ZUrV9bc+/Ldu/nkD2c29Dk3rOXNZ7ZkWDNrrvFSLcerOY5Xcxyv5jhezXG8muN4Naed43XgQLLU84wzzmh6b/BMvMgphDBAklazjmTm/QNl956SXgf4OfBSkiB+EHgjsAt4GXDtIexyS61b0Vtx/vjB2XbJlCRJUjdYqn3gWyaEsBq4CXgOyf7uF8UYHy0rMgV8CNgAXF42y74f+EwI4W6Sl0pdGEI4M03TmdPmzZtb+REasm3btrrPfnzZTvjuzDb244X+tvSxk8w1XqrleDXH8WqO49Ucx6s5jldzHK/mtHO8tmzZsuC6HR3AhxA2kuw882ySQP2NMcZ/Ly8TY3wIeHu9NmKMPwghfAs4G3g5C19g2zaDLmKVJElSqmNTaEIIJ5DMnD8bmCCZef/sApu7Iz0e24q+HWpDLmKVJElSqiMD+BDCacD3gROBA8B5McYvzFG+EELor3cfKC0OyOQG6utXLaenbHnDnoMTjE6YBy9JktSNOi6ADyGcDHwTOBJ4HHhJjPHrc5S/miQw/8oczT49PW5rVT8PpZ6eAhsGKr+fDPsyJ0mSpK7UUQF8CGEVyYLVw0l2m3lBjPGWeardQZLLf1YIoSZFJoRwOsm+8FPAv7a2x4dOdRqNAbwkSVJ3aksAH0IYCiFsCiGcWHXrPUAgCbZfHWPc2kBzN5BsH9kPXBdCOL7sOc8imZnvAT4eY7y/JR+gDXwbqyRJkqB9u9BcBlwBPAgcB5DmsL85vX8AuGqeN7peGGPcHmMcDSG8iiTt5pnAvSGEe4Feki8DkOxk88et/hCHkgtZJUmSBJ21jeSpwGHpz6uB35yn/IrSDzHGO9OFr+8g2SryJGAE+B7waeAzMcbWv3L2EKrdStIUGkmSpG60JAF8jPE7zOz8Mtv9K4Erq67dPledBp65nWSWPdMz7fVUp9AMOwMvSZLUlTpqEavqM4VGkiRJYACfGTUz8PtNoZEkSepGBvAZUR3A79jrDLwkSVI3MoDPiMGaFBpn4CVJkrqRAXxGVAfwu/aPMjWV6Y11JEmStAAG8BnR39fLmhUzmwZNFeHxA87CS5IkdRsD+AzZ6EJWSZKkrmcAnyE1efAuZJUkSeo6BvAZUr0TzU5n4CVJkrqOAXyG1ATwzsBLkiR1HQP4DKndStIAXpIkqdsYwGdIzdtY3QtekiSp6xjAZ8iQM/CSJEldzwA+Q1zEKkmSJAP4DBl0EaskSVLXM4DPkOoUmuH9oxSLxTb1RpIkSe1gAJ8hq/v76O+b+S07OD7F/rHJNvZIkiRJh5oBfIYUCoVZdqIxjUaSJKmbGMBnjDvRSJIkdTcD+IypXsi6Y6870UiSJHUTA/iMmW0hqyRJkrqHAXzG1G4l6Qy8JElSNzGAz5iaRazOwEuSJHUVA/iMcRGrJElSdzOAz5jqGfid+0yhkSRJ6iYG8BlTG8A7Ay9JktRNDOAzZrB6Fxpn4CVJkrqKAXzGrF+1nJ7CzPnukXHGJqba1yFJkiQdUgbwGdPbU2DDgHvBS5IkdSsD+Ayq2UrSNBpJkqSuYQCfQdV58DtcyCpJktQ1DOAzyBl4SZKk7mUAn0GDA24lKUmS1K0M4DNoaE31VpIG8JIkSd3CAD6DfBurJElS9zKAz6ChqkWsptBIkiR1DwP4DHIGXpIkqXsZwGfQYE0A7wy8JElStzCAz6DBqjex7to/xtRUsU29kSRJ0qFkAJ9BK5b1sqa/b/p8cqrIEyPjbeyRJEmSDpW++Ys0L4TQA9wCnBhjHFpA/fXAFcD5wFHADuAbwPtijA/OUe8NwGXAqcAocAfwkRjjV5r+EB1uaE0/e0cnps+H942yoWpmXpIkSfmzVDPwVwHPXkjFNHi/GbgcWA9sBVYClwB3hBBOq1PvauAfgWcC95EE/WcBN4YQ/mwhfelk1TvR7DAPXpIkqSu0NIAPIRRCCFcC715EM58CNgFfB54UY3wmcDTwGWAd8MUQQm/Vc88F3gnsAp4TYzw1xngy8EqSmfj3hhB+cxF96jjVb2MddicaSZKkrtCyAD6EcCRwA0nqy0Lb2ARcAOwDXh9j3AsQYzwIXApsAzaTpNaU+x/p8V0xxh+WLsYYbwTeCxRY3JeKjlP9NlZ3opEkSeoOLQngQwhnA/cC5wHbWXiwfBFJsH1TjHFX+Y0Y4yRwbXr62rJnnwQ8FxgHPj9Lm/+QHs8OIaxbYL86TvUMvAG8JElSd2jVDPxTgdXAZ4FTgFsX2M5z0uPNde6X2n3eLHW2xhj3V1eIMT4G3A8sA85cYL86ztAaU2gkSZK6UasC+B8Az4gxviHGOLyIdk5Kj7+oc7+0A80RIYTVDdYpr3fSHGUyZWjAFBpJkqRu1JJtJGOM9WbMm7UxPdb7ElCeVjNEkis/X53yeg1tablt27ZGirXUyMhIU8/eN3yw4vxXO3a3pd/t0ux4dTvHqzmOV3Mcr+Y4Xs1xvJrjeDUnq+PVaS9yWpkeR+rcL7++supYr075vZVzlMmUdSsqf+ueODjZpp5IkiTpUFqSFzktwiRzf6kov1csqzOfUr3inKVSmzdvbqRYS5W++TX67CcdHIcvPzR9vme02JZ+t0uz49XtHK/mOF7Ncbya43g1x/FqjuPVnHaO15YtWxZct9Nm4EuLUFfUuV++crM0qz5fnfJ6c83SZ8qa/j6W98389o2MT7K/7M2skiRJyqdOC+BLeewb6twfLPt5R4N1yuvtmKNMphQKhZqFrO5EI0mSlH+dFsDfkx6Pq3P/2PT4SIzxQIN1yuvdt+CedaDqrSR3uBONJElS7nVaAH97eqy3X3vp+m2z1Dk9hFCTRhNCOBw4HpgCflh9P8sG3UpSkiSp63RaAH99enxlCKEiJSaE0AtcnJ5+rnQ9xvgA8GOSPPeLZmnz0vT49Rjj463sbLsNrfZlTpIkSd2mLQF8CGEohLAphHBi+fUY41bga8Ba4LoQwmBafgVwDbAZiMANVU2+Pz1+OITwgrLnvAL4c5LdZz64BB+lrQarAnhn4CVJkvKvXTPwlwHbgP+Y5d6bSN6c+kLglyGE24Ffk8y+7wbOjzFOlVeIMV4HfJok8P92COGuEMK9wI0kM/N/GmP83hJ9lrYZWl29iNUAXpIkKe86LYWGGONDwBnAx0h2jTkNmAC+ADwrxljvVVmXApcAPyBZ0HoMcAvwOzHG99epk2kb11TPwJtCI0mSlHdL8iKnGON3gMIc968Erpzj/jBwefqr0WcWgWvTX11hcMAUGkmSpG7TcTPwatzQGnehkSRJ6jYG8BlWOwNvCo0kSVLeGcBn2IaB5RTKEpV2j4wzNjFVv4IkSZIyzwA+w3p7CmxYVZlGs2u/s/CSJEl5ZgCfcdUvczIPXpIkKd8M4DNucLULWSVJkrqJAXzGVc/AD7uQVZIkKdcM4DPOFBpJkqTuYgCfcdUpNMMuYpUkSco1A/iM21g9A7/XGXhJkqQ8M4DPuOoZ+B2m0EiSJOWaAXzGuYhVkiSpuxjAZ5zbSEqSJHUXA/iMq56B37V/jKmpYpt6I0mSpKVmAJ9xK5b1sqa/b/p8YqrI7pHxNvZIkiRJS8kAPgdqt5I0jUaSJCmvDOBzoDqNZsdeF7JKkiTllQF8DjgDL0mS1D0M4HOgegbelzlJkiTllwF8DgxWB/DuBS9JkpRbBvA5sNEUGkmSpK5hAJ8D1TPwLmKVJEnKLwP4HKjOgXcGXpIkKb8M4HNgqCqFZuc+A3hJkqS8MoDPgeoUmmEXsUqSJOWWAXwOrF3Rx/Lemd/KA2OTHBibaGOPJEmStFQM4HOgUCjUvMxppwtZJUmScskAPidqXubkQlZJkqRcMoDPidoZeAN4SZKkPDKAz4narSRNoZEkScojA/icqEmhcQZekiQplwzgc6J6L3hn4CVJkvLJAD4nqmfgd/gyJ0mSpFwygM+J6kWswwbwkiRJuWQAnxM1OfC+jVWSJCmXDOBzomYbSWfgJUmScskAPic2rFpOoTBz/sSBccYnp9rXIUmSJC0JA/ic6OvtYf2qyln4Xe5EI0mSlDsG8DlSvZWkaTSSJEn509eqhkII64ErgPOBo4AdwDeA98UYH2yinQeAYxss/sIY43fK6t4EnDtH+YdjjMc02pesGVrdz72P7ps+dyGrJElS/rQkgE+D95uBTcBeYCtwAnAJcEEI4awY49YGm/sh8NAc948HjgZGZyl3anq8FZicpe5jDfYhkwardqJxK0lJkqT8adUM/KdIgvevA6+LMe4NIawAPg5cDHwxhHBqjHG2oLpCjPHV9e6FEIaAn6Sn/z3GeF/ZvbUkM/d7Y4zPXfAnyTBTaCRJkvJv0TnwIYRNwAXAPuD1Mca9ADHGg8ClwDZgM0lqzWL9PXAkcH2M8dNV90qz73e34DmZ5F7wkiRJ+deKRawXAQXgphjjrvIb6Yz7tenpaxfzkBDCK0i+BOwBLpulSCmAv2sxz8kyZ+AlSZLyrxUB/HPS48117t+aHp+30AeEEHqBq9PTq2KMj8xS7LT02LUB/OCAM/CSJEl514oc+JPS4y/q3C/tQHNECGF1jHFfnXJzeSNJGs7DwMfqlCnNwD8YQvgD4MXAepKFrtfHGG9cwHMzZWiNi1glSZLyrhUB/Mb0OFznfnlazRBJrnzDQggF4G3p6V/HGOtFpaekx88Aq6vuvSGE8G/Aaxb4BSITBgdMoZEkScq7VgTwK9PjSJ375ddX1ikzl5eQ7HCzm2QRa40QwlOAdenpz4F3AN8H+oFXAB8GXkaSj193l5uSbdu2LaCbizMyMrLoZ49OTFWc79w7yt13302hUFhU3zpRK8armzhezXG8muN4Ncfxao7j1RzHqzlZHa9WBPCTzJ1LX36vuID235wer4kx7qlTZgr4ELABuLxsln0/8JkQwt3ALcCFIYQzY4y31mkn0/r7eli5rMDIeDLMk0XYNzbFmv7eNvdMkiRJrdKKAH4/yez3ijr3yxOz683SzyqEMACck55+rl65GONDwNvnuP+DEMK3gLOBlzOzsHZWmzdvbqabLVH65rfYZx++djsPDh+YPt9w9HGcdHh1RlH2tWq8uoXj1RzHqzmOV3Mcr+Y4Xs1xvJrTzvHasmXLguu2YheaUu77hjr3B8t+3tFk22eTfAG4N8Z4R7Mdq1Kqf+wi2+lotXvBmwcvSZKUJ60I4O9Jj8fVuV8KmB+JMR6oU6aec9Pjv8xXMIRQCCH0z1GklAie670VXcgqSZKUb60I4G9Pj2fWuV+6ftsC2n5uevzOXIVCCFeTBOZfmaPY09NjtlYpNKl2K8lcf1+RJEnqOq0I4K9Pj68MIVSk0aQvYLo4Pa2bwz6bEMIqIKSnP5qn+B0k+fxnhRBqUmRCCKeT7As/BfxrM/3ImiFn4CVJknJt0QF8jHEr8DVgLXBdCGEQIISwAriG5AVMEbihvF4IYSiEsCmEcGKdpk9J+7c9xrirTpmSG0i2j+xP+3B82XOeRTIz3wN8PMZ4f5MfMVOqZ+B9G6skSVK+tGIXGoA3Ad8DXgj8MoSwDTiB5E2ou+U5YIUAACAASURBVIHzY4xTVXUuA64geVPrcbO0eVR6fHy+h8cYR0MIrwK+CTwTuDeEcC/Qy8ws/leBP27iM2WSi1glSZLyrRUpNKVtHM8APkay08xpwATwBeBZMcaF5J2Xdq/Z3WAf7kyf+1HgAeAk4EiSLxaXAK+IMeZ+Orp6EeuwAbwkSVKutGoGnhjjMHB5+quR8lcCV85x/9PAp5vsw3aSWfbcz7TXYwqNJElSvrVkBl6dY2igehcaZ+AlSZLyxAA+Z9au7GNZb2H6fP/YJCNjk23skSRJklrJAD5nCoUCgwMuZJUkScorA/gcGlrjXvCSJEl5ZQCfQ7Uz8C5klSRJygsD+Byq3gvehaySJEn5YQCfQ6bQSJIk5ZcBfA5VbyVpCo0kSVJ+GMDnkDPwkiRJ+WUAn0NuIylJkpRfBvA5VLuI1RQaSZKkvDCAz6Gh1abQSJIk5ZUBfA5tGFhOoTBz/viBcSYmp9rXIUmSJLWMAXwO9fX2sH5V5Sz8rv2m0UiSJOWBAXxODQ5Up9EYwEuSJOWBAXxOVS9kNQ9ekiQpHwzgc2qwaiHr8H4DeEmSpDwwgM+pmhn4vabQSJIk5YEBfE65laQkSVI+GcDnVG0OvDPwkiRJeWAAn1ODLmKVJEnKJQP4nKpOoXERqyRJUj4YwOeUi1glSZLyyQA+p6oD+OH9oxSLxTb1RpIkSa1iAJ9TK5f3MrC8d/p8fLLInpGJNvZIkiRJrWAAn2M1C1nNg5ckSco8A/gcq9kLfq8BvCRJUtYZwOdY7VaSLmSVJEnKOgP4HJttIaskSZKyzQA+xzaaQiNJkpQ7BvA5VruI1RQaSZKkrDOAz7Halzk5Ay9JkpR1BvA5NliVQjPsDLwkSVLmGcDnWM0M/D5n4CVJkrLOAD7H3AdekiQpfwzgc+ywlcvo6ylMn+8fm2RkbLKNPZIkSdJiGcDnWKFQqMmDN41GkiQp2wzgc672ZU4uZJUkScoyA/iccytJSZKkfDGAz7narSQN4CVJkrKsr1UNhRDWA1cA5wNHATuAbwDvizE+2GRbg8DOeYr9RYzxT6vq9QJvAX4POBnYB9wGXB1j/G4zfciLjTVbSZpCI0mSlGUtmYFPg/ebgcuB9cBWYCVwCXBHCOG0Jps8NT0OA9+v86viS0EIoQB8DvgosBnYBhwAfhv4Tgjh4mY/Vx64iFWSJClfWjUD/ylgE/B14HUxxr0hhBXAx4GLgS+GEE6NMTa6h2Ep4P9CjPEtDdZ5M/A64H7gnBjjz9Kg/veBvwM+EUL4rxjjLxpsLxdqX+bkDLwkSVKWLXoGPoSwCbiAJF3l9THGvQAxxoPApSQz4ZtJUmsaVZqBv6vBPvQBb09P3xRj/Fnah2KM8RMkXzD6gbc10YdcGHQRqyRJUq60IoXmIqAA3BRj3FV+I51xvzY9fW0TbTYVwAMvAJ4CPBJj/OYs969JjxeGELpq4W7121hdxCpJkpRtrQhmn5Meb65z/9b0+LxGGkvTXk5JTxsN4Ofrw4+AMeAI4DcabDMXTKGRJEnKl1bkwJ+UHuvllpcWmx4RQlgdY9w3T3snAAPAduDwEMI7gP8GFIE7gWtKKTKN9iHGOBlCeBg4Pi17zzx9yI0NA5Uz8I8fGGNicoq+3q76hwhJkqTcaEUAvzE9Dte5X55WM0SSKz+XUvrMYcBPgd6yey8F3hpCeEuM8ZNN9KHUj+PTPsxp27Zt8xVpuZGRkSV79tr+HvaMTgFQLMJtd97FhpUt20G0LZZyvPLI8WqO49Ucx6s5jldzHK/mOF7Nyep4tWIadmV6HKlzv/z6yjplypV2oFnJzO42/SSpL58ElgEfDyGc20Qfyu810odcOWxFb8X57pFGNwOSJElSp2nFNOwkc38RKL9XbKC9H5EE6j+NMf5t2fWfAW8KIYwDlwEfAr5a1of5lPoxbx82b97cQHOtVfrmtxTPftJ3n+BXu2f+IWTN4U9i88kb56jR+ZZyvPLI8WqO49Ucx6s5jldzHK/mOF7Naed4bdmyZcF1WxHA7wfWASvq3C9fRTnXDDkAMcavMhOYz+b9JAF8CCGcnObD70/v1etDeT/m7UPeVG8lOexCVkmSpMxqRQpNKe98Q537g2U/71jsw2KMjwCPpafHNtiH8n4sug9Zs7FmJxq3kpQkScqqVgTwpR1djqtzvxRkPxJjPNBIgyGEZSGE3jmKFNJjaSp5zj6kL3p6Unp6XyN9yJPBqp1odhjAS5IkZVYrAvjb0+OZde6Xrt/WSGMhhF+RBOavqXP/aGZ2nSktGS714Tm1NQB4Bsni12G6MIAfWmMKjSRJUl60IoC/Pj2+MoRQkcKSzqJfnJ5+rsH2Si9vekOd+29Lj/8VYyylw3wX2AkcG0J4ySx1Lk2PX4gxTjXYj9yofZmTM/CSJElZtegAPsa4FfgasBa4LoQwCBBCWAFcA2wGInBDeb0QwlAIYVMI4cSqJj+UHs8JIXwghLA8Ld8bQvgT4K0ku868s6wPk8AH09NrQwilrSgJIfw+SQA/Cnx0sZ83iwZXV6bQOAMvSZKUXa16HeebSN64+kLglyGE24Ffk8y+7wbOn2Xm+zKSFJj/KL8YY/wW8J709F3AY2l724G/IgneL4kxVqfk/A3w78AxwI9DCHeEEB4EPkGSM39JjPH+FnzWzHERqyRJUn60JICPMT4EnAF8jGSXl9OACeALwLNijE293irG+H7gRcBXgPG0vTHg88AzY4z/NEudceBckhSbu4AArCf5gnB2jPHzC/pwOTDbDHyx2MiW/JIkSeo0rdgHHoAY4zBwefqrkfJXAlfOcf/bwLeb7MME8JH0l1KrlvexankvB8aS912NTU6x5+AEh61c1uaeSZIkqVmtSqFRh6uehTeNRpIkKZsM4LtE9U40LmSVJEnKJgP4LjE44EJWSZKkPDCA7xIb11QvZDWAlyRJyiID+C5RnUKzwxQaSZKkTDKA7xKDA87AS5Ik5YEBfJcYWmMOvCRJUh4YwHeJ6kWs7kIjSZKUTQbwXaJ6Easz8JIkSdlkAN8lareRdAZekiQpiwzgu8RhK5fR11OYPt83OsHB8ck29kiSJEkLYQDfJXp6CgyuNo1GkiQp6wzgu4gLWSVJkrLPAL6LuJWkJElS9hnAd5Ghmpc5OQMvSZKUNQbwXaR6Bn6HM/CSJEmZYwDfRQYHXMQqSZKUdQbwXWRotYtYJUmSss4Avou4jaQkSVL2GcB3EWfgJUmSss8AvotsdBtJSZKkzDOA7yIbqhax7jowxuRUsU29kSRJ0kIYwHeRZb09rFu1bPq8WIRd+02jkSRJyhID+C5TvZXk8H7TaCRJkrLEAL7LVC9k3bnXGXhJkqQsMYDvMjUBvAtZJUmSMsUAvssMuRe8JElSphnAd5naGXhTaCRJkrLEAL7LDNa8zMkZeEmSpCwxgO8yptBIkiRlmwF8l6mZgXcfeEmSpEwxgO8yG2u2kXQGXpIkKUsM4LvMYHUKzf4xisVim3ojSZKkZhnAd5mB/j5WLuudPh+bmGLv6EQbeyRJkqRmGMB3oZpZeNNoJEmSMsMAvgtV7wXvQlZJkqTsMIDvQjUvc3IGXpIkKTMM4LtQzV7wzsBLkiRlhgF8F3IGXpIkKbsM4LtQ9SLW4f0G8JIkSVnR16qGQgjrgSuA84GjgB3AN4D3xRgfXEB7m4B3AC9K2xsB7gSuiTF+tk6dm4Bz52j24RjjMc32JW9qZ+BNoZEkScqKlgTwafB+M7AJ2AtsBU4ALgEuCCGcFWPc2kR7Lwe+BKwADgL3AEcAzweeH0I4B7goxlj9BqJT0+OtwOQsTT/W8IfKsZptJPc5Ay9JkpQVrZqB/xRJ8P514HUxxr0hhBXAx4GLgS+GEE6NMc4WVFcIIRwB/DNJ8P4p4I9ijAfSe68E/gn4XeA24GNl9dYCxwJ7Y4zPbdHnyqWNbiMpSZKUWYvOgU9TXS4A9gGvjzHuBYgxHgQuBbYBm0lSaxpxKbAG+BHwplLwnrb5ZeDd6elbq+qVZt/vXsDH6CqDLmKVJEnKrFYsYr0IKAA3xRh3ld9IZ9yvTU9f22B7L0iP18cYp2a5/9X0eFyaulNSCuDvavA5XWvdymX09hSmz/eOTnBwfN5/HJEkSVIHaEUA/5z0eHOd+7emx+c12N6fkaTdfLnO/YGyn8tTgE5Ljwbw8+jpKTA4UL0TjWk0kiRJWdCKHPiT0uMv6twv7UBzRAhhdYxx31yNxRhvZSbon8156XEHsLPsemkG/sEQwh8ALwbWAw+RzObfONdzu83g6n4eK0udGd43ypPWrWxjjyRJktSIVgTwG9PjcJ375Wk1QyS58gsSQjiSZGtJgM9X7UJzSnr8DLC6quobQgj/Brxmvi8QANu2bVtoFxdsZGTkkD57ZWG84vzH237Osr2rDsmzW+FQj1fWOV7Ncbya43g1x/FqjuPVHMerOVkdr1ak0JSmbUfq3C+/vuAp3hDCAElazTqSmfcPlN17Snod4OfAS0mC+EHgjSRfIl7GTD5+11u3orfi/IkRc+AlSZKyoBUz8JPM/UWg/F71vu0NCSGsBm4iybefJNkD/tGyIlPAh4ANwOVls+z7gc+EEO4GbgEuDCGcmabp1LV58+aFdHNRSt/8DtWzT7y/yH/eP/OPEcvWbmDz5pPmqNFZDvV4ZZ3j1RzHqzmOV3Mcr+Y4Xs1xvJrTzvHasmXLguu2IoDfTzL7vaLO/fI9C+vN0tcVQthIsvPMs0kC9TfGGP+9vEyM8SHg7fXaiDH+IITwLeBs4OXMnWPfFWq3knQRqyRJUha0IoWmlPu+oc79wbKfdzTTcAjhBJKZ82cDEyQz759tuoeJO9LjsQusnytDNS9zci94SZKkLGhFAH9Pejyuzv1SwPxI+UuZ5hNCOA34PnAicAA4L8b4hTnKF0II/fXuk+xVD+BUMzC0unIbyZ37DOAlSZKyoBUB/O3p8cw690vXb2u0wRDCycA3gSOBx4GXxBi/Pkf5q0kC86/M0ezT02O2lhkvkZoZ+H1+r5EkScqCVgTw16fHV4YQKtJoQgi9JC9lAvhcI42FEFaRLFg9nGS3mRfEGG+Zp9odJPn8Z4UQalJkQgink+wLPwX8ayP9yLvqAN4ZeEmSpGxYdAAfY9wKfA1YC1wXQhgECCGsAK4BNgMRuKG8XghhKISwKYRwYlWT7wECSbD96rT9+dxAsn1kf9qH48ue8yySmfke4OMxxvub/5T5s2GgOoVmjDt+9USbeiNJkqRGtWIXGoA3Ad8DXgj8MoSwDTiB5E2ou4HzY4xTVXUuA64geVPrcQBpDvub0/sHgKtCCHM998IY4/YY42gI4VUkaTfPBO4NIdwL9JJ8GYBkJ5s/XsyHzJPlfT087ei13PXrPdPX3valO/jaHz6PFct656gpSZKkdmpFCk1pG8czgI+R7DRzGsmuMV8AnhVjbDTv/FTgsPTn1cBvzvNreuvKGOOd6XM/CjwAnESSQ/894BLgFTFGE73L/MlLK78c/XzHfj7yzXvb1BtJkiQ1olUz8MQYh4HL01+NlL8SuLLq2u3M7BazkD5sJ5lld6a9AS8Mh/PaZz6Z/337r6avfeq793P2U4/gmcfV2xVUkiRJ7dSSGXhl15+eu5mjD5t5B1exCH/yL3dyYGyijb2SJElSPQbwXW7NimX85YWnV1x7YPgAf/mN2KYeSZIkaS4G8OL/OHmIi858SsW1z9z8ALf8fLhODUmSJLWLAbwAePfLNvPkDSsrrr39ujvZN2oqjSRJUicxgBcAA/19/FVVKs1Dj4/wga/74lpJkqROYgCvaWeeMMgbf/O4imv/fNsv+e7PdrSnQ5IkSaphAK8K73jpJo4fGqi8dt1W9hwcb1OPJEmSVM4AXhVWLu/lQ68+jZ6y3fgf2X2Qq756d/s6JUmSpGkG8KpxxrEb+L+fd0LFtS/d/hD/ec+jbeqRJEmSSgzgNau3/tZvcNLhqyuuvetff8ITB8ba1CNJkiSBAbzqWLGslw+/+nR6y3JpHts7yntvMpVGkiSpnQzgVdfpT17HH5x1YsW1G378MP9+1/Y29UiSJEkG8JrTH774ZDYduabi2ntu+Am79ptKI0mS1A4G8JrT8r4ePvya0+krS6XZuW+MP7vxp23slSRJUvcygNe8nnb0YbzlRSdXXPva1kf46tZft6lHkiRJ3csAXg357y88kVOetLbi2p99+afs2Dvaph5JkiR1JwN4NWRZbw8ffvXTWd4780fm8QPj/I8bfkKxWGxjzyRJkrqLAbwaFo5cwx/9VmUqzTfvfpQv3/Fwm3okSZLUfQzg1ZT/53kn8PQnr6u4dsWNd7F998E29UiSJKm7GMCrKX29PXzo1afT3zfzR2fPwQneff1WU2kkSZIOAQN4Ne2kw1fz9peGimvfjjv4l9sfalOPJEmSuocBvBbkjb95PM86bn3Ftfd99W4efmKkTT2SJEnqDgbwWpDengJ/deHprFzWO31t3+gE77zOVBpJkqSlZACvBTtuaIB3vWxTxbXv3beTf77tl23qkSRJUv4ZwGtRXn/msTz3hMGKa+//+jZ+OXygTT2SJEnKNwN4LUpPT4G/vPA0BpbPpNIcGJvk7dfdydSUqTSSJEmtZgCvRXvyhlW85/98asW1236xi3+85YG29EeSJCnPDODVEr/z7CfzvJOHKq598Bv3cP+OfW3qkSRJUj4ZwKslCoUCH3zVaazp75u+dnB8irdft5VJU2kkSZJaxgBeLXP0upX8+csrU2m2PPg4//C9+9vUI0mSpPwxgFdLXXjGMbx40+EV1z70/97Lzx7d26YeSZIk5YsBvFqqUCjwgQtO5bCVy6avjU1M8Sf/cicTk1Nt7JkkSVI+GMCr5Q5fu4L3nfe0imt3PrSbT/5/ptJIkiQtlgG8lsQrTj+ac552ZMW1v/7WvWx7ZE+beiRJkpQPBvBaEoVCgavOP4UNA8unr41PFnnbl+5k3FQaSZKkBTOA15IZWt3PVa88peLa3Y/s4W//87429UiSJCn7DOC1pH771KN4+elHV1z7X9++j58+vLtNPZIkSco2A3gtufe94mkMre6fPp+YSlJpRicm29grSZKkbDKA15JbP7CcD1xwasW1+Ohe/uZbP2tTjyRJkrLLAF6HxG899QgueMaTKq594r9+zo9/+XibeiRJkpRNfa1oJISwHrgCOB84CtgBfAN4X4zxwUPVXgjhDcBlwKnAKHAH8JEY41ea7YNa74qXP43v37eTR/eMAjBVhPP/7maW9RZY1ttDX0+B5X09LOtNfvX1Flhe9vOy3p70vMDBA/vp6ykweOfB9H4Py9Myy/p6WNYz83N1u8t6C6xZ0cfG1SvYuKafwdXLWdbrd1lJkpQNiw7g02D7ZmATsBfYCpwAXAJcEEI4K8a4danbCyFcDbwTKAJ3ASuAs4CzQgh/HmP8nwv/lGqFw1Yu44OvOo2Lr/1hxfXxySLjkwvMh39wfwt6BhsGlrNxdT8b15T9KjsfSn9et3IZPT2FljxTkiRpIVoxA/8pkmD768DrYox7QwgrgI8DFwNfDCGcGmNsNEJrur0Qwrkkwfsu4JwY4w/T6+cB/xt4bwjhP2OM31/8x9VivCAczuue9WS++MNftbsrFXbtH2PX/jHio3vnLNfXU5gO5quD/OprA/0t+QcuSZKkCouKMEIIm4ALgH3A62OMewFijAdDCJcCzwE2k6TCXLeE7f2P9PiuUvCe1rsxhPBe4P3Au4FzF/Fx1SJ//vKnsm90gm9te5SD49l6qdPEVJHtew6yfc/BecuuWt47HdCXgv71A8spkPwzEcUipD8Xi1CkmB6nb1EkuZBcm7lPVR1K92e5VwSeePxxegoFNt5313S6Ul9vkmrUl6YV9VX8PJO21NdTSNOSStdmuZ+mOfX1pPXLrvf6LxaSpEUoFotMFWGqWGQq/X/hVNm14lRynJzt/lT5eWU7U1Pw8+FR1vT3sLndH7JJi50ivAgoADfFGHeV34gxToYQrgX+EngtDQTwC2kvhHAS8FxgHPj8LG3+A0kAf3YIYV2M8YkmPp+WwKrlffzt7z4DSP5ijU9NMTFZZHxyirHJKcYni0xMTiXnE0UmpmZ+Hp+cYmJqivsf+BUTU0UOP/IoJiaLab2pip9rzieSZ41NTLF7ZJwde0fZsXeUXQfGpoPgVjowNsmDwwd4cPhA6xtfqLjnkD+yUICeQoGeQvKG3p7p80LFveS8/H5avqfJ8rO13zNTvne2uj2lusm1vXv2UCjA+p+OlZVpru8UChRgumwBptOvSnXTYhRIy0zXSX8uu1ZTZ/rntE7PTDuUXaf6Gek5Zefl5ZO2k/JMl0/7PUtbFOBX20cA2N0/PN0e5fVKfSrrT/mV2vuFWcsXqspTdb/mzx6z36hbvsl25jLzdbrWLx4fS75lPzL738f5/ntUanu2cuXXZitXrChbnOVabcmZCYWZ8/K61RMOs10vVlwve2553em2K8s+9NB+isCDk9uTkmUTHZUTH5V9nr5XPgmSNlxer6Z8emH6GWU/TxWLs5YvBY2lcU3Kzt5mqWzNZ6i6PvOs4nRbU0Uqyk6VtUl6/sTuPRSLRdb8eGS6/ampWepXtF3Z5nQfy89JP1NFkDxzPlWsbqPs2eXBNlXnVcfytsrLLLVz7hnn7/6vZ2QmTXaxAfxz0uPNde7fmh6ft4TtlepsjTHWJETHGB8LIdxPkkd/JsliWHWInp4C/T29NJttclQx+X63efMxi+7D+OQUu/aPJQH9vtHpwL78fGd6vnd0YtHP6zbFIkwWiyQ5b4fgv8Itta/dHciYR9rdgYx5uN0dyJhH292BjGnNGrFu8Y27tvPTX+/mtGPWtbsrDVlsAH9SevxFnfulHWOOCCGsjjHO93/DhbQ3X51SvRPKykrTlvX2cMTaFRyxdsW8ZUfGJtm5b5THqgL88oC/FOyPTWYrPUiSpG61vLeH9auWt7sbDVtsAL8xPQ7XuV+eBjPE/NNZC2lvvjrl9YbmeT4A27Zta6RYS42MjLTt2VnU7vFaBRzbC8ceBhwGyV+lPmAASP7pb//4FI+PTPL4yCS70uO+sWQeusBMisLMOWUpC5X/bF+Z6lD2c3phJi1itnIFxsfHmCpCT28fE8Ukl39yqsjEFOmxyOQUTBTLfk6vz1amVLemnWJtXUmSFmsmvXAmNbGHyvNS2uJMueT/pRX1mLnXUyhAcYo1/T2c99T17Hv0QbZl5B96FhvAr0yPI3Xul19fWafMYtubr075vUb6IC1aoVBg9fJeVi/v5cmHtbs3M194Vq48tH8FSjmMQE0OZ3l+6PS1qvPK8uU5mGnbUJmHWXZeyh+tzKWszFet14fR0TGKQF/f8iQfk7JnTrdRnT86S7vT9WaSh0qfg7Rc+mNFnm3lceZ6+ThShKm0cqk/5fnBM78HaTvpSXlbxaoypd+z2a9X9nXmZ5icSr6p9RRm3qcwXY/KhxWr71dlVVX3rfRTTZ+rH1SlXrJW3SSuOkm2ddsp1s+ZL6l3u/Rns6en/vsn5svCLdT8UPXFvvTzLAVnv197raJc1Q+F8imGOhMMyXnleobqMoXZ+l+o7OvUVDLx0dfbW1m/FIzN0ufqdR4VEyTTPxdm6e8s60LS8j1lzyhfY9JTKG+7eq0JZX2oXDsy65qSivLMrIUpPYfC9PN6quun5cbHxykA/f3Ly+qlwWpap2f6MxWmP0Oh/NmlILisD9PPqw6Ky8eqULaGp/ycys9Ru+anOtCuPC/1Yym06/+Pi7XYAH6Sud/mWn6vkeTXhbTXyPaUpXoNJeBu3nzo1yKXZpLb8ewscrya43g1x/FqjuPVHMerOY5Xcxyv5rRzvLZs2bLguot9/WRphUS95OH+sp/nmiFfTHvz1Smv10gfJEmSpI612AC+lHe+oc79wbKfdyxRe/PVKa/XSB8kSZKkjrXYAP6e9HhcnfvHpsdHYoyNbIa9kPbmq1Ne774G+iBJkiR1rMUG8LenxzPr3C9dv20J2yvVOT2EUJNGE0I4HDieZL3XD6vvS5IkSVmy2AD++vT4yhBCRQpLCKEXuDg9/dxStRdjfAD4MUme+0WztHlpevx6jPHxBvshSZIkdaRFBfAxxq3A14C1wHUhhEGAdCb8GmAzEIEbyuuFEIZCCJtCCCe2oj3g/enxwyGEF5Q95xXAn5PsPvPBxXxWSZIkqRMsdhtJgDcB3wNeCPwyhLCN5K2n64HdwPkxxurXuVwGXEHyhtTjFttejPG6EMKngUuAb4cQ7gaWASenRd4TY/xeCz6rJEmS1FaLTaEhxvgQcAbwMZJdXk4DJoAvAM+KMTb1qsxFtHcpSQD/A5IvBccAtwC/E2N8f506kiRJUqa0YgaeGOMwcHn6q5HyVwJXtqq9tE4RuDb9JUmSJOXSomfgJUmSJB06BvCSJElShhjAS5IkSRliAC9JkiRliAG8JEmSlCEG8JIkSVKGGMBLkiRJGVIoFovt7kPH2LJli4MhSZKkQ+aMM84oNFvHGXhJkiQpQ5yBlyRJkjLEGXhJkiQpQwzgJUmSpAwxgJckSZIyxABekiRJyhADeEmSJClD+trdgTwKIawHrgDOB44CdgDfAN4XY3yw3e11ohDCJuAdwItIPuMIcCdwTYzxs020MwjsnKfYX8QY/3ShfW23Vn/GEMKTgfcC5wCDwK+BG4H/GWMcXkxf2ymE8ABwbIPFXxhj/M487eX2z1YIoQe4BTgxxjg0R7k3AJcBpwKjwB3AR2KMX1ngc1va3qHSyHiFEFYCfwi8BvgNkv/fPgh8BfjLGON8f5aq27sJOHeOIg/HGI9pps1DpcHxaunnCyH0Am8Bfg84GdgH3AZcHWP8bqPttMNc4xVCuJIkHmjEP8YYL27wmZn787WQuCFP/w0zgG+xNNi+GdgE7AW2AicAlwAXhBDOvgAWdwAADdBJREFUijFubVd7nSiE8HLgS8AK4CBwD3AE8Hzg+SGEc4CLYoyN7Hl6anocTtuZTda/9LTsM4YQjgNuJRnvXcBPSP6sXU7y5+u5McaHF9Xb9vkh8NAc948Hjib5j+5c5Ury/GfrKuDZJJ9tViGEq4F3AkXgLpK/r2cB/3975x4zR1UF8F/BUlreLQIKKW0pHiBQpBYLoqEilmqAEiiIApVHIyAhSgSEEqFGLRAxGKNSpC0VgYpgQSkYAwqNj9SiFcujOVSRZygQCqU8pI+v/nHu8C0fu7Mz+93db2b2/JJmvtk798ye27Nnztx77r2Hi8jlqvqdPDeMLa/DpLaXiAwHHgDGYfo9jfm2scBFwMkicoSq/jvHPRP7WwpsqlP+Ug5ZnaapfRFRPxEZBNwMnBxkPYJ1TnwemCIiZ6nqgqzyBoC09noG+EtK3WHAQeHv/+S4Z6nsq5W4oWo+zAP4+NyABUD3Aier6joR2Rq4Djgd+KWIHKCq9X4gnZBXKERkV+AWzPBvAL6uqm+FsuOAm4AvYT0nP8ogclw4LlTV8+N/40IQU8fbMac3D/iqqq4XkR2BhViP/I3A5H7eY0BQ1RMblYnIzthDHUzvLIFU5WwrBDpXAJc2ue5o7EG1Bpiiqg+Fz6cCtwHfFpE/qmpaYNE2eZ0ia3th/nkcFlScpKqPhPojgVuBw4DbRGRClo4JEdkeG01ap6qH9kOFjpLDvmLrdx4WvD+J2deq8F3OBn4KzBGRJar63wj3ikaW9lLV+cD8FBlzsQD+QWB2xvuWyr5aiRuq6MM8Bz4iYTjneGyo7jRVXQegqv8DZgArgX2xVJiOyysoM4DtgOXAOcmPEEBV76LXkV2QUV7Si/BYtG9YPKLoKCKTgQlY7+C5qroeQFVfw4b9XwE+KyIT+nOfgvIzYDdgUXggZqFStiUiuwF3km04fmY4XpI8qABU9TdY+tUgmge17ZTXdrK2l4jsAZwI9ACnJME7gKo+A0zDfPp4rLcwC4ntPZ7zaw8YOe0rmn4i8gFslAPsmbIKQFU3q+ocLOAbAnyjv/eKSc72aiRjKpYytBaYnqNjr2z21UrcUDkf5gF8XE7F/tPuVtU1tQXhh3RjOP3CAMkrIpPCcZGq9tQpXxyOo0I6UTMqFWQ1IJaO08PxVlXdUFsQXhZvC6dltq/3ISLHYi+9r2O5i1mpjG2Fl7cngKnAalIeNCIyFjgU2ID1HvdlXjhODqM3ze4dVV4nyNNe2BD6IOBJVV3et1BVVwN/D6fjM36FUtlezvaCuPpNAkYCL6jqfXXK54bjtJBrPuC00F71ZAwFfhJOZ6rqszmql8q+yBk3VNWHFcJ4K8TEcPxrg/Kl4fipAZJXRL6FpQLd1aB8m5q/U1O+wvDj/uG0LI4oF5F17Ab7eg9hYttV4fS7qvpCxnpVs639gG2BX2B6LU25NrGTFar6Zt9CVX0JS1UYDByS4d6x5XWCPO21BOuB/2bKNYlfy5rGmqRvlcX28rQXxNWvmV9bDqzHUgc/EuF+McjbXvW4ANgdSw2ck7Nu2ewrb9xQSR/mOfBxGRuOjfLqkgluu4rItqr6RoflFQ5VXUq6s5oaji/TfAWQMdgPdzWwi4hcjOUCbqZ3Zvqq/n3jASeKjqHnaXQ4bWZfYxuUl5EzsLSz58k2pyKhara1DBivqg8DiEjatc38EJitjCGbrcSW1wkyt5eqPgfc0ahcRPYEDgynWVMWkh7Sp0XkXOAzwE7Y5OtFYdi+SOSxL4irX6p9qeomEXke839jaTwhvZPkba/3ECZNJy+MMxv0SqdRKvtqIW6opA/zAD4uHwzHRjPta9NgdsbyIDspr1SEnMCLw+mtGSZ7JU5oB+BRYMuasqOAC0TkfFW9Pu437SixdBxeU7eZfQ0XkS1aeCgUitCLnuS9/lBV38lRvVK2paqNeifr0cwPQa+tNFyCso3y2k7O9mrG1cBWwIvAHzLWSUZ/FmA9tbVMF5HfYZNlC/EMaKG9YuqX1b5GUx37+gqwPfCoqi5udnEdSmVfadSLG0Skkj7MU2jiMjQc325QXvv50AbXtFNeaRCRbbDhsR2xN+grM1RLhgGH0rt6zxBsmPR6bDjrujB7vKzE0rHWXprZ16Bwj7JzJNZea7FJrHnoBttqRDM/VFsWw6/llVcaRORCeueUzAwLEjSrMxLzg2DLAh6FBVkjsBGlNcDn6J0TVSraoF9X2VdICzw3nF7TQv3K2FdK3FBJH+Y98HHZRPpLUW1ZljXNY8srBSKyLXA3lme2CVvL9cUMVZdjwdSjqvrjms9XAeeIyAZs0uI19E5yKRuxdMyyOkHV7Ou8cJyrqq/nrNsNttWIPLaS1a/FlFcKROR84Pvh9OYcqx/1YHY1HPhaTS/om8ACEXkc2/RnmogcEtILykRs/brNvo4hTNql/oTKZlTCvprEDZX0YR7Ax+VN7M1v6wbltb2YaW9u7ZJXeMJQ12JsE4se4AxV/X2WumHoMC14mo0FWSIie5csZxmIqmPtxJutsV7pviT21YNtdlRaQs/MlHB6c9763WBbKSS20sgPQa+tZPVrMeUVHhG5ApgVTu/BlvrLRMipvyilfJmI3I/t13AMrU2AHDDaoF+32de0cPxV39XEslAF+8oQN1TSh3kKTVySfKjhDcpH1Pz98gDIKzQiMgZ70/84sBF7g667HXIrhBVHkt3k9owlt0jk0HEdthIDNLevV7JsNlNwJmMO9YlkolhMKm5bzfwQ9NpKDL+WV15hEZEtReQGeoP3O4Hjkz0XIpLYdNVsLyGPfl1lX1h6C9iupO2isPaVMW6opA/zAD4uyWz2UQ3KE+N/oXbjgQ7KKywiMg7bHnov4C1gqqoubEHO4ODUGjEoHGM/QDtGDB3DhNSkl3hUg8sS+8qz3XtRSXLTb29VQDfYVgOa+SHIZyux5RUSERmCrUYzI3w0HzixleBdRAYFeY0ote1F1i/VvsJGT7uH09LaV+ATWBD5HBbEtkRZ7StH3FBJH+YBfFySzTkarfuZfP63AZJXSERkb+A+bGfMV4EjVfXeFuQ8izmYkxqUf5je2eMrW/u2A0tkHbvCvgLJ9uAPtlK5G2wrhcRODhSR9w0Zi8gu2IoePcBDfcs7IK9whBe9W4DjwkdXq+pZOXbGrJV1FWZ7v0257KPhWDrba4N+iX1NbFA+Hpt0/grlD+ATv7ak1VHSstpXzrihkj7MA/i4LArH48K6rO8SHPrp4TRrDm5seYVDRIZhE092wWaNT1LVVnsSkk0opjcoT5YQXKKqZR06jaljYl+nichWtQUish29wWpp7QvetbFkYeX37YyZkW6wrbqo6lPAP7EUpFPrXJL0MN+rqq92Wl5BmQWcEP6+TFUv6Yesh7H5aoeHNeTfg4gciK3b3QP8uh/3GShi6/cn7Fmyp4gcWac8sa+FZV8aF9uLAlr3a1BC+8obN1TVh3kAHxFVXYFNUNoeuENERgCEN7S52AYyiuVBvouI7Cwi+4jIXjHklYzLsOCqBxteXtGsQqP2oncJrSkicmUSlIY81Auxneo2kb5DYtHJraOIfCi018g+su4BVmA9BT8PThER2QHLpxwB3K+q/2irRu1nf8zXrVbVNWkXdrltpTE7HH8gIpOSD0XkWOBybKWFq2srhJSjfcK/Yf2VVxZEZF/g0nA6T1Vnp11fU69Re92JLe83BHsOjK6pczDWc7oFcJ2qPhlFic7Skn4iMqymvQYnn4dRjsR2bgxpFkmds7Hg6h3g2jbq1CmSDcGa7qBaMfvKHTdQQR82aPPmss9NKxYisgfwZyz/6S1syGkMtqvZWuBQVV3Zp84s4ArgaVUd1V95ZSHk3L2IbY7zBrajZRrTVHV1k/aaCXwvnK7Fhkj3xDZT2Aicpao3xdJhIMiro4gsAL6M9Q5P6iNrHJZWshPwGubIBVsH+Blgoqqubp827UdEpmJrA69U1f2aXDuLLrSt8AB6AJuwXHfjERGZB5wZTh/H0hD2DueX9Q1URWQUvTsVflpVH+yPvCKR1l4iMgc4O5wuJ30VivnJcpJp7RV6Qe/D0rQ2Ak9gm4klI0uLgRPaMDk2Cs3sqxX9amQCjA69oknZYKyH9igsyHsE83FJJ8YpqtrKkosdIcvvMVz3KrZS3URVXdZE5igqYF+txg2hbqV8mPfARyYsyfQxbJv2l7ENYDYCC4GD8wbbseUVjAOwHyFYwHhYk39pSzYBEH4wR2C9Bhuw9lqPrY87oawBVi0xdQw9Fwdhm3S8jfXoJBsdlT54DySrAdRbKjMz3WBbTZiBPayWYZO39sAmzn2xxQdVbHlF4ZM1f48n3af1HRWri6r+C7O3a4GnsO3Zd8M6d84Eji1CcNUqsfULyykejaW2PYYFojthO99OLnLwnpWQRps8P/vr28pkX/2JGyrlw7wH3nEcx3Ecx3FKhPfAO47jOI7jOE6J8ADecRzHcRzHcUqEB/CO4ziO4ziOUyI8gHccx3Ecx3GcEuEBvOM4juM4juOUCA/gHcdxHMdxHKdEeADvOI7jOI7jOCXCA3jHcRzHcRzHKREewDuO4ziO4zhOifAA3nEcx3Ecx3FKhAfwjuM4juM4jlMiPIB3HMdxHMdxnBLhAbzjOI7jOI7jlAgP4B3HcRzHcRynRHgA7ziO4ziO4zglwgN4x3Ecx3EcxykRHsA7juM4juM4TonwAN5xHMdxHMdxSsT/AWLrvMlCbRakAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 248, "width": 376 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", "w = 0.5 # on choisit w \n", "error = [np.square(x - np.ones(4)).sum()]\n", "for i in range(20):\n", " x = w * (N @ x + b) / M + (1-w) * x\n", " error.append(np.square(x - np.ones(4)).sum())\n", "plt.plot(range(len(error)), error);" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "A priori it seems good, except that in fact you can't see anything because the scale prevents you from seeing what is happening at\n", "the end.\n", "\n", "Let's look at a logarithmic scale:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 246, "width": 376 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(len(error)), error)\n", "plt.semilogy();" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "Wow, the ending is scary...\n", "\n", "Morality: **Always look at an error in logarithmic scale.**\n", "\n", "Since we measure something\n", "which must tend towards 0, with a normal scale we are quickly crushed and therefore we do not see if we are at\n", "$10^{-3}$ or $10^{-6}$ while it is very very different.\n", "\n", "Similarly if we diverge we will not see the beginning because a linear scale will adjust to the last values ​​which\n", "can be very large." ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "Let us resume our calculation on more iterations." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 264, "width": 375 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", "w = 0.5 # on choisit w \n", "error = [np.square(x - np.ones(4)).sum()]\n", "for i in range(200):\n", " x = w * (N @ x + b) / M + (1-w) * x\n", " error.append(np.square(x - np.ones(4)).sum())\n", "plt.plot(range(len(error)), error)\n", "plt.title('Erreur absolue')\n", "plt.semilogy();" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "So we approached the solution and then we diverged, which is better than diverging directly.\n", "\n", "#### Relative error\n", "\n", "Could we have seen it if we had not known the solution? Let's look at the gap between 2 successive ${\\bf x}^k$s." ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "It seems that there is a strong relationship between the gap between two successive **x** and the absolute error.\n", "Let's check:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération présentant le minimum : 12 14\n", "Erreur absolue minimum : 0.004062676542953207\n", "Erreur absolue minimum devinée à partir du minimum de l'écart : 0.004333899458825818\n" ] } ], "source": [ "k_min = np.argmin(error)\n", "k2_min = np.argmin(error2)\n", "print('Itération présentant le minimum : ', k_min, k2_min)\n", "print('Erreur absolue minimum : ', min(error))\n", "print(\"Erreur absolue minimum devinée à partir du minimum de l'écart : \", error[k2_min])" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "The gap between 2 successive **x** is a simple and relatively efficient way to know when to stop an algorithm\n", "iterative." ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "#### Residue\n", "\n", "Finally we can calculate the residue namely $||A \\, {\\bf x} - {\\bf b}||$ but it is $n^2$ operations:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 264, "width": 376 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = x0 # on reprend la même valeur initiale sinon la comparaison serait faussée\n", "w = 0.5 # on choisit w \n", "residu = []\n", "for i in range(200):\n", " old_x = x\n", " x = w * (N @ x + b) / M + (1-w) * x\n", " residu.append(np.square(A @ x - b).sum())\n", "plt.plot(range(len(residu)), residu)\n", "plt.title('Résidu')\n", "plt.semilogy();" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "### Let's test other matrices with this algorithm" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def mk_A(seed):\n", " np.random.seed(seed)\n", " return np.random.randint(10, size=(4,4))\n", "\n", "A = mk_A(234)\n", "b = A.sum(axis=1) \n", "\n", "M = np.diag(A) \n", "N = np.diag(M) - A \n", "\n", "x0 = np.random.random(4)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def plot_error(M, N, b, x0, w, n=200):\n", " x = x0 \n", " error = [np.square(x - np.ones(4)).sum()]\n", " error2 = []\n", " for i in range(n):\n", " old_x = x\n", " x = w * (N @ x + b) / M + (1-w) * x\n", " error.append(np.square(x - np.ones(4)).sum())\n", " error2.append(np.square(x - old_x).sum())\n", " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n", " ax1.plot(range(len(error)), error)\n", " ax1.set_title('Erreur absolue')\n", " ax1.semilogy();\n", " ax2.plot(range(len(error2)), error2)\n", " ax2.set_title('Erreur relative')\n", " ax2.semilogy()\n", " print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 17 40\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 264, "width": 822 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_error(M, N, b, x0, w=0.5);" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "We find the same behavior (convergence then divergence) but much more chaotic.\n", "\n", "We can reduce the oscillations by increasing the inertia, i.e. by decreasing $w$:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 81 209\n" ] }, { "data": { "image/png": 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hG5I+yJDsSROBx+ha+LwthDA4t/FmOQfQVfHzeIwx213ceXr7d5xI+TP67s+7/g7g3O4eMITwMeBokvfU9BjjPb2KVJIkSUqfgby+6pXc/poPkuwx0wAcDNxabn4IYTBJQmMByevw7RhjW3ePkVuPdK675gDnlVvz5PbYmZj3q/7Y0wZgGknb7dHAu0MIP6drf8+7YoxzStwnf+10SAihLtdWu6QQwlHAp0ie810xxumbInBJm49SGztLktLn2rzrX8y1FCvn3cBJwCnA54HX88YW5F3ft5tj/DtJ+69KGJN3fVm5SSGE3UieW6fu4tsphNBdG7UzSM6sgvU33BxK0tf4bODM3AKtnPyqmGUAub1tOj+QDwc+1839yT1Op7/0MDdfb/+OH+pm7F66zhg7MIRwaLmJuUXm13PHO4vKnAEnSZIk9ZeBvL7qi/zX4awe1j//QVKZcirwgZ4SNjn5a70VPZykdhpdFTlQ+vXqvP8Gf5+ZW7P9LnfzMJIT8Tq7E1xV5j6zgUdzN8cBHyt3/Fw3hYuB95OsO3fZ0Fglbb5M2khSbbgeeDx3fRJwdQihaM+UEMKeJGeBdfpGQen5P0nOEIPki/qpJY4xBfjWJom6d57Lu35qqQm5lmTXA0Pyft1TT+if5+5XeKyPkyy2AF4Dftg5FmN8nq6zqN4EnF8mngB8IHdzJfBA3vDXgc7X/MIQwnspEEKoCyF8HTg296sXgL7sKZN/ptf7QghFC8Tc37Zsr+XchqTfyPvV1WWO0wz8Edg296sngBv6EKskSZKUNgN5fdUXP6erxfNhwA9CCEVdeUIIR5Csczpd3Mvjz6Yr0dKS29+mSAjhs8BXCn5dar3XuQfoxp5EdmXusomuNdFK4Jpu7nNh3vX/y1XTrCeXsPkR8Obcr14BfrlxoUraHNkeTZK6TAohvKfnaUXmxhj/ucmjyZMrXT+BJDkwguRsr1khhF8CT5FUiBwAfJSuM5LuAr5XcJylIYSrgRNzv7o2hHAl8A+gmaQ1QOdZYA8AU/rzeeX8jKTtFsAnQwgTSM74egXYOhfTVIr/zSq3VwvAQmAr4IEQwi9InkszSdl750KqA/hEjHFhwX3PIHnt6oDzQwjH5uKZCwwj2X/nJLoSSJfGGBd13jnG+HAI4X9IFjXNJK/xjSQLw0XATiR/pz1zd1kHfCSvxUKPYoytuU06D849xp0hhJ+S7Ak0nCQZdBzQRrKQ3KfMob4LHAEcQ7Lx5v0hhD8AdwCrSFpGfJLkbDJIFjIf664VgCRJkpTj+qo666teizGuCCF8kKQtWhPJSXRHhBCuAp4GtiRJ5ryPrnZlv4kxXlvqeCWOPz+EMJ1kDVYH3Jxbnz0MrCVpGfcBkhPmCpVa780jabe2ewjhEuAhYFGM8W+9iScvrodCCK25Y3Xuh/qnGGPZzg8xxutCCD8mqTgaCtwUQrie5IS210gqaj5GVzu4duCkGOOKUseTpO6YtJGkLifkfvrqSpIv8ftVjDGGEA4kOfunBdgO+J8y0/8MnFimZP00ki/jp5B8MD8l99NpHUklSjMVWFTEGK8NIXwHOD33q7fnfgrNAT4N3EjS2mzvbg57FcmH/JOB/8z95FtG8gG6qCVZjPHuXDXOT4DBwFtyP4U6SPo4/2+JY1wSQlhOctbWYJKkyDEljjEb+GCM8cFunks5JwK3ARNIFg2nF4wvBz4BHEqZpE2MsSOEcDxwGUnP5QaSTTg/XGL6PJI2CI+XGJMkSZIKub5KVHR91Vcxxr+HEA4naRu9Pcm+MheUmf5jitdWPTmF5KSwFpLXoGR3BeAPJCecdVb07A0UJmN+DXwtd/1LucuHKb1e68mVrF89dGW5iXlOJTlB8Mska6d35X4KLSY5QfCmDYhLkmyPJkm1JMY4A9iD5Av7P5F8kb469/Mc8BvgnTHG42OMy8sc4zXgbSRf0t9BUv2xhiSB8DNg3xjj//XzUymM6Ysk1TZ/JinPX0dS6TGX5Mylk4E3xRhvBe7O3W3PXLuCcsc8heSsrTuBJbnjzQS+CYQY43Xd3PfXJIuKi0jOiFtMUrWyBPgXyRl2b44xntHNMX5AklC5kOQMsMUkr/Mc4CaSv+GbNjBh09nKbQ/gi8B9ec9xFkkFzR4xxu7K+zuPsyb3Wu0D/IDkzMKlJM93Icl75PPA5Bjj/WUPJEmSJNWYgbq+6qsY490ka5fPkpwk9xJJJcxKIJI8jykxxs/0ci+b/GPPB/YjSbI8QLInUHvu8kmS9nMHxRhPIEncdLZT+2iJw10M/Bcwg2Tts5qe22aX82uSE/EAXgRu78VzycYYzyVpqfcNkiTTayRrp9eAe0j2LQ0xxr9uYFySRCab7W4PMEmSJEmSJEmSJFWClTaSJEmSJEmSJEkpYNJGkiRJkiRJkiQpBUzaSJIkSZIkSZIkpYBJG0mSJEmSJEmSpBQwaSNJkiRJkiRJkpQCJm0kSZIkSZIkSZJSwKSNJEmSJEmSJElSCpi0kSRJkiRJkiRJSgGTNpIkSZIkSZIkSSlg0kaSJEmSJEmSJCkFGqodQNo88sgj2WrHIEmSJKXFvvvum6l2DKodrqckSZKkLhuynrLSRpIkSZIkSZIkKQWstClj3333rcrjtra2AtDS0lKVx1f1+R6Q7wH5HpDvAUH13wePPPJIVR5XA4PrKVWL7wGB7wP5HpDvAVX/PbAx6ykrbSRJkiRJkiRJklLApI0kSZIkSZIkSVIKmLSRJEmSJEmSJElKAZM2kiRJkiRJkiRJKWDSRpIkSZIkSZIkKQVM2kiSJEmSJEmSJKWASRtJkiRJkiRJkqQUMGkjSZIkSZIkSZKUAiZtJEmSJEmSJEmSUsCkjSRJkiRJkiRJUgqYtJEkSZIkSZIkSUoBkzaSJEmSJEmSJEkpYNJGkiRJkiRJkiQpBUzaSJIkSZIkSZIkpYBJG0mSJEmSJEmSpBRoqHYA6tLW3sFtzy4jA0zcrYOGenNqkiRJktRbD76wkgXL29h+l3UMH9RY7XAkSZKkPjNpkyJnXPMEf3p0IQCzVz7Jtz6wV5UjkiRJUjW8tmItD76wkgmjm6odilQzrrpvDuffPh+Am567h1tPP4S6ukx1g5IkSZL6yFKOlMhms9zw5Mtv3J7+5EtVjEaSJEnVsHpdO/93+9O87ZI7OP/2+Xz82rm0vvx6tcOSasKNT85/4/qzC1fQOt//diRJklR7rLRJiUwmw5q2jjdur17XQUdH1jPDJEmSNgPZbJa/Pv4Sl9w4k5eWrn7j920d8NfHX6Jl2+FVjE6qDe0d2fVuL1vdVqVIJEmSpA1n0iZF6jKQv87oyGapw6SNJEnSQPbI869xwbQZPDZvScnxvceNrHBEUm1qali/kUT+SXGSJElSrTBpkyL1dRk62ruyNu3ZrH8gSZKkAeqF11ZyyU2R6x8v3RZ3eHMdn9p3S45609gKRybVpuaCpM1akzaSJEmqQeYEUqQukwG6kjYdrjEkSZIGnOVr2rj8zmf42T9ml6wEaKzP8PEDduaocR0MbaqvQoRSbWpuLKy0aa9SJJIkSdKGM2mTIknSpktHNltmpiRJkmpNe0eWax95gW/cElm4bE3JOUdO3oazjm1hlzFb0NraWuEIpdrWVF+QtFnnWXCSJEmqPSZtUqS+bv2kTbtJG0mSpAHhvmcXccG0Gcx4+fWS45O3Hc45U1s4cPyYCkcmDRzNDetXpq1tN2kjSZKk2mPSJkUKcjZkXWNIkiTVtDmvruCiG1q5ZcYrJce3GtbMGUcG3rfvDkUn8Ejqm6L2aOtsjyZJkqTaY9ImReqstJEkSRoQlq5ax2V3PM0V985hXXvxZ7qmhjpOOXgXTj10AkOb/Uiu9AshbA88CXwgxnhbteMppag9Wok9oyRJkqS0c4WYIvUFe9q0d5i0kSRJqiVt7R387sG5fOe2p1m8Ym3JOe/aazvOPDqww6ghFY5O2jAhhHHAzcCoasfSncJKm7UmbSRJklSDTNqkSGGlTdZKG0mSpJpxZ1zA16a38vSC5SXH9x43knOnTmbfnVL9vbf0hhBCHfAx4JtA6vv3Fe5pY6WNJEmSapFJmxQpbGNuezRJkqT0e/qVZVw4vZW7Zi0sOb7diEGcecwk3rXndkUn6UgptyfwI+CHwG3A9OqG072mhsL2aO5pI0mSpNpj0iZFbI8mSZJUOxavWMt3bp3Fbx+cW/Jz25Cmek49ZDwnH7wrg5vqSxxBSr25wIQY4wshhEOrHUxPmhtsjyZJkqTaZ9ImRYrbo1UpEEmSJJW1tq2Dq+6bw/duf5plq9uKxjMZeN8+O3DGUYFthg+qfIBSD0IIDcDJ3UxZFmP8TYxxMbC4QmFtNNujSZIkaSAwaZMidVbaSJIkpVY2m+WWGa9w8Q2tzFm0suSct+4ymvOmTmb37UdUODqpTwYBl3cz/jzwmwrFsskUt0czaSNJkqTaY9ImReoLKm3c00aSJCkdnnppKRdMm8H9z5UuOthx9BDOPnYSR71pLJmM+9Yo3WKMy4EB90a1PZokSZIGApM2KVK4L23WpI0kSVJVLXh9Nd+8JfLHR14o2bp2WHMD/+/wCXz8wJ2LWjNJqqzCpM2atvYqRSJJkiRtOJM2KVLcHq1KgUiSJG3mVq9r52f/eI4f3vksK9cWf/Fbl4EPT9mR04/YjS2HNlchQkmFbI8mSZKkgcCkTYoUtUdzTxtJkqSKymazXP/Ey1xy40xeXLKq5JyDJ47hnOMmE8YOq3B0krpTWO1m0kaSJEm1yKRNihT2P++wPZokSVLFPDr3NS6YNoN/zl1Scnz8VltwznGTOTRs5b41qpgQQh1wHzA+xjimm3mjgPOB44FtgYXATcBXY4zPVyLWamtutNJGkiRJtW/AJm1CCIcBFwF7AouBX5IsWNqqGlg36tdfY5i0kSRJqoCXlqzikptm8pfHXio5PnJII6cfsRsfnrIjjYUf2KT+dyHwVmBRuQm5hM29wCRgGfAEsCvwSeC9IYRDYoxPbEwQMcY7gVRnK5sK/vtcs849bSRJklR7BmTSJoQwBbgR+Cvwv8DewFeB4cAXqhhat+qL9rQxaSNJktRfVqxp40d3PctP/v5cyTPyG+oyfPzAnfn8OyYyYkhjFSLU5iyEkCGpnDmrF9N/SpKwuQH4YIxxWQhhEHA5cBJwdQhhjxjjgM5iDCqotFnrJqGSJEmqQQMyaUOSqGkFTogxZoGbQghrgG+EEC6NMZY+jbLKitujVSkQSZKkAayjI8s1/3yBb94cWbBsTck575y8DWcf28IuY7aocHQShBDGAj8C3t2LuZOA9wLLgRNjjMsAYoyrQwgnA1OAFpK2adf0W9AFWltbK/VQb5i/bN16t5evXFOVOFRdq1Yl+5H5t9+8+T6Q7wH5HlAtvwcGXH+HEEIzcBhwXS5h0+kPQD1wdFUC64X6Ove0kSRJ6k8PPLeIf/vB3XzpmidKJmwmjR3Gb0+ewk8/tp8JG1VFCOFIYBZJwmY+PVfafJSkbdn1McbF+QO5yppf5m6esIlDTZ2m+vXXU+vaXU9JkiSp9gzESptdgSYg5v8yxvhiCGEVyVlmqWR7NEmSpP7x/KIVXHzDTG56an7J8TFDm/nvI3fj/fuNKzqRRqqwycBQ4FfA6cAePcyfkru8t8z4/bnLgzc+tN5raan8smvJyrXA3Ddut5OpShyqrs6zaf3bb958H8j3gHwPqNrvgUceeWSD7zsQkzYjcpevlxhbRrKvTSoV5GystJEkSdpIr69ex2V3PMMV98wpub9FU0MdJx+0C589bAJDmwfiR2PVoAeBfWKMjwGEEHqaPyF3ObvM+PO5y21CCENjjMs3PsR0am6oX+92qb2qJEmSpLQbiCvTnlq+pTYTUtQezTWGJEnSBmlr7+B3D83jO7fOYvGKtSXnTN1zW848ehLjRg+pcHRSeTHGchUz5WyVu1xUZjy/ZdoYkr1vBqSmhvWXgmvaOshms0V7h0qSJElpNhCTNktyl8NKjA0DllYwlj5xTxtJkqSN9/dZC7lw+gxmvVL6u+m9xo3kvKkt7LvT6ApHJvWLwbnLVWXG838/uMycAaG+LkN9BvK3slnXnqWpwaSNJEmSasdATNo8C7TT1YoPB/kAACAASURBVCYAgBDC9iSLlNZqBNUbhWeAtZu0kSRJ6rVnFizja9Nb+VtcWHJ82xGD+NLRgXfvtT117lujgaOd7rsN5I8N+AVGU32GVW1dT3NNW3tRBY4kSZKUZgMuaRNjXBNCuBN4bwjhkhhjZ5OxDwBtwB1VC64H9YV72nQM+DWVJEnSRnttxVq+e9ssfv3AXNpLfH4a3FjPZw4Zz6ffviuDm+pLHEGqaSuAkcCgMuPNedfLVeMMGI1FSZuOki0YJEmSpLQacEmbnAtIkjPXhhB+CuwJfBW4PMY4t6qRdaO4PVqVApEkSaoBa9s6uOq+OXz/9qd5fXVbyTnv22cHzjgqMHZEue+zpZq3iCRpU67f35Z510uXoQ0gjQVnwq1tc6NQSZIk1ZaqJm1CCHXAfcD4GOOYbuaNAs4Hjge2JVls3AR8Ncb4fOH8GONdIYT3kCRq/gS8Alycu51aRe3RzNpIkiQVyWaz3DrjFS6+cSazX11Rcs5bdh7FuVMns+cOIyscnVRxM4HxwM5lxnfKXb4cY1xZkYiqqKkgabPGpI0kSZJqTLUrbS4E3kpydlhJuYTNvcAkYBnwBLAr8EmSFmiHxBifKLxfjPF64Pr+CLq/1GcKK21M2kiSJOWb8dLrXDh9Bvc+W/rj47jRgznrmBaO2X1s0Qkx0gD1MHAcsD9weYnx/XOXD1QsoioqTtq0VykSSZIkacNUZUfGEEImhPAV4KxeTP8pScLmBmD7GON+wHbAFSRtAK4OIQyI5uTF7dFM2kiSJAEsWLaaL1/7BMf93z9KJmyGNjfw5WMmcevph3DsHtuasNHm5Lrc5XtCCOu1SMutk07K3fx1JYOqlsY626NJkiSptlW80iaEMBb4EfDuXsydBLwXWA6cGGNcBhBjXB1COBmYArSQtE27ZlPG2drauikP1yvLlr2+3u15816ktXFpxeNQda1alewPW433oNLB94B8D8j3QJe17R38acZSfv/EkvU2F+9Ul4GjJw7jxL1HM3LwWmY/M6sKUfYP3wfqjRjjEyGE6STVNteEEN4fY1wUQhhEUnnTAkSSttEDnu3RJEmSVOsqmrQJIRxJklwZBswHvkey10w5HwUywPUxxsX5AzHG9hDCL4FLgRPYxEmbaqizPZokSRKQ7Fvz9zkr+MUji1mwoq3knDdvO5hT3rIlu4xqqnB0Uup8BrgbOAyYG0JoJWkpPQpYChwfY9wssheNhUmbdZvF05YkSdIAUulKm8nAUOBXwOnAHj3Mn5K7vLfM+P25y4M3PrT1tbS0bOpD9mj0E2tIiooSY7fdjpaWHSoeh6qr82zaarwHlQ6+B+R7QJv7e+CxeUu4YNoMHnn+tZLju261Becc18JhYesB3Qat2u+DRx55pCqPq76LMb4QQtgXOI+ko8GewBLgd8D5McanqxlfJRUmbda2u6eNJEmSakulkzYPAvvEGB8DCCH0NH9C7nJ2mfHnc5fbhBCGxhiXl5lXEwq/dGi30kaSJG1GXl66iktvivzp0RdLjo8Y3MgXjpjIR/fficb6qmzNKFVcjPFOku4DPc1bBJyW+9lsFbVHs9JGkiRJNaaiSZsYY7mKmXK2yl0W7zabyG+ZNob8MpUaVPjdQ0eHSRtJkjTwrVzbxo/ueo6f/P1ZVpf4grWhLsOJB+zEaYdPZOQQW6FJKs89bSRJklTrKl1p01eDc5eryozn/35wmTk1o3hPmyoFIkmSVAEdHVmue/RFvnHzTF55fU3JOUe0bM1Zx7YwfquhFY5OUi1qrCtoj2bSRpIkSTUm7UmbdqC73hf5YzWf4qirsz2aJEnaPDw4ezEXTp/BEy8sLTk+aewwzjluMgdNHFPhyCTVssI9bda0uaeNJEmSakvakzYrgJHAoDLjzXnXy1Xj1Iz6wkobS20kSdIAM3fRSr5+Uys3PDm/5PiYoU3815GBD+w3jvq6HrfxkKT12B5NkiRJtS7tSZtFJEmb0WXGt8y7vrD/w+lfhd9LdFhpI0mSBohlq9dx2d+e4Zd3z2Fte/GXqE31dXzyoF343GHjGTaosQoRShoIiittTNpIkiSptqQ9aTMTGA/sXGZ8p9zlyzHGlRWJqB8VtUez0kaSJNW4tvYOfv/wPL59yywWrVhbcs5xe2zLl4+ZxLjRQyocnaSBxkobSZIk1bq0J20eBo4D9gcuLzG+f+7ygYpF1I8K26NZaCNJkmrZP55eyIXTWomvLCs5vucOIzh36mTesnO5ompJ6pum+vW3RHVPG0mSJNWatCdtrgPOB94TQhgdY1zcORBCqAdOyt38dRVi2+SKKm3M2kiSpBr07MLlXDS9ldtnLig5Pnb4IL50dOA9e29f9PlHkjZG4/o5G9ZaaSNJkqQak+qkTYzxiRDCdJJqm2tCCO+PMS4KIQwiqbxpASLwp2rGuanUZWyPJkmSateSlWv57m1P8+v7n6etxOeYQY11/Mfbx/Mfh+zKkKZUfwyVVKMaiyptTNpIkiSpttTCavkzwN3AYcDcEEIrsCswClgKHB9jHBCfxAvWF2SttJEkSTVgXXsHv7rveb53+9MsXbWu5Jz3vnl7zjg6sO2IwRWOTtLmpGhPm3UDYqkoSZKkzUjqkzYxxhdCCPsC5wHvBvYElgC/A86PMT5dzfg2peJKmyoFIkmS1AvZbJbbWxdw0Q2tPPfqipJz9ttpFOdOncxe40ZWODpJm6PGgqTNWhdVkiRJqjFVTdrEGO8EemxkHmNcBJyW+xmwipI2VtpIkqSUan35dS6cPoN7nllUcnyHUYM565gWjt1jLJmM+9ZIqoziSpv2KkUiSZIkbZjUV9psTuoLNuK1PZokSUqbhcvW8O1bZ/H7h+ZSavu9oc0NfPaw8XzybbswqLG+8gFK2qwVVtq4p40kSZJqjUmbFCnI2dBe6psQSZKkKli9rp1f3jOHH/ztGZavaSsar8vACW8ZxxffGdhqWHMVIpSkEu3RTNpIkiSpxpi0SZG6OtujSZKkdMlms9zw5Hy+flMr8xavKjnnbRO25JzjJtOy7fAKRydJ6ytqj9ZmezRJkiTVFpM2KVKfKWyPVqVAJEmSgCdeWMIF02bw0JzXSo7vOmYLzj62hcNbtnbfGkmpUJy0sdJGkiRJtcWkTYrUFXzZYXs0SZJUDfOXrubSm2dy3T9fLDk+YnAjpx0+kY/uvxNNDXUVjk6Symussz2aJEmSaptJmxQpao9m0kaSJFXQyrVt/OTvz/Hju55j1brilkL1dRlO3H8nTjt8IqO2aKpChJLUPSttJEmSVOtM2qRIwfqCrP3RJElSBXR0ZPnzYy9y6U2R+a+vLjnnHZO25uxjW5iw9dAKRydJvdfonjaSJEmqcSZtUqSo0sakjSRJ6mcPz1nMBdNm8PgLS0uOh22Gcc7UFg6euFWFI5OkviustLE9miRJkmqNSZsUKd7TpkqBSJKkAW/e4pV8/caZTH/y5ZLjW27RxBeP3I0T9htHQ7371kiqDcWVNi6qJEmSVFtM2qRIYdLG9miSJGlTW7Z6HT+881l+fvfskmegN9XX8YmDduZzh01g+KDGKkQoSRvOPW0kSZJU60zapEjhSaztHSZtJEnSptHekeUPD8/jW7dEXl2+tuScY3Yfy1nHtLDjlkMqHJ0kbRr1GajLQOdSqr0jS1t7hxWDkiRJqhkmbVKkqD2alTaSJGkTuOeZV7lg2gxmzl9Wcnz37Ydz7nGTmbLrlhWOTJI2rUwmQ2NdhjXtXWuptSZtJEmSVENM2qRIcXu0KgUiSZIGhOcWLueiG1q5rXVByfFthjdzxlGTeO+bt6euLlNyjiTVmsb6gqRNWwdDmqoYkCRJktQHJm1SpL7gyxLbo0mSpA2xdOU6vnf701x13xzaSnyeGNRYx6ffPp7PHLIrQ5r8OChpYHFfG0mSJNUyV+kpUniGa4elNpIkqQ/WtXfwm/uf57u3P82SletKzjn+zdtzxlGB7UYOrnB0klQZjYVJm3UmbSRJklQ7TNqkSGFXEpM2kiSpN7LZLH+LC/ja9FaeXbii5Jx9dxrFuVMns/e4kRWOTpIqq7DSZm17e5UikSRJkvrOpE2K1GdsjyZJkvomzl/GhdNn8I+nXy05vv3IwXz5mElM3XNbMhn3rZE08BVW2qy20kaSJEk1xKRNihS3R6tSIJIkKfVeXb6Gb986i6sfnFvyM8MWTfV89rAJfOqgXRjUWF/5ACWpShrr3NNGkiRJtcukTYrUFZz92mHWRpIkFVjT1s4V98zhsjueYdmatqLxTAZO2G8cXzxyN7YeNqgKEUqqdSGEBuA/gVOAnYH5wF+A82OMy6oYWq8UtUczaSNJkqQaYtImRerr1r/d7p42kiQpJ5vNctO/5nPxjTOZu3hlyTkH7Lol506dzOTthlc4OkkDzEXAF4CLgb8Dk4CvAgeEEN4WY0x1FqQwabOmzT1tJEmSVDtM2qRIUaWNORtJkgQ8+cJSLpg+gwdnLy45vvOWQzj72BbeOXkb962RtFFCCENIEjbfjDGen/v17SGEV4GrgUOBO6oUXq8U7mljezRJkiTVEpM2KWJ7NEmSlO+V11dz6U2R6x59gVIFuMMHNfD5wyfysQN2pqmhrniCJPXdKOCnwB8Lfj8zd7ldZcPpO9ujSZIkqZaZtEmR+oINM9tN2kiStFla3dbBtU8t5drfPs+qdcVtferrMnx0yo6cdsRujN6iqQoRShqoYowvAp8rMfSe3OW/KhjOBrHSRpIkSbXMpE2KFLdHM2kjSdLmpKMjy18ff4kLr5/HqytL78FwWNiK/zmuhQlbD6twdJJqXQihATi5mynLYoy/KXG/A4AvA9NijI/1V3ybSmOde9pIkiSpdpm0SZGCtYVJG0mSNiOPPL+Yr05r5fF5S0qOT9x6KOdMncwhu21V4cgkDSCDgMu7GX8eWC9pE0I4FPgLMBs4qb8C25RsjyZJkqRaZtImRWyPJknS5ueF11by9RtnMu2Jl0uOj96iidPfuRsfess4Gurdt0bShosxLgcyPU7MCSGcBPwYeAo4Jsa4qJ9C26QKkza2R5MkSVItMWmTIpmi9mhVCkSSJPW75Wva+OHfnuFnd88ueRZ4Qx188qBd+dxhExgxuLEKEUranIUQvgqcC9wM/Hsu4VMTiva0WWfSRpIkSbXDpE2KFFba2B5NkqSBp70jyx8fnsc3b5nFq8vXlJzzth2H8Ml9t+TwKS0Vjk6SIIRwJknC5grglBhjW3Uj6pvCpM3adve0kSRJUu0waZMi9Rnbo0mSNJDd++yrXDCtldaXXy85/qbthnPu1MmMWLOgwpFJUiKEMBG4EJgJ/ATYL4SQP+XZGOPCasTWW0Xt0ay0kSRJUg0xaZMiBTkb26NJkjRAzH51BRfd0MqtM14pOb7VsGa+dFTgffvsQF1dhtZWkzbS5i6EUAfcB4yPMY7pZt4o4HzgeGBbYCFwE/DVGOPzG/DQx5OsEycB95YYPwX42QYct2Ia69zTRpIkSbXLpE2KFLVHM2sjSVJNW7pyHd+/42muum8O69qL/11vbqjj02/flc8cMp4tmv1YJmk9FwJvBRaVm5BL2NxLkmBZBjwB7Ap8EnhvCOGQGOMTfXnQGOOlwKUbGnQaFFbalNo3TJIkSUorvx1IkcKkTbt72kiSVJPa2jv47YNz+c6ts3ht5bqSc96993Z86ehJbD9ycIWjk5RmIYQMSeXMWb2Y/lOShM0NwAdjjMtCCIOAy4GTgKtDCHvEGDerTV2K2qO1bVZPX5IkSTXOpE2K1BW1RzNpI0lSrflbXMDXprfyzILlJcffvONIzp06mX12HFXhyCSlXQhhLPAj4N29mDsJeC+wHDgxxrgMIMa4OoRwMjAFaCFpd3ZNvwVdRmtra6UfEoBVq1aRbV8/Wb7wtaVVi0eVt2rVKqB670Glg+8D+R6Q7wHV8nugrtoBqEtdxvZokiTVqlmvLONjv3iQT/zyoZIJm+1HDub7H3oz1516oAkbSUVCCEcCs0gSNvPpudLmo0AGuD7GuDh/IFdZ88vczRM2caip11hQaVOqPaUkSZKUVlbapEjRnjauLSRJSr1Fy9fwndtm8bsH59Fe4h/vIU31fO6wCXzqoF0Y1FhfhQgl1YjJwFDgV8DpwB49zJ+Su7y3zPj9ucuDNz60vmtpaanGw9La2srQwev/v7hp0JCqxaPK6zyb1r/55s33gXwPyPeAqv0eeOSRRzb4viZtUqSw0qbUFz+SJCkd1rS1c+W9c/i/O55h2eq2ovFMBt6/7w7895GBrYcPqkKEkmrMg8A+McbHAEIIPc2fkLucXWb8+dzlNiGEoTHG0j0bB6DGOve0kSRJUu0yaZMidUWVNiZtJElKm2w2y81PvcLFN7by/KKVJefsv+tozjluMrtvP6LC0UmqVTHGchUz5WyVu1xUZjy/ZdoYkr1vNgtN9YVJm44qRSJJkiT1nUmbFKkv3NPGpI0kSanyrxeXcsG0GTwwe3HJ8Z22HMLZx7Zw5ORtyBT8uy5Jm9jg3OWqMuP5vx9cZs6A1NSw/tatq9dZaSNJkqTaYdImRQoKbWj3hDBJklJhweur+cbNkWv++QKlzqkYNqiBz79jIh87cCeaG9y3RlJFtAN13Yznj21WZ4M1F1TarF7nwkqSJEm1w6RNitgeTZKkdFm9rp2f/v05Lr/rWVauLT5Tu74uw4ffuiNfOGIiWw5trkKEkjZjK4CRQLlNs/L/p1SuGmdAam5Yf121ykobSZIk1RCTNiliezRJktIhm83y18df4pIbZ/LS0tUl5xyy21acc1wLE7cZVuHoJAlI9rIZCYwuM75l3vWF/R9OehTuaWN7NEmSJNUSkzYpUleQtGnvMGkjSVKl/XPua1wwbQaPzl1ScnzC1kM557gWDg1bVzgySVrPTGA8sHOZ8Z1yly/HGFdWJKKUKKy0WWN7NEmSJNUQkzYpUlfQkbrDpI0kSRXz4pJVXHLjTP76+Eslx0cNaeSL79yND711Rxrqu9tGQpIq4mHgOGB/4PIS4/vnLh+oWEQp0ViXIZPhjT3I1rZ30N6Rpb5wE1FJkiQphUzapEjhIsKcjSRJ/W/FmjYuv/NZfvqP51jTVnw2dmN9ho8fsDP/7/CJjBjcWIUIJamk64DzgfeEEEbHGBd3DoQQ6oGTcjd/XYXYqiqTyTCooX69vWxWr2tni2aXv5IkSUo/TxNNkaL2aO5pI0lSv2nvyPKHh+Zx6Dfv5LK/PVMyYXPk5G245fRDOGfqZBM2klIlxvgEMB0YDlwTQtgSIIQwCPgZ0AJE4E9VC7KKBjfVr3fbfW0kSZJUKzzVKEUKkza2R5MkqX/c9+wiLpg2gxkvv15yfPK2wzlnagsHjh9T4cgkqU8+A9wNHAbMDSG0ArsCo4ClwPExxs1yQ5dBDeufn7jKpI0kSZJqhEmbFClssdxhpY0kSZvUnFdXcPGNrdz81Cslx7ca1swZRwbet+8O7n0gKfVijC+EEPYFzgPeDewJLAF+B5wfY3y6mvFV06DGwkqbzTJ3JUmSpBpk0iZFSu1pk81myWT80kiSpI2xdNU6Lrvjaa64dw7r2otPimhqqOOUg3fh1EMnMNQ9DySlQIzxTqDHhUCMcRFwWu5HOcVJGyttJEmSVBv8ViJFMpkMGSD/q6SOLNSbs5EkaYO0tXfwuwfn8p3bnmbxirUl57xrr+048+jADqOGVDg6SVJ/GdS4fns0kzaSJEmqFSZtUiaTgfyuaB3ZLPU9n2AnSZIK3DVrIRdOm8HTC5aXHN973EjOnTqZfXcaVeHIJEn9zfZokiRJqlUmbVKmLpNU13Rq78hSsN6QJEndeGbBMi6c3sqdcWHJ8e1GDOLMYybxrj23o859ayRpQBpcsIhaZaWNJEmSaoRJm5Spz2Roy2uQ1pEt7rsvSZKKLV6xlu/eNovfPDCX9o7ifz+HNNVz6iHjOfngXRnc5BkRkjSQuaeNJEmSapVJm5TJFJzwW+I7J0mSlGdtWwdX3TeH793+NMtWtxWNZzLwvn124IyjAtsMH1T5ACVJFVeYtLHSRpIkSbXCpE3KFHZpKXWmsCRJgmw2yy0zXuHiG1qZs2hlyTlv3WU0502dzO7bj6hwdJKkahrUWLfe7TUmbSRJklQjTNqkTF0mA3nt0bK2R5MkqchTLy3lwmmt3PfcopLjO44ewtnHTuKoN40lU1jGKkka8Irbo3VUKRJJkiSpb0zapIyVNpIklbdg2Wq+dfMs/vDIPEqd1zCsuYH/d/gEPn7gzjQ3uG+NJG2uBtseTZIkSTXKpE3K1BWcDdxupY0kSaxe187P757ND//2DCvWFn/xVpeBD0/ZkdOP2I0thzZXIUJJUpoUtkdbbdJGkiRJNcKkTcoUVtqYs5Ekbc6y2SzXP/Eyl9w4kxeXrCo55+CJYzjnuMmEscMqHJ0kKa0K26NZaSNJkqRaYdImZQrb7tseTZK0uXp07mtcMG0G/5y7pOT4+K224JzjJnNo2Mp9ayRJ63FPG0mSJNUqkzYpU1/YHs2kjSRpM/PSklVcetNM/vzYSyXHRw5p5PQjduPDU3aksb6u5BxJ0uatMGmzxkobSZIk1QiTNiljezRJ0uZqxZo2fnzXs/zkH8+VPCO6oS7Dxw/cmc+/YyIjhjRWIUJJUq0YbHs0SZIk1SiTNilT1B7NrI0kaYDr6Mhy7T9f4Bs3RxYsW1Nyzjsnb8PZx7awy5gtKhydJKkWDWpcvxJztUkbSZIk1QiTNilTZ3s0SdJm5IHnFnHB9Bn868XXS45PGjuM86ZO5sAJYyocmSSplhW2R7PSRpIkSbXCpE3KFLdHM2kjSRp4nl+0gotvmMlNT80vOT5maDP/feRuvH+/cdQX/uMoSVIPCpM2pdpuSpIkSWlk0iZlCr+Xsj2aJGkgeX31On5wxzP88p45rG0v/gKtqaGOkw/ahc8eNoGhzX5MkSRtGNujSZIkqVb5bUjK2B5NkjQQtbV3cPVD8/jOrbNYtGJtyTlT99yWM4+exLjRQyocnSRpoBlcVGlj0kaSJEm1waRNymSK2qNVJw5JkjaVv89ayIXTZzDrleUlx/caN5Lzpraw706jKxyZJGmgsj2aJEmSapVJm5SpL2yPZqWNJKlGPbNgOV+bPoO/xYUlx7cdMYgvHR14917bU+e+NZKkTagwabPKShtJkiTVCJM2KVPUHs1SG0lSjXltxVq+e9ssfv3A3JInHwxurOczh4zn02/flcFN9SWOIEnSxrE9miRJkmqVSZuUKW6PZtJGklQb1rZ18Kv7n+d7t83i9dVtJee8b58dOOOowNgRgyocnSRpc9LcULfe7TVtHXR0ZK3slCRJUuqZtEmZwjVEu62XJUkpl81mua11ARfd0MrsV1eUnPPWnUdz7tTJ7LHDiApHJ0naHNXVZWhuqGNNW9eCak1bhxWekiRJSj2TNilT2B6tw0obSVKKtb78OhdMm8G9zy4qOT5u9GDOPqaFo3cfS6awnFSSpH40qLF+vaTNqnXtJm0kSZKUeiZtUqaw0qajxF4AkiRV28Jla/j2rZHfPzSPUv9UDW1u4D/fMYGTDty5aDNoSZIqYUhTPUtXrXvj9ir3tZEkSVINMGmTMoWVNu1W2kiSUmT1unZ+cc9sfvi3Z1m+pnjfmroMfPCtO/LFd+7GmKHNVYhQkqTEkIKqmpUl/t2SJEmS0sakTcoUVdqYs5EkpUA2m2X6ky/z9Rtn8sJrq0rOOXjiGP7nuBYmjR1e4egkSSq2RfP6y90Va620kSRJUvqZtEmZwqRNe0dH6YmSJFXI4/OWcMG0GTz8/Gslx3fdagvOOa6Fw8LW7lsjSUoNK20kSZJUi0zapExRezRzNpKkKnl56SouvSnyp0dfLDk+YnAjpx8xkY/svxON9XUVjk6SpO5t0WSljSRJkmqPSZuUqbfSRpJUZSvXtvHju57jx39/ltXriv8daqjLcOIBO3Ha4RMZOaSpChFKkvpTCOEU4HRgF2Au8EPg+zHGmmrePKSgPdrKtVbaSJIkKf1M2qRMfUF/tDY3tZEkVUhHR5Y/Pfoil948k1deX1NyzhEtW3PWsS2M32pohaOTJFVCCOE/ge8DFwF3AAcA3wKGAxdUMbQ+26KgPdqKNVbaSJIkKf1M2qRMcaWNSRtJUv97aM5iLpg2gydeWFpyfNLYYZxz3GQOmjimwpFJkiolhFAHnAX8JsZ4Tu7Xd4QQJgKfp8aSNkOarLSRJElS7TFpkzKFlTYmbSRJ/Wne4pVcfGMrNzw5v+T4mKFN/NeRgQ/sN67o3yhJ0oCTBd4JLC/4/VqgufLhbJwtmq20kSRJUu0xaZMyhZU2tkeT9P/Zu/P4qOp7/+Pvmcm+kz0kYUkIJ4kCKgruiAvutVprbWur19vFtrdWrfZWrbWtWq9Le7U/W23tqvVq1WoXccMFBAVBFFkSDnsgIWSF7OvM+f2REDJLQghJ5kzyej4ePoZzvmfmfKqnIWfe5/P9AqOhqb1Lv353u/64Yqc63f7r1kS4nLr+9On6zsJ8xUeFB6FCAMBY612zpkSSDMNwSJok6QpJX5X0aBBLGxa/TpsuOm0AAABgf4Q2NkOnDQBgNLk9lv62Zo9+ucRUbXNnwGMunpWlH15YqNzkmDGuDgAwWgzDCJP0tUEOaTJN85l+22dKWtr754/Vs65NSPHttGml0wYAAAAhgNDGZnxnnqHTBgAwUt7fVqt7XinR5n1NAcdn5yTqrkuKddK05DGuDAAwBqIkPT7IeJmk/qHNNklnScqR9BNJHxmGcZJpmlWjVeBI8+20aWFNGwAAAIQAQhubcTl8Om0CTFkDAMCR2FHTrJ+/Wqq3SqsDjmckROoH5xfq8uOz5WTdGgAYl0zTbJY05B/ypmlWSKqQJMMwPpS0VT2dOveNSoGjIDaCThsAAACEHkIbm3E6vbfdNNoAAIbpQGunocfl9wAAIABJREFUHn17q55eWRawczMq3Klvnpmvby7I83saGQAw8RiGkSjpUknvm6a58+B+0zS3GYbRKCk3aMUNQ0wknTYAAAAIPXxDYzN+nTYeOm0AAEemy+3RM6vK9MjbW3WgtSvgMVccn63bLjCUlRg9xtUBAGzMI+mPkp6U9J2DOw3DOFVSgqR1QaprWOJ81rRpaie0AQAAgP0R2tiMy6fThjVtAABDZVmW3jWrdd/iUm2vaQl4zIlTJ+lHlxTruNykMa4OAGB3pmk2GYbxsKT/Ngxjv6R3JBVJulvSJ5L+HMTyjlh8VLjXdlN74AcZAAAAADshtLEZ/zVtCG0AAIdn7mvSvYtLtHxrbcDx7KRo3X5RoS6elSWHg3VrAMDODMNwSlopKd80zdRBjpuknkDlcklZkmokvS7pZ6Zplg3z9D9Sz1o235L0fUn1kp6T9CPTNNuH+ZlBER/lfbtLpw0AAABCAaGNzfiuaTPUTpvG9i79a91emfualBgdrvOPydSsnMRRqBAAYCe1zR365ZItem71bgX6KyM2wqXvnD1D1582XVHhLv8DAAB2dK+keZLqBjqgN7D5QFKhpCZJ6yXlSbpe0hWGYSwwTXP9kZ7YNE2PpF/3/hPSEnw6bRrptAEAAEAIILSxGf81bQ4f2nywrVbfffYT1bV09u177N1tuurEHN3z2WMVGcaXdAAw3nR0u/Xn93fpsXe2qanD/8lhh0P6wom5umXRTKXHRwWhQgDAkTIMw6Gezpnbh3D4k+oJbF6VdHXv1GZRkh6XdJ2k5wzDmGWapnu06rW7mAiXXE5H3z1Ve5dHXW6Pwn3npAYAAABshNDGZnzvH9zW4KHN6p31uu5Pa9Tp9viNPf9RuepbOvXbr5wol5OpcABgPLAsS69v3Kf7X9us3fWtAY85NT9FP7q4WMWTE8a4OgDAcBmGkSnpCUmXDeHYQklXSGqW9BXTNJskyTTNdsMwviZpvnrWorlc0oujVrTNORwOxUWGqaHtUIdNU3u3kmMjglgVAAAAMDhCG5s5kk6b5o5ufffZjwMGNge9VVqtX7+7TTeeUzBiNQIAgmNDeYPuWVyi1TvrA45PT43VHRcV6dyidNatAYAQYhjGIvWEK/GS9kl6VNL9g7zlGkkOSf82TdPrLwXTNN2GYfxJ0oOSvqAghTalpaXBOK3a2tq8zh/lstTQb/yTjZs1OSE8wDsxXvheA5iYuA7ANQCuAYTyNUBoYzMun+/Yut0Dhza/fnebqho7vPZ9ef4UfbC9TjtrW/r2PfbuNl06Z7Kmp8aOaK0AgLFR1diuh94w9fePyxWoATMhKkw3nlOgr54yTRFhTPkCACGoWFKcpKcl3Sxp1mGOn9/7+sEA46t6X884+tJCW2y499+LrV0DP/AGAAAA2AGhjc04nb6dNoFvKvbUt+oPy3d67fvGmXm646IiVTW266JHl/etcdPZ7dHd/9qkp66fNzpFAwBGRVunW08u36Enlm1Xa6f/kgQup0PXzJ+im86dqUlM9QIAoWy1pBNM01wnSYZhHO74Gb2vOwcYL+t9zTAMI840zeajL/HIFBUVjfUpJR16kvLg+VPfO6Ad+w81I6Vk5agoPzUotWFs+F4DmJi4DsA1AK4BBPsaWLt27bDfS2hjM36dNgNMj/bXVWVe06JlJETqe71ToGUkROmuS4p109/W9Y2/t6VGn+45oDm5SSNfNABgRFmWpaU7W/TXfyzV3ob2gMcsNNJ058VFmpEeP8bVAQBGmmmaA3XMDCSt97VugPH+U6alqmftmwkpIcr7lrepvTtIlQAAAABDwxwqNuPfaeMf2rR3ufX8R3u89t107kzFRh66IbnsuMmaNy3Z65gnlm0fwUoBAKNhbdl+3fzqXj24vDpgYFOQHqe/XD9Pf/qPeQQ2ADBxRfe+tg0w3n9/9ADHTAjxUd7r1zS2dQWpEgAAAGBo6LSxmaF02ry2sVL7Ww/dbCREhemzx2V7HeNwOPSds2do9R9X9+17fdM+ldW1aGoKa9sAgN2U72/VA6+b+venewOOJ8dG6ObzZuqLJ+UqzMUzFwAwwbk1+AN4/ccGXiRzAkiM9g5tGghtAAAAYHOENjbj8um08QQIbV7+xPsLvSvn5io6wuV33JkFqSrOSlBJZaMkybKkF9eW6/uLDjtHNgBgjDR3dOvxpdv0++U71dHtv45ZuMuh/zhtur6zcIbfF08AgAmrRVKSpKgBxiP7/XmgbpwJIdlnzbf9rZ1BqgQAAAAYGh7VtRmXwzu08e20aWzv0srttV77vnBSbsDPcjgcuvbUqV77Xvq4ImAQBAAYW26PpefX7NHCh5fq1+9uDxjYnH9MhpbcvEB3XFREYAMA6O/gWjbJA4yn9PtzzSjXYmuTYrz//qxvodMGAAAA9kZoYzO+M974rmmzzKxRl/vQvumpsZqZETfg5100K0tR4Yc+tOJAm1btGGi9UgDAWFi5vU6X/r8V+sHf16umqcNvPD85Qg+cn6XffuVETUtlSksAgJ/Nva/TBhg/+ORWpWmaraNfjn1N8u20aaHTBgAAAPZGaGMzTr81bbyfvF5SUuW1fV5xhhw+3Tn9xUeF64JjMr32/XNd4PUSAACja1dti77x1Ef64pOr+qau7C8tPlIPXjlbj16crdmZE3rdaADA4D7qfT15gPGD+z8cg1psbVIM06MBAAAgtBDa2Izv9Gj9O23cHktLzWqv8UXFGYf9zMtPyPHafqu0yq+DBwAwehraunTf4hKd97/L9KZP+C5JkWFO/dfCGXr31rN01Ym5fuubAQDg46Xe188ahuE1RZphGC5J1/Vu/nUsi7KjJJ/p0QhtAAAAYHeENjbj+0Vd/zVtNu9rVGN7d992YnS4jp8y6bCfeUpeiuKjwvq261o6tbZs/whUCwAYTLfbo6dX7tLCh5fqyeU7vaa3POgzcybrnVvP0q3nG4qLDPP/EAAAfJimuV7SYkkJkl40DCNFkgzDiJL0e0lFkkxJLwetSJtI9p0erZU1bQAAAGBvfDtkMy6fh6v7d8Ss3lnvNTZvevKQnsaOCHPq7MJ0r2nR3ty0T/OmD7RuKQDgaC3bUqN7XynR1urmgOPH5SbprkuKNXfq4cN3AAACuEHSCkkLJe02DKNUUp6kSZIaJF1umqZnkPdPCH7To7V0yrKsQaeYBgAAAIKJThubcToHnh7NN7SZfwShy/k+69q8Veo/PQ8A4Ohtq27SdX9arWv/uDpgYDM5MUqPXn2cXvrWqQQ2AIBhM02zXNJcSb+SVCNptqRuSc9KOsk0zdIglmcbUeEuxUS4+ra7PZYa27oHeQcAAAAQXHTa2Ixvp83B6dEsy9KaXf6dNkO1YGaawl2Ovql5dtW1ak99q3KTY46uYACAJKm+pVOPvLVFz3y4O+C6YTERLn1rQb6+dkaeovt9eQQAgC/TNJdKOmwriGmadZK+1/sPBpAWH6myuta+7eqmdiX6rHUDAAAA2AWdNjbjO93ZwS/+dtS2qLb50KKZsREuFWclDPlzYyPD/J7oXr619igqBQBIUme3R79fvkNnPfSunlpZ5hfYOBzSlXNz9O6tZ+m75xQQ2AAAMMbS4yO9tqubOoJUCQAAAHB4dNrYjO8SNQc7bTaUN3jtP2HqJIW5jixzO6MgTat2HOrWWbGtRl+aP2V4hQLABGdZlpaUVOn+1zZrZ21LwGPmTU/Wjy8p1rHZiWNcHQAAOCg9Pspru7qpPUiVAAAAAIdHaGMzLodvp03P2qEllY1e+4fzBeDpM1L10Btm3/b72+rk9lh+3T0AgMGV7G3UPa+UaOWOuoDjU5JjdMdFhTr/mEwWOgYAIMjSfDttGum0AQAAgH0R2tiMb/NMd+8aNCV7vUObI5ka7aBjsxOVGB2uhrYuSVJDW5dK9jZqVg5PgAPAUFQ3teuXb27R3z7aI8t/2RrFR4bpv86eoetOm6bIMKZBAwDADtITmB4NAAAAoYPQxmZ8O208liXLsvw6bYonH3lo43I6dHJest7YVNW3b82uekIbADiM9i63/rBip37z7ja1dLr9xp0O6Yvzpujm82YqNS4ywCcAAIBgSfP5u7mqkenRAAAAYF+ENjbj12njsVTV2KH6ls6+fdHhLk1LiR3W5580zT+0uf706cP6LAAY7yzL0ivrK/U/r21WxYG2gMecUZCqH11cLCMzfoyrAwAAQzE5Kdpre6C/0wEAAAA7ILSxGf81bSyVVDZ47SvMih/2OjTzpid7ba/ZVS/LslhzAQB8rNtzQPe8UqK1ZfsDjuelxepHFxdpoZHOz1AAAGwsd1KM1/aeekIbAAAA2Behjc34ZjHdbmtE1rPp/97YCFff9D61zZ3aWduivLS4YX8mAIwnlQ1tevB1Uy9/UhFwPCkmXDedU6AvnzxV4b7tkQAAwHaykqLkdEie3vXoaps71NbpVnQE688BAADAfghtbMa3g8btsbSjpsVrX+FRTMET5nLqhKmTtHxrbd++NbvqCW0ATHitnd16YtkO/e697Wrv8viNhzkd+uop03TjOTOUFBMRhAoBAMBwhLucmpwUrfL9hzpsyve3qiCDqU0BAABgP4Q2NuPy7bTxWNpV5x3aTE89uoDlxKnJXqHNuj0N+sJJR/WRABCyPB5LL39SoQff2Kyqxo6Ax5xblK7bLypSPgE3AAAhKXdSjFdos4fQBgAAADZFaGMzTp9OG49lqayu1Wvf1BTvOZmP1JzcRK/t9eUHjurzACBUrdlVr3teKdH68oaA44WZ8brrkmKdNiN1jCsDAAAjKTc5Wit3HNre7XOPBQAAANgFoY3NhPksj1Df0um1He5yaHJS9FGdY3ZOkte2ua9J7V1uRYUzpzOAiWFPfavuf61Ur27YF3A8NS5C319k6KoTc/2mrQQAAKEnd5L3g297+nXdAAAAAHZCaGMzEb7zo/nITY456i8Qk2MjlJscrT31PTcq3R5LJZWNOmHKpKP6XACwu6b2Lv363e3644qd6nT7r1sT4XLq+tOn6zsL8xUfFR6ECgEAwGiY4jNbwZ56Om0AAABgT4Q2NhN+mEBmWkrsiJxndnZSX2gjSev3HCC0ATBuuT2W/rZmj365xFRtc2fAYy6elaUfXlio3OSjm4ISAADYTw6dNgAAAAgRhDY243A4FO50qMtjBRw/2vVsDpqdk6jFGyr7tgdazwEAQt2KrbW6d3GJNu9rCjg+KztRd11SrHnTk8e4MgAAMFZyk72nmN5T3yrLsuRwMA0qAAAA7IXQxoYiwxzq6gwc2oxYp43Pujaflh8Ykc8FALvYXtOsny8u1dubqwOOZyRE6gfnF+ry47PlZN0aAADGtbS4SMVFhqm5o1uS1NzRrarGDmUmRgW5MgAAAMAboY0NhQ+yrs1IddrMykmUwyFZvdnQjtoWNbV3sYYDgJB3oLVTj769VU+vLFN3gK7FqHCnvnlmvr65IE8xEfw1CADAROBwOJSfHqdP9xx6WG1rdROhDQAAAGyHb6tsKHLQ0GZkOm3iIsOUnxanbdXNknrCm40VjTolP2VEPh8AxlqX26O/rirTo29v1YHWroDHXH58tn5wgaGsxOiA4wAAYPwq8A1tqpp1RkFaECsCAAAA/BHa2NBgnTZZI/gk2OzsxL7QRpI27W0gtAEQcizL0rtmte5dXKodNS0Bj5k7dZLuuqRYx+UmBRwHAADjX0F6nNf21n73QgAAAIBdENrYUMQAoU1ybISiwl0jdp7iyQl66ZOKvu2BFukGALsy9zXp3sUlWr61NuB4dlK0br+oUBfPymKhYQAAJriCDO/QZls19z8AAACwH0IbGxpoerTMhJGdb7kwM8Fre/O+xhH9fAAYLbXNHfrlki16bvVuBVi2RrERLn174Qz95+nTRzTsBgAAoasgPd5re0tVsyzL4sEOAAAA2AqhjQ0NND3a5KQRDm2y/G9aut0ehbmcI3oeABgpHd1u/fn9XXrsnW1q6uj2G3c4pC+cmKtbFs1UejwLCwMAgEOyk6IVFe5Ue5dHktTQ1qXa5k6lxUcGuTIAAADgEEIbG4oMCxyaZI7gejaSlBoXqdS4CNU2d0qSOrs92lXXqhk+cz0DQLBZlqXXN+7T/a9t1u761oDHnJKXorsuKVbx5ISA4wAAYGJzOh2akR6njRWHZhjYWt1EaAMAAABbIbSxoYE6bbISo0f8XIWZCVqx7dBaEJv3NRLaALCVDeUNumdxiVbvrA84Pi0lRndcVKTzijOY3gQAAAyqID3eK7TZVt2sU/NTg1gRAAAA4I3QxoYiBgxtRn6qn8LMeK/QxtzXpEtmj/hpAOCIVTW266E3TP3943JZAdatSYgK043nFOirp0xTxAAdigAAAP0VZHg/oLa1qjlIlQAAAACBEdrYUOQAoc1IT48mSUam97o2pZVNI34OADgSbZ1uPbl8h55Ytl2tnW6/cZfToWvmT9H3zp2p5NiIIFQIAABCVUG69/3P1mrufwAAAGAvhDY2NND0aJNHYXq0oizvtR/MqsYBjgSA0eXxWPrXp3v1wOubVdnQHvCYs4w03XlRkQoy4gOOAwAADKbAZyroLVXNsiyLKVYBAABgG4Q2NjSWnTYz0uPkdEie3qmH9tS3qbmjW3GRXBoAxs7asv2655USrdtzIOB4QXqcfnRJsRbMTBvjygAAwHiSmxyjqHCn2rs8kqT6lk7VNHUoPWHk77UAAACA4eCbeRsK1GkzKSZcUeGuET9XVLhL01Njtb2mpW+fua9Rc6cmj/i5AMBX+f5WPfC6qX9/ujfg+KSYcN2yyNAXT8pVmIt1awAAwNFxOR0yMuL1aXlD377SfU2ENgAAALANQhsbiggQ2uRMihm18xVmJniFNlurmgltAIyq5o5uPb50m36/fKc6uj1+4+Euh647dZr+6+wCJUaHB6FCAAAwXhVlJXiHNpWNdPMCAADANghtbCjQ9GjTUmNH7Xz5PvM6b69pHrVzAZjY3B5Lf19brofeNFXT1BHwmPOPydDtFxaN6s89AAAwdIZhPCrpRknhpml2B7ueo1WY6b023uZK1vUEAACAfUyY0MYwjGxJGyRdZZrmW8GuZzApsf7/WaaljF6nTX6a9xej/btuAGCkrNxep3teKVHJAF+MFGcl6K5LinVKfsoYVwYAAAZiGMY5kr4b7DpGUlFWgtd2aWVTkCoBAAAA/E2I0MYwjFxJb0iaFOxahmJ2RrTfvvT4yFE7X34anTYARs+u2hb9/NVSvVlSFXA8LT5Sty0y9Lm5OXI5/TsNAQBAcBiGkSTpz5LKJeUGt5qRU5jpHdpsr2lWR7dbkWEjv4YoAAAAcKTGdWhjGIZT0lclPSwpZL4JTIp2aWpKjMrqWvv2zclNGrXz5fl02uypb1V7l1tR4dy0ABi+hrYuPfbOVv35g13qclt+4xFhTn39jOn61lkzFBc5rv86AgAgVP1a0g5JyyTdFeRaRkxiTLiyk6JVcaBNktTtsbStulnHTE4McmUAAACA5Ax2AaNstqQnJD0l6StBruWI3H1pcd+fT81P0azs0buBiIkIU3bSoe4ejyWvwAgAjkS326OnV+7SwoeX6snlOwMGNpfOmax3vr9At51fSGADAIANGYZxlaTPSPoPSZ4glzPifNe1YYo0AAAA2MV4/6Zst6QZpmmWG4ZxVrCLORJnF2Zo+Q8Wand9q07OS5HDMbqNQnlpsX1PmknSjppmGT43MgBwOMu21OjeV0q0tTrwNIvH5SbprkuKNXdqSMxWCQDAuGIYRpikrw1ySJNpms8YhjFZ0uOSbjNNc4dhGGNT4BgqykrQ25ur+7Y3D7DmHgAAADDWQjK0GerNhmma9ZLqx6isEZebHKPc5JgxOVd+WpyWb63t22ZdGwBHYlt1k+5dXKqlZk3A8cmJUfrvCwt16ezJcrJuDQAAwRKlnjBmIGWSnpH0R0kfmab5xJhUFQSFWT6dNvsIbQAAAGAPIRnaaOg3GxiifJ91bbbXtASpEgChpL6lU4+8tUXPfLhbbo//NGjR4S5966x8ff2MPEVHsE4WAADBZJpmsw6z1qdhGN+WdIqkOb0Py0mHptV2GYbhMU0z5KdLK8pK8NourWySZVkjOsNBR7dbJXsbVd3UIUnKSoxSYWaCIsLG+yzlAAAAOBohGdoM5WYDRyY/Lc5rm04bAIPp7PboqZW79Ku3t6qxvdtv3OGQPndCjm4731BGQtTYFwgAAIbrKkkJknYGGGuX9FNJPxnLgkbDtJRYRYU71d7Vkz/Vt3SqpqlD6SPwe0vJ3kY9sWy7lpRUqa3L7TUWG+HSwsJ0/cdp0zR3avJRnwsAAADjT0iGNhh5+ek+oU1184g/aQYg9FmWpTdLqnT/q6XaVdca8Jh505P140uKdWx24hhXBwAARsA3JfkubvkNSV+XdLKkPWNe0ShwOR0yMuL1aXlD377SfU1HFdq0d7n1P69t1p8/2DXgMS2dbr2yvlKvrK/UecUZuvvSYuVMGpspsQEAABAaCG0gSUqPj1RcZJiaO3qemG/pdKuqsUOZiTwhD6DHpr0NuveVUq3cURdwPDc5WndcWKQLjs0k8AUAIESZpmn67jMM45LeP641TdO/xTZEFWYmeIc2lY1aMDNtWJ9V29yh//jTGm2oaDj8wb2WlFRp1Y46Pfi52bpwVtawzgsAAIDxh9AGkiSHw6H8tFivm5btNc2ENgBU3diuh9809cLacln+y9YoPjJM/3X2DF132jRFhrFuDQAAI8EwDKeklZLyTdNMHeS4SZLulnS5pCxJNZJel/Qz0zTLxqLWUFWU5d1QtLmycVifU9fcoat+u1I7AqwLmpEQqWMmJ8pjWdq0t1E1vevbHNTU3q1vPfOx7rioUN84M39Y5wcAAMD4MuqhDTcboWNaqndoU1bXqtNmBLEgAEHV3uXW75fv0G+Wbldrp9tv3OmQrp43RbecN1OpcZFBqBAAgHHtXknzJAVucVXfPdQHkgolNUlaLylP0vWSrjAMY4FpmuuPthDTNH+icbCOja/CrASv7dLKpiP+jPYut7721Ed+gU1ucrR+fMkxOrcova8D2bIsvb+tTr9YYuqT3Qe8jv/5q5tV39Kl/77AoGMZAABgghuLThtb3GyYprlUEr/9DmJqsvdcymX1/k+KARj/LMvSvz7dqwdfN1VxoC3gMWcUpOrOi4tUmJkQcBwAAAyPYRgO9TzMdvsQDn9SPfdQr0q62jTNJsMwoiQ9Luk6Sc8ZhjHLNE3/py+gIp/fY7bXNKuj231EncM//fcmvwDmjIJU/ebLJyg+Ktxrv8Ph0OkFqTo1P0V//mCX7n+tVF3uQ23MTyzbrtgIl757TsEw/tcAAABgvBi10IabjdAzNSXWa7usNvAi4wDGr49379c9r5T4fflwUF5arH50cZEWGuk8BQoAwAgzDCNT0hOSLhvCsYWSrpDULOkrpmk2SZJpmu2GYXxN0nxJReqZyeDFUSt6AKWlpWN9SklSW1vbEZ0/Ldalmpae28xuj6U3Vm1QQcrQOojfL2vRs6urvPYdlxWtW+fHq3zntkHfe0qK9LNzMvWzd/aprftQcPOLJVtkte7XeTPiB3k3BnOk1wDGJ64DcA2AawChfA2MSmgzHm42QuUmYyRZze1e21v21ofkRR3qQvkHCkZGMK6B6uZu/enjei3d2RxwPD7SqS/PmaSLjQSFWfXavLl+zGqbiPg5AK4BSFwHE41hGIvUc78TL2mfpEcl3T/IW65Rz0wC/zZN0+svZtM03YZh/EnSg5K+oCCENqFiRnKkaloOPay2ta5jSKFNU4dbj62q9dqXnRCuO89KV4RraA+2HJcVrQcumKw73qxUc6enb/+jH9QoOyFcxemsLwoAADARjXhow81G6MqK974cKpu6ZFkWT9MD41hbl0cvbDygv29qUGe/6TkOcjmkSwsT9KU5kxQfOfSpQgAAwBErlhQn6WlJN0uadZjj5/e+fjDA+Kre1zOOvrQjV1RUFIzT9oWcQz3/aZVhWrlnS992rTt6SO+96x8bdaD90EQQ4S6HfnvtfB2bnXhE9RZJysyeomv+8KE6u3uCG7clPfxBvRbfeIaSYyOO6PNw5NcAxieuA3ANgGsAwb4G1q5dO+z3jkanzbi42QiVm4yRZFmWYv5R0bfgeFu3pfQp+SwwPsaC/QMFwTcW14DHY+nFj8v18Bumqps6Ah5zblGG7rioUHlpcaNWBwLj5wC4BiAF/zo4mpsMDMtqSSeYprlOkgzDONzxM3pfdw4wXtb7mmEYRpxpmoHbaSe4WTlJXtvryxsO+54tVU3664dlXvu+s3DGEQc2B82bnqz/veo4fef/Pu7bV9nQrlueX6c/XnuSnE4eogMAAJhIRiO04WYjRDkcDk1JjtHmfU19+8rqWgltgHFm1Y463fNKiTbtbQw4XpSVoLsuLtKpM1LHuDIAACYu0zQHeohtIGm9r3UDjPefxSBVPdNRw8csn6DF3Nek9i63osIH7jD+1dtbZfVrUJ6aEqMbFuQfVR0Xz87Suj3T9eTyQ7fFS80aPbtmt748f+pRfTYAAABCy4iHNtxshLapKd6hze76Fs2dOimIFQEYKbtqW3T/a6V6Y1NVwPHUuEjddv5MXTk3Vy6e6AQAwO6ie1/bBhjvvz96gGMmvOTYCOVMilb5/p5/Xd0eS5v3Nem43KSAx2+rbtLiDZVe+26/sHDQkGeofnBBodaW7dfHuw/07bv/1c1aaKRrchL/CQEAACYKZ7ALEDcbtjI1JdZru6yudYAjAYSKhrYu3be4ROf977KAgU1EmFPfWZivpbedpS+cNIXABgCA0OA+zHj/ez3/hevQZ3aOd7fNJ7v3D3js/3tnm1eXTWFmvBYVZ45IHeEupx69+njFRhwKgJo7unXHyxtkWfwnBAAAmCjsENpws2EjU5JjvLYJbYDQ1e326OmVu7RuCragAAAgAElEQVTw4aV6cvlOdbn9f4ReOmey3vn+At12fqHiIkdjxkwAADBKWnpfowYY7z/H8UAPyEHS8bneMwus2VUf8LjtNc3696d7vfbdeE7BiK45k5sco/++sNBr31KzRq9v3Ddi5wAAAIC92eEbuhZJSeJmwxampviGNi0DHAnAzpaa1bpvcam2VgeeUfK43CTddUkx0x8CABC66tRzH5U8wHhKvz/XjH45oWvedO9/hat31suyLDkc3mHMr9/ZJk+/Z2CMjHhdcMzIdNn0d838qXplfaVW7zwUHt27uFQLC9NHZBo2AAAA2JsdOm0OrmXDzYYNTPOZHm13PZ02QCjZWtWka/+4Wtf9aU3AwGZyYpQevfo4vfStUwlsAAAIbZt7X6cNMH5w9fpK0zT5pX4Qx0xO8Oo4rm3u1PYa79+jdtW26B/rKrz2ffecGSPaZXOQ0+nQfZ891mvK2ooDbfrdeztG/FwAAACwHzuENtxs2EhWYpTC+t0c1DZ3qrmjO4gVARiK+pZO3fWPjbrg0eVatsU/346JcOn7583U298/S5cdlz0qXzAAAIAx9VHv68kDjB/c/+EY1BLSwlxOv4dZVu3wniLtsXe9u2xmpMfpwmOzRq2mgox4XXvKNK99v1m6TVWN7aN2TgAAANiDHUIbbjZsJMzlVM6kaK99u1nXBrCtjm63nnxvhxY89K6eXlUmt8d73RqHQ/r83By9e+tZ+u45BYqOYEoNAADGiZd6Xz9rGIbXrAWGYbgkXde7+dexLCpUzc/znvhh5Y66vj+X1bXo5U98umzOnuHVCTMavndugVJiI/q227s8euydbaN6TgAAAASfHUIbbjZsJjfZe12b8v2ENoDdWJal1zfu06L/fU/3vVqqpnb/jrj505P17/86XQ99fo4yEgZaNgwAAIQi0zTXS1osKUHSi4ZhpEiSYRhRkn4vqUiSKenloBUZQk7OS/HaXmbWqKPbLUl67J1tXg/G5KXF6pLZk0e9psTocN103kyvfc+u3s1DdQAAAONc0EMbbjbsx7fTpuJAW5AqARDIhvIGXf27Vbrhr2tVFuCmfWpKjJ64Zq6e+8bJOjY7MQgVAgCAMXKDpDJJCyXtNgzjI0l71fPgW4Oky03T9ASvvNAxJydJqXGRfdvNHd1asbVWm/c16sWPy72OHYsum4O+cGKucpMP3Z91eyw98taWMTk3AAAAgiPooU0vbjZsJGeSd6dNxX5CG8AOKg606ea/rdOlj63Qhzvr/cbjo8J050VFevPmM3XBsZlyOFi3BgCA8cw0zXJJcyX9SlKNpNmSuiU9K+kk0zRLg1heSHE5HTqvOMNr3/99uFs/f3WzrH6zz+anxerSMeiyOSgizKmbz/Xutnl5XYW21zSPWQ0AAAAYW2HBLkDqudkwDGOupB9Lukw9NxsH1HOzcbdpmluDWd9Ek53k3WlTTmgDBFVTe5ceX7pdf1ixUx3d/vm1y+nQl+ZN0U3nFiil3xOiAAAgdJmmuVTSYZ/AME2zTtL3ev/BUfj8iTl6dvXuvu23N1f7HfPDC4sU5hrbZx8vOy5bjy/drq3VPUGNZUm/XbZdD145Z0zrAAAAwNgY9dCGm43Qk830aIAtdLk9em71bj3y1lbVtXQGPGbBzDT96OIiFWTEj3F1AAAA48vxuUmanZOo9eUNAcfnTU/WuUXpY1xVzwM6/3X2DH3vuXV9+17+pEI3nTtTk30euAMAAEDos8v0aLAR1rQBgsuyLK3a3aLzH3lPd/1zU8DApjAzXk9dP09/uX4egQ0AAMAIcDgcuvOiooBjsREuPfi52UGbfvbiWVmamnJoGusut6Unl+8ISi0AAAAYXYQ28JMeH6Wwfgtr1rd0qrWzO4gVARPHhvIG/fDNSv303SrtqGnxG0+Pj9SDn5utxTeeoTNnpgWhQgAAgPFrfl6KfnxJsfrdDikxOly/v/YkTUuNDVpdYS6nbliQ77XvudV7dKA1cDc2AAAAQpct1rSBvbicDmUlRWlP/aEOm4r9bTzND4yiigNtevgNUy9/UhFwPDrcpW8uyNPXz8hTbCQ/ugEAAEbL9adP15kzU/XO5molRIXrvOIMW6wbeMUJ2XrkrS2qauyQJLV1ufX8R3v0jTPzD/NOAAAAhBK++UNAOUkxXqFNOaENMCqa2rv0+NLt+sOKnero9viNOx3SVSfm6pbzZio9ISoIFQIAAEw8M9LjNSPdXvc/kWEuffWUaXroDbNv31Mry/Sfp+fJ5QzOtG0AAAAYeYQ2CCjbZ12bcta1AUZUl9uj51bv1iNvbQ24Zo0knTkzTXdcVKjCzIQxrg4AAAB29MV5U/To21vV2fuwT/n+Nr1dWqVFx2QGuTIAAACMFEIbBJSd5B3aVOwntAFGgmVZeru0Wve/VqrtAdaskaRpkyL0tbnJuubcuWNcHQAAAOwsOTZCl82ZrBfWlvft+8vKXYQ2AAAA4wihDQLK8e202d8apEqA8WNDeYPue7VEq3bUBxxPj4/UrYsMFcc0McUFAAAAArr21Gleoc372+q0taqJ6awBAADGCWewC4A9+U6PVsH0aMCw7T3Qplv+tk6XPrYiYGATHe7STecW6N1bz9JVJ+US2AAAAGBAx2Yn6qRpk7z2PbWyLEjVAAAAYKTRaYOAcpJivLaZHg04ck3tXXp86Xb9YcVOdfTOO96fwyFdNTdX3180U+kJUUGoEAAAAKHo2lOnac2u/X3b/1xXoTsvLlJUuCuIVQEAAGAkENogoMzEKDkdksfq2a5u6lB7l5ubAGAIut0ePbtmjx5ZskV1LZ0BjzlzZppuv7BQRVkJY1wdAAAAQt2i4kylxEb0/a7Z2N6tNzbt02XHZQe5MgAAABwtpkdDQBFhTmX4PPlf2dAepGqA0GBZlt4qqdL5j7ynu/6xMWBgU5gZr79cP09PXT+PwAYAAADDEhHm1OXHewc0L3xUPsDRAAAACCV02mBAk5OivYKayoY2TU+NDWJFgH1trGjQfYtLtXJHXcDx9PhI3brI0Ofm5rBmDQAAAI7a50/M1e9X7Ozbfn97rfbUtyo3OWaQdwEAAMDuCG0woMxE706bfXTaAH72HmjTw2+YeumTioDj0eEufXNBnr5+Rp5iI/mRCwAAgJFhZMZrTk6iPi1vkCRZlvT3j8t107kzg1wZAAAAjgbfIGJAWUyPBgyoqb1LTyzbrt8v36mObo/fuMMhXTU3V7csmuk31SAAAAAwEj5/Ym5faCP1TJF249kFctLZDQAAELIIbTAgOm0Af91uj55ds0ePLNkScM0aSTpzZppuv7CQNWsAAAAwqi6dM1n3vFLS9xBRxYE2fbizXqfkpwS5MgAAAAwXoQ0GlJUY7bVNpw0mMsuy9M7mav381VJtr2kJeExhZrxuv6hIC2amjXF1AAAAmIgSo8N1wbGZ+ue6vX37Xlm/l9AGAAAghBHaYEB+nTaNbUGqBAiujRUNum9xqVbuqAs4nhYfqVsXzdSVc3PlYioKAAAAjKHPzJnsFdq8tnGffvKZYxTucgaxKgAAAAwXoQ0GlMX0aJjgKhva9NAbpl7+pEKW5T8eHe7SNxfk6etn5Ck2kh+nAAAAGHtnFKQpISpMje3dkqT6lk59sL2O7m8AAIAQxbeMGFBafKScDsnT+2V1bXOnOrrdigxzBbcwYJQ1d3Trt8u268nlO9Te5fEbdzikq+bm6pZFM5WREBXgEwAAAICxERHm1IXHZulvH+3p2/fvT/cS2gAAAIQo+qUxoHCXU2nxkV77qhs7glQNMPq63R7934e7ddZDS/X/3tkWMLA5oyBVr954hh64cjaBDQAAAGzh0jmTvbbf2LhPHd3uIFUDAACAo0GnDQaVmRitqn5BTWVDu3KTY4JYETDyLMvS0i01uv/VUm2pag54jJERrzsuLuKJRQAAANjOyXnJSo2LUG1zpySpqaNby8waLTomM8iVAQAA4EgR2mBQWQlR+rTfdmVDW9BqAUZDaWWjfv5qqZZvrQ04nhoXqe8vmqnPz81RGIu5AgAAwIbCXE5dNCtLT60s69v3r0/3EtoAAACEIEIbDCoz0Xv6p30N7UGqBBhZVY3t+uWbW/T82j2yLP/xqHCnvnFGnr6xIF9xkfyoBAAAgL1dOmeyV2jz7uZq1iQFAAAIQXwTiUFl+YQ2lYQ2CHGtnd363Xs79NtlO9TW5T/Pt8MhXXF8jm49f6ayEqODUCEAAABw5OZOmaS0+EjVNPVMb93S6dbK7XU6y0gPcmUAAAA4EoQ2GBSdNhgvPB5LL31SoYfe2Oy1TlN/p+Sl6M6Li3RsduIYVwcAAAAcHafToXOL0vXs6j19+5aUVBHaAAAAhBgWaMCgfDsNKhsJbRB61pbt1+W/eV+3vvBpwMAmPy1Wf7j2RP3f1+cT2AAAACBkLSr2XsNmSUmVPJ4AcwEDAADAtui0waB8p0fb19AWpEqAI1fZ0KYHXtusf6zbG3A8OTZCN59boKvnTVG4iwwbAAAAoe2U/BTFRLjU2tkzDXB1U4fWVzTouNykIFcGAACAoSK0waDSEyK9tqubOtTl9vAFN2ytvcutJ9/bod8s3R5w3ZqIMKeuP226vr0wXwlR4UGoEAAAABh5UeEuLZiZptc27uvbt6RkH6ENAABACOGbdwwqMsyllNiIvm3LUt/CloDdWJalVzdU6pxfLNMvlmwJGNhceGym3r5lgX54YSGBDQAAAMadRcdkeG0vKakKUiUAAAAYDjptcFjpCVGqa+ns265u6tDkpOhB3gGMvU17G/Szf5fow531AccLM+N196XH6JT8lDGuDAAAILQYhrFfUqDWjCzTNPcF2A8bWWiky+V0yN27ls2Wqmbtqm3RtNTYIFcGAACAoSC0wWGlx0eqtPLQdnVje/CKAXw0tHbpF0tM/XVVmQKtsZocG6HvL5qpq0+aIpfTMfYFAgAAhBDDMKapJ7C5UdIan+G6MS8IRywpJkLzpiVr5Y5D/7ne3lyt/zx9ehCrAgAAwFAR2uCw0uP917UBgs2yLP394wrd/2qpVyfYQWFOh649dZpuPKdAidFMgwYAADBEx/W+vmiaZuWgR8K2zi3O8Apt3ttSQ2gDAAAQIghtcFjpCT6hDZ02CLLN+xp11z82as2u/QHHzzLS9KOLizUjPW6MKwMAAAh5x0mqJrAJbQtmpuqefturdtSpvcutqHBX0GoCAADA0BDa4LDS46O8tum0QbA0tXfpkbe26s8f7Oqbo7u/qSkxuvvSYp1dmBHg3QAAABiC4yQ1GIbxT0kLJTkkLZZ0M0FO6MhPi1N2UrQqDrRJkjq6PVq9s15nzkwLcmUAAAA4HEIbHFaGb6cNoQ3GmGVZ+vf6St37SknA6y8yzKlvnzVD31yQx9ODAAAAARiGESbpa4Mc0mSa5jPqCW1SJD0p6WFJxZJ+KmmZYRgnmKbZPOrF4qg5HA6dOTNVz67e07dv2ZYaQhsAAIAQQGiDw0rz67RhejSMnd11rbrzHxu0fGttwPGzC9P1k0uP0ZSUmDGuDAAAIKRESXp8kPEySc9IukZSo2ma63v3LzcMY6OkFZKuk/TYaBaJkbNgZppXaPPelpogVgMAAIChIrTBYaXH+65pQ6cNRl+326M/vr9Tv1yyRe1dHr/x7KRo3X1psc4rzpDD4QhChQAAAKGjt0PmsL80maa5IsC+9w3DaJA0ZzRqw+g4dUaqXE5H37TCW6ubtfdAmyYnRQe5MgAAAAyG0AaHleYT2tQ2d8jtseRy8kU5RsfGigb98KX12ljR6DcW4XLqG2fm6TsLZyg6gqnQAAAARophGCmSPitphWmaZr/9TkkRkgK3PsOWEqLCdcKUJK3Ztb9v33tbanT1vClBrAoAAACH4wx2AbC/qHCXEqPD+7Y9llTXTLcNRl5bp1v3v1aqy379fsDA5tT8FL1+0xm69XyDwAYAAGDkdUl6QtJtPvs/Iyla0rtjXhGOypkF3mvYLGOKNAAAANuj0wZDkh4fqYa2rr7t6qYOpSdEDfIO4Mi8v61Wd7y8QWV1rX5jidHhuvPiIn1+bg5ToQEAAIwS0zQbDcP4haQfGIZRJ+lNSbMl/UTSYtM03wxmfThyC4w0/WLJlr7tFdtqmTUBAADA5ghtMCQZCVHaWt3ct13d1C4pMXgFYdxo7ujWfYtL9ezq3QHHL5mdpbsvPcZvmj4AAIDxqnc6spWS8k3TTB3kuEmS7pZ0uaQsSTWSXpf0M9M0y4Z5+jsl7ZX0TUk3qmdKtMcl/XSYn4cgOnZyoibFhGt/a88DeE3t3dq0t0Gzc5KCXBkAAAAGQmiDIUn3+cK8upHp0XD0Ptheq9teWK+KA21+Y1mJUbr3s8fqnKKMIFQGAAAQVPdKmiepbqADegObDyQVSmqStF5SnqTrJV1hGMYC0zTXH+mJTdN0S/pV7z8IcU6nQyfnpei1jfv69q3aUUdoAwAAYGOsaYMhSUvwCW2aCG0wfK2d3br7nxv1pSc/9AtsHA7p2lOmasktCwhsAADAhGIYhsMwjJ9Iun0Ihz+pnsDmVUnZpmmeKGmypD9LSpL0nGEYLAIInZyX4rW9cvuAWSAAAMC44PFYqmvtVqfbCnYpw0KnDYYkPd57/Zqe6dGAI/fRrnrd+sKn2hVg7Zq8tFg9dOVszZ2aHITKAAAAgscwjExJT0i6bAjHFkq6QlKzpK+YptkkSaZpthuG8TVJ8yUVqWfatBdHrehBlJaWBuO0amtrC+r57ShDnV7bq3bUauOmknG7rg3XACSuA3ANgGtgIvFYliqburW1tkNb63r+2VbfobYuS1FhDv30nHbNzowOdplHhNAGQ8L0aDha7V1u/XLJFj25fIcsn5Db4ZCuP226bjvfUFQ4D4QCAICJxTCMReoJV+Il7ZP0qKT7B3nLNZIckv5tmmZ9/wHTNN2GYfxJ0oOSvqAghTawjylJ4UqMcqqh3SNJauuytK2uQ0Za1GHeCQAAYC/WwYDmYDjT+9raFbijpr3b0gsbDxDaYHzyDW2qQmx6NI/HUktntxwOh2IjXHI4xudTZXa1aW+DvvfcOm2rbvYbm5Ico4c/P0fzptNdAwAAJqxiSXGSnpZ0s6RZhzl+fu/rBwOMr+p9PePoSxueoqKioJz34NO0wTq/XZ1e0K7FGyr7tvdZCfpsUX4QKxo9XAOQuA7ANQCugfHAsiztqW/T+ooD2lDRoA3lDdpY0aDG9u4j+pzpmSlBuQ7Wrl077PcS2mBIMhK8n8KqabT/9Gjl+1v197UVesesVmllozq7e54si41wqXhygk6bkaorjs/RlJSYIFc6flmWpT+9v0v/89pmdbo9fuNfOXmqfnhhoWIj+VEEAAAmtNWSTjBNc50kGYZxuONn9L7uHGC8rPc1wzCMONM0/Z+cwYRycl6yV2izcnudblgwPkMbAAAQeizLUvn+Nm2oaND63nBmQ0WDGtq6hv2ZcRFOnZwbox9cUDiClY4NvinFkKQneHfa1DR3yOOx5LThPMiN7V365Ztb9NdVZer2+LfGtXS6tWbXfq3ZtV+PvLVVp89I1c3nFbCOygirbe7QbS98qnfNGr+xyYlRevDKOTq9IDUIlQEAANiLaZoDdcwMJK33daAV5ftPmZaqnrVvMIGdkp/itf3Rrnp1uT0KdzmDVBEAAJioLMtSxYE2bewNaDb0BjQHWocf0MRHhWl2TqKOzU7U7OwkzcpOVHPVLjkcDqX5zCAVCghtMCQxEWGKjXCppdMtSepyW2po69Kk2IggV+Zt094GffuZj1UWYJH7gazYVqsV22p1blGGfnrZMcpOCq05Du1o+dYa3fL8p6oJMI3elXNz9ONLi5UQFR6EygAAAMaFg7+wtg0w3n8/v9xC+WlxSo2LVG1zz+/nLZ1ubaho0AlTJgW5MgAAMJ5ZlqXKhva+7pn1FT2v9S2dw/7M+MiwnnDmYEiTk6gpyTF+y2GUVtuv2WCoCG0wZKnxkWrpF4bUtXTYKrRZs6te1/1xdV+w5Cs63CW3ZfVNk+brrdIqrdxeq9svKtKX509h3Zth6Oz26BdLTP122Q6/sfjIMP38ilm6dM7kIFQGAAAwrrglDdYi0X8s8KqsmFAcDodOzkvWK+u9p0gjtAEAACPFsizta2zXhn7dMxvKG1R3FAFNXGSYjpmcoNk5iZqV09NBMzU5xpazP40kQhsMWWpcpFcHS01Tp2akB7GgfjaUNwQMbHImReuGBflaVJyh9IQoWZalvQ3tWmbW6MW1e/Tx7gNex7d0uvWjf2zUB9tr9cDnZiuebpAhK6tr0Y3PfqJPyxv8xk6YkqRHrz5eucmsHwQAADACWiQlSYoaYLz/HBADdeNggjk5L8UrtFlbtj+I1QAAgFBX1dh+aHqz8gPaUNHY19U7HLERLh2TnahZ/bpopqfEjvuAJhBCGwxZapx3V83R/J9wJNU0degbT3/kF9h8ef4U3XVJsaLCXX37HA6HspOi9aX5U/Sl+VO0akedHnh9sz7xCW9e3bBPpZVNeuKauTIy48fkf0coe+njct31j41+/w0cDum7C2foxnMKFMZ82QAAACOlTj2hzUCLMvZfwMR/gUFMSCdN875c1pbtt+06pQAAwF6qG9u1oXcNmoPTnAVaFmGoYiJcOmZygmZlJ2lWTs9rXurEDGgCIbTBkKXEeS/aZIfQxrIs3fL8OlU2tHvtv+18Q99ZOOOw7z85L0V/v+FUPbN6t/7n1VKv0GFnbYs+9/gH+s2XT9CZM9MG+ZSJq6m9Sz/+5ya9/EmF31hmQpT+9wvH+S16CgAAgKO2WVK+pGkDjE/tfa00TXPoiz1iXCtIj1N8ZJiaOrolSQ1tXdpR26wZ6TykBgAADqlp6ugJZvqmOTugqsbhfw8cHd4T0Bxcf2ZWdqLy0uLkIqAZEKENhizVJ7Spax7+fIQj5W9r9mj51lqvfdefNn1Igc1BTqdDXzl5qs6YkapvPfOxSisb+8aaO7p1/Z/X6OeXz9JVJ+WOWN3jwad7DujG5z7xmjLvoEXFGXrgc7NtteYRAADAOPKRpIslnSzp8QDjJ/e+fjhmFcH2nE6Hjp86Se9tOdR8tbZsP6ENAAATWG1zhzZUNGhjeU/3zMaKBr+H449EZJizdw2apL6QJp+A5ogR2mDI0mw2PVptc4fuW1zqtW/e9GTdcVHhsD5vWmqsXv72qfrxPzfq+Y/K+/Z3eyz94O/rVb6/VTefN1MOx8T+IePxWPrd8h16+A1T3R7vdW0jw5z60SXFumb+lAn/7wkAAGAUvSTpbkmfNQwj2TTN+oMDhmG4JF3Xu/nXINQGGzsxQGjzhZOmBLEiAAAwVupbOvutP9OgDeUN2nuUAU1RVkLf+jOzcxI1Iy2OJRJGAKENhsy30ybYoc0jb23pa+2XeuZC/MXn5xzVD4aocJce+NxszcyI132vlsrql0n86p1t2t/apZ9+5pgJO79idWO7bnn+U63YVus3ZmTE61dfPJ41gAAAAEaZaZrrDcNYrJ5umxcNw/i8aZp1hmFEqafzpkiSKenlYNYJ+5k7dZLX9kdl+4NUCQAAGE37DwY0veHMhooGVRxoG/bnRfQGNLOyEzQ7u6eLpiAjTuEENKOC0AZDlhrvHdrUBHF6tO01zXp29R6vfbecN1O5yTFH/dkOh0NfOyNP2UnRuulv69TR7ekbe3pVmVo6uvXglbMnXGr8zuYq3frCetW3+P93/8rJU3XnxUWKCncFoTIAAIAJ6QZJKyQtlLTbMIxSSXmSJklqkHS5aZqeQd6PCWhObpKcDulgw/yOmhbVt3QqmWmNAQAIWQ2tXYcCmoqeLpo99UcR0LicKsyK16zsnvVnZuUkamZGPAHNGCK0wZD5ddo0Ba/T5tfvbpO739RcU1Ni9NVTpo3oOS6claX0hCj951/W6EBrV9/+lz6pUEtnt371xeMVGTb+Q4qObrf+57XN+tP7u/zGkmLC9cDnZuv8YzLHvjAAAIAJzDTNcsMw5kr6saTLJM2WdEDSs5LuNk1zazDrgz3FRYapKCtBm/YeWsfzk937dU5RRhCrAgAAQ9XQ1qVNFT3rzxzsotld77/e9FCFuxwyMuM1KztJs3qnOJuZEa+IMAKaYCK0wZCl+KxpU9fSIcuyxnztkj31rfrnur1e+2473xiVHyZzp07S375xir7yhw9V3S+kemNTlb72l4/026/MVUzE+P2/0bbqZn332U9UWtnoNzZ/erIeufo4ZSVGB6EyAACA8cs0zaWSDvtLtmmadZK+1/sPMCRzp07yCm0+KiO0AQDAjhrbu7SxokEbKxq0vrzndVfd8AOaMOfBgKane2ZWdqKMzPgJ8VB6qBm/3zZjxMVHhikizKnO3unC2rs8aul0Ky5ybC+jP6zY6dVlk5cWq4uOzRq18xmZ8XrhhlP05d9/qPL9h1oLl2+t1Vf/sFp/uO4kJUaHj9r5g8GyLP3f6t2655UStXd5z6rhcjp00zkF+vbCGXJN0LV9AAAAgFA1d+okPbWyrG97LevaAAAQdE3tXdq0t9EroNlR2zLsz3M5HZqZEa/Z2Yk6NidRs3sDGpY2CA2ENhgyh8OhtLhIr0Wraps6xjS0aeno1otry7323bAgX85RDg+mpsTqhRtO0TW//1Dbaw79wPyobL+++LtV+sv185Tms+ZPqKpv6dR//329lpRU+Y1lJ0XrV1883m8BUwAAAACh4YQp3r/Lf7rngLrcHuapBwBgjLR0dGvT3katLz/QE9JUNGhnbYss6/DvDcTldKggPa5verNjsxNVlJVAQBPCCG1wRFLjIrxDm+YOTUuNHbPz/+vTvWru6Paq57PHZY/JubMSo/X8N0/RV/+42ms6gZLKRl35xAd6+vr5mpISMya1jJYVW2t1y/PrvKaCO+iS2Vm67/JZ466rCAAAAJhIciZFKyMhUlWNPb/zd3R7VFrZqNk5//Bx+GoAACAASURBVJ+9+46P7Krv//8e9T6q20bavnu2SLter7sxmOaYGNwC2CR0zDeUEH5AQkK+SQzEIQlJIJBvgokJGLAxBAebYnoxGC8uu/Za2na2eJtmi1Zt1Ntofn/c0azuSKMyVeX1fDz8mL1t7pHnajRn3vdzTnmGWwYAwMLTN+QENE3N4Tlo/AEdu9ATd0CT5ZE2LClVfTigaaj1avOyMhXmEdAsJIQ2mJXqEnc1SWvPUFrP/+DTJ13Ld1xel9aJsapK8vWNd1+ld93/rHaPG0bgZFuf/uDeXfraO6/Q5uVlaWtPsgyOBPUvP7G674njE7YV5WXr4zdv1Rt21qZ9/iIAAAAAyeXxeHRJXbl+sv9iZf0LzQFCGwAAEtQ/FNSBs87wZk3+gJqanYBmNIGAZl1NSWT+mW21TgXNQp5fGw5eYcxKVUmea7m1Z2JFRqrYc93a579Y4eLxSHdevjJt5x/jLczV1951hd734HN63F6IrL/QPag7vvg7/ffbL9flqyvT3q542XPd+tC39urA2a4J27bXevW5O3ektZoKAAAAQGptq3WHNo2nO6WrVmWwRQAAzC8Dw0EdOOtU0IzNQXOkpTvugMYzFtD4nICmodarLcvLVJzmucQxN/CqY1YmVtqkL7T57l6/a/kl66tVV5mZ4ciK8nJ031sv0599+wV9d++ZyPqugRG9+UtP69/uuESvaViekbbN1HBwVPc+fkyf/+URDQfdf1E8Hun916/XB1+1gbGtAQAAgAVme1RVTWNzIEMtAQBg7hsYDurg2S5n/plwFc2Rlh4F40xoPB5pTXWxtvm84WHOyrVlRVla5w3H3MaVgFnJVGgTCoVc4YiktM1lE0tudpY++8ZLVFGUp/t3nYisHxwZ1XsffE4fefVG/ckr1s/JIcUOnu3Sn337BdfcPGNWeAv02Tsu0ZVrqzLQMgAAAACp1lDrdS0faelW7+AId/MCABa9geGg7LluNfoD2tccUKM/oCPnuzUSbwmNnIBmbHizep9XW1eUqbSAOaMRG5/IMCvVpVGhTXd65rR57lSn/J39keX8nCz9Xv2ytJx7KllZHt39ui2qKs7Tv/7ssGvbv/7ssI609OjTr9+mgty5MRnYwHBQ//n4Mf3nr45O+sfmpm3L9albG+Qt4g8HAAAAsFB5C3O1prpYx1t7JUmjIWmfP8CNWwCARWVwxAloxuafafIHZM8lFtCsrioKV884AU29z6syAhrMEqENZqU6ak6btt70VNr8dP851/KrNi+dMyWDHo9HH3jlBi0py9f/fWSf6439ey+c0eHz3fp/f3ip1i8pyWArpV8cPK+Pf3+/Trf3T9hWVZynT95Sr5u2ze0h3QAAAAAkx/ZabyS0kZwh0ghtAAAL1dDIqA6f744Mb9bk75Q91z1hyoDZWFlZpIZaZw6abT6vtvq88hYS0CBxc+Nbb8wbE4dHS0+lzc8OnHct3zgHqmyi3XH5Sq2sLNZ7H9yjzr7hyPpD57r1un//rT5xy1a9YWdt2odLO9nWq7/7wQH9/GDLpNtfu225PnHzVlVFvbYAAAAAFq5tteV6dNwQ1C80d2awNQAAJM9wcFTH2gd1pHVQDxxqUpM/oENnuzUUHI37OesqC9Xg86rBV64Gn1f1vjKVF+VNfyAQB0IbzMqE0KY79ZU2R1t69OK4O8Bysz263tSk/LzxuHpdlb77/mv1rq/u1tGWnsj6/uGgPvpwox5rPKu/v61etRVFKW/L+a4Bff4XR/StZ09PWtZZXZKve27dqhvrqa4BAAAAFpvtde55bRqbAxlqCQAA8RsOjurI+R7t8wfU6O9Uk79LB892aWgk/oDGV14YGd5sW61X9Su8qigmoEH6ENpgVsoLc5Wd5VEwHAJ0D45ocCSo/JzUzdkSXWVz1dqqOT1Z16qqYj3yvmv0fx/Zp++9cMa17deHL+iGz/5G77t+nd75kjUqykv+r2BzR5/uf/KEHnj6pAaGJ/6ByvJIb716tT706o2UbAIAAACL1JblXlff7lR7nzp6h/hSCgAwZ40ER3X0Qo8amwNOSNMc0MGzXRpMIKBZ4S2IDHHWUOtU0VTytxAZRmiDWcnK8qiiKNc1LFpn37CWlqUutPn1YfewXjdsWZqycyVLaUGuPnfnJbp2fZXu/t5+V3jSNxTUv/z0sO7fdVLvf/k6veGyuoTn5wmFQnruVIe+8uQJ/WjfuUjHK9plqyr0yVvqtWVFWULnAwAAADC/FeZla+PSUh082xVZ1+gP6GUb5+aoBgCAxSU4GtKxcEDT1NypJn9AB852TXqD8kwt9xY41TM+r+rDQU30qELAXEBog1mrKMpzhTZtPUNaWlaQknP1Do5oz8kO17rrzZKUnCvZPB6P7rh8pS5fXam//E6Tnjne7tre2jOoT3z/gP7lJ1a3XerTLZf4dOnKihk/f3A0pCZ/QL84eF7f3XtGp9r7Yu67srJIH7lho163bYWystI7pw4AAACAuWl7rdcd2pzuJLQBAKRdcDSkFy/0qClcPbPPH9D+M13qHw7G/ZxVhdnaUJ2vq01tZKizmlICGswPhDaYtegSwfbeoRh7Ju7p420aDl6sGllTXay6ytTPB5NMa2tK9M13X6Vv7T6tf/zRIQX6h13be4eCeuCpU3rgqVOqLM6TqczRhqp87Rz0a0lpgYrysjUyGlLXwLDae4Z0pKVHh893a/eJdnUNjEx57iWl+frTV27QHZfXKTc7K5U/JgAAAIB5Zlttub757OnI8gvMawMASLHR0ZBebO1Vk79TTc1davJ3av+ZLvUNxR/Q1JTma5vPe3GYM59Xbf7jkqTNmzckq+lA2hDaYNaqStyhTVvvYMrO9cSRVtfyS9ZXp+xcqZSV5dGbrlip329Yrv/6zTF9+bcnJr1boL13SL/rHdLvTvfpa3s7JnmmmdmwpER3XbdGt1ziU0Fu6oauAwAAADB/bav1upb3+QltAADJMzoa0vG23sj8M03+gPb7A+pNIKCpLsmPVM6MBTWTjQDU5k+k5UBmEdpg1iqK3KFNRworbX4bFdpct2F+hjZjvIW5+vPf26S3XbNaDzx1Sg89c0oXupMTeuXlZOmVm5bozitW6qUbquXxMAwaAAAAgNg2Li1VXnaWhoLO/ADnugZ0oXuQ4WMAALM2OhrSyfY+NfmdOWgam50hznoGpx4lZipVxXmu6pmGWq+WlRXwnRcWPEIbzFpVmoZHa+91hgIbk+WRrlpXlZJzpduS0gJ9+NUb9YFXrNfPD5zXj/ad069si7qnGe4sWnlRrq5dV62XmRrdWL9MZQW5KWoxAAAAgIUmLydLm5aXqnHcsGj7/AG9fNP8mEcUAJAZoVBIp9r7IvPPNDYHtO9MYNbfa41XWZwXqZ6p93m1rdar5V4CGixOhDaYteg5bdpSFNrsOekeHmzLirIFF0rkZmfpNQ3L9ZqG5RoJjurQuW79+NlDag4MqddTqEDfsPqHg8rySGWFuSoryFVdZZE2Li3RpmVl2rSsVFlZ/PECAAAAEJ96n9cV2jQR2gAAxgmFQjrd3q8mf0CN/k7t8wfU1ByYdp7lqZQX5UaqZ8aGOvOVFxLQAGGENpi1iqjQpqMvNaHN7hPtruXLVlWm5DxzRU52lup9XmV3lUmSNm/enOEWAQAAAFjo6le457VpYl4bAFi0QqGQmjucgKYpHM40+QMK9A/H/ZzewtzI0GZjQU1tBQENMBVCG8xaVbF7fOO2ntSENs9GhzarK1JyHgAAAABYrBp87tBmH6ENACwKoVBI/s7+yPBmTX5nqLOOvvgDmtKCnEhAs81XrgafV3WVBDTAbBHaYNaih0dLxZw2A8PBCXd4LfRKGwAAAABIt43LSpSb7dFwMCRJOhsYUGvPoKpL8qc5EgAwX4RCIZ0NDLiqZ5r8gYS+0yvNz1F9VAXNqqoiAhogCQhtMGvRoU0qhkdrbA5EOg2SVFtRqGXegqSfBwAAAAAWs/ycbJllpdrn74qs2+cP6HrDvDYAMB+FQiGd7xpUY7Mz/0xjuIKmNYGRckryc7R1RVlk/pltteVaVVnEPMtAihDaYNYqinNdyx19wxodDSX1jXr3yej5bBgaDQAAAABSocHnJbQBgHnqfNeAmpovhjONzQG19gzG/XzFednaGq6cGQtp1lQVE9AAaURog1nLz8lWaX6OugdHJEnB0ZAC/cOqiKrAScTuEx2u5ctWMzQaAAAAAKRCvc8r6XRkOXqoagDA3NDSPXBxeLPwY0t3/AFNUV62tq4oU4OvXA21zuOa6mJlE9AAGUVog7hUFOdFQhtJau8bSlpoEwqFtPd0p2vdZauptAEAAACAVKhf4XUtj6+6AQBkxoXuwUjljDMHTafOd8Uf0BTmZmvLirLI/DPbar1aW1NCQAPMQYQ2iEtlcZ5OtfdFltt7h7SuJjnPfTYw4JoIrTA3WxuWlCbnyQEAAAAALmZZqXKyPBoZdeYV9Xf2q713aMJ8pgCA1GjrGXRVzzT5AzobGIj7+fJzssIVNF411JarwefVuppi5WRnJbHVAFKF0AZxqYr68N6WwGRm0fZFleJvWVFG6g8AAAAAKVKQm62NS0t14Kx7XpuXbkzSnXkAgIj23iE1Reaf6dQ+f5f8nf1xP19+TpY2Ly+LzD+zrdar9TUlBDTAPEZog7hED4XW0ZfE0OaMuxS/fkVZ0p4bAAAAADBRg8/rCm2aCG0AIGGdfUORypmmZmeos0QCmrxwQNPgK9M2X7nqfV5tWFqiXAIaYEEhtEFcoittxg9nlqj9UZU2W33eGHsCAAAAAJKhvtarb+0+HVmOHgEBADC1QN+w9p1xgpl9/oAa/Z063Z5AQJOdpU3LSyNz0DTUerVxaSkBDbAIENogLtFjGyd1eLQz7s5B9KSYAAAAAFLHGHOVpH+QdIWkHkk/lvTn1tqWjDYMKdUQdbNcE6ENAMQU6B/W/nAFTWN4qLOTbX3THxhDbrZHZlmpGnzO/DPbwgFNXg4BDbAYEdogLqkaHq2le0DnuwYjy3nZWdqwtCQpzw0AAABgasaYnZJ+JekXkm6TtEJOgLNB0jUZbBpSbNOyUmVneRQcDUmSmjv61dE7NKHvBwCLTffAsPb5u9Tk71STv0tNzZ06kUBAk5M1FtA41TMNPq/MslLl52QnsdUA5jNCG8Qleni0tiQNj7Y/aj6bTcsp+wQAAADS6NOSGiXdYq0NSpIxpkvS54wx6621RzPaOqRMQW62Niwp0aFz3ZF1+84EdN0G5rUBsHj0DI5oX7hyZmyYsxdbe+N+vuwsjzYuLVWDr0wNteXaFg5oCnIJaADERmiDuEQPj9beOxhjz9mZMJ8NQ6MBAAAAaWGMqZJ0vaR3jQU2kmSt/Y6k72SqXUifBp/XHdr4uwhtACxYvYMj2n+mS03+gJqaO9UUDmhCofieLzvLow1LSlwVNJuXlxHQAJg1QhvEJTq06egdTsrz7vO7K22ix1UGAAAAkDLbJGVJajHGfF3SrZI8kh6V9AFrbUcmG4fUa6j16tt7miPL+5jXBsAC0Tc0ogNnuiLVM43+gI5d6Ik7oMnySBuWlKo+PP9Mvc+rLcvLVJhHQAMgcYQ2iEt0aNOWpEqbg+fcoc3WFWVJeV4AAABgMTPG5Ei6a4pduiWN3Yl1n6QfyQlt1suZ02a9MeYaa+1oShuKjKqPummuidAGwDzUPxTUgZYBHWkb1H1Ne7XPH9DRlh6NxhnQeDzS+pqSSPXMtlqngqYoj69VAaQG7y6IS0l+jvKyszQUdPpsA8Oj6hsaSegP1sBwUKfa3RO5bVhaklA7AQAAAEiSCiR9YYrtJyX9dfjfz1trxwKeXxhjApIeknSjpB+mronItC3Ly5Sd5VEw/M3mqfY+BfqG5S3KzXDLAGByA8NBHTjbpabmQHiYs4COtHQnFNCsqwkPcRYe5mzL8jIV5/MVKoD04R0HcfF4PKooztX5rosVNm09QyqqjP+SOtriLkutqyzkrgUAAAAgCay1PXKGOovJGHNL+J/RwcyPw487JtmGBaQgN1sblpS457U5E9C166sz2CoAcPQPOQHNPr8T0OzzB3SkpScSNMdjbU3xxYDG59VWn1clBDQAMox3IcStsjjfFdp09A2prrIo7uc72tLjWt6wpDTu5wIAAAAwa0fCj/lR68fKLPrT2BZkyNYVXldo0+QntAGQftEBTVNzQEcvJBbQrKkudlXQbF1RptICKgkBzD2ENohb1YR5bYYSer7D57tdywyNBgAAAKTVQUknJN1pjPk3a+3YN2OvDT8+kZFWIa0afGX63+cuLjOvDYBUcwKaQHiIs65wBU38Q5xJ0orSHK2vytdLttSp3udVvc+rMgIaAPMEoQ3iVhEV2rT3JBbaHImqtNlIpQ0AAACQNtbakDHmzyX9j6RvG2O+KMlI+pSkR621z2a0gUiLhlqva3k/oQ2AJEpFQLOysihSPbMtPMTZmRNHJUmbN69LUssBIH0IbRC36Eqbjr4EQxsqbQAAAAAZY7Ik/U7SOmttzHGpjDEVku6WdJuk5ZIuyJl/5pPW2pPxnNta+7Ax5mZJfyvp+5LaJX1R0l/H83yYf7Ys9yrLo8gXqCfa+tQ1MMwd6gBmbSygaWy+OAfN0ZaehAKaVVVFqh83B039Cq+8RRPfn84k0G4AyDRCG8StMonDow0MB3Wqvc+1bv0SQhsAAAAsSvdIukJSW6wdwoHNLkmbJHVLapS0VtI7Jd1ujHmZtbYxnpNba38g6QfxHIv5rzAvW+uXlOjw+YsjIezzB3TNOua1ARBb39CIDpzpcuafSUFAs83n1dYYAQ0ALDSENohb9PBoHQmENscuuP+Q11YUqiiPyxMAAACLhzHGI6dy5mMz2P0+OYHNDyXdaa3tNsYUSPqCpLdL+qYxpsFaG0xVe7Fw1fu8hDYAYooOaJqaAxO+15mt1VEVNFt9XnkLCWgALE58K464VRZFzWmTQGhzNHo+m6XMZwMAAIDFwxizTNK9km6Zwb6bJN0uqUfSW6y13ZJkrR0wxtwl6UpJm+UMm/Zwyho9hYMHD2bitOrv78/o+ReKmuwB1/KTB07rupr4+3vDwZA6+oPyeKTKwmxlZ3kSbWJMXAOQuA6SaWB4VMc6hnSkdVBH2wZ1pG1QzV3DCQU0K0pztL4qXxuq8rW+Kl/rq/JUkpcd3jokDV/QmRMXEhrijGsAXAOYz9cAoQ3iVlHsvuMhkTltDkfPZ8PQaAAAAFgkjDE3yAlXSiWdk/Q5Sf8wxSFvluSR9H1rbfv4DdbaoDHmK5I+LekOZSi0wfy2virftXy0ffZ9veBoSE+e6tUPbZcOtAxqOPwNb2GORw3LCnWTKdPlvkJ5PKkLcADMTv/wqI61D+loW3IDmrFwZkNVvta5AhoAwGQIbRC3qmL3B/lEKm2OnHdX2myg0gYAAACLxxZJJZK+LulDkhqm2f/K8OOuGNufCj9el3jT4rN58+aMnHfsTspMnX+hWLl2RB/9yRmFwl/U+ruGVbtmvUoLZjZU0dGWbn30Wy+oyR+YsK1/JKRnmvv0THOfLl9doU+/frvWVBcnre1cA5C4Dmaid3BEB852qanZmX+m0e8McRZKIKBZU10cHuKsTPVjc9BkaIgzrgFwDSDT18CePXviPpbQBnGbWGkzHPdzHW/tdS2vq0neh3YAAABgjntG0qXW2r2SZIyZbv/14cfjMbafDD8uNcaUWGt7YuwHTKo4P0frakpcw1jvPd2p6zbUTHvsrw616L0P7tHA8Oi0+z57okM3ff4J/ccfXqqXb1qSUJsBxNY7OKL94Tlo9oXnoUlmQNPgK9dWX5nKZhjsAgCmRmiDuFVEzWnT2Tek4Gho1uMTj46GdLK9z7VubTXDowEAAGBxsNbGqpiJZeyb87YY28cPmVYtZ+4bYFZ2rqxwhTa7jrVNG9r8ZP85vf/B5zQyyVhKVcV5GhkNKdDvvtmvbyiou762W59543bdcokvOY0HFrFUBDRrIwGN16mgIaABgJQitEHccrOzVFqQo+6BEUnSaEjq6h9WRXHeNEe6ne0a0NDIxbuwyoty5S3ijz8AAAAQQ2H4sT/G9vHrC2PsA0zpmvVV+tbu05HlXUdbp9z/aEuPPvytvRMCmxu3LtOHb9iojUtLFQqF1Ngc0Gd/fliP2wuRfYKjIX3kf15QaUGOXrFpaXJ/EGABGx/QNDV3qskf0IutvQQ0ADDPEdogIZXFeZHQRpLa+4ZmHdqciBoabXUVQ6MBAAAAUwhKyppi+/htCXx1h8Xs6nVVruUmf0CB/uFJ56foHRzRex/Yo96hYGSdxyN94uatestVq+TxeMLrPNpeV66vvP1yfXXXCX3yBwciE5yPjIb0gW88r+/+ybVav4Q5ToFo4+egaUpyBc222nBAs6JsxnNXAQBSh9AGCakoytPJtotDm7X3Dmnd9MMcu0TPZ5PMSSgBAACABahXUrmkghjb88f9O1Y1DjClJaUF2ri0RIfPO0OkjYakp15s0+9tXebaLxQK6WPfadKRFvcofJ+4eaveevXqSZ/b4/Ho7deuUWVJvj74zecjXzr3DgX1ngee0/f+5FoV5fF1BRavvqERHYhU0DgBzdFEA5qaYjWMr6AhoAGAOYtPQUhIZVRVTXvv0KyfI7rSZlVVUUJtAgAAABa4NjmhTWWM7eNLJC7E2AeY1jXrqiOhjST96lDLhNDm60+d1PdeOONad9sOn95y1appn//m7SvU3jOoj3//QGTd0ZYeffrHVh+/eWuCrQfmh/6hoA6cdcKZxvA8NEdbejTJ1FAz4vE4N8MS0ADA/EVog4RUFLlDm454QptxlToSlTYAAADANA5JWidpdYztY9+Wn7XW9sXYB5jW9aZG9+86EVn+6YHzuufWUeVkOyPwPXeqQ3/3gwOuY8zSUv39bfWRIdGm87ZrVquxOaDvPO+PrLt/1wndWL9MV62tmuJIYP5xApou7fMH1NjsBDRHWrqTFtA0+Lza6vOqJJ+v+wBgPuNdHAmpLHbfqdHeF09ow5w2AAAAwCzslnSTpKskfWGS7VeFH59OW4uwIF2zrlplBTnqCs9j2t47pF8eatENW5eprWdQ73/wOQ0HL37bXJKfoy+8+dJZDW3m8Xj0d7fWa/fJDp1qv5gx3v3d/XrsT18SCYiA+WYkOKrD53u093SnXjjdqReaO3WkpUfBeBMaMQcNACwWhDZISEVxYpU2wdGQTkVV2hDaAAAAAFP6jqS7Jd1qjKm01raPbTDGZEt6e3jxgQy0DQtIXk6Wbtq2XA89czqy7r9/e1wv3Vij93/jOZ0NDLj2/+fXb9PampJZn6c4P0f//PptuuO/noqss+e79dCzp2c0zBqQaaFQSP7O/khAs/d0p5r8AQ0Mj8b9nGvGApqxIc58ZSojoAGARYHQBgmpmjCnzfCsjj8b6NdQ8OKHmIqiXHmL+BACAAAAxGKtbTTGPCan2uZhY8wbrLVtxpgCOZU3myVZSY9ksp1YGP7wilWu0Obp4+3a+Xc/U+9Q0LXfu69bo9c0LI/7PFeurdLtO3yuYdI+81Orm7etoI+IOSfQP6zG5k7tPeVU0Ow9HVBrz2Dcz7e6qkj1Y0Oc1Xq1dYVX3kKuewBYrAhtkJAJc9rMcni0E61RVTbMZwMAAADMxHsk/VbSyyWdMsYclLRWUoWkgKTbrLXx3+INhDXUenXdhmo9caQ1si46sLlidaU+euOmhM/10Rs36Uf7zql/2Hn+jr5h3fubY/qLJDw3EK/gaEj2XLd2n2zX3lNOFc2Lrb3THxjDqnEBzbbwHDQENACA8QhtkJDKCZU2swttjjOfDQAAADBr1tpmY8xOSX8r6RZJ2yR1SnpI0t3W2iOZbB8Wlr++aYtu/n+/1eDIxBxww5ISffEtO5WbhLlnlnkL9P6Xr9O//PRwZN3Xdp3QH790rcqjbhgEUqV/KKi9pzu1+0S7nj3ZoedPdqh7cCSu56ouydMldeW6pK5c2+vKtc1XTuUYAGBahDZIyIQ5bWZZaXOyldAGAAAAGM9a+7gkzwz2a5P0wfB/QMqYZaX63J2X6IPf3OsKbhp8Xn3pbZdN6Bcm4l0vWav7d51Qa4/Tt+wdCuorT57Qh169MWnnAMZr7RnU7hMdkZBmvz+gkdHQrJ+nMDdbDT6vttd5dUldhbbXeeUrL5THM+3bOQAALoQ2SEhlUWKVNifbo4dHK0q4TQAAAACA5Lqxfrl+/mGvHn3er46+YV2yslyvqV+WlAqb8QrzsnXXdWv1jz86FFn3lSeP667r1qiUSdiRoFAopBdbe7XnRIeePdGu3Sc7dDyOoc6yPNLGpaXaXluuS1aWa3ttuTYuLVFOkn8fAACLE6ENElJWmKssjzR2E0r3wIiGg6Mz/uB+Oiq0qasktAEAAACAuaiuskgfeOWGlJ/nzVet0r2/PqbOvmFJUtfAiL7x9Cn98cvWpfzcWFiGRka170xAu0+0a/eJDu052aG2Wd5sKknlRbm6bFWldq6q0I6V5ar3eVWSz1dqAIDU4C8MEpKd5VF5UZ6rwqajd0hLygqmPTYUCsnf0e9aV1dBaAMAAAAAi1lJfo7eee0afeZnF+e2+fpTJ3XXdWuVncVQU4gt0D+s50516MfPtetAy4AOP3hi0rmYprOqqkiXrarU5asrdNnqCq2tLlEW1x4AIE0IbZCwiqJcV2jT3jez0Karf8Q1mV9+TpaqS5hcEgAAAAAWu7dctUr/8aujkS/cmzv69atDLXrVlqUZbhnmEn9nvzMXTbiSxp7vVmiW09FkZ3lUv6JMO8Mhzc7VFVpSOv13GgAApAqhDRJWWZynYxcujgE703ltTne4h0arrWCCPgAAAACAVFGcp5u3r9C39zRH1n31dycIbRaxkeCoDp3r1p6THdp9skN7TrTrTGBg1s9TnJetS1dVRCppLllZrqI8k54KVwAAIABJREFUvh4DAMwd/FVCwiqK3NUxHb3DMzquOWpotFqGRgMAAAAAhL316tWu0OaJI606dqFH62pKMtgqpMvYUGfPnXTmotl7ulN9Q8FZP8+ysgJdtrpCl6925qTZtKxUOTOchxcAgEwgtEHCqqKGNGvvm1mlTfMklTYAAAAAAEhSQ61XO1aW6/lTnZF1//PsaX3s9zdnsFWJCYVCOtLSo33+gI629Oh4a69aewbV0TesnoGLw4d7PFJpQY7Ki/JUUZSryuI8rfAWqrayUHUVRaqrLFJNSf6CmWdlJDiqIy09amoO6PnTTkhz+HzPrJ/H45HM0lKtLZO2Li3QLdfUy1fOqB4AgPmF0AYJm1hpM9PQhkobAAAAAEBsb7lqlSu0eeR5vz564yZlz6OwYmA4qF8eatFP9p/Tk0fb1NozOKPjzgam3l6Qm6VVlcVaXV2k1dXFWlNVrDXVzn81pflzNqgYCY7q6AUnoGnyO/8dONMVmb9oNvJzsrS9rlyXr3aGO7t0ZYW8Rbk6ePCgJL5nAADMT4Q2SFhlcVSlzYxDGyptAAAAAACx3Vi/TH/z6D71hofFauke1JNHW/XSjTUZbtn0zgb69aUnjuvbu0+ra1wVTbIMDI/Knu+WPd89YVtxXrZWhUOc1dVFWh35d7GqivPSEugMjgR1ur1PR8736EhL+L/z3XrxQq+GgrMPaCSpuiRPO8Pz0Vy6qkINPq/ychjqDACwsBDaIGETKm1mPDyau9KmrpI7YAAAAAAAFxXl5eg1Dcv18Li5bf73ueY5Hdp09g3pMz87rIeeOaXhYCgjbegdCurA2S4dONs1YVtpQY4rxKmtKFRFUZ68hbkqL8qVtzBX+TlZysnOUm62R7lZTigyFBzV4PCoBkeCGhwZVWffsNr7htTRO6SOviGd7xpUc0ef/J398nf0q6V7ZhVFsYwNdXbpqgpdtqpCO1dVaGVl0ZytIAIAIFkIbZCweCptQqHQJMOjUWkDAAAAAHC7/VKfK7T5yf5z6h4YVmlBbgZbNVEoFNL/PufXPY8dUGffcMz9ivOydfmaSm1aVqb1S0q0orxAFUV5KivM1diob8HRkAL9w+rsG1ZH35BauwfV3NGv0x19Ot3uPHbHWb3TPTASGZZsLqkpzVeDz6t6n1c7V1XokrpyeQvn1msMAEA6ENogYRXFs6+0CfQPq2fw4gfMgtwsVUU9DwAAAAAAV62pkq+8UP5O58a/geFR/WT/eb1+Z22GW3ZRoH9Yf/VIkx5rPDvp9qriPN18yQrd1LBc2+vKlZs9/ZBetRWxt4VCIXX0Det4a69OtPbqRFuvjrf2RpbHhpObq2pK81W/okwNteVq8HnV4PNqadncnYcHAIB0IrRBwiqjh0frjX1H0ZiJVTaUOAMAAAAAJsrK8ujWHSv0H786Fln3o6azcya0OdHaq3fc/6yOt/ZO2FZXWaj3Xb9et1/qU35OdtLO6fF4VFmcp8piZ46X8UKhkC70DOpEa59OtPbqeJsT5Bxv7dXJtj71D6cn0PF4pKWlBVq/pETrl5Ro49JSbVhaovU1JRNu/gQAABcR2iBhFcXucuW23unHrW3u6HMtMzQaAAAAACCWmxrcoc0TR1rnxBBpe0526K6vPquOqOHQCnKz9IFXbNC7XrJGBbnJC2tmwuPxaElpgZaUFuiKNZWubaFQSOe7Bp2KnHCY09I9GB6KbUid/cPq6h/R0EhQI6MhjQRDGgqOSpLyc7KUl5Ol/Jxs5edkqawwV5XFuSovylNlkRMg+SoKVVteqNqKIi3zFigvZ/qKIgAA4EZog4SV5OcoN9sTmWBxYHhU/UNBFebF/mDKfDYAAAAAgJnavLxUq6uKdKLNuQFwKDiqXx5q0S2X+DLWpudPdeit//30hKHItiwv0+fftEPrl5RkqGWxeTweLfMWaJm3QFevq5rRMaFQKHIsAABIPW55QMI8Ho8qooZIa59mXpvT7e5Km7qKoqS3CwAAAACwMHg8Ht1Yv9y17odNk88fkw77/AG97cvPTAhsbtvh0yPvv2ZOBjbx8ng8BDYAAKQRoQ2SorI4el6bqUObyea0AQAAAAAglt9vWOZaftxeUO/gSNrbcS4woHfc/6y6Btzn/sAr1uszb9ye1LlrAADA4kNog6SIDm3aZx3aMDwaAAAAACC2Bp9XvvKLfcfBkVH9+vCFtLZhYDioP/76bl3ods/l+qev3KCP3GCoSAEAAAkjtEFSVERX2kwxPFooFFJzh3t4NEIbAAAAAMBUnCHS3NU2vzzUktY2/M2j+/RCc8C17l0vWaMPvWpDWtsBAAAWLkIbJEVl9Jw2U1TadPYNu8b9LczNnlCpAwAAAABAtFduWuJafty2aHQ0lJZz/6jprL69p9m17hWbluivfn8zFTYAACBpcjLdgGQzxuRI+hNJ75a0WtI5Sd+VdLe1tjuDTVvQJlTaTBHaTDY0Gh9wAQAAAADTuWx1pUryc9QTnsumtWdITf6AtteVp/S8LV0D+qtHmlzr1tYU69/uvETZWfRnAQBA8izESptPSfq0pIcl3SzpM5LeJumnxpiF+PPOCZVFua7l9imGR2NoNAAAAABAPPJysnTdhmrXunQMkfZXj+xTR99wZDk326N/f9MOlRXkTnEUAADA7C2oEMMYUyTp/5P0L9bau621v7DW/oek90m6StL1mWzfQjax0mY4xp6Sv9NdaeMjtAEAAAAAzNDLo4ZI+5VNbWjzy0Pn9fOD513rPvTqjdq6wpvS8wIAgMVpQYU2kiok3Sfp21HrD4UfV6S3OYtH9Jw0U81pEz08mq+8KCVtAgAAAAAsPC837tCmsTmglu6BlJxrYDioT3z/gGvdjpXl+uOXrkvJ+QAAABbUnDbWWr+k90+y6dbw4740NmdRqSiKqrSZYng0Km0AAAAAAPGqKc3X9lqvXmgORNb99kirbr+0Nunn+u/fHtfJtotDfGd5pHturWceGwAAkDLzJrQxxuRIumuKXbqttQ9OctzVkv5S0g+stXtT1b7FLrrSpm2KShv/hEobQhsAAAAAwMy9bGONO7Q5mvzQpqN3SPc+fsy17o+uXMWwaAAAIKXmTWgjqUDSF6bYflKSK7Qxxlwv6buSjkt6e6oahomhTUfvkEKhkDyeiXcfRVfa1FJpAwAAAACYhWvXV+vzvzwaWX7yaKtCoVBSz/FfT7yo7sGRyHJ5Ua4+csPGpJ4DAAAg2rwJbay1PZJmXH9sjHm7pC9K2i/pNdbathQ1DZIKcrNVlJetvqGgJGlkNKTuwRGVFeS69usZHFGgfziynJedpZqS/LS2FQAAAAAwv+1YWaHC3Gz1Dzt90PNdgzp2oSdpz3+he1D3P3nCte69L1un8qihwQEAAJItK9MNSAVjzCclfUXSryS91Fp7PsNNWhQmzGszyRBp0UOjLS8vUBZjAQMAAAAAZiEvJ0tXrKl0rfvtkdakPf8Xf30sEghJUnVJvt569eqkPT8AAEAsCy60Mcb8haS/kXS/pNeGK3SQBtFDpLVPFtp09rmWmc8GAAAAABCPl6yvdi0/eSw5A2wE+of10DOnXOve//J1KszLTsrzAwAATGXeDI82E8aYDZLukXRI0n9JuswYM36XY9baC5lo22JQET2vTd/0lTaENgAAAMDcEZ4X9FdT7PJxa+0n0tQcYErXRoU2Tx1rU3BnkbITHM3hoWdOqXfoYpVNTWm+3nTFyoSeEwAAYKZSEtoYY7Ik/U7SOmtt9RT7VUi6W9JtkpZLuiDpx5I+aa09Gcepb5PzM22StGuS7e+W9KU4nhczUFnknr+mrWdiaNPcGRXaVBDaAAAAAHPIc5KunmT9PZIul/RQepsDxLZpWamqivPUFh7loXtwRIfbBrW5piDu5xwaGZ0wl83brl6lglyqbAAAQHqkqtLmHklXSIpZmxwObHbJCVi6JTVKWivpnZJuN8a8zFrbOJuTWms/LenT8TYaiaksznctt81gThsqbQAAAIC5w1rbJemp8euMMTdLeqWkN1hrD2ekYcAksrI8umZ9tb7/wpnIur1n+hMKbR5rOqNzXQOR5YLcLP3RlasSaicAAMBsJHVOG2OMxxjzcUkfm8Hu98kJbH4oyWetvUzSCjlz0ZRL+qYxhltZ5pGaUndo09I1OGEfP5U2AAAAwLxhjCmU9O+SHrPWPpzp9gDRrl1X5Vp+7mx/jD1n5qu73IN+vGFn3YShwAEAAFIpaZU2xphlku6VdMsM9t0k6XZJPZLeYq3tliRr7YAx5i5JV0raLGe4s4x0DA4ePJiJ06q/vz+j50/ESE+3a/mov0UHD7rHEj55wb3PQNsZHRximqHx5vM1gOTgGgDXALgGIHEdYM74oCSfnEobYM6Jntfm0IUBDYyMxvVcB892ae/pTte6d75kTdxtAwAAiEdSQhtjzA1ywpVSSeckfU7SP0xxyJsleSR931rbPn6DtTZojPmKnGHO7lCGQhvMXmWhuzCqoz/oWh4KhtQ+bp1HUnVRqkboAwAAADCeMSZH0l1T7NJtrX1w3P55ckKbb1prj6a6fUA86iqLVFdZqNPtTtA9MiodbBnQjjie65vPnHItX7u+Smuqi5PQSgAAgJlL1jfmWySVSPq6pA9Japhm/yvDj7tibB8bQ/m6xJsWn82bN2fkvGN3Umbq/InIquiWfnYustwbzHb9HCdaeyUdjywvLSvQtvot6WzivDCfrwEkB9cAuAbANQAp89fBnj17MnJepFSBpC9Msf2kpAfHLb9e0jJJ/5zKRgGJumZttb7Vfjqy/MK5Af3hLJ+jfyioR573u9a96YqVSWgdAADA7CQrtHlG0qXW2r2SZIyZbv/14cfjMbaPDSK71BhTYq3tSbyJSLUJc9p0u+e0YT4bAAAAIHPC/SrPtDte9HpJ+621L6SoSUBSXL2uSt/aPT60mf28Nj9sOquugZHIclVxnm7Ysiwp7QMAAJiNpIQ21tpYFTOx1IQf22JsHz9kWrWcuW8wx1UU5So326PhYEiS1DM4or6hERXlOZeZvyMqtCkntAEAAADmImNMrqTfk/RPmW4LMJ2r11W5lg+3DqpncEQl+TP/yuN/n2t2Lf/Bzlrl5WQlpX0AAACzkalPIGP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"text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 264, "width": 822 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "error2 = plot_error(M, N, b, x0, w=0.1, n=1000) \n", "# w 5 fois plus petit donc je fais 5 fois plus d'itération pour \"avancer\" d'autant (grosso modo)" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "The oscillations are gone! But we paid a high price since we had to do 5 times more iterations.\n", "\n", "It can be seen that in both cases the relative error (between 2 successive x) does not give the correct minimum.\n", "So stopping an iterative algorithm based on relative error is not always the most efficient.\n", "\n", "Let's see what the residue gives:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 218\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 264, "width": 376 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = x0 \n", "w = 0.1\n", "residu = []\n", "for i in range(1000):\n", " x = w * (N @ x + b) / M + (1-w) * x\n", " residu.append(np.square(A @ x - b).sum())\n", "plt.plot(range(len(residu)), residu)\n", "plt.title('Résidu')\n", "plt.semilogy();\n", "print(\"Itération du minimum :\", np.argmin(residu))" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "### Exercise 20.1\n", "\n", "How is it that the curve of the residual has the same shape as that of the relative error?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Réponse**\n", "\n", "..." ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "#### New Matrix" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 153 153\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 264, "width": 827 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "A = mk_A(123)\n", "b = A.sum(axis=1) \n", "\n", "M = np.diag(A) \n", "N = np.diag(M) - A \n", "\n", "x0 = np.random.random(4)\n", "\n", "plot_error(M, N, b, x0, w=0.5)" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "Here is a case with perfect convergence. Note that we stopped at iteration 150 when we passed\n", "below machine precision (following values ​​must be 0 and as log(0) = $-\\infty$,\n", "matplolib does not display them).\n", "\n", "Let us nevertheless verify that the basic Jacobi method would not have\n", "it does not work :" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x_0 = [0.398 0.738 0.182 0.175]\n", "x_1 = [4.127 1.837 1.029 2.203]\n", "x_2 = [-0.526 -0.195 0.907 -0.906]\n", "x_3 = [3.427 1.782 1.133 3.759]\n", "x_4 = [-1.56 -0.204 0.913 -0.86 ]\n", "x_5 = [3.395 2.118 1.134 3.775]\n", "x_6 = [-1.907 -0.196 0.876 -1.616]\n", "x_7 = [3.877 2.342 1.133 3.784]\n", "x_8 = [-2.133 -0.357 0.851 -2.12 ]\n", "x_9 = [4.364 2.49 1.151 4.165]\n", "x_10 = [-2.525 -0.574 0.834 -2.467]\n", "x_11 = [4.804 2.671 1.175 4.665]\n", "x_12 = [-3.027 -0.792 0.814 -2.89 ]\n", "x_13 = [5.293 2.898 1.199 5.17 ]\n", "x_14 = [-3.581 -1.027 0.789 -3.421]\n", "x_15 = [5.87 3.159 1.225 5.719]\n", "x_16 = [-4.194 -1.298 0.76 -4.026]\n", "x_17 = [6.531 3.45 1.255 6.35 ]\n", "x_18 = [-4.891 -1.608 0.728 -4.704]\n", "x_19 = [7.277 3.779 1.29 7.073]\n" ] } ], "source": [ "x = x0\n", "for i in range(20):\n", " print(f\"x_{i} = {x}\")\n", " x = (N @ x + b) / M" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "The basic Jacobi diverges, so it is indeed inertia that made it possible to converge." ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "#### New Matrix" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 0 0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 264, "width": 827 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "A = mk_A(16)\n", "b = A.sum(axis=1) \n", "\n", "M = np.diag(A) \n", "N = np.diag(M) - A \n", "\n", "x0 = np.random.random(4)\n", "\n", "plot_error(M, N, b, x0, w=0.5)" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "Direct divergence but if we reduce $w$ we see that we are in the 1st case:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 32 38\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 264, "width": 817 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_error(M, N, b, x0, w=0.01)" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "But it's still not good. At best we are not even at $10^{-1}$." ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "## Normalize\n", "\n", "This last remark only makes sense if we know what we are comparing to.\n", "\n", "* If the solution is a billion, having an error of 0.1 is fine.\n", "* If the solution is 0.01, an error of 0.1 is huge.\n", "\n", "We can therefore only judge an error according to a reference. If we know the exact solution, then\n", "it is the right reference.\n", "\n", "$$\n", "\\frac{||{\\bf x}^k - {\\bf x}||}{||{\\bf x}||}\n", "$$\n", "\n", "Similarly, the error between 2 successive iterations only makes sense when normalized.\n", "If $||{\\bf x}^k|| = 1 000 000$ then $||{\\bf x}^k - {\\bf x}^{k-1}|| = 1$ is fine but it is not\n", "if $||{\\bf x}^k|| = 1$.\n", "\n", "Also we compare the difference between 2 iterations with the current **x** or the previous one:\n", "\n", "$$\n", "\\frac{||{\\bf x}^{k+1} - {\\bf x}^k||}{||{\\bf x}^k||}\n", "$$\n", "\n", "Let's do that and look at our previous results." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def plot_error_normalized(M, N, b, x0, w, n=200):\n", " x = x0 \n", " error = [np.square(x - np.ones(4)).sum()]\n", " error2 = []\n", " for i in range(n):\n", " old_x = x\n", " x = w * (N @ x + b) / M + (1-w) * x\n", " error.append((np.square(x - np.ones(4)).sum())/4) # normalisé par rapport à la solution\n", " error2.append((np.square(x - old_x).sum())/np.square(x).sum()) # normalisé par rapport à x\n", " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,4))\n", " ax1.plot(range(len(error)), error)\n", " ax1.set_title('Erreur absolue normalisée')\n", " ax1.semilogy();\n", " ax2.plot(range(len(error2)), error2)\n", " ax2.set_title('Erreur relative normalisée')\n", " ax2.semilogy()\n", " print(\"Itération du minimum :\",np.argmin(error), np.argmin(error2))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 60 70\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 264, "width": 821 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "A = mk_A(799)\n", "b = A.sum(axis=1) \n", "\n", "M = np.diag(A) \n", "N = np.diag(M) - A \n", "\n", "x0 = np.random.random(4)\n", "plot_error(M, N, b, x0, w=0.1, n=1000) " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 60 70\n" ] }, { "data": { "image/png": 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T73i6gz6fbpblkZkLq9JsF1V3rQu8p5fnMuiqIMHx1c3ZwD6NARuAqiPzLsqoKCip9ysv4e5PagjY1Pb1L7pPyqGMTqt3NOVEG0pN4qadg+r+Wsr3csDHe2nLsyyaFdWbO4Cjm5T0+gVltFvNzxoCNjWnUwIy0B3cqBmqz0F/1W+naRCo+jz9jhLgu7nqBAIQERsCh1U3b6T8yNAjIytLHem30/06fKphlUPq2vLtJj8Y1LZzOd0jK5enScaOJEkaEexjLZ57WLI+VqPv1gVsGg3H+deb665/oknApraP0ymBFShZIKsPYB+9qkpr1YJ2K1LmhmnmbXXXz2xYdjzdA8je1BiwqdvPxyjZ+QBvirpI02L6fot+5f0sOpCqsf90ON0/5l+cmZ9ocYyfS/d7Ow74TB/tObE/jaaUnD6iMfsnM68Abq6768qGgE19ux6rbi7Sf4oyx8+u1c3rWgU4s5TY+1rdXUPRf7q4xet6I2Uw282UOYGeLykXZQ6fWj/1YeCAhoBNbRtPUDLDZlV3HVtl6NS2M5K/x6QRwaCNpGb+1uQH3lb+2suyt9Rd/37LtYDMvIBSKgrgDdWP80NpIM+xmasp5bD2pOcPuI3q5zhZpuVa5eSwMQug3ncoqexQJmKsVyt1tkpEvLfZgzPz7sxcLzN3q08rrkpM1ebyeAr4di9tADi57nqz2s5DaXvgBdX132cvkzJm5jOUk00oo4ResYT7/nUvy+onuV+1YVltFNZC4It97OPzlBFpAAf2st711fPrj19mkwkwq/vurburaTm2qnNamyunMfA1FJ+Dgagv8fehiFi+2UqZ+cbMfFFmHpiLlmV7E92j3H6YvUzsmpn/pGRUAbw0Iuo74/3+rqMEwWrvx769rShJkkYV+1gDNyivA4t//vUhYGtKtk1vZcmglJGqGaxz3Zr6QNhbWqxTC9o8yaJZK6vT/eP4PzPz/1rtpPrRvPZajqE7y2hxLWn/CUr/qDffpruv8roocxA1c19m3tPHtmouahaIqNxZd723cta1flZj/+k/lPLlL6MEp3oz1P2nwyNizWYrZeb7MnObzNynoc/9WkrJa4CfZ+asJg+vbeNBuo/FDVh0Dp2R/D0mjQiWR5M6368oqcMDcXcfy5uO6lqMdXetu75RRDQGGho9TEl7XYFSM/aWAbRjoAbyHHuoTmjvo0Ud4mo0/1RKTdv6yTPHNVu/cmWzUf51+3wiIm6hnOysFxHrZXf5rF9QJrKHkip+JKVe7x+BqxpHCTXYju6TwKuy77lGrqMEd1YEXhIR43r7sXuQ1R9TY/txTE2su74Ti2bEDMQzfZzk15/UT6hdqTpJm1Y3M1uXO6ut8GBVjmwbynu8fovA1ECO3x4j6erUt/uOXtZ7htKZWuT4HaLPwUBcQMk6WobSGb03Ii6kpPr/uR+lL+qPpzX6cTzVj67ckTL3T+N2tqzKU/TmYUpnbcuIWK63zo4kSWoL+1iLZ4n6WAPc3pCff1X9olto8ZpFxBqUvtTLWHQy+sE6162146aqtPGLgL0jYoX6rJ+IeDHdA9t+1VA+7aV115/rx/GyUt31nVqu1T8397Ksaf+pskt1OYvuQVNNZebsqhzZGyl9vx2AK5qs2o7+EzQMlq+Cmg/SHYRYRERMoJREewmLDpAcrGPqCkrgaF3KnDx3RsTvKSXILs3MvuZZqv/cLdeP46l+8OBOdGdyjeTvMWlEMGgjdb7bcmA1cfvjib5X6de669ddH2j91TUY2n/EA3mOvYqIjSkT3m9LmZRwE0qHoNkIkDFN7qu5q5dlNffQPUJlbcqEgVAydPagu+7w1tXfccCzEXE5JYhzXmb+t2Gba9Vd/3dfDcjMroi4G3gh5cR4ZbrTv4da/TG1Hz0zjnqzxhLst9VIq5r6k9H6931Ar23lTrrT6Neku8RbvYEcvzP6uV5vmTt9jpgcxM9Bv2XmYxFxKGXCykmUY/Ed1V9XREyjlEY7t0V96/rj6dNNlvdmDXi+REB953YgP/CMoZTPMGgjSdLIYh9r8QxaH6u37Q33+Vc1sn9PyvwcUymDsjahZxZF/T4G208o/cDJwAGUOTNr6gdHNZZGqz9eXkqZJ7W/lqT/BL33oZr2n6rM+dqAwrublcxqoj77pWnmCCOz/7QWJdj0Ikr/aVNKRkqz32oHq/80LyIOpvSRVqRUpDio+iMibqfMB3oecEWTzLn64+k9DKxcev3xNJK/x6QRwZQySc20zPYY4LorLkEbVliCx/bHQJ5jUxGxUkT8jHKS+A1KevOelBOtscA8ygR+F/Zzk8/2Y536E8Pn5+ao5pt5MyVocwXdc29AOel9PWXivwci4n+rkmg19a91f0tu1a+3XD8fMxjadUz1KC+2GPsczNd2IMfvvL5XWXxD8DkYkMw8jxIoOoOSAVYzhjLy8Tjg+oi4KiK2bHj4YBxPS7KN+u1IkqTRzT7WAPVShWDYzr8iYjfKD8R/pswRejAlm6MWsJlBycy6s+kGBs/P6T6vf760VDVPSG3unTsy86qGx7XteGlWonmA+xyt/adJEfF1yuC871PmbHkVJRA4ntKX/welmsagq46RLYFvAo0DOl8AfJhSmvDmau6ZeoN1PI3k7zFpRDDTRtJQepbuf6hTGtK0h8rkYdgHETEZuJzyozDAc5QTm38At1HSr2/KzOci4t30rx5wf9pefxLabMK/XwO/rlL1XwO8nDKXS20kywTgI8BqwKHVffWjzJbtRxugTOJZ09+T6YFo9VrUB7bel5nfHYJ9D6aR+NoOmiH6HAxYZt4OvDMi3kMpE/gqyrG/A92lBHYBLouIF2bmQ9V99cfT1My8bTF2X7+NRzJzrZZrSpIkLblR28cagGE5/4qIPSjlpmsD3h6gnPveDCTlPPfOat0r6C6LPOgy89GqjNU+wCsiYo2qgsIr6M4u+WmTh9a/Vl/KzGOHqo2DZLT3n8YA59M9p+x8ygC36yl9p+nAtMycFRGvoPUcRkukmm/mQxHxEUrZslcDe1H6TLXjfUvgjxGxS2ZOq+6rP55el5mXLGYT2vE9JnUUgzaShtLDdP8jXpfFH31UnzXS1/fWSn0sHywfpvuH6huAN9b9ENyoVdp8o/X6sc5m1WUXzctmAVCdwP+0+iMitgbeTxnFA/D2iDg5MxOob/dm9KEqD7BJdfM5+l8abSDvY6uRNw/XXV+3n/ttpwG9tpX6eti9zoEzAgzF52CxZeY84C/VHxGxCnAgZQLT1Sip9B8EPlk95GFKlg6U42lxgjZPUj4Hk4FVI2KynQ5JkjSERnMfq7+G6/zrNLp/wD4ZOLGXuTyH/FyXUiJtH8qgpAMp7XtrtayL5kGbjuo/ZeZTEVGbs3LjiBjbjxJpndR/OpjugM29wKurAWjNDEf/aSFwdfX32ar04Bso/aeNKe/DsXQfZ4N1PA3W95g0ahm0kTSUrqF7QsSX08s/4mrEyY8oqcj3AKdlZq3ubH0qc8tU2IhYhu5gwlDbp+760b38UA2wfd313mrR7tjbDiNiHUoNZSiT2j9R3b8q5cTqBZT62z1O1jPzZuD9EbEmpQYylDlpEvgX3Z2eXSNiSjXpZiu70J3xc2OTOret9Pd93JzWo/nqJ6J8OfCZ3nYYEe+gnBTfA1ycmX/vV0sHSWb+t5r/Z+PSnFgvM1t2JCJifcrEk1BGDfZ2XI0EQ/E56LeIeD1l/p/1MvODjcsz83Hg9Ih4GLiguvtFdatcQxlVBuV4+nMf+zuFEvy5B/hJZt5bzfF0HaXG+XhKps+lvWxjCqVD/d9qO19dzNIRkiRp6TSa+1j9MhznX1WfpNb3ugc4vlW/p/qhuz5wMBRz2gBcBDwOrALsGxE/pHuOz79m5j1NHlPff9qjryBIRLwGeDflOf81My8ejIYP0LWUrI/lgJ2BxpJvz6uOz1oJr/mULKiRrL7/9NleAjYwNP2n3YEXU/qcH8vMReZ2qm7/MiJuAWrZNY39p9o8Ni8HftjH/j5OGSR3D3B2Zt5Ut53B+B6TRi3ntJE0lM6tu/7RqpRSK/sChwFHAB8Cnq5bVl9ndYdetnEQpfzXcFit7vrMVitFxAsoz62mt/ZtGBG9lY86mu5ST/WTbS5Hmc/jk8AnqpOaVuqzYmYCZOZcoHYyvgJwZC+Ph+4sBYDf9rFuvf6+j72lgF9F9+iel0bEnq1WrE7gv1ht7ziGZ/RbM+dVl2Mpo5R6cyzd/5sH8tq2y1B8DgbiaMp7/IGI6C3o2eO4r5xXd/09EbF6qw1ExIuAjwPvBD7VsJ3677rj+vgM/n+UkZHvAw42YCNJkgZoNPexBmKoz7/qz3Of6WOg2ofpzsiB5q9X7fGL/Ttc1W+rzXOyF2UwXq1CwZktHnM38M/q5vrAO1ptv6qo8AXgTZTz7I0Xt61LqP4c/ZMt1yqOpDvo+JfMbNknGSH6239ajdLvqBmsz+A7ga9QAi+v72W9Vv2niykDPgEOqvp5TVWDTk+ilGX/DN2fARi87zFp1DJoI2koXQjcWF3fgjJio0dd2ojYljJyoubUhrTzf9A9GeBLI+INTbaxE+XkY7jcVXf9fc1WqEqSXUhJKa7pqx70D6vHNW7rfygnKABPAN+pLcvMe+keQbUVZYLMZu0JSjo2lBqy19Yt/iJQe81PjogDaBARYyPii3Sf3D0ADGROmfpRXgdGRI/OYfXetgxsVJORnlp31y9bbGcScDawdnXXNOB3A2jrYPoa3bWV3x8RH2i2UkQcSfexNBP40jC0bUkN1eegv+qDl6dHRI+yetXkrPWdvctqVzLzxqptUDpQv606SI3bWJ/Seaz9GPD9Koun5od0l8LbC/h2RPTIZo6IV1I+azVfaPG8JEmSWhnNfayBGOrzr7vp/pF5ajW/TQ8R8X7gxIa7m53r1voDSzqQ7CfV5US6+0XPAuf08piT665/s8qmWUQVsPku3VkVjwA/XrKmLrYf0f3e7h0RX6zat4iqz/q56uZ8er4PI1F9/+k9LZ7XBpSsqvq5moai//TViGhVor2+okV9/+m/wOnVzYnABRHRIxMvIlaiVDqYUt11UVX9o2awvsekUcvyaFLn2yIi9ut7tR7uy8x/DHpr6lRp64dQggMrUkZI3B4RPwZuoWSI7AK8ne6RI38Fvt6wnaci4peUERoA50bET4ArgEmUdNraCLBrKRPpDbUf0F2L9l0RsRlltMgjlHkzXk4pWdb4PdtqrhaAR4HVgWsj4keU5zKJkvJe60QtBN6ZmY82PPZoyms3FjihKht1LnAfZWLG7SijU2o/nJ+SmTNqD87M6yPiU5QOzSTKa/x7ysnUDGBDyvtUm/9jHvC2gaQlZ+b0aoLO3ap9XB4Rp1PmQlmBEgzam3LC/Q8WTQev9zXglcDrKJNuXhMRv6bMYzKbkmb9LspIMiidmHf0oxbykMjMByLiCOBnlB/9vxkRb6YElR6kBJbeBLysekgX8N7MvKvZ9kaYofgcDMSPgQ8AW1OOzbuqz85tlBFgG1FGE9ZGgN1Gz87n4ZSJP9enfB/dUX1H3UDpiLyIcjwtW7eNRUb8ZeYz1Xt6afWY9wGvjIgzgTuAVSk/JhxId+DnZ5lZP8JMkiSNHPax2tPH6rehPv/KzIcj4mLKuexY4A/Veeb1wFxKybiDKYPmGjU7172fUm5t64j4EvB/wIzMvKzJur216/8iYnq1rdoP7r/pLcMkM8+LiO9RMo6WAy6JiAspg9qeoGTUvIPucnALgMMy85lm2xtqmflsw3v7CeD1EXEWpTzWKsAbWTRT5DOZefVwt3Ux/IjyPowBXgX8IyJ+ShkQuSrls3sg3cGOmkHpP2XmHyLij5QS0esCt0XEGcBNlAyW9YBD6M6+ewT4asNmPkHpu76IUmbt5uo5XEX5vWIrSh9r1bptLDLAb7C+x6TRzKCN1PkOqf4G6ieUH/GHVGZmRLyUMvJnKrAOpbRQM+cDh7ZIV/8w5YfXnSgnbkdUfzXzKJkokxiGDkVmnhsR/wscVd21e/XX6B5K6vHvKaXNXtjLZs+knLAcTvkhujEjYybl5LlH2azMvLLKxvk+5QTvJdVfo4WUGs6fbbKNL0XELMqIrSmUoMjrmmzjbuDNmXldL9LAIIUAACAASURBVM+llUOBPwGbUU7EjmpYPouSsr0nLYI2mbkwIvYHvkWptzyeMjHiW5usfj+lBMKNTZYNm8z8RUTMoYwIXIlSd3nXJqs+Rgkw/X4427e4huhzMJD9z42IvSkdzq0oHbiPt1j9BmD/xklqq3mHdgF+DbyU8v40Hpc1VwIHNesUZ+bfIuIVlNFr61Lqmn+ucb3K9+j5+ZYkSSOHfaxiWPtYAzUM519HUAaGTaW8Bk0zyynnkf+gO6PnhdRlJ1TOAv5fdf2Y6vJ6mvfZ+vITFs0e+kmrFeu8jzJI8FhK/+mN1V+jxymDBC9ZjHYNmrr39leU43sbmlcieBY4MjPPGMbmLbYq6PZRSgbbWMrgyu2arPoY5XeB0yiD/Lbpaz6iAXgz5Xthd8rAtFbl0f8NHJiZjzQ8h9kRsRfl94t9KL8dvIfuuW7q3Urpg/WY13UQv8ekUcnyaJKGXGbeSjnJOhT4DeWH9Oeqv7soGQivysz9GyfCq9vGE5Qfud9NOXGeQZk8827KaP8dMvObQ/xUGtv0UUqWwfmU9O15lEyP+yg/Ih8ObJWZl1J+7AXYtkrxbbXNIygjti4Hnqy2dxvwZSAy87xeHnsW5WTn85QRK49TslaepEzI+HXgRZl5dC/b+DYloHIyZfTX45TX+R7gEsp7uNViBmxqpdy2AT4KXF33HG+nZNBsk5m9pfbXtjOneq22B75NGY3zFOX5Pko5Rj4EbJmZ17Tc0DCq3ruNKfPrXEk5EZ9HGVV1GaUjtVmnBGxqhuJzMMD930cZ5fVuSo3lByjH7HPAvZTMn7cCO2bm/S228Z/M3JUywuvnlO+VZ6vt3E8pjXYgsHtjp6VhO1dSPj/vpwSoHqSMxHwWSMp31U6Z+V47HJIkaUmM1j7WQA3l+VdmPkyZtP0YSv/qaUoWytOUzIQfAS/LzEMogZtaObW3N9ncF4CPUX7Enk15nxa35NVZlMF4AP8B/tyP59KVmZ+hlKI6lRJkeoLSf3oC+Dslmzwy84LFbNegqntvP0jJunmE0td4iJLVcQywSacEbGoy82uUwWI/p/SZ5lI+dw9SBjgeBWxeDdb8Y/WwlSlVKQZj/09QBkkeTOkr3U05JudS+lK/p2QDbZWZ01ps46nM3Lfazo8o/flZlPfnYUo/8J3ACzPz9l7assTfY9JoNaarq7e51Ea2iFiX8o/y4Mz8U8OyvSg/XG5L+dHxx8BJ/kgiSZIkSZIkSZJGoo7NtKkmBb6UJpO4VZPl/Z4SoT2QMgr7WMpIdUmSJEmSJEmSpBGn4+a0iYixlAnSvkz3ZHKNPgtMBw7JzC7KJGtzgFMj4pTMfHB4WitJkiRJkiRJktQ/nZhpsy3wXcqEV4c2LoyIScBewHlVwKbm15TJj187HI2UJEmSJEmSJEkaiE4M2txHmaj5o5SJ5RptAkykTDj3vMz8D2ViralD3kJJkiRJkiRJkqQB6rjyaJn5OPB4L6usWF0+3WTZTGCFQW+UJEmSJEmSJEnSEuq4oE0/9JU91NXHckmSJElSnYhYF7gJODgz/9Tu9kiSJEmjVSeWR+vLk9Xl8k2WLQ88NYxtkSRJkqSOFhHrA5cCK7e7LZIkSdJoNxozbe4EFgCb1d9ZjQybAkxvR6MkSZIkqZNExFjgHcCXgTFtbo4kSZK0VBh1mTaZOQe4HDig6mTUHAzMB/7SjnZJkiRJUofZFvgucCZwaJvbIkmSJC0VRmOmDcDnKMGZcyPidEpn4yTgtMy8r60tkyRJkqTOcB+wWWY+EBF7trsxkiRJ0tJgyII2VZbL1cCmmblaL+utDJwA7A+sDTwKXAKclJn3Ls6+M/OvEbEfJVDzG+AR4AvV7V7dcMMNXYuzT0mSJGk02mGHHSyLNcpExHjg8F5WmZmZP8vMx4HHB7Jt+1OSJElSt8XpTw1lps3JwI7AjFYrVAGbq4AtgJnANGAT4F2U8mZ7ZOa0Vo/PzMtpUVs5My8ELlzcxkuSJEnSKDUZOK2X5fcCPxumtkiSJEmqM+hBm4gYQ8mcOa4fq59OCdj8DnhzZs6MiFoH4jDglxGxTWYuGOx29mWHHXYY7l0CMH36dACmTp3alv2r/TwG5DEgjwF5DAjafxzccMMNbdmvhl5mzqLF4LfBYn9K7eIxIPA4kMeAPAbU/mNgSfpTgxq0iYi1KBNV7tuPdbcADgBmAYdm5kyAzHwuIg4HdgKmUsqmnTOY7eyP2ps63GbPnt3W/av9PAbkMSCPAXkMCDwOJEmSJGlpNHawNhQRrwZupwRsHqbvTJu3U0Z3XVjVSn5elVnz4+rmIYPVRkmSJEmSJEmSpJFqMDNttgSWA34KHAVs08f6O1WXV7VYfk11uduSN23g2pU21e60LbWfx4A8BuQxII8BQfuPA8ujSZIkSdLwG8ygzXXA9pn5L4CI6Gv9zarLu1ssv7e6XDMilqvqLkuSJEnSUiMixgJXA5tm5mq9rLcyZW7R/YG1gUeBS4CTMvPeVo+TJEmSNLIMWtAmM1tlzLSyenU5o8Xy+pJpq1HmvpEkSZKkpcnJwI607jfVAjZXAVsAM4FpwCbAu4ADImKPzJy2JI3IzMsp5a0lSZIkDaFBm9NmMUypLme3WF5//5QW60iSJEnSqBMRYyLiRPqeKxTgdErA5nfAupn5YmAd4AxgJeCXETFuiJoqSZIkaRANZnm0gVpA70Gj+mVdQ9wWSZIkSRoRImIt4LvAvv1YdwvgAEplgkMzcyZAZj4XEYdT5hKdSimbds6QNbpBbU6m4TZ79uy27l/t5zEg8DiQx4A8BtTZx0A7M22eqS4nt1g+qe56q2wcSZIkSRo1IuLVwO2UgM3D9J1p83ZK2bILM7O+xDSZuQD4cXXzkEFuqiRJkqQh0M5MmxmUVP1VWixfte76o0PfHEmSJElquy2B5YCfAkcB2/Sx/k7VZas5Rq+pLndb8qb139SpU4dzd8+rjaRs1/7Vfh4DAo8DeQzIY0DtPwZuuOGGxX5sOzNtbqsuN2qxfMPq8qHMfHbomyNJkiRJbXcdsH1mviMzZ/Rj/c2qy7tbLL+3ulwzIpZb4tZJkiRJGlLtDNpcX13u3GJ57f5rh6EtkiRJktR2mXlVZv5rAA9ZvbpsFeCpL5m22uK1SpIkSdJwaWfQ5rzqcr+IWKREWkSMAw6rbp41nI2SJEmSpA4ypbpsNQ9o/f1TWqwjSZIkaYRoW9AmM6cBFwMrAOdExKoAETEZ+AEwFUjgN+1qoyRJkiSNcAv6WF7f5+sayoZIkiRJWnLj27z/9wJXAnsB90XEdGATYGXgKWD/zFzYxvZJkiRJ0kj2DLASMLnF8kl111tl40iSJEkaIdpZHo3MfADYAfgG8CiwLTAf+AXwksyc3sbmSZIkSdJIV5vLZpUWy1etu/7oELdFkiRJ0hIaskybzLwcGNOP9WYAH67+JEmSpKXeXY/O4rfTn2KL1SYxdWq7W6MR7jZgU2CjFss3rC4fysxnh6VFbXTdA8/y6DPzWXfjeawweUK7myNJkiQNWLvLo0mSJEmqzJm/gG/++d+c9tc7WbCwTD+y5robsMumq/bxSC3Frgf2BnYGTmuyfOfq8tpha1GbnHn1PZzw54cB+P2df+fSo/Zg7Ng+xxFKkiRJI0pby6NJkiRJKqY98CT7fPPvfOuyfz8fsAG48t9WtFKvzqsu94uIRUqkRcQ44LDq5lnD2ah2+P1NDz9//c5Hn2H6w0+3sTWSJEnS4jFoI0mSJLXRnPkLOOWS29j/O1eRj8xcZNnYMbD75qu3qWXqBJk5DbgYWAE4JyJWBYiIycAPgKlAAr9pWyOHybwFCxe5/cycBW1qiSRJkrT4LI8mSZIktcmN9z/Jx8++kTv+O6vHslWmjOPDL12dnTaxNJr69F7gSmAv4L6ImA5sAqwMPAXsn5kLe3n8qDBx/KJjEhuDOJIkSVInMGgjSZIkDbPn5i3ga3+6g+//7U7qKqE978Dt1+OQF4xj+Unjhr9x6jiZ+UBE7AAcD+wLbAs8CfwCOCEz72hn+4bLhHGLBm3mzjdoI0mSpM5j0EaSJEkaRv+87wmOPmca/26SXbPmCpP4wgHb8PIt1mT69OltaJ1Gmsy8HBjTj/VmAB+u/pZKPYI2ZtpIkiSpAxm0kSRJkobBc/MW8L+X3s7pV9zVNLvmTTusx6ffsCUrTpkw/I2TRoGJ4xeNbVkeTZIkSZ3IoI0kSZI0xG649wmOOedG7nz0mR7L1lphMl84cBv2ijXa0DJp9GjMtDFoI0mSpE5k0EaSJEkaIs/NW8BX/pj84Mq76WqSXXPIi9fnU2+YygqTza6RltTExqDN/CYfOkmSJGmEM2gjSZIkDYEb7n2co8+exl2P9cyuWXvFyXzxwG3Z4wWrt6Fl0ug0YfyiQZs5ZtpIkiSpAxm0kSRJkgbR7LkL+PIfkx/9vXl2zVt2XJ/jXm92jTTYembaGLSRJElS5zFoI0mSJA2S/7vncY45Zxp3N8muWafKrtnd7BppSEwYN2aR285pI0mSpE5k0EaSJElaQrPnLuCUP9zGGVfd0zS75q07bcBxr9uC5c2ukYbMhMZMG4M2kiRJ6kAGbSRJkqQlcO1dMzjm3GncO+PZHsvWXWkKXzpwW162+WptaJm0dJnYMKfN3AVNIqiSJEnSCGfQRpIkSVoMz86dzymXJGdcdU/T5W/feQOOfd1UlpvkKbc0HBozbeY6p40kSZI6kD1ISZIkaYCuuWsGx5wzjfse75lds97KUzjlwG156WZm10jDaaLl0SRJkjQKGLSRJEmS+umZOfP50iW3cebV9zZd/o5dNuQTr92CZc2ukYbdhHFjFrlt0EaSJEmdyN6kJEmS1A9X3fkYnzh3Gvc/PrvHsvVXmcIpB27HLpuu2oaWSQKYMN5MG0mSJHU+gzaSJElSL56ZM58v/H46Z11zX9Plh710I45+TZhdI7VZY3m0ufO72tQSSZIkafHZs5QkSZJa+Pu/S3bNA0/0zK7ZYJVlOOWgbdl5E7NrpJFgYkOmzVwzbSRJktSBDNpIkiRJDWbNmc/nfzedn1/bM7tmzJju7JplJno6LY0UExoybebNN2gjSZKkzmMvU5IkSapz5R0lu+Y/T/bMrtlo1WU45aDt2HHjVdrQMkm96RG0MdNGkiRJHcigjSRJkgTMfG4en//ddH5x3f09lo0ZA+/adWM+/upgysRxbWidpL5MGDdmkduWR5MkSVInMmgjSZKkpd7fbn+UY8+dxoNPPddj2carLcupB23Lizcyu0YayRrntDHTRpIkSZ3IoI0kSZKWWk8/N4//d9F0fnV98+yaw1+2MR97dTB5gtk10kg3saE82lzntJEkSVIHMmgjSZKkpdLl+V+OO+8mHmqSXbPJ6iW7ZocNza6ROkXPOW262tQSSZIkafEZtJEkSdJS5anZ8zj5ols5+4YHeiwbOwaO2G0TjnrVC8yukTpMz6CNmTaSJEnqPAZtJEmStNS47LaSXfPw0z2zazZdfVlOfdN2bL/Bym1omaQlNXH8mEVuzzVoI0mSpA5k0EaSJEmj3lPPzuOki27l3H80z655z+6b8pFXbm52jdTBzLSRJEnSaGDQRpIkSaPan6c/wid/cxOPPD2nx7LN11iOU9+0HS9cf6U2tEzSYJo4ftGgzdz5Bm0kSZLUeQzaSJIkaVR68tm5nHThrZz3z//0WDZ2DLx3j0350CvMrpFGi56ZNl1taokkSZK0+AzaSJIkadS59NaSXfPozJ7ZNS9YczlOPWg7tjO7RhpVegRtzLSRJElSBzJoI0mSpFHjiWfm8tkLb+H8fz3YY9m4sWN43x6b8sFXbMak8WbXSKPNxIagzVzntJEkSVIHGrVBm4g4AvgIsBFwH3Aa8K3M9MxdkiRpFPrDLQ/zqd/czGOzembXxJrL8+U3bcc2663YhpZJGg4Txo1Z5PY8gzaSJEnqQKMyaBMR7wG+B3wT+C2wG/A1YArwpTY2TZIkSYPs8WfmcuIFt3DBjc2za47cc1M+8PLNe0xSLml0GT9uLGPHwMJqKpuFXbBgYRfjxo7p/YGSJEnSCDIqgzbAu4ErM/ND1e0/R0QAH8CgjSRJ0qhxyc0P8enzb+axWXN7LNtirZJds/W6ZtdIS4vxY8cwd0HX87fnzl/IlImWQ5QkSVLnGK1BmynAYw33zQBWbUNbJEmSNMhmzJrDCRfcwkXTHuqxbPzYMRy512YcuddmZtdIS5nxY2Hugu7bcxcsZAoGbSRJktQ5RmvQ5mvA9yPi7cCFwM7A/wA/bWurJEmStMR+d9NDfOb8m5nxTM/smqlrr8CX37QtW61jdo20NBo/dgzQnWnjvDaSJEnqNKM1aHMWZR6b+iDNH4EPtqc5kiRJWlKPzZrDCb+9hYtvap5d88GXb87799qUCePMrpGWVhMa5q8xaCNJkqROM1qDNr+lBG0+AVwLbAOcCJwbEftmpmfukiRJHeSiaQ9y/G9v4fEm2TVbrbMCpx60HVuus0IbWiZpJJkwriFoM7+rxZqSJEnSyDTqgjYR8VLgtcD7MvO71d1/jYi7gIuBfYDz29U+SZIk9d+jM+dw/G9v5vc3P9xj2YRxY/jQyzfnvXuaXSOpGN+QaTN3wYIWa0qSJEkj06gL2gAbVpd/b7j/b9XlVhi0kSRJGtG6urq4cNpDnPDbm3ni2Xk9lm+97gp8+U3bscVaZtdI6ja+IdNmrpk2kiRJ6jCjMWhzW3W5G3BT3f27Vpd3DW9zJEmSNBD/nfkcnzn/Zv5wyyM9lk0YN4aPvPIFvGf3TcyukdTDhIavBee0kSRJUqcZdUGbzPxnRJwLnBoRy1PmtNmKMqfNv4Bz29g8SZIktdDV1cUFNz7ICRfcwpNNsmu2XW9FTj1oO2Kt5dvQOkmdoLE8mkEbSZIkdZq2Bm0iYixwNbBpZq7Wy3orAycA+wNrA48ClwAnZea9TR7yVuDTwHuBk4D7gDOq9XvOXitJkqS2+u/Tz/Gp82/m0lt7ZtdMHDeWj7xqc96z2yaMN7tGUi8mNJZHM2gjSZKkDtPuTJuTgR2BGa1WqAI2VwFbADOBacAmwLuAAyJij8ycVv+YKjBzfPUnSZKkEaqrq4vz//UfTrzgVp6a3TO7Zrv1V+LLB23L5muaXSOpb42ZNnPnG7SRJElSZ2lL0CYixlAyZ47rx+qnUwI2vwPenJkzI2IycBpwGPDLiNgmMxcMVXslSZI0+B55+jk+9Zub+NP0//ZYNnH8WD76qhdw+Ms2NrtGUr/1LI/W1aaWSJIkSYtn2IM2EbEW8F1g336suwVwADALODQzZwJk5nMRcTiwEzCVUjbtnMFs5/Tp0wdzc/02e/bstu5f7ecxII8BeQxotB8DXV1d/PmuWXzvuhnMmttzFHysNomP7ro6G6w0lztuzza0cGQY7ceBNBQmNMR4ndNGkiRJnWZYhy1GxKuB2ykBm4fpO9Pm7cAY4MLMfLx+QZVZ8+Pq5iGD3FRJkiQNgceemc+Jf3mEr1z5aI+AzYSxY3j3DqvwldetwwYrTWxTCyV1sp6ZNgZtJEmS1FmGO9NmS2A54KfAUcA2fay/U3V5VYvl11SXuy150xY1derUwd5kv9RGUrZr/2o/jwF5DMhjQKPxGOjq6uKcGx7gpItuZeZz83ss336DlTjloO3YbI3l2tC6kandx8ENN9zQlv1KS2LCOOe0kSRJUmcb7qDNdcD2mfkvgIjoa/3Nqsu7Wyy/t7pcMyKWy8xZS95ESZIkDaaHnprNcefdxOX5aI9lk8aP5ejXBO/cdWPGNYyQl9QeETEe+ABwBLARpUrCb4ETaiWrR6rGTJu5ZtpIkiSpwwxr0CYzW2XMtLJ6dTmjxfL6kmmrUea+kSRJ0gjQ1dXF2dc/wOcuupWZc3pm17x4w5U55aBt2WR1s2ukEebzwEeALwB/A7YATgJ2iYhdM3PERkImNJZHM9NGkiRJHWa4M20Gakp1ObvF8vr7p7RYR5IkScPswSdnc+x5N/G323tm10yeMJajX7MFh710I7NrpBEmIpahBGy+nJknVHf/OSIeA34J7An8pU3N69P4cY1z2nS1qSWSJEnS4hnpQZsFwNheltcv82xckiSpzbq6uvjV/93PyRdPZ1aT7JqXbLQypxy0HRuvtmwbWiepH1YGTgfObrj/tupyneFtzsCMb+g9Wh5NkiRJnWakB22eAVYCJrdYPqnueqtsHEmSJA2D/zw5m2PPncYVdzzWY9nkCWP5xGu34H922YixZtdII1Zm/gc4ssmi/arLm4exOQM2oSHTZq7l0SRJktRhRnrQZgYlaLNKi+Wr1l3vWXtDkiRJQ66rq4tfXHc/n/9d8+yaHTdehVMO3JaNzK6R2ioixgOH97LKzMz8WZPH7QIcC1yUmf8aqvYNhvENQWEzbSRJktRpRnrQ5jZgU2CjFss3rC4fysxnh6VFkiRJet4DTzzLsefexJX/7pldM2XCOI593RYcuvOGZtdII8Nk4LRelt8LLBK0iYg9gd8CdwOHDVXDBstEM20kSZLU4UZ60OZ6YG9gZ5p3LnauLq8dthZJkiSJrq4ufnbtfXzhd9N5Zu6CHst33mQVTjlwOzZYdZk2tE5SM5k5C+h3BDUiDgO+B9wCvC4zZwxR0wbNhIYA8Zz5Pb+fJEmSpJFsbN+rtNV51eV+EbFIibSIGEf3SK+zhrNRkiRJS7P7H3+Wt/3gWj59/s09AjbLTBzH5/bdip8fvrMBG6mDRcRJwI+By4DdM/ORNjepX8y0kSRJUqcb0UGbzJwGXAysAJwTEasCRMRk4AfAVCCB37StkZIkSUuJhQu7+OnV9/Car/2Nq+7sOeB+l01W5Q8f2Z1Dd9nIcmhSB4uITwCfAc4A3lBl6HSECQZtJEmS1OFGenk0gPcCVwJ7AfdFxHRgE2Bl4Clg/8z0TFySJGkI3TfjWY4590auuevxHsuWnTiO414/lbfuuIHBGqnDRcTmwMmU+UW/D7w4IupXuTMzH21H2/qjMWgzx6CNJEmSOsyID9pk5gMRsQNwPLAvsC3wJPAL4ITMvKOd7ZMkSRrNFi7s4qfX3MsXf38bs+f1nBti181W5YsHbMv6q1gKTRpMETEWuBrYNDNX62W9lYETgP2BtYFHgUuAkzLz3sXY9f6UfuIWwFVNlh9BqXowIk0ca6aNJEmSOltbgzaZeTn9mAizmvDyw9WfJEmShsG9M57hmHOmce3dzbNrPrX3lrxlx/UZM8bsGmkInAzsCPSsRVipAjZXUQIsM4FplKoE7wIOiIg9qpLT/ZaZpwCnLG6j281MG0mSJHW6ET2njSRJkobfwoVd/Pjvd/Par13RNGCz2+ar8YejduetO21gwEYaZBExJiJOBI7rx+qnUwI2vwPWzcwXA+tQ5qJZCfhlRIwboqaOSM5pI0mSpE434sujSZIkafjc81jJrrnunp7BmuUmjefTe0/lkJeYXSMNhYhYC/gupSx0X+tuARwAzAIOzcyZAJn5XEQcDuwETKWUOztnyBrdwvTp04d7lwAsnD93kdtPznymbW1Re8yePRto3zGokcHjQB4D8hhQJx8DZtpIkiSJhQu7+OGVd/Par/+tacBm9xeszh+P2p0372h2jTQUIuLVwO2UgM3D9J1p83ZKqekLM3ORD21mLgB+XN08ZJCbOqI1zmkzb2FXm1oiSZIkLR4zbSRJkpZydz06i2POmcb19z7RY9nyk8bzmTdsyZtevJ7BGmlobQksB/wUOArYpo/1d6our2qx/Jrqcrclb9rATZ06tR275b4nb1zk9phxE9rWFrVHbTSt7/vSzeNAHgPyGFC7j4EbbrhhsR9r0EaSJGkptaCau+bUP2TTybr3jNX5wgHbsPaKU9rQOmmpcx2wfWb+CyAi+lp/s+ry7hbL760u14yI5TJz1pI3ceSb2DCnTbPvNkmSJGkkM2gjSZK0FLrz0VkcffaN/OO+J3ssW37yeI5/w5YctIPZNdJwycxWGTOtrF5dzmixvL5k2mqUuW9GvQkNQZu5CwzaSJIkqbMYtJEkSVqKLFjYxQ+vvIuv/PH2piPQX77FGnx+/21Ya8XJbWidpAGopcDNbrG8/v6lJl1uQsOcNnPmLWhTSyRJkqTFY9BGkiRpKfHv/87i6HNu5J9NsmtWmDyeE964FQdsv67ZNVJnWACM7WV5/bKuIW7LiNFYHs1MG0mSJHUagzaSJEmj3IKFXZx+xV189dLbmdsku+YVW6zB5w/YhjVXMLtG6iDPACsBrT64k+qut8rGGXUay6PNmb+Qrq4ug9GSJEnqGAZtJEmSRrE7HpnJx8+Zxo3398yuWXHKBE7cZ0v2e6HZNVIHmkEJ2qzSYvmqddcfHfrmjAzjxo5h7BhYWOUWdXXB/IVdPYI5kiRJ0khl0EaSJGkUmr9gId+/4i6+dukdTcsDvXLqmnx+/61Zw+waqVPdBmwKbNRi+YbV5UOZ+eywtGiEmDBuDHPmd1eEmzN/IRPG9VZJTpIkSRo5DNpIkiSNMrc/MpOjz76RGx94qseylZaZwGf32Yp9tlvH7Bqps10P7A3sDJzWZPnO1eW1w9aiEWJiQ9Bm7vyFixaLkyRJkkYwhxtJkiSNEvMXLOTbl/2bN3zjyqYBm1dvuSZ/PGp39rUcmjQanFdd7hcRi5RIi4hxwGHVzbOGs1EjwYSxi36/NZvLS5IkSRqpDNpIkiSNArc9/DT7f+cqTv1D9iiHtvIyE/jGW17E9w7dgTWWtxyaNBpk5jTgYmAF4JyIWBUgIiYDPwCmAgn8pm2NbJOJDfPXzJm/oE0tkSRJkgbO8miSJEkdbN6ChXz38jv5xl/uYN6Crh7LX7vVWnxuv61ZfXlrA0mj0HuBK4G9gPsiYjqwCbAy8BSwf2YudWkmE8aZaSNJkqTOZdBGkiSpQ01/6Gk+fvaN3PLg0z2WrbLsRE7aLLgjhgAAIABJREFUdyv23mZtS6FJo1RmPhAROwDHA/sC2wJPAr8ATsjMO9rZvnZpLI82x6CNJEmSOohBG0mSpA4zb8FCvnPZnXzrsubZNXtvszaf3XcrVlvO7BqpU2Xm5UCfEdfMnAF8uPoTPTNtDNpIkiSpkxi0kSRJ6iC3PPgUR589jVsf6plds+qyEzlp363Ze9u129AySRoZegZtnNNGkiRJncOgjSRJUgeYO38h377s33z7sn8zf2HP7Jo3bLs2n91nK1Y1u0bSUm6ic9pIkiSpgxm0kSRJGuFu/s9THH3ONKY3ya5ZbbmJfG7frXndNmbXSBI4p40kSZI6m0EbSZKkEWru/IV86y938J3L72yaXbPPdutw4j5bscqyE9vQOkkamcy0kSRJUiczaCNJkjQC/XvGHI76w5Xc9vDMHstWW24SJ++3Na/deq02tEySRrbGOW0M2kiSJKmTGLSRJEkaQebMX8BP/vE4v775SZok17DfC9fhhDduxcpm10hSU41BG8ujSZIkqZMYtJEkSRohpj3wJEefPY18pGd2zerLT+L/7bc1r97K7BpJ6s3EsY2ZNgva1BJJkiRp4AzaSJIktdmc+Qv4+p/u4Ht/u4sFTdJrDnjRuhz/xi1ZaRmzaySpL2baSJIkqZMZtJEkSWqjG+9/ko+ffSN3/Pf/Z+++49uq7v+PvyVvx1l29t4nznCAQBJ2KbuMkEUXbSmjg1L40jaBUMoqM6Htl35LgUIpLVDaXwYrhVAoUDYhAeIM52Q7O3HsxHG8Ld3fH1KIZUlJnNi6kvx6Ph7u1b3nSvpALx73o/c5+8PGurXP0H2TRuucEd1dqAwAEhNr2gAAACCR0bQBAABwQU29T//75hr96d11EdeuOWdwjn7z7VPUMTst9sUBQAIjaQMAAIBERtMGAAAgxj7ftEfT5xZqbYR0TfcOGbrupM4a1yebhg0AHIX0pkkbH00bAAAAJA6aNgAAADFSU+/T795YrSfeWx8xXTNtbB/ddvEIbdu4NvbFAUCSSPM2SdrU+1yqBAAAAGg+mjYAAAAxsKR4j2bMXap1JZVhYz06ZOr+KaN1lukmSdoW6+IAIImQtAEAAEAio2kDAADQimrqffrNv62efH+DnAjpmq+f2Fe/vDhfHTKZCg0AWgJr2gAAACCR0bQBAABoJUuKyzR9TqHW7w5P1/TsmKkHphTozGFdXagMAJJX2PRoNG0AAACQQGjaAAAAtLDqOp8e+rfVUx9ETtd8c1xfzfwa6RoAaA1NkzZ1NG0AAACQQGjaAAAAtKBPN5ZpxtxCbYiQrundKUv3Tx6tM0jXAECrYXo0AAAAJLKkbdoYYyZIul/SOEn7JS2UNN1au8vVwgAAQFKqqmvQ7Netnv5wY8R0zbfG99PMC4erPekaAGhV6WFJG59LlQAAAADNl5RNG2PMWElvS/qPpEmSeinQwBkq6RQXSwMAAEnok/WlmjGvUMWlVWFjvTtl6cEpBTptaBcXKgOAtoekDQAAABJZUjZtJM2SVChporXWJ0nGmH2SHjbGDLHWrnW1OgAAkBSq6ho0a2EgXRPJFRP66ZYL85WTkay/cgFA/AlP2tC0AQAAQOJIujsIxpg8SV+RdPWBho0kWWvnS5rvVl0AACC5fLSuVDfPK9SmsvB0TZ/OWZo1pUCnDCFdAwCxluYlaQMAAIDElXRNG0kFkrySdhljnpF0mSSPpBcl/dRau8fN4gAAQGKrrG3QgwtX6W8fFUcc/+7J/XXzBcPVjnQNALiCpA0AAAASWTLeTega3D4h6TUFmjZDFFjTZogx5hRrLb+1AwCAZvtw3W7NmFuoLXuqw8b65mZp1pQxOnlwnguVAQAOaLqmDU0bAAAAJJJkbNqkB7efW2uvCT7+jzGmXNLzki6Q9KorlQEAgIS0v7ZBD7xWpGc/3hRx/MpTBmjGBUbZ6cn4qxUAJJbw6dF8Uc4EAAAA4k8y3lmoCG6bNmYWBrfHRxgDAACI6IO1gXTN1r3h6Zr+edl6cEqBJgwiXQMA8YKkDQAAABJZMjZt1gS3GU2OpwW34XdcAAAAmqioqdf9r63S3z8JT9d4PIF0zfTzSdcAQLxp2rSppWkDAACABJKMdxmKJG2U9A1jzP9aa53g8YuD2/dcqQoAACSM99aU6JZ5yyKmawbkZWv2tDE6aUCuC5UBAA4nzRu63+B35PM7SmkybRoAAAAQj5KuaWOtdYwx0yX9P0lzjDGPSzKS7pP0orX2U1cLBAAAcauipl73vVqk5xdtDhvzeKSrTh2oX5xnlJWe4kJ1AIAj4fF4lJ7qDZkWra7Bz/duAAAAJARXmzbGGK+kjyQNttZ2OcR5nSXdIWmSpJ6SShRYo+Zua21x0/OttXONMZdKul3SK5LKJD0u6bYW/4cAAABJ4b+rSzRzXqG2ldeEjQ3q0k6zpxVobH/SNQCQCDJo2gAAACBBuZ20uUfSOEml0U4INmw+lDRcUoWkQkmDJF0labIx5kxrbWHT51lrF0ha0BpFAwCA5LGvpl73LijSPxdHTtdcc9pA/fw8o8w0bvYBQKLISPWqotF+bYNPB5c5BQAAAOKXK00bY4xHgeTMzCM4/QkFGjavSvqGtbbCGJMp6VFJV0r6hzFmtLXW11r1AgCA5PS23aVb5y/T9kjpmq7tNHvqGI3t39mFygAAxyIjNbTRXtsodQMAAADEs5g3bYwxPSQ9JmniEZw7XNJkSfslfcdaWyFJ1toaY8w1ksZLyldg2rS5LVlnUVFRS77cEauurnb1/eE+rgFwDYBroPXtr/PpT5+W6o21+8PGvB5p8oiOuuK4zsqo2qGioh0xr49rABLXAXAs0lO9Ift1Ppo2AAAASAzew5/Scowx50larUDDZocOn7S5QpJH0ivW2rLGA8FkzV+Cu19v4VIBAECSWrSlSj96cUvEhk3fjmn6zYW9dPWJecpIjemvSQCAFpSeEvo9vLaepg0AAAASQ6yTNiMk5Uh6RtJNkkYf5vzxwe2HUcY/Dm5PP/bSQuXn57f0Sx6RA5+kdOv94T6uAXANgGugdZRX1evuBSs177Pw5IzXI/3gjMH6n3OGxsXaNVwDkNy/DpYsWeLK+wItISONpA0AAAASU6ybNosknWCt/UKSjDGHO39IcLshynhxcNvdGJNjrQ3/yCwAAGjz/lO0UzPnL9OuitqwsaHdcjR72hgd17eTC5UBAFpDeNKGJVABAACQGGLatLHWRkvMRNM1uC2NMt54yrQuCqx9AwAAIEnaW1Wnu19Zqfmfbw0bS/F69MMzBumGs+MjXQMAaDkkbQAAAJCoYp20aa6s4LY6ynjj41lRzgEAAG3QGyt36tYXlqkkQrpmWPccPTRtjAr6kK4BgGTEmjYAAABIVPHetPFJOtQqwI3HnFauBQAAJIA9lXW665UVevGLbWFjKV6PfnzmYP307CHKSCVdAwDJqun3eJI2AAAASBTx3rSplNRJUmaU8YxGj6OlcQAAQBvx+ood+uULy7V7f3i6ZniP9po9dYxG9+noQmUAgFhKT22StGlgTRsAAAAkhnhv2pQq0LTJjTKe1+hxSeuXAwAA4lFZZZ3ufHmFXl4anq5J9Xp03VcG6/qvDg27iQcASE5Nv9/XNZC0AQAAQGKI96bNKkmDJQ2IMt4/uN1ura2KSUUAACCuLFy+Xbe9uFy799eFjQ3v0V4PTRujUb1J1wBAW5JB0wYAAAAJKt6bNoslXSRpgqRHI4xPCG4/iVlFAAAgLpTur9UdL6/QgsLtYWOpXo9+ctYQ/eSsIaRrAKANarqmTU09TRsAAAAkhni/izE/uL3MGBMyRZoxJkXSlcHdZ2NZFAAAcNery7brvN+9G7Fhk9+zg166/lTddO4wGjYA0EZlpDVJ2vho2gAAACAxxPWdDGttoaR/Seogaa4xJk+SjDGZkp6UlC/JSnrBtSIBAEDM7N5fq58895mue+4zlVaGToeWluLRTecM08vXn6qRvZgODQDasqbTo9XU+1yqBAAAAGieeJ8eTZJ+JOl9SWdJ2mSMKZI0SFJnSeWSJllr+dgUAABJbkHhNt3+0gqVVYavXTOyVwc9NG2M8nt2cKEyAEguxphrJd0kaaCkTZL+KOn31lrH1cKaITMtdHq0Wta0AQAAQIKI66SNJFlrt0gaK+n3kkokFUhqkPS8pJOstUUulgcAAFpZSUWtfvzsEl3/98/DGjZpKR79/NxhevEnp9KwAYAWYIy5XtLjCkxVfZGkv0n6jaTb3KyruUjaAAAAIFG5mrSx1r4jyXME55VKujH4BQAA2gDHcfRK4Xbd8dJy7amqDxsf1TuQrhneg2YNALQEY4xX0kxJz1lrDzRp3jLGDJV0g6Rfu1ZcMzVN2tC0AQAAQKJIhOnRAABAG7Oroka/enG5Xl+xM2wsPcWrG88Zqh+cMUhpKXEfGgaAROJIOlfS/ibH6yRlxL6co5eZFvrzgenRAAAAkCho2gAAgLjhOI5eXrpNd7y8QnsjpGsK+nTU7KljZHq0d6E6AEhuwTVrVkqSMcajwDqikyV9V9LDLpbWbBmpJG0AAACQmGjaAACAuLBrX41++eJyvbEycrrmf84dqh+cPkippGsAoNmMMamSrjnEKRXW2uca7Z8h6Z3g488UWNcmYZC0AQAAQKKiaQMAAFzlOI5e/GKr7nx5pcqrw9M1Y/p20kNTCzS0O+kaADgGmZIePcR4saTGTZu1kr4iqY+kOyUtNsacZK0N76zHIZI2AAAASFQ0bQAAgGt27qvRL19YpjeLdoWNpad69bNzh+ma0waSrgGAY2St3S/J04zzt0raKknGmE8krVEgqXNvqxTYwkjaAAAAIFHRtAEAADHnOI7mf7ZVd72yQvtqGsLGj+vbSQ9NK9CQbqRrACBWjDEdJV0i6QNr7YYDx621a40x+yT1da24ZgpP2tC0AQAAQGKgaQMAAGJqR3mNbn1hmd5aFZ6uyUj16ufnDdPVpw1SiveIPxAOAGgZfklPSXpC0k8OHDTGnCKpg6QvXKqr2cKTNkyPBgAAgMRA0wYAAMSE4ziau2SL7l6wUhUR0jUn9Ouk2dPGaHDXHBeqAwBYayuMMQ9JutkYs0fSW5LyJd0h6XNJT7tYXrM0TdrUkrQBAABAgqBpAwAAWt328mrNnL9M79iSsLGMVK+mn2/0/VMHkq4BAEnGGK+kjyQNttZ2OcR5nRVoqEyS1FNSiaSFku621hYf5dvfpsBaNj+W9HNJZZL+Iek2a23NUb5mzGWQtAEAAECComkDAABajeM4mrN4i369YKUqasPTNSf276xZUws0iHQNADR2j6RxkkqjnRBs2HwoabikCkmFkgZJukrSZGPMmdbawua+sbXWL+mR4FfCykxjTRsAAAAkJpo2AACgVWzbW61b5i/Tu6vD0zWZaV5NP3+4rjxlAOkaAAgyxngUSM7MPILTn1CgYfOqpG8EpzbLlPSopCsl/cMYM9pa2yYjJhmpJG0AAACQmGjaAACAFuU4jv756Wbd868i7Y+QrjlpQGfNmjpGA7u0c6E6AIhPxpgekh6TNPEIzh0uabKk/ZK+Y62tkCRrbY0x5hpJ4xVYi2aSpLmtVvQhFBUVufG2qq6uliStW23lkeQEj9f7HC1fsZIPCrQBB64Bt65BxAeuA3ANgGsAiXwNeA9/CgAAwJHZurda331qkW6ZvyysYZOVlqI7Lhmhf/7gZBo2ANCIMeY8SasVaNjs0OGTNldI8kh6xVpb1nggmKz5S3D36y1casLweDxKTwlt0NT5nChnAwAAAPGDpA0AADhmjuPo+UWbdd+rkdM14wbmavbUAvXPo1kDABGMkJQj6RlJN0kafZjzxwe3H0YZ/zi4Pf3YSzs6+fn5rrzvgU9S5ufnKytjs2qr6r8cGzB4qHLbpbtSF2Kn8TWAtovrAFwD4BqA29fAkiVLjvq5NG0AAMAx2bKnSrfMW6b31+4OG8tKS9EtFw7Xdyb0l5cpaQAgmkWSTrDWfiFJxpjDnT8kuN0QZbw4uO1ujMmx1u4/9hITT9N1bWrqWdcGAAAA8Y+mDQAAOCqO4+i5Tzbp/leLVFkXfiNswqBczZoyRv3ysl2oDgASh7U2WmImmq7BbWmU8cZTpnVRYO2bNiczLSVkv7bB71IlAAAAwJGjaQMAAJptc1mVbp5XqA/Xhd8vzE5P0cwLh+vb40nXAEAryQpuq6OMNz6eFeWcpEfSBgAAAImIpg0AADhifr+j5z4p1v2vrVJVhHTNyYPyNGtqgfrmkq4BgFbkk+Q9xHjjMaeVa4lbJG0AAACQiGjaAACAI7KptEoz5i3Vx+vLwsbapado5tfy9a1x/UjXAEDrq5TUSVJmlPGMRo+jpXGSHkkbAAAAJCKaNgAA4JD8fkfPfFysB15bpeoIN7xOG9JFD0wZrT6dSdcAQIyUKtC0yY0yntfocUnrlxOfSNoAAAAgEdG0AQAAURWXVmrG3EJ9siE8XZOTkapfXpSvb5zUVx4P6RoAiKFVkgZLGhBlvH9wu91aWxWTiuJQRmpo04akDQAAABIBTRsAABDG73f01482atZCGzFdc/rQLnpgSoF6d2qz61sDgJsWS7pI0gRJj0YYnxDcfhKziuJQRlro9GgkbQAAAJAIaNoAAIAQG3cH0jWLNoana9pnpOq2i/N1+YmkawDARfMl3SHpMmNMrrX2y2/YxpgUSVcGd591oba4kUnSBgAAAAnIe/hTAABAW+D3O/rz+xt0wcPvRmzYnDmsq16/6Qx9/aR+NGwAwEXW2kJJ/5LUQdJcY0yeJBljMiU9KSlfkpX0gmtFxgGSNgAAAEhEJG0AAIDWl+zXjLmFWly8J2ysfUaqfnXJCE0b24dmDQDEjx9Jel/SWZI2GWOKJA2S1FlSuaRJ1to23aVomrSpJWkDAACABEDSBgCANsznd/Tke+t14cPvRWzYnGW66t8/O4Pp0AAgzlhrt0gaK+n3kkokFUhqkPS8pJOstUUulhcXmiZtmB4NAAAAiYCkDQAAbdS6kv2aPmepPtu0N2ysfWaq7rhkpKac0JtmDQDEmLX2HUmH/eZrrS2VdGPwC02EJW2YHg0AAAAJgKYNAABtjM/v6M/vr9dv/r064g2srw7vpvsmjVaPjpkuVAcAQMsgaQMAAIBERNMGAIA2ZO2u/Zo+d6k+j5Cu6ZCZqjsvHalJx5OuAQAkvszU0KYNSRsAAAAkApo2AAC0AT6/oyfeW6/fvrFadRFuWp2T3033Thqt7h1I1wAAkkNmWuj0aCRtAAAAkAho2gAAkOTW7KzQL+YWaunm8HRNx6w03XXpSE08rhfpGgBAUmk6PRpJGwAAACQCmjYAACSpBp9ff3pvvf73jTWq84XfqDp3RHfde9kodSNdAwBIQpmpJG0AAACQeGjaAACQhFbvrND0OUu1dEt52Fin7EC65tIxpGsAAMmLpA0AAAASEU0bAACSSIPPr8ffXa+H34ycrjl/ZHf9+rJR6taedA0AILmRtAEAAEAiahNNG2PMw5JukJRmrW1wux4AAFrDqh37NH1OoZZtDU/XdM5O090TR+nigp6kawAAbQJJGwAAACSipG/aGGPOlvRTt+sAAKC11Pv8euyddfr9W2tU73PCxi8c1UN3Txylru0zXKgOAAB3ZIQlbWjaAAAAIP4lddPGGNNJ0tOStkjq6241AAC0vKLt+/SLOUu1Ytu+sLHcdun69cRRuqigpwuVAQDgrsywpA3TowEAACD+JXXTRtIjktZL+q+kX7lcCwAALabe59cf316nP7wdOV1zUUFP3X3pSOXlkK4BALRNTZM2tSRtAAAAkACStmljjLlc0qWSxkj6rsvlAADQYlZsK9f0OYVauT08XZPXLl2/vmyUvjaadA0AoG3LTGs6PRpJGwAAAMS/pGzaGGN6SXpU0nRr7XpjjNslAQBwzOoa/Hrk7bV65O21avCHp2suGdNLd14ygnQNAACSMsKmRyNpAwAAgPiXlE0bSU9JWmytfcztQgAAaAnLt5brF3OWatWOirCxLjnpuueyUbpgFOkaAAAOyEwlaQMAAIDEk3RNG2PMdZJOljTGGHPgn+/AR6xSjDF+ay0fsQIAJIS6Br/+8NYa/fGddRHTNROP66U7Lhmp3HbpLlQHAED8SkvxyOORnOCPzwa/owafX6kp3kM/EQAAAHBR0jVtJF0uqYOkDRHGaiTdJenOWBYEAMDRWLalXNPnRkvXZOjeSaN0/sgeLlQGAED883g8ykxNUXWjhE1tA00bAAAAxLdkbNr8UFL7Jsd+IOlaSRMkbY55RQAANEOdz9HzS/dozooN8kVI10w6vrduv3iEOpOuAQDgkDLSvGFNm3Ys/QYAAIA4lnRNG2utbXrMGHNx8OESa21DjEsCAOCIFW7ZqxsWbFHx3vqwsa7tM3TfpNE6d0R3FyoDACDxBNa1OfgzlXVtAAAAEO9cbdoYY7ySPpI02Frb5RDndZZ0h6RJknpKKpG0UNLd1triWNQKAEBrqm3w6eE31+jxd9dHTNdMPiGQrumUTboGAIAjlZEWOhVabQPLmwIAACC+uZ20uUfSOEml0U4INmw+lDRcUoWkQkmDJF0labIx5kxrbeGh3sRae6dYxwYAEKe+2LxX0+cs1Zpd+8PGurXP0P2TR+vsfNI1AAA0VyBpcxBJGwAAAMQ7V1ZgNMZ4jDF3Spp5BKc/oUDD5lVJva21J0rqJelpSZ0k/cMYkxL96QAAxKeaep8eeG2VJv/xg4gNm6lj++iNm86kYQMAwFHKJGkDAACABBPzpI0xpoekxyRNPIJzh0uaLGm/pO9YayskyVpbY4y5RtJ4SfkKTJs2tyXrLCoqasmXO2LV1dWuvj/cxzUAroG2YVVJjX77QYk2l4evXZOb5dWPT+yo0wala1vxWm1zoT64i+8DkLgOgJaQQdIGAAAACSamSRtjzHmSVivQsNmhwydtrpDkkfSKtbas8YC11ifpL8Hdr7dwqQAAtIraBr/+vLhUP39tW8SGzXlD2uvh87tqbM9MF6oDACC5sKYNAAAAEk2skzYjJOVIekbSTZJGH+b88cHth1HGPw5uTz/20kLl5+e39EsekQOfpHTr/eE+rgFwDSSvJcV7NH3uUq0vqQwb69kxU/dPHq2vmG5cA+AagCT3r4MlS5a48r5ASyJpAwAAgEQT66bNIkknWGu/kCRjzOHOHxLcbogyXhzcdjfG5FhrwxcEAADAZTX1Pv3m31ZPvr9BjhM+/o2T+urWi/LVITMt9sUBAJDEWNMGAAAAiSamTRtrbbTETDRdg9vSKOONp0zrosDaNwAAxI3FG8s0Y26h1u8OT9f06pip+6cU6MxhXSM8EwAAHCuSNgAAAEg0sU7aNFdWcFsdZbzx8awo5wAAEHPVdT499G+rpz6InK755rh+uvVrw9WedA0AAK0mK71J0oamDQAAAOJcvDdtfJK8hxhvPBbhlhgAALH36cYyTZ+zVBtLq8LGenfK0gNTRuv0oaRrAABobZlNkjbVNG0AAAAQ5+K9aVMpqZOkzCjjGY0eR0vjAAAQE1V1DZr9utXTH26MmK759vh+uuVC0jUAAMRKVnqTpk0da9oAAGLHifSHYdRzm/narVVH88poVt1OM169uf8+mjqwjl2kqVHjpWYSCK2rut6vrLRD5UHiV7w3bUoVaNrkRhnPa/S4pPXLAQAgsk/Wl2rGvEIVR0nXzJpaoFOHdHGhMgAA2q7MtCZr2jSQtAEQP/x+R3U+v+p8ftU3HNg6qvP5VNcQGKv3+VUXHKtr8KvB58jnOPL5g4/9B/YdNfgc+R1HDf6D+1+e63fk8zU61+/I7z94rs8fuDXtdxw5jiO/P/hYgRv+fiew73cC+86X+4HHjff9jho97+BrSQdf4+DzQvcbc5yDt8sd5+DN8wPnOWp8k9wJOd7Q0CBJ8qZsPvj84AmNntLo9UPfK/iKIa+paMejPB/xYqPbBcBFfTum6c+5fTSse3u3S2mWeG/arJI0WNKAKOP9g9vt1trwu2QAALSyqroGzVoYSNdE8p0J/XXzhcOVkxHvP3IBAEg+TZs21XU0bQAcOZ/f0f7aBlXU1KuipiHscXWdTzX1PlXX+1Rd51d1fXC/LnisyX5NvV91DT7V+wINGZ+fu/utj4Ql0JZtLq/XrIWr9OT3TnK7lGaJ9ztIiyVdJGmCpEcjjE8Ibj+JWUUAAAR9tK5UN88r1Kay8M8N9OkcSNecMph0DQAAbslq0rSpJWkDtEl+v6Py6nqVVdWprDLwtaeyTmVVwW1lvfZU1WlPVV2gIVMTaM5U0ugFgISXnpp4U6TFe9NmvqQ7JF1mjMm11pYdGDDGpEi6Mrj7rAu1AQDaqMraBj24cJX+9lFxxPHvntxfN18wXO1I1wAA4KrMJvOYk7QBkk+Dz6/t5TXavKdKO/fVaEd5rVYV79buKp+q3i7Trn212lVRo3ofqRbEP4+nmec367WP/OxmltGsuj3NefVj+PdxYDq8aP/crVVza/5/iObxO36ZLpmaeWG+26U0W1zfTbLWFhpj/qVA2mauMWaatbbUGJOpQPImX5KV9IKbdQIA2o4P1+3WjLmF2rKnOmysX262HpxSoJMH50V4JgAAiLWmSZvqCIsRA4h/tQ0+rS+p1PqSSm0qq9KmsiptDm637q1O6GnG0lO9Sk/xKj3Vq7QUT3Db+FjgcVrwvFSvR6kpHqV6PfJ6A9sUr1cpXinV61WKt+lY+LlNx1M8ga3HI3k9Hnk9Bx4HbngHjgVuRjfe93oCt7I9B/a9ga10cPzAazV+7QOve/BY4KZ445vdBx57PAdvl3s8B2+efzn+5f+EvsaaNWskSWbYsIjP/3LjUaPx0Pdq+ppNjx/u+c1pkqDlFRUVSZLy8xPvhj1axoFroG9utsuVNF9cN22CfiTpfUlnSdpkjCmSNEhSZ0nlkiaxqR1kAAAgAElEQVRZa5mgEgDQqvbXNuiB14r07MebIo5fecoAzbjAKDs9EX60AgDQNjRd06amnj8dgXjW4PNrXUml7M4KrdlZodU7K7Rm134Vl1a51pjJyUhV+8zAV+BxmnIyU9U+I1VZ6SnKSgt+pacos9HjrLTAfnb6wf2M1EAj5kAzJtXr4cZ+KynJDHz/z22X7nIlANB8cX9nyVq7xRgzVtLtkiZKKpC0V9Lzku6w1q5xsz4AQPL7YG0gXbN1b3i6pn9etmZNKdD4QaRrAACIN02bNiRtgPjh9ztav7tSy7buVeGWchVuKdeKbeWt1lxtn5Gq3Jx0dc5OV167dHVul67cdoH93HZpym2XoU7ZaepwoCmTmaqc9FR5vTRVAACx5WrTxlr7jo5g6j5rbamkG4NfAADEREVNve5/bZX+/kl4usbjkb5/ykBNP98oKz0lwrMBAIDbmv6MrqVpA7im3ufX8q3lWrShTJ9sKNOnG8tUUdPQIq/dJSdDfXOz1Ktjlrp1yJC3Zp/yslN1/PBB6tExU907ZJCIBwAkDH5iAQAQwXtrSnTLvGUR0zUDu7TTrKkFOmlArguVAQCAI5WZ5g3ZJ2kDxI7jOFpXUql37C79d3WJlhTvUVXd0f832LtTloZ0y9HALu3UNzdb/YJffTpnqV1G6O2tL9eyYK1JAEAComkDAEAjFTX1uu/VIj2/aHPYmMcjXX3qQP38PNI1AAAkgizWtAFiqqbep4/Wleptu0tv213aXBb+AajD6ZKTrpG9OmpY9xwN7d5ew7q315BuOcrJ4BYWAKBt4CceAABB/11dopnzCrWtvCZsbFCXdpo9rUBj+5OuAQAgUbCmDdD6aht8enf1br26bLveWLlT+2uPfMqzjllpKujTUQV9Omp0704q6NNRPTtmyuNhHRkAQNtF0wYA0Obtq6nXvQuK9M/FkdM1154+SD87d1jYjR8AABDfmv7srjmGqZkAHOQ4jj7ZUKY5i7fo3yt2qOIIGzVdcjI0flCuxg/M1fiBeRraLUdeLw0aAAAao2kDAGjT3ra7dOv8ZdoeKV3TtZ1mTx2jsf07u1AZAAA4Vk3XtKlpoGkDHIvt5dWat2SL5izZouLSqsOen57i1fhBuTrLdNMZw7pqcNd2pGgAADgMmjYAgDapvLpe9yxYqTlLtoSNeT3StWcM0k3nkK4BACCRpad45fVIfiewX+9z1ODzKzXFe+gnAviS4zj6eH2Znvpgg/5TtPPL/56i6ZKTofNHdtdXh3fTyYPzlJ3OrScAAJqDn5wAgDbn7VW7dMv8Qu3cVxs2NqRbjmZPLdDx/UjXAACQ6Dwej7LSUlTZaFq0mga/cmjaAIdV2+DTK0u366n3N2jl9n2HPLdLToYuHNVDFxX01EkDcpXClGcAABw1mjYAgDajvKpedy9YqXmfRU7X/PDMwbrx7KGkawAAaMQY87CkGySlWWuPfIXxOJHZpGlTXedTTgZ/CgPRVNU16LmPN+nxd9dr9/7wDzkdkJ7i1Xkju+vyE/vq1CFdaNQAANBC+E0VANAm/Kdop2bOX6ZdFeF/eA7tlqPZ08bouL6dXKgMAID4ZYw5W9JP3a7jWDT9MEZNPevaAJFU1TXomY+K9ad316u0si7qecN7tNc3Tuqry47vrU7Z6TGsEACAtoGmDQAgqe2tqtPdr6zU/M+3ho2leD360ZmDdMPZQ5WRSroGAIDGjDGdJD0taYukvu5Wc/Qy00KnQqNpA4SqbfDpmY+K9cd31qksSrPG45HOG9FdV506UOMG5srjIVUDAEBroWkDAEhab6zcqVtfWKaSCOka0729Zk8rUEEf0jUAAETxiKT1kv4r6Vcu13LUstJDP5hRTdMGkCQ5jqNXl+3QgwtXaVNZVcRzstNT9I2T+unKUwaoX152jCsEAKBtomkDAEg6eyrrdNcrK/TiF9vCxlK8Hl33lcG6/qtDSNcAABCFMeZySZdKGiPpuy6Xc0wyU5tOj+Z3qRIgfny2aY/u/VeRlhTviTjeLj1F3ztlgK45fZBy2zEFGgAAsUTTBgCQVF5fsUO/fGF5xEVTh/dor9lTx2h0n44uVAYAgLuMMamSrjnEKRXW2ueMMb0kPSppurV2vTEmNgW2EpI2wEF7q+p0/6ur9M/FmyOO52Sk6spTBujq0waqM80aAABcQdMGAJAUyirrdOfLK/Ty0vB0TarXo+vOGqLrzxqi9FRvhGcDANAmZCrQjImmWNJzkp6StNha+1hMqmplmWlNmjZ1NG3Q9jiOo5e+2KZfL1ip0gjr1qR4Pfr2+H668eyhysvJcKFCAABwAE0bAEDCW7h8u257cbl27w//AzS/ZwfNnlqgUb1J1wAA2jZr7X5Jh1w93BhznaSTJY0JJnMk6cAnHlKMMX5rbULNL9a0aVPbQNMGbUtxaaVue3G53luzO+L4OfnddMuF+RrSLSfGlQEAgEho2gAAElbp/lrd8fIKLSjcHjaW6vXo+q8O0XVfIV0DAEAzXC6pg6QNEcZqJN0l6c5YFnSsstJCfw8gaYO2wnEcPffJJt37r6KI0wIO7tpOd08cpVOHdHGhOgAAEA1NGwBAQnp12Xb96sXlEad3GNGzg2ZPK9DIXqRrAABoph9Kat/k2A8kXStpgqTIC2HEsaZJmxrWtEEbsGtfjWbMK9Q7tiRsLD3Vq5+eNUQ/OHOQMlJTIjwbAAC4iaYNACCh7N5fqzteWqF/LQtP16SlePTTrw7Vj78yWGkppGsAAGgua61teswYc3Hw4RJrbUOMSzpmWU3XtKlPqNndgGZ7bdl23frCMu2pqg8bO3VInu65bLQGdmnnQmUAAOBI0LQBACSMBYXbdPtLK1QWIV0zqncHzZ46Rvk9O7hQGQAALcsY45X0kaTB1tqocxcZYzpLukPSJEk9JZVIWijpbmttcSxqjXckbdBW1NT7dNcrK/T8ovBAXE5Gqm6/eISmndhHHs8hl7YCAAAuo2kDAIh7JRW1uv2l5Xpt+Y6wsbQUj248e6h+eCbpGgBAUrlH0jhJpdFOCDZsPpQ0XFKFpEJJgyRdJWmyMeZMa23hsRZirb1TCbaOTWM0bdAWbCqt0o+fW6IV2/aFjZ00oLN+e/lx6pub7UJlAACguWjaAADiluM4eqVwu+54aXnE6R1G9+6o2dMKNLwH6RoAQHIwxngUSM7MPILTn1CgYfOqpG9YayuMMZmSHpV0paR/GGNGW2vbdJciKy30Qx2RFmQHEtkbK3fqZ//vC1XUhM5emJbi0c/ONfrBGYOU4iVdAwBAoqBpAwCIS7sqavSrF5fr9RU7w8bSU7y68Zyh+uEZg5RKugYAkCSMMT0kPSZp4hGcO1zSZEn7JX3HWlshSdbaGmPMNZLGS8pXYNq0ua1WdBRFRUWxfktJUnV1ddj779kdmjzYUVLmWn1ofZGugWTl8zv66+dlmrO8PGysV/tUzTyzu4bk1Wm1XeVCde5qS9cBIuMaANcAEvka4E4XACCuOI6jl77YqvN+927Ehs2YPh214IbT9JOzhtCwAQAkDWPMeZJWK9Cw2aHDJ22ukOSR9Iq1tqzxQDBZ85fg7tdbuNSEk5Ea+vtCbYPfpUqAllNZ59fdb++M2LA5tX87/f7iPhqSl+FCZQAA4FiRtAEAxI1d+2r0yxeX642VkdM1N507TNeePpBmDQAgGY2QlCPpGUk3SRp9mPPHB7cfRhn/OLg9/dhLa778/Hw33vbLT1I2fv9i3w7pvV1f7qdn57hWH1pfpGsg2Wwuq9KNf/1Uq3dWhRxP9Xo082v5uurUAfJ42vZ0aG3hOsChcQ2AawBuXwNLliw56ufStAEAuM5xHL34xVbd+fJKlVeHr10zpm8nPTS1QEO7t3ehOgAAYmKRpBOstV9IkjHmcOcPCW43RBkvDm67G2NyrLX7j73ExJSVnhKyX8OaNkhgn24s0w+fWaKyyrqQ4907ZOiP3z5BY/vnulQZAABoKTRtAACu2rmvRr98YZneLNoVNpae6tXPzx2mq08jXQMASG7W2miJmWi6BrelUcYbT5nWRYG1b9qkrLTQpk11HU0bJKYXP9+qGXMLVecLneKvoE9HPfHdE9W9Q6ZLlQEAgJZE0wYA4ArHcTT/s62665UV2lfTEDZ+fL9Omj11jIZ0y3GhOgAA4l5WcFsdZbzx8awo57QJmWmhH/yoaaBpg8TzxLvrde+r4QspXzS6px6aNiYsUQYAABIXTRsAQMztKK/RrS8s01urwtM1Gale/eI8o6tOG6gUb9ueixsAgEPwSTpUDLXxmNPKtcQ1kjZIZH6/owcWrtKf3l0fNnbj2UN149lD5eV3ZgAAkgpNGwBAzDiOo7lLtujuBStVESFdM7Z/Z82aWqDBXUnXAABwGJWSOkmKNh9SRqPH0dI4bUJmWtM1bfxRzgTiS73PrxlzC/XC51tDjqelePTQtDGaeFxvlyoDAACtiaYNACAmtpdXa+b8ZXrHloSNZaR6Nf18o++fSroGAIAjVKpA0ybaquN5jR6H//BtQ8KbNiRtEP+q63z68XNLwn53zslI1ePfGatTh3RxqTIAANDaaNoAAFqV4zias2SLfh0lXXNiMF0ziHQNAADNsUrSYEkDooz3D263W2urYlJRnGq61gdNG8S7ytoGXf3XT/Xx+rKQ411y0vX098dpVO+OLlUGAABigaYNAKDVbNtbrVvmL9O7q8M/4JuZ5tWM84fre6cMIF0DAEDzLZZ0kaQJkh6NMD4huP0kZhXFqczU0KV/qut9chxHHg+/fyD+VNTU6/t/+VSLi/eEHO+fl62/XTVO/fPauVQZAACIlUMtXAkAwFFxHEf/WLRJ5/3u3YgNm3EDcrXwxjN01WlMhwYAwFGaH9xeZowJmSLNGJMi6crg7rOxLCoepaZ4lZZy8PcNvyPV+VjXBvGnvKpeV/x5UVjDJr9nB8390Sk0bAAAaCOSMmljjEmVdL2kaxWYLmCHpJck3WGtrXCxNABIelv3VuuWeYV6b83usLGstBTNuMDoeycPkJdmDQAAR81aW2iM+ZcCaZu5xphp1tpSY0ymAsmbfElW0gtu1hkvMlNTVO87OE1rTb1fGakph3gGEFt7Kut0xZ8/0Ypt+0KOF/TpqL9dNU6dstNdqgwAAMRaUjZtJN0n6X8k3S/pXUnDJd0t6WRjzKnWWj5WBQAtzHEcPb9os+57tUj7a8PXrhk/MFezphbwCUEAAFrOjyS9L+ksSZuMMUWSBknqLKlc0iT+9gnITE9RRW3jpo1PHbPSXKwIOKi8ql7ffvITrdwe2rA5vl8n/fWqceqQybUKAEBbknRNG2NMtgINm4estXcED//HGLNb0j8kfUXSWy6VBwBJacueKt0yb5neXxuerslOT9EtFw7XFeP7k64BAKAFWWu3GGPGSrpd0kRJBZL2SnpegVkG1rhZXzzJTAudGbym3udSJUCoipp6ffcvi8IaNuMG5Oqp75+knIyku20DAAAOIxl/+neW9ISkOU2Orwpue8W2HABIXn6/o78v2qT7Xy1SZV34zY8Jg3I1a8oY9cvLdqE6AAASl7X2HUmH/bSDtbZU0o3BL0SRlRY6FVo1TRvEgaq6Bl399GIt3bw35Pgpg/P05PdOVHZ6Mt6yAQAAh5N0vwFYa7dK+kmEocuC2+UxLAcAktbmsirdPK9QH64rDRvLTk/RzK/l69vj+pGuAQAArgtr2kT4sAkQSzX1Pv3gb0u0aGNZyPFxA3P15++dpKx01lwCAKCtSrqmTSTGmJMl3SJpgbX2C7frAYBE5vc7eu6TYt3/2ipVRbjhccrgPD04pUB9c0nXAACA+JDRpGlTU89SP3BPXYNf1z33WdjUwsf17aSnrqRhAwBAW5f0TRtjzFckvSRpg6QrXS0GABLcptIqzZi3VB+vLwsba5eeolsvyte3xvWTx0O6BgAAxI+mSRvWtIFbfH5HN/3zC721alfI8RE9O+iv3x/HGjYAACC5mzbGmCslPS5phaQLg/M9AwCaye939MzHxXrgtVUR54A/bUgXPTBltPp0Jl0DAADiD2vaIB44jqM7X16hfy3bHnJ8aLccPXP1OHXMTnOpMgAAEE+StmljjLlb0q8kvS5pqrV2v8slAUBCKi6t1PS5hVq0ITxdk5ORql9elK9vnNSXdA0AAIhbTaebijTFK9Da/vDWWj3zcXHIsQF52XrumvHKy8lwqSoAABBvkrJpY4y5WYGGzdOSrrXWNrhbEQAkHr/f0V8/2qgHF66KOO/76UO76IEpBerdKSv2xQEAADRD06ZNdR1/IiK2/rFok37zxuqQYz06ZOq5ayeoW4dMl6oCAADxKOmaNsaYoZLukbRK0p8knWiMaXzKOmttiRu1AUCi2LC7UjfPLdSijeHpmvYZqbrt4nxdfiLpGgAAkBiy00jawD1vrNypW19YFnKsQ2aq/nrVOD4ABQAAwrjatDHGeCV9JGmwtbbLIc7rLOkOSZMk9ZRUImmhpLuttcVNTp+kwD/XcEkfRni5ayU9eezVA0Dy8fkdPf3hRs1+PXK65sxhXXX/5NHqxR+XAAAggWQzPRpcsnhjma7/+2fyOwePZaR69eT3TpLp0d69wgAAQNxyO2lzj6RxkkqjnRBs2HyoQBOmQlKhpEGSrpI02RhzprW28MD51tpZkma1ZtEAkIzWl+zXjLmFWly8J2ysfWaqfnXxCE0b24d0DQAASDhZ6aF/+lbX07RB61tXsl9X/3WxahsOfhjK65H+75vHa9zAXBcrAwAA8czrxpsaYzzGmDslzTyC059QoGHzqqTe1toTJfVSYL2aTpL+YYxJif50AMCh+PyOnnh3vS58+L2IDZuzTFf9+6YzmA4NAAAkrPCkDWvaoHWVVdbpqqc/VXl1fcjxeyeN1nkje7hUFQAASAQxT9oYY3pIekzSxCM4d7ikyZL2S/qOtbZCkqy1NcaYaySNl5SvwJRoc1uyzqKiopZ8uSNWXV3t6vvDfVwDiOU1sLm8Tr/9oESrSmrDxtqlefXDcXk6Z3CO9m7bqL3bWr0cBPF9AFwDkLgOgJbE9GiIpdoGn374zGIVl1aFHL/pnGH65rh+LlUFAAASRUyTNsaY8yStVqBhs0OHT9pcIckj6RVrbchq2NZan6S/BHe/3sKlAkBS8/kdzV2+Vz95eWvEhs24Ptl6bGIfnTukPekaAACQ8LKbTo9G0watxHEc3TJvmT7dGJpgnza2j244e4hLVQEAgEQS66TNCEk5kp6RdJOk0Yc5f3xw+2GU8Y+D29OPvbRQ+fn5Lf2SR+TAJynden+4j2sArX0NrN1VoZlzCvXF5r1hYx0yU3XnpSM16fjeNGtcxPcBcA1Acv86WLJkiSvvC7QGkjaIld//Z61e+HxryLEJg3J176TR/H4NAACOSKybNosknWCt/UKSjDGHO//Ax1A2RBkvDm67G2NyrLX7j71EAEhODT6/nnhvg3735mrVNVoM9YBz8rvrvkmj1K1DpgvVAQAAtJ6sJk0bkjZoDS99sVW/e3N1yLFBXdrpsSvGKj3VlSWFAQBAAopp08ZaGy0xE03X4LY0ynjjKdO6KLD2DQCgiTU7K/SLOUu1dEt52FjHrDTddelITTyuF5/+AwAASSksaVPf4FIlSFaLN5Zp+pzCkGOds9P01JUnqVN2uktVAQCARBTrpE1zZQW31VHGGx/PinIOALRZDT6/Hn93vR5+c43qfOHpmvNGdNc9k0apW3vSNQAAIHkxPRpa05Y9VfrhM0tCft9OT/Hq8e+cqAFd2rlYGQAASETx3rTxSTpUhrjxmNPKtQBAQrE7KjR97lIVRkjXdMoOpGsuHUO6BgAAJL+s9NA/fZkeDS2lus6nH/xtiUor60KOPzh1tMYNzHWpKgAAkMjivWlTKamTpGgfAc9o9DhaGgcA2pR6n1+P/3edfv+ftRHTNReM7KFfXzZKXdtnRHg2AABA8slOI2mDluc4jqbPXaqV2/eFHL/h7KGadHwfl6oCAACJLt6bNqUKNG2ifTwlr9HjktYvBwDiW9H2fZo+d6mWb90XNpbbLl13Txypi0b3JF0DAADalKyw6dFY0wbH7tH/rtOCwu0hx84f2V3/c/ZQlyoCAADJIN6bNqskDZY0IMp4/+B2u7W2KiYVAUAcqvf59eg76/R/b61RvS98tsivje6huyeOUpcc0jUAAKDtyUj1yuuR/MFfk+p9jup9fqWlHGo2biC6t1bt1OzXbcixYd1z9JvLj5PXywekAADA0Yv3ps1iSRdJmiDp0QjjE4LbT2JWEQDEmZXbAumaFdvC0zV57dJ198RRuqigpwuVAQAAxAePx6Ps9FTtrz2YsKmq86ljFk0bNN+6kv268fkv5DT6rFTHrDQ98d0TlZMR77dZAABAvIv331DnB7eXGWNCpkgzxqRIujK4+2wsiwKAeFDX4Nf/vrlal/7h/YgNm4sKeurfN51BwwYAAEDhU6RVs64NjkJ5db2u/etiVTRqAHo90iPfOkH989q5WBkAAEgWcd20sdYWSvqXpA6S5hpj8iTJGJMp6UlJ+ZKspBdcKxIAXLBiW7kmPvKB/vfNNWrwh06H1iUnXY9++wQ98q0TlMd0aAAAAJKkbNa1wTHy+x397J9faP3uypDjt34tX6cN7eJSVQAAINkkQm73R5Lel3SWpE3GmCJJgyR1llQuaZK11u9ifQAQM3UNfv3h7bX649trw5o1knTJmF6669KRym2X7kJ1AAAA8SsrrWnThqQNmueRt9fqP6t2hRybfHxvXX3aQJcqAgAAySjumzbW2i3GmLGSbpc0UVKBpL2Snpd0h7V2jZv1AUCsLN9arl/MWapVOyrCxrrkZOiey0bpglE9XKgMAAAg/jVN2lTX07TBkXtvTYl+++bqkGMFfTrqvsmj5fF4XKoKAAAkI1ebNtbadyQd9rcba22ppBuDXwDQptQ2+PSHt9bqj++sky9Cumbicb105yUj1Zl0DQAAQFTZ6aF//pK0wZHaurdaNzz/uZxGv4p3zk7To1eMVWaTBBcAAMCxivukDQC0ZYVb9mr6nELZneHpmq7tM3TvZaN03kjSNQAAAIcTlrRhTRscgdoGn657don2VNV/eczjkX7/zePVu1OWi5UBAIBkRdMGAOJQnc/R7NdX6bH/ro+Yrpl8fG/dfskIdcomXQMAAHAkmjZtSNrgSPx6wUot3VIecuzn5w7T6UO7ulQRAABIdjRtACDO2N01+u37JdpUXh821q19hu6bNFrnjOjuQmUAAACJK4vp0dBM8z/bomc/3hRy7Ozh3XTdV4a4VBEAAGgLaNoAQJyoqffp4f+s0eP/3aYI4RpNOaGPbr94hDpmp8W+OAAAgAQXPj0aTRtEV7R9n259YVnIsX652frt5cfJ6z3s0rwAAABHjaYNAMSBzzft0fS5hVq7a3/YWPcOGbp/8mh9dTjpGgAAgKPF9Gg4Uvtq6vWjZ5eopt7/5bGMVK8eveIEPkAFAABaHU0bAHBRTb1Pv3tztZ54d33EdM20sX1028Uj1DGLPw4BAACORVbTpk19g0uVIJ45jqNb5hWquLQq5Pg9l43SyF4dXaoKAAC0JTRtAMAln23ao+lzlmpdSWXYWF52ih76+gk6y3RzoTIAAIDkk53G9Gg4vGc/Ltary3aEHPvmuH6admJflyoCAABtDU0bAIixmnqffvvGaj35XuR0zflD2+vaE/N0Ig0bAACAFpOdHvrnL9OjoanlW8v16wVFIcdG9OygOy4Z4VJFAACgLaJpAwAxtKS4TNPnFGr97vB0Tc+OmXpgSoG6+Xa7UBkAAEByazo9GkkbNFZRU6/r//6Z6nwH17Fpl56iR759gjKbpLQAAABaE00bAIiB6jqfHvq31VMfbJATIV3zzXF9NfNr+eqQmaaiIpo2AAAALS276Zo2daxpgwDHcXTrC8u1sck6NvdPKdDALu1cqgoAALRVNG0AoJV9urFMM+YWakOEdE3vTlm6f/JonTGsqwuVAQAAtB1NkzZMj4YD/vHpZr2ydFvIsW+O66dLx/RyqSIAANCW0bQBgFZSXefTrNdX6ekPN0ZM13xrfD/NvHC42memxb44AACANqbpmjbV9TRtIBVt36c7X14Rcmx4j/asYwMAAFxD0wYAWsEn60s1Y16hiptMsSAF0jUPTinQaUO7uFAZAABA2xQ+PRpNm7ausrZBP/n7Z6ptOLiOTTbr2AAAAJfRtAGAFlRV16BZC62e/nBjxPErJvTTLRfmKyeDb78AAACxlNXkJnw1TZs2zXEc/erF5VpfEjqF8b2TRmlw1xyXqgIAAKBpAwAt5uP1pZoxt1CbysLTNX06Z2nWlAKdMoR0DQAAgBuaJm0q6xpcqgTxYM6SLZr/+daQY5ef2EeTju/jUkUAAAABNG0A4BhV1jbowYWr9LePiiOOf/fk/rr5guFqR7oGAADANU3XtGF6tLZr7a79uv2l5SHHhnXP0V2XjnKpIgAAgIO4gwgAx+DDdbs1Y26htuypDhvrm5ulWVPG6OTBeS5UBgAAgMYy07zyeCTHCezXNfjl8ztK8XrcLQwxVdvg0w3Pf66a+oPr2GSlpeiRb52grHTWsQEAAO6jaQMAR2F/bYMeeK1Iz368KeL4lacM0IwLTNgnOgEAAOKdMWaPpE4Rhnpaa3fEup6W4vF4lJ2WospGCZuquga1z0xzsSrE2qyFViu37ws5dtfEkRravb1LFQEAAITibiIANNMHawPpmq17w9M1/fOy9eCUAk0YRLoGAAAkHmPMAAUaNjdI+rTJcGnMC2phWempIU2b6jofTZs25B27S39+f0PIsYsLemraWNaxAQAA8YOmDQD8f/buO07K6uz/+Hd2tleW3jucpe2iKCpWNLbYEHuiPiYx5WeMvcdKVIwlRvPkSYxGY+yCIIKKvSEqisJSlgPSO0vb3nd+f8ws7DDTjhQAACAASURBVOzs7FJ2557yeb9evm7mnHt2rnVuljl73dd19lFJZY0mv7tML38TWF3jcnmra24+leoaAAAQ0Ub7jlOttZsdjaQdpDZpf8W+NrGjsKRKN01Z6DfWq0OKHjh3lFwuWuQBAIDwwW8WAWAffLGiULe9sajZ6pr+nVL18Pl5GjugowORAQAAtKnRkrZFY8JGImkTq+rrPbppykJtL63eMxbnkp64eLSyUqi0AgAA4YWkDQC0oKSyRg++U6BX5q0PmHO5pF8ePUA3nWLYtBQAAESL0ZKKjDEzJI2X5JL0tqTroyGR0/QzW0VNrUORIJSem7tGny0v9Bu75qQhOqw/N10BAIDwQ9IGAIL4bHmhbn8jX5uKKgPmBnZO0yMX5GpMPxZ6AAAg/Blj4iVd2cIpJdbal+RN2nSS9LSkRyUNl3SfpM+MMYdaa0vbPdh21LTSpqyKSptot2RTkf787jK/scP6Zevq8YMdiggAAKBlJG0AoIniyho9MKtAr33XfHXNlccM0I2nGCUnUF0DAAAiRrKkf7Qwv1bSS5IulVRsrc33jX9hjFksaY6kKyT9b3sG2d7Smuw9WF5NpU00q6iu0zWv/KDquvo9YxnJ8frrxaMV745zMDIAAIDgSNoAQCOf2G26Y9oibW6uuqZLmh45P09j+mU7EBkAAMCB81XItLrburV2TjNjXxpjiiTltUdsoZSe5L8ELqXSJqpNmrVUKwvL/MYmTxyl3tmpDkUEAADQOpI2ACCpqKJG989aqinzNwTMxbmkXx87UNefPJTqGgAAELWMMZ0kTZA0x1prG43HSUqUtN2p2NpKWtOkTWWNQ5Ggvc1evFmvzFvnN3bBmN46M7enQxEBAADsG5I2AGLex8u26vZpi7S1uCpgblCXND16QZ4O6Ut1DQAAiHo1kv4p6Xn5739ztqQUSZ84EVRbapq0Kaum0iYaFZbV6ta3F/mNDeicpnvPHuFQRAAAAPuOpA2AmFVUXqNJs5bqje+br675zXGDdN1PhlBdAwAAYoK1ttgY85ikW4wxOyS9LylX0r2S3rbWvu9kfG0hPcn/c11pFXvaRJt6j0ePzdmmooq9VVQJbpeevPiQgKQdAABAOOITC4CY9OHSrbpj+iJtKwmsrhnSNV2PXJCn0X06OBAZAACIdb52ZF9JGmSt7dzCedmS7pF0rqQekgolzZY0yVq79gBf/o+SNkn6raRr5G2J9g9J9x3g1wsrAZU2JG2izoylRVq4xX9/yptOMRrVO8uhiAAAAPYPSRsAMWV3ebUmzVyqaT9sDJhzx7n02+MG6pqTqK4BAACOul/SWEk7gp3gS9jMlZQjqURSvqSBkn4paaIx5nhrbf7+vrC1tk7Sk77/ok7AnjYkbaKK3VKi577f5Td21MBO+vWxAx2KCAAAYP+RtAEQMz7wVdcUNlNdY7pl6JELcpXbm+oaAADgDGOMS97Kmdv34fSn5U3YvCPpYmttiTEmWd6qmCskvWqMGeVLwsAnnUqbqFVVW6drX/1BNfWePWOZyfF67MI8xcW5HIwMAABg/5C0ARD1dpVV676ZS/Tmgk0Bc+44l646YZCuPnGwkuKprgEAAM4wxnSX9E9J5+zDuTmSJkoqlXSZtbZEkqy1lcaYKyUdIWmYvG3TprZb0BEosD0aOa1o8Zf3l2vZlhK/sT9NGKmeHVIciggAAODAkLQBENXeW7JFf5y+WNtLA6trcrpn6JHz8+hvDQAAHGWMOUXe5EqGpC2SnpA0uYWnXCrJJWmmtXZn4wlrbZ0x5jlJD0u6SA4lbQoKCpx4WVVUVLT4+tu3+e91Uri7xLFY0Xbyt1ToX59v9hs7YUCahiYVq6Cg2KGo4KTWfhYg+nENgGsAkXwNkLQBEJV2llXr3reW6K2FgdU18XEuXTV+sK4eP1iJ8XEORAcAAOBnuKR0SS9Iul7SqFbOP8J3nBtk/mvf8diDDy26pCT4f/arqKl3KBK0lbLqej02p1CeRmOdUuJ01RGdHYsJAADgYERt0sYYM17Sg5JyJe2U9JykSdZamhYDUW724s26883F2l5aHTA3rEemHjk/VyN7UV0DAADCxjxJh1prF0iSMaa18wf7jquDzK/1HbsZY9KttaUHH+L+GTZsWKhfUtLeOymDvX76znLprQ17HtfK7VisaBvXv7ZA28r8l/k3HdtNY0ePdCgihIPWfhYg+nENgGsATl8D8+fPP+DnRmXSxhhzhKR3Jb0l6T5JoyVNkpQp6ToHQwPQjnaUVumet5ZoVv7mgLn4OJeuPnGwrjqB6hoAABBerLXBKmaC6eI77ggy37hlWmd5976BpPQme9qUVnFPXySblb9J03/Y6Dc2cXiWRvdgHxsAABC5ojJpI2+ipkDSRdZaj6TZxpgqSY8YYx621gb2SwIQ0d5ZtFl3vblYO8oCq2uG98jUIxfkakRPqmsAAEBUaPiNdEWQ+cbj/Pa6kbQmSZuy6jp5PB65XC6HIsKB2lJUqT9OX+w3ltM9Q/9zaLZDEQEAALSNqLvd3BiTJGm8pGm+hE2D1yW5JZ3mSGAA2sX20ir9/qXvddVL3wckbBLcLt1w8lDNuPpoEjYAACCa1LUy33id5wl6VgxKjI9Tonvv/566eo+qatnXJtLU13t005SFKqqo2TOW6I7T4xeN9nt/AQAAIlE0VtoMlJQoyTYetNZuNMZUSKKRIRAFPB6P3l60WXfPWKKdzVTXjOyVqUfOz9OwHpkORAcAANCuyiR1kJQcZD6p0Z+DVePErLQkt6rL9yZqSqtqlZzgdjAi7K//zF2jOT9u9xu76dShGtYjUwW7NwZ5FgAAQGSIxqRNw+30xc3Mlci7r03YWrfb+8tnMktAcIUlVbp7xmK9u3hLwFyC26VrTxqi3x4/SAncZQcAAKLTDnmTNh2DzHdq9OfC9g8nsqQlxWtX+d4KjbKqWnVOT2rhGQgnK7aW6KHZy/zGjhzYUVceM9ChiAAAANpWNCZtWvstbdi2B/jfj1fo0fc3SJJurkzT78cPdjgiILx4PB69tXCT7n1rid9Cu8GoXll69II8me4ZDkQHAAAQMsskDZLUP8h8P99xs7W2PCQRRZD0JvvalFbVOhQJ9ld1bb2ufXWBqhu1tMtIitejF+QpLo59iQAAQHSIxtvQd/uOzf3WNkNSUQhj2Wcej0fPzFm95/HTX6ySxxO2+SUg5LaVVOq3L8zXta8uCEjYJLrjdPOpRtOvGkfCBgAAxILvfMcjg8w3jH8TglgiTlqTpE1ZVWtbBCFc/PXD5Vq62b+pxqQJI9Q7O9WhiAAAANpeNCZtVsq7MadfmYoxppekFEkFTgTVGpfLpeJGmyjuLq9RXT1JG8Dj8ejNHzbqlMc/1/tLtwbM5/XO0qxrjtHvxw9WPO3QAABAbJjmO04wxvi1SDPGuCVd4Xv4YiiDihSBSRsqbSLB/LU79c/PVvqNnZHbQxNG93IoIgAAgPYRdb/htNZWSfpU0kRjTOPv70JJtZI+diKufdF0/42aOpI2iG3biiv16//O13WvLdDuZqprbj0tR2/8v3Ea2o3qGgAAEDustfmS3pZ3v86pxphOkmSMSZb0jLxbZFpJ0x0LMoylJ7n9HtMeLfyVV9fqxtcXqvF9jd0yk/TAhJFyuWiLBgAAoks07mkjSX+SNznzhjHmaUm5kiZJ+oe1dp2jkbUg0R2nqka9eavr6pUidwvPAKKTx+PR9B826r6ZS1VUEbh3TV6fDnr0/FwNIVkDAABi1+8kzZE0XtI6Y0yBpIGSsuVtCX2utba+hefHrLREKm0izcOzrdbs8N+e6ZHz89QhNdGhiAAAANqPo0kbXyXMV5IGWWs7t3BetqR7JJ0rqYekQkmzJU2y1q5ter619jNjzAR5EzXTJW2VNNn3OGwlxMdJVXsf19SxxkLs2VpcqTumLdJHy7YFzCXGx+nGk4fqV8cMoBUaAACIadbaDcaYMZLulnSOvDeq7Zb0iqR7rLUrnIwvnDVtj0alTXj78sft+s/cNX5jPz+ir44b2sWZgAAAANqZ05U290saK2lHsBN8CZu5knIklUjKl/cOsl/K2wLteF97AD/W2pmSZrZH0O0lwe1f1k3SBrHE4/Hoje83atLMJSquDFw4H9K3gx45P0+Du6Y7EB0AAEDoWGs/ldRqzydr7Q5J1/r+wz5KD9jTps6hSNCa4soa3TLVf7nft2Oq7vjpMIciAgAAaH+OJG2MMS55K2du34fTn5Y3YfOOpIuttSW+Xs3/kHeDzVeNMaOstRH/STtgT5ta9rRBbNhSVKnbp+XrE1sYMJcUH6ebTjH65TED5I6jXzUAAAAOTtNKm7JqKm3C1Z9mLtXG3RV7Hrtc0qMX5AW8hwAAANEk5J90jDHdJf1T3hL+1s7NkTRRUqmky6y1JZJkra00xlwp6Qh5N9k8V9LUtoyzoKCgLb/cPvHU+S8Wlq1YobJt9OiNNRUV3kWJE9dgqHk8Hn3wY6n+9e0OldUEVpYN75Kk64/uot5ZVVpulzkQoTNi6RpA87gGwDUAiesAaC8Zyf7L4JLKwD0U4bwPl27VlPkb/MauPGaAxg7o6FBEAAAAoRHSTSGMMadIWi5vwmaLWq+0uVTetgAzrbU7G0/4Kmue8z28qI1DdURCk3ejto5KG0SvwrJa3f3RFj0+tzAgYZPoduk3h3XUw6f1VO8sEpcAAABoO5kpCX6PiyuotAk3u8qqddu0RX5jg7um68ZTjEMRAQAAhE6oK22GS0qX9IKk6yWNauX8I3zHuUHmv/Ydjz340PwNGxb6HrnpH26Xdu+9y6t3v/4a1rtDyOOAsxrupnXiGgwFj8ej179br/tnFaikmU1fD++frYfPz9OAzmkORBceov0aQOu4BsA1AMn562D+/PmOvC7Q3ppW2hRTaRN27pyxWNtLq/Y8dse59JcL85Sc4HYwKgAAgNAIddJmnqRDrbULJMmYVu+SGew7rg4yv9Z37GaMSbfWlh58iM4J2NOmLrBdFBDJNu6u0G1v5OuLFdsD5pIT4nTLqTm6Ylx/xbF3DQAAANpJZnKTSptKKm3CycyFm/R2/ma/savHD1YuNzQCAIAYEdKkjbU2WMVMMF18xx1B5hu3TOss7943Eatp0qa6lvZoiA4ej0evfrteD7xdoNJmqmvG9u+oh8/PVf8Yrq4BAABAaGSlNNnTpoJKm3CxrbhSd81Y7Dc2slemrj5xcJBnAAAARJ9QV9rsrxTfsSLIfOPxlCDnRIxEKm0QhTbsKtft0xY1W12TkuDWracZXX4U1TUAAAAIjQwqbcKSx+PRbdMWaXf53iRaojtOf7lwdMANjgAAANEs3JM2dZJa+nTWeC7iy1IS3P6/tCZpg0jm8Xj08rx1evDtApVV1wXMHzHAW13TrxPVNQAAAAidwPZoVNqEgynfbdDHy7b5jd14ylAN7ZbhUEQAAADOCPekTZmkDpKSg8wnNfpzsGqciMGeNogW63eW67Zp+fryx8DOhqmJbt12eo4uPaIf1TUAAAAIueSEOCW4Xaqp8973V11br8qaOja5d9CGXeWaNGup39hh/bJ15bEDHYoIAADAOeGetNkhb9KmY5D5To3+XNj+4bSvhPgme9rURXzxEGJMfb1HL81bp8nvFKi8meqaowZ20p/Py1XfTqkORAcAAABILpdLGckJ2llWvWespLKWpI1D6us9unlKvt/elykJbj16QZ7c3OQFAABiULgnbZZJGiSpf5D5fr7jZmtteUgiakcBe9rUUmmDyLF+Z7lumZqvr1Y1X11z+0+H6edj+1JdAwAAAMdlJsf7JW2KK2vUJSOphWegvfz3qzUBa4g7fpqj/p1powwAAGJTuCdtvpN0hqQjJf2jmfkjfcdvQhZRO2JPG0Si+nqPXvxmrR56d1mz1TXjBnmra/p0pLoGAAAA4SGj6b42Fexr44RVhaV6aPYyv7Fjh3TWpUf2C/IMAACA6BfuSZtpku6RNMEY09Fau7NhwhjjlnSF7+GLDsTW5tjTBpFm7Y4y3TI1X9+s3hkwl5bo1h/PGK5LxvaRy0V1DQAAAMJHZor/UriksjbImWgvdfUe3ThloSpr9q57M5Lj9efzclk/AACAmBbX+inOsdbmS3pbUqakqcaYTpJkjEmW9IykYZKspOmOBdmGmiZt2NMG4aq+3qP/fLlap/31i2YTNscO6az3rj9OPzuiLwsuAAAAhJ3MppU2lVTahNq/56zSD+t2+43de9YI9eyQ4lBEAAAA4SHcK20k6XeS5kgaL2mdMaZA0kBJ2ZKKJJ1rrY2KkpTEeP+kTS2VNghDa7Z7q2vmrQlM1qQnxevOM4bposOprgEAAED4ykj2XwoXV1BpE0o/bivVo+8v9xs7eXg3TTy0l0MRAQAAhI+wrrSRJGvtBkljJD0pqVBSrqRaSa9IOtxaW+BgeG2KPW0QzurrPXp2zmqd9sTnzSZsjhvaRe9df5wuHkt1DQAAAMJb00qbEiptQqau3qNbpi5Ude3e9W6H1AQ9cO5I1hEAAAByuNLGWvuppFY/lVlrd0i61vdf1KI9GsLVqsJS3TI1X9+t3RUwl5EUr7vOHK4LDuvNIgsAAAARITOF9mhOee7L1fq+SVu0+84eoa4ZyQ5FBAAAEF4ioT1azGiatKHSBk6rq/fouS9X65H3rKpqA6/H44d20UPnjVKPLPpOAwAAIHLQHs0ZqwpL9ch71m/s5OHddHZeT4ciAgAACD8kbcJIYtOkTTO/JAdCZWVhqW6esjDgLjjJu8i9+8zhOn8M1TUAAACIPLRHCz1vW7R8v5vBslIS9MAE2qIBAAA0RtImjLCnDcJBXb1H/56zSo+9v7zZ6prxposmT8xV9yzaFwAAACAyBbZHo9Kmvf1n7pqAdsv3nj1cXTNZVwAAADRG0iaMJMSzpw2c9eO2Ut08daF+aKa6JjM5XvecNUITD+3FnXAAAACIaIHt0ai0aU+rt5fpkfeW+Y2dlNNVE0b3cigiAACA8EXSJoywpw2cUlfv0dNfrNJfPliu6maqa07K6aoHJ45SN+6CAwAAQBRo2h6tmPZo7aa+3qNbpi5UZc3edUZmcrwenDiKm8EAAACaQdImjCQnuP0el1dToo/2t2JriW6amq+F6wOra7JSEnTv2cM1YTTVNQAAAIgeHVL9kza7yknatJfnv1qjb9f4t0W7+6wR3BAGAAAQBEmbMJLdZOGws6zaoUgQC2rr6vWvL1bprx+sUHUzVV0/GdZND547kh7TAAAAiDrZqYl+j3eVVcvj8XCjUhtbu6NMf57t3xZtvOmi8w6lLRoAAEAwJG3CSMe0pgsH7vZC+1i+tUQ3T1mohRuKAuY6pCbovrNH6Oy8nixaAQAAEJVSEt1KSXCroqZOklRb71FJVW1A2zQcOG9btHy/tmgZyfGaPDGXdQYAAEALSNqEkaZJm53lVNqgbdXW1eupz1fpiQ+br645ZXg33X/uSHXNoLoGAAAA0a1jWqI27q7Y83hXWTVJmzb04jdr9c3qnX5jd505XN2zWGsAAAC0hKRNGKFEH+1p2ZZi3TwlX4s2BlbXZKcm6L5zRuqs3B5cbwAAAIgJTZM2O8qq1a9TmoMRRY91O8r10Lv+bdGOH9pFF4zp7VBEAAAAkYOkTRhJTnArJd6lilqPJG+JfnFlrbJSuNsLB66mrl7//HSlnvx4hWrqPAHzp43orj9NGKkuGUkORAcAAAA4IzugPTWdDtpCfb1Ht7yxUOXVdXvGMpLiNXniKG4QAwAA2AckbcJMZrJbFaW1ex7vKqsmaYMDVrC5WDdNWaglm4oD5jqmJWrSOSN0xiiqawAAABB7Oqb6r7N2krRpEy/NW6evV/m3RbvzzGHq2SHFoYgAAAAiC0mbMJOZ5NbWRkmbHWXV6t+ZEn3sn5q6ev3fJyv1v580X11zxqgeuu+cEeqcTnUNAAAAYlPHNP/PwrvYU/Sgrd9ZrsnvFPiNHTuksy48rI9DEQEAAEQekjZhJis5zu8xJfrYX0s2FenmKflaujmwuqZTWqImnTNSZ+T2cCAyAAAAIHx0TPOvtNnB2uugeDwe3fpGvl9btPSkeD10Xi6V/QAAAPuBpE2YyUpy+z3eyd1e2EfVtfX6+yc/6u+f/Kja+sDqmjNze+i+s0eoE9U1AAAAAHvatLGX563T3JU7/Mbu+Okw9aItGgAAwH4haRNmMpObJG1YOGAfLN5YpJumLNSyLSUBc53TE/Wnc0bq9FFU1wAAAAANOqb6J212ltU4FEnk27CrXA++7d8W7ZjBnXXJWNqiAQAA7C+SNmGG9mjYH9W19frfj1fo75+uVF0z1TVn5/XUvWePUMcmdxECAAAAsa7pZ2T2tDkwHo9Ht72xSGWN2qKlJbo1eeIo2qIBAAAcAJI2YSazSXs0+iojmEUbinTz1GDVNUm6f8JInTayuwORAQAAAOGvadKGLgcH5tVv12vOj9v9xm7/6TD16ZjqUEQAAACRjaRNmGmatKHSBk1V1dbpbx/9qH981nx1zYTRPXXPWSMCenQDAAAA2Kvp52WSNvtv4+4KPdCkLdq4QZ30s7F9HYoIAAAg8pG0CTNZTfe0oUQfjeRv2K2bpizU8q2lAXNdMpL0wISROmUE1TUAAABAazqkJMjlkjy++6CKKmpUW1eveHdcy0+EpIa2aPkqrardM5aa6Nafz8tVXBxt0QAAAA4USZsw03RPG+72guStrnniwxV66vNVzVbXTDykl+4+a7g6pFJdAwAAAOyLeHecslIStLu8Zs/Y7ooadU5PcjCqyPH6d+v1xYombdFOz6EtGgAAwEEiaRNmmrZHI2mDBet36+YpC7ViW2B1TdeMJD147ij9ZHg3ByIDAAAAIlvHtES/pE1hSRVJm32wuahC98/yb4t25MCO+vkR/RyKCAAAIHqQtAkz6YlxinNJDcUUJZW1qqmrVwIl+jGnsqZOf/1whf71+Uo1U1yj8w7trbvPHK6s1ITQBwcAAABEgW4ZyVpVWLbn8baSKg3r4WBAEcDj8ej2aYtU0qgtWkqCWw+fl0dbNAAAgDZA0ibMuONcSk+MU3FV/Z6xXWXV6pqZ7GBUCLWCwkpd/c4XWtloAdmgW2aSJk8cpRNzqK4BAAAADka3TP+qmq1FlQ5FEjmmzt+gT22h39itpxn17URbNAAAgLZA0iYMZSW7/ZI2O8tJ2sSKypo6PfPdDk1fWtRsdc2Fh/XWH88YrqwUqmsAAACAg9WtyTprazFJm5ZsKarUpFlL/cbG9u+oy4/q70xAAAAAUYikTRjKSnJrvfb2VWZfm9gwf+0u3Tx1oV97hgY9spI1eeIonWC6OhAZAAAAEJ2a3hy3tYSkTTAej0d3TF+kksq9bdGSE+L08Pm5tEUDAABoQyRtwlBmsv/+NSRtoltFdZ0ee9/q31+ulqeZ6pqLD++jO84YpsxkqmsAAACAthTQHq24yqFIwt+07zfq42Xb/MZuOTVH/TunORQRAABAdCJpE4aykt1+j3eRtIla363ZqZun5mv19sDqmp5ZyZp8Xq6OH9rFgcgAAAAQq4wxR0qaLGmspFJJsyXdbK3d1uITI1DT9mhb2NOmWVuLK3XfzCV+Y4f3z9YV4/o7ExAAAEAUI2kThjKT/JM2O8tqgpyJSFVRXadH3rN6bm7z1TWnD83Qwz87ShlU1wAAACCEjDFjJH0i6SNJ50rqKW8CZ4ikcQ6G1i56dUjxe7xxd4VDkYQvj8ejO6YtUnGjtmhJ8XF6+Pw82qIBAAC0A5I2YSgrqWl7NEr0o8m81Tt1y9SFWrOjPGCuV4cUXXV4lg7tmUrCBgAAAE54WFK+pHOstXWSZIwplvSEMWawtfZHR6NrY90ykxUf51JtvfdOqp1l1SqrqlVaEkvlBm8u2KiPmrRFu/lUowG0RQMAAGgXfBINQ03bo+0sp9ImGpRX1+rh2VbPf7Wm2eqanx/RV7ednqMNq6NqHQwAAIAIYYzpJOkESb9qSNhIkrV2mqRpTsXVntxxLvXskKJ1O/feULVxd4WGdstwMKrwsa24Uve+tdRvbEy/bP3i6AEORQQAABD9SNqEocymSRsqbSLeN6t26JY38rU2SHXNw+fn6ujBnR2IDAAAANgjV1KcpG3GmBckTZDkkvSmpD9Ya3c5GVx76Z3tn7TZsKucpI18bdGmL1ZRxd6bCL1t0XLlpi0aAABAuyFpE4bY0yZ6lFXV6s+zl+m/X61tdv6yI/vp1tNzlE77BQAAALQjY0y8pCtbOKVEUsPC42lJ78qbtBks7542g40x46y19e0aqAN6Z/vva7OumRutYtFbCzfpw4KtfmM3njJUg7qkOxQRAABAbIi63xT7FiNXS/q1pP6StkiaIekea22Jg6Hts6xk/z1tdpVVOxQJDsbcH7frljfytWFX4GamvbO91TXjBlFdAwAAgJBIlvSPFubXSrrT9+cfrLUNCZ6PjDFFkl6RdJqkd9ovRGf06+S/N8vq7WUORRI+tpVU6p63lviNHdK3g351zECHIgIAAIgdUZe0kfSgpOvkvRvsc0k5kiZJOsoYc3Qk3BmWFVBpUy2PxyOXixL0SFBSWaPJ7y7Ty9+sa3b+8qP66dbTctjcFAAAACFjrS2Vt9VZUMaYc3x/bJqYme07HtLMXMRrWjmysjC2kzYej0d3vblYuxvtrZoYH6dHaIsGAAAQElH1W2NjTKq8CZtHrbX3+IY/MsZsl/SqvJtqfuxQePssKd6lpPg4VdV680vVdfUqq66jhVYE+Hx5oW6ftkgbdwdW1/TtmKo/n5erowZ1ciAyAAAAoFUrfMekJuMJvmPgh9woMLirf6XNysJShyIJD7PyN+u9Jf5t0W44eagGd2WfHwAAgFCIa/2UiJItb//lKU3Gl/mOPUMbzoFxuVzqlJboN0aLtPBWXFmjW6fm6/Jn5wUkbFwu6RdH99fsypXRJwAAIABJREFU644lYQMAAIBwViBpjaSLjTGNSyrO9B2/CHlEIdC3Y5pfBcnmokqVVtU6GJFztpdW6e4Zi/3G8vp00JXHDHAoIgAAgNgTVaUb1tqNkn7fzNQE33FxM3NhKTstUZuKKvc83lFWrT4dUx2MCMF8smybbp+2SFuKKwPmBnRO08Pn5+rw/h0diAwAAADYd9ZajzHmZkmvS5pijHlKkpG3BfWb1tpvHQ2wnSTGx6l/p1S/tmgFm4tj8jP83TMWa1fjtmjuOD16fq7i3dF2vycAAED4ipikjTEmXtKVLZxSYq19qZnnHSXpNkmzrLUL2iu+ttY53b8jQWFJlUORIJii8hpNmrVUb3y/IWDO5ZKuPGaAbjjZKCXR3cyzAQAAgOYZY+IkfSVpkLW2cwvnZUu6R9K5knpIKpR3/5lJ1tq1B/La1tqpxpizJd0taaaknZKeknTngXy9SDGyV5Zf0mbRhqKYS9q8nb9Z7yza4jd23clDNKQbbdEAAABCKWKSNpKSJf2jhfm1kvySNsaYEyTNkLRa0hXtFVh76JJB0iacfbB0q/44fZG2NfO+DOqSpofPz9OYftkORAYAAIAocL+ksZJ2BDvBl7CZKylHUomkfEkDJf1S0kRjzPHW2vwDeXFr7SxJsw7kuZFqVK8szViwac/jxRuLHIwm9LaXVumuJm3Rcntn6TfHDnQoIgAAgNgVMUkba22pJFerJ/oYY66Q946wJZJOt9YGXfCEo65NkjbbSgJbbyH0dpVV676ZS/RmowVdgziX9JvjBum6nwxRcgLVNQAAANg/vn1k7pF0+z6c/rS8CZt3JF1srS0xxjTc6HaFpFeNMaOstXXtFW80Gdkry+/xt2t3OhSJM+6esVg7G+2jmuiO0yPn59EWDQAAwAFR+QnMGDNJ0nOSPpF0nLV2q8Mh7TcqbcLP7MWbdfLjnzebsBnaLV3Trzpat52eQ8IGAAAA+80Y013SdHmTNq2dmyNpoqRSSZdZa0skyVpbKW9L6QJJw+Rtm4Z9MLpPByU2SlCs31mhDbvKHYwodGblbwpoi3bNSYNlutMWDQAAwAkRU2mzr4wxt0q6S9J/JP3aWlvrbEQHpmtGst/j5tpwITR2lFbpnreWaFb+5oA5d5xLV50wSFefOFhJ8SRrAAAAsP+MMadImiopQ9IWSU9ImtzCUy6VtwvBTGutX0mItbbOGPOcpIclXeT7uiFXUFDgxMuqoqLigF9/aOdELd66t8PBlM8X6bShmW0WWzjaXVGnO2as9xsb0ilRJ3Srcew9PFgHcw0genAdgGsAXAOI5GsgqpI2xpgh8vZ/XibpX5IOM8Y0PmWltbbQidj2F5U24eHt/M26e8Zi7WjUKqBBTvcMPXpBXkArBQAAAGA/DZeULukFSddLGtXK+Uf4jnODzH/tOx578KHFjtE9UvySNl+tL4/6pM3fv9mu4qr6PY/j46Qbju4qd9w+dyYHAABAG2uXpI0xJk7SV5IGWWs7t3Betrzl/+dK6iGpUNJsSZOstWsP4KXPlfd7ylHzC5hfS3rmAL5uyDXd04akTWgVllTp7hmL9e7iLQFz8XEuXX3iYF11wmAlxkdlh0EAAACE1jxJh1prF0hSkxvPmjPYd1wdZL5hLdXNGJPu2x80pIYNGxbql5S0907KA3n9n3co1osLvtjz+IfNFerUe0BAF4RoMSt/k+asXeU3dv3JRqePGxzkGZHhYK4BRA+uA3ANgGsATl8D8+fPP+Dntlelzf2SxkraEewEX8JmrrwJlhJJ+ZIGSvqlpInGmOOttfn786LW2oflbQMQ8ZqrtPF4PHK5uOOpPXk8Hr21cJPufWuJdpXXBMyP6JmpR87P0/Ce0X3HHQAAAELHWhusYiaYLr5jsPVW45ZpneXd+watyOmeoYGd07Rqe5kkqabOo5e+XqfrTx7qcGRtb3tple6escRvLLd3ln573ECHIgIAAECDNi0TMMa4jDH3Srp9H05/Wt6EzTuSellrD5PUU969aDpIetUYE7ObhKQlxSstce+3X11Xr6KKwCQC2s624kr95oX5uvbVBQEJmwS3SzeePFRv/v5oEjYAAABwWorvWBFkvvF4SpBz0ITL5dKlR/bzG3vpm7Wqqq1zKKL24fF4dNebi7WzUQvoRHecHr0gT/FuOgkAAAA4rc0+kRljukuaLm+7s9bOzZE0Ud47vi6z1pZIkrW2UtKVkgokDZO33VnMYl+b0PB4PHpj/gb95C+f6YOlWwPmc3tnadYfjtUfThqiBBYxAAAAcF5rWYTGH1o97RlItLngsN5KT9rbkGJ7abWenbPGuYDawaz8zQFtoK/9yRAN7ZbhUEQAAABorE3aoxljTpE0VVKGpC2SnpA0uYWnXCrJJWmmtbZx6b6stXXGmOfkbXN2ke/rhlxDz7tQq6io2PP66e56v7lvl6xQ7U5ulGtL28tq9eRXhfp2Y+BNivFx0mWjO+q8EVmq37VBBbtCE1PjawCxiWsAXAPgGoDEdYAWlcnbnSDYZiuN7/4KVo2DZmQkJ+jCw/ro2S/3bhf0t49X6JzRPdWzQ+SvxRr27mwsj7ZoAAAAYaWtygaGS0qX9IKkkZK+buX8I3zHYL2bG55/7MGHFrmyU/y7w+2qqHUokujj8Xj03opi/W7GhmYTNqZzkv5+Vm9dOKqD3HHsIwQAAICw0rCXTccg850a/bmwnWOJOn84cbA6pCbseVxeXaebpixUXX1kFy01tEVr3AqatmgAAADhp00qbSTNk3SotXaBJBljWjt/sO+4Osj8Wt+xmzEm3Vob8o0zhw0bFuqXlLT3Tsphw4Zp0Ip6fbG2bM9cQkYnDRs2yJG4osnG3RW6fdoifb58e8BcUnycbjxlqH51zEDHkjWNrwHEJq4BcA2AawCS89fB/PnzHXld7JNlkgZJ6h9kvmFjls3W2vKQRBRFstMSdfOpRn+cvrciZe7KHfrnZyv1+/GDW3hmeJuZv1mzl/i3Rbvu5CEaQls0AACAsNImt9NYa+c2JGz2URffcUeQ+cYt0zofWFSRr2um/542m4sqHYokOng8Hr38zTqd+vjn+nx54A2Hh/XL1rvXHqvfHDeI6hoAAACEs+98xyODzDeMfxOCWKLSJYf31bhBnfzG/vLBcs1fuzPIM8JbYUmV7mnaFq1PB/3mWNqiAQAAhBunaqAbmgEH66/ceDzyGwcfoN7ZqX6PN+yiHfWBWrejXJf++xvdMX2RSqv828wlJ8TprjOH67XfHqWBXdIdihAAAADYZ9N8xwnGGL8WacYYt6QrfA9fDGVQ0SQuzqXHLxqtjmmJe8bq6j265pUFKqqoaeGZ4cfj8ej2aYsC26Kdn0tbNAAAgDDk1Ce0ulbmG8cV2Y2DD0LvbP98FUmb/VdX79G/56zWqX/9XF/+GFjYNXZAR82+9jj96pgBVNcAAAAgIlhr8yW9LSlT0lRjTCdJMsYkS3pG0jBJVtJ0x4KMAt0yk/XoBbl+Yxt3V+iP0xfJ44mcZerr363XhwVb/cauP3kobdEAAADCVFvtabO/yiR1kJQcZL5xX7CYzVQEJm1oR70/Vmwt0S1v5OuHdbsD5lIT3br1tBxddmQ/xZGsAQAAQOT5naQ5ksZLWmeMKZA0UFK2pCJJ51pr6x2MLyqcmNNNvzx6gJ79cu92rLPyN+u4IV104eF9HIxs36zdUab7Zi71Gzukbwf9+tgBDkUEAACA1jhVadNQ8tAxyHzj5sGBm4/EiC7pSUqK3/sWlVTWRlwpvhOqa+v15EcrdMaTc5pN2Iwb1EnvXXec/mdcfxI2AAAAiEjW2g2Sxkh6Ut41U66kWkmvSDrcWlvgYHhR5dbTjYb3yPQbu+etJVpZWOpQRPumrt6jG15fqPLqvY0uUhPdevzC0bRFAwAACGNOVdoskzRIUv8g8/18x83W2pgtL3G5XOqVnaJVhWV7xtZsL1Nenw4ORhXe8jfs1i1T87VsS0nAXEZyvO48Y5guPKyPXC6SNQAAAAhP1tpPJbX6gdVau0PStb7/0E6S4t168pJDdNbf5qiixpsAqaip0zWv/KBpV41TUrzb4Qib98/PVmr+2l1+Y3eeMVz9O6c5FBEAAAD2hVO313znOx4ZZL5h/JsQxBLWBndJ93u8fGtgMgJSZU2dJr9boAl//7LZhM3Jw7vpwxuO10WH9yVhAwAAAGC/DO6arnvPHu43tmRTsR7/YIVDEbVs8cYiPf7Bcr+xE3O66pKx4d/SDQAAINY5lbSZ5jtOMMb4tUgzxrglXeF7+GIogwpHQ5tsDknSJtA3q3bo9Ce+0FOfrVJ9k/1AO6Ul6m+XHKJ/XTZG3TKDbaEEAAAAAC278LA+OmNUD7+xpz5fqXmrdzoUUfMqa+p0/WsLVNtocdQxLVEPnTeKG9gAAAAigCNJG2ttvqS3JWVKmmqM6SRJxphkSc9IGibJSpruRHzhZGh3/6SN3RrefZNDqaSyRne+uUgX/etrrd5eFjB/7iG99MENx+usvJ4sTgAAAAAcFJfLpQfPHaUeWXtvBvN4pBteX6CSyvDZe/Shd5dpxTb/deOD545S1wxuYgMAAIgETu4++DtJayWNl7TOGPOdpE3yVtkUSTrXWlvvXHjhIadJ0uaHdbtU17ScJAZ9Yrfp1Mc/14tfrwuY65GVrGevOEyPXzRaHdMSHYgOAAAAQDTKSk3Qoxfk+Y1t2FWhSTOXOhSRv/eXbNF/5q7xG7tgTG+dNrK7MwEBAABgvzmWtLHWbpA0RtKTkgol5UqqlfSKpMOttQVOxRZOBndJV4fUhD2PSyprtWRTkYMROauwpErXvPKDfvHct9pUVBkwf+mRffX+9cfpxJxuDkQHAAAAINodPbizfnn0AL+xKfM3aPbiLQ5F5LVxd4VunprvN9Y7O0V3nzU8yDMAAAAQjuLb44taaz+V1Go/KmvtDknX+v5DM+LiXDpqYCe922gB8M6iLcrt3cHBqEKvvt6j175br8nvFKi4sjZgvn+nVD10Xq6OHNjJgegAAAAAxJJbTjP6YkWhXxuyO6Yv0qH9OjjShqymrl7XvPKDiir2tmmLj3Ppb5ccoozkhBaeCQAAgHDjZHs07KPxOV39Hr/0zVqtLIydvW1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" ] }, "metadata": { "image/png": { "height": 264, "width": 822 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_error_normalized(M, N, b, x0, w=0.1, n=1000) " ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "The normalized relative error stabilizes in this case whereas unnormalized it always increased.\n", "\n", "However, to converge the gap between 2 iterations must tend to 0.\n", "\n", "Sometimes we can have a surprise:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Itération du minimum : 500 499\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 264, "width": 821 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "A = mk_A(308)\n", "b = A.sum(axis=1) \n", "\n", "M = np.diag(A) \n", "N = np.diag(M) - A \n", "\n", "x0 = np.random.random(4)\n", "plot_error_normalized(M, N, b, x0, w=0.1, n=500) " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004062676542953207" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "min(error)" ] }, { "cell_type": "markdown", "metadata": { "lang": "en" }, "source": [ "We converge but near the desired value. It is rare and it is due to the very bad conditioning\n", "of the matrix A. This bad conditioning generates calculation errors which make it impossible to arrive\n", "to the exact solution." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.1405202107473442e+17" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.cond(A)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ] }