{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# UNIST\n", "## Mathematical Sciences( http://www.math.unist.ac.kr )\n", "### 2015 CMA Summer Workshop : Mathematical Bigdata Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Reference : IPython Interactive Computing and Visualization Cookbook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "https://www.packtpub.com/big-data-and-business-intelligence/ipython-interactive-computing-and-visualization-cookbook" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "import pandas.io.data\n", "import datetime" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Logistic Map" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f(a, x):\n", " \"\"\" Logistic Function \"\"\"\n", " return a*x*(1-x)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "init = x = 0.2\n", "values = np.array(init)\n", "for i in xrange(100):\n", " x = f(4, x)\n", " values = np.append(values, x)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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amCBrbMwg1YPfzMpqgKHXsuUbIk2ySyOCMgreW7+dFTP79uBBB1qfUFO+OgUf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\n4I8Bt1RS444BGyMmHEG6gk9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VGUWgs6S6lMGLmeDXIjWLZiiCt0G4qRH8s9EV\nuhSq152iPQOLF2Q9h/j609Qe95M+onwB8H66jSKjFbybUSTCTvP9D3Qogxczwa9FqoIf0qK5p/As\nVvdaKQRf10CfDVydo1AN13Xf4xTtGWA5eDhbNPXoouBfAHy84ygyxaJxv/cc4BqleHWJkexM8Gsx\nRYumD/Vur3UKHRuoWU3wKcA/5Cta7XXdjmWSCt6oPQX8TqF00j5hM75yWjT7SVDwxh55PvDpiO/6\nzrcXnaoZsjrmqnKgO5m/7VgGL2aCX4tUgv9h4LUDNMIl+lsdcQmtKGOIsi5o/Z3AzYEpZamos2im\nqOABbkITQYl00j6RUn+87VGEHWj/OkZY2fMdAB5Rilsjvus737nATZFLSdhyPJ+Z4HtFKsE/lrDV\nH3Ojb4L/WuC62+53qs+ztP8OazuWqe3k5OIm87NEOmmfSKk/TVlt+835YhYadJVzV/Vuz3c6cfaM\n/d5m4HnAZzKUoxYzwa9FdJqkCGc73+m7Eb4MOK+nkcMScfaM/U4dwZf03+uuO0mLxiD3bO2hsESc\nPWO/00TwtySeLyfBQxrBPwW9iFwxa3cm+LVIyaJ5FfAehmmEj6BHD32MHHISfGkFX73u84D/PEUf\nu8Bs7aGQWn987TFm0Tv3fGMh+BdR0J6BmeDrkGLRvAp470CN0C7W1cfIoTPBm+3+ngh8MWO5Gq8r\nwjPRa24/i+n72FNGbgX/k8DLIjvtY+iEiDPQm3N0hSX40Bx493szwQ+AKIIX4fFoBf3JYiVqRp/D\n9wPA/xbZoKoK7OnAl5XicPbSrb2ufY8XA18z/5+6jz1l7Af+dUL98bXHx6GXGojptJfQgc2rImMB\nTeeDNAX/3cwE3ztiFfwPAR/MVFmi0fPw/Q50xkBsg3KfZx/++/J1RdgDvBr4QRbDx54y7gaeTLf6\nA4AIz0UHKSGu014CdpHHngF4E3oy2nsjrb8l4Ajw5UzlqMVM8GsRS/CvQs9CWw+wsyljG1SV4Ev7\n7+51/xXwl0rxlQXxsacMm5LYpf5Y/Ef0bm6xnbYVYrkI/hT0Esix1t8S8NmIVTCTMBP8WgRn0Yhw\nJnoG28eLlmg8SLGDqs/z+4Gf6iHYaYnhfwd+u+B1ZoQjR/1BhKeihcLbEjrtJfT+wp+N+E4THjA/\nY62/JQrbMzATfB1ismj+V+DDSnGkYHlGg0Q7yA12vh49rO4j2LkEfBc6uLpeOuBRo2v9cfBzwK8l\nLs/xU+hd4C7PJDBSY2CPBn6otNBpJXgROV9EbhCRG0XkTZ5jftP8/Qsi8vT8xewVMRbNzwLPmGLq\nXY+wXvgzgV9jxX8vHexcQu/V+86Jb1a93rFKcJk5Jy8hfVS20/zLIjA6xMBuBp6aqxw+NBK8iGwA\n3gacjw6uXSQiT6occwHwRKXUAeDfAm8vVNa+0ErwImwU4f9BL0H7FCJfkoic16WAE8MSWq38EVo9\nvQJH8RR8Fm9Er+Hysql0vuusXjTCeRbuCPCdwCfQux+l7ptsl8cYOpvKdghFy9Gm4J8D3KSUukUp\ndRS9tOYrK8e8Avh9AKXUVcBeETkte0n7QyPBi3Aq8DHgacCnzMexL+m81MJNED8G/C/o5/qXNYrn\nvELXPRkQ4KVMJ+/9vKELMCKcZ37aEeCZwA+glwU4QPo7Hcus4F7K0UbwZ8CqxXhuM5+1HXNm96IN\nhrrVD08S4SUifBa9YtyZwEXo9LsxVJYx40Tz8yz6JdquGznMGAdeB7wePcHOzp1IfqdjmRXcVzna\nvObQRXyk8nvM4j9jw1uBHSLcB3wLrRg2A/cDh4At6JmYb1eKC4ELhyroRGDX2eibaF+L7lAuHrox\nz+iEHazku18D/B3zOw2GKOXnYhF5HnCpUup88/vPAseVUr/sHPPbwEGl1PvN7zcAL1ZK3Vk515RJ\nf8aMGTMGg1KqKqKD0KbgrwYOiMh+9JK0F6KtCRdXAJcA7zcdwr1Vcu9SwBkzZsyYkYZGgldKLYnI\nJcBH0VHrdymlrheRi83f36GU+oiIXCAiN6Ej1D9WvNQzZsyYMaMVjRbNjBkzZsyYLorPZA2ZKLWo\nEJF9IvJxEfmyiHxJRH7afH6SiHxMRL4iIn8hIpPI084BEdkgIteIyIfM7+vyWYjIXhH5gIhcLyLX\nichz1/Gz+FnTRq4VkfeKyJb18ixE5HdF5E4Rudb5zHvv5lndaDj1+9rOX5TgQyZKLTiOAv9eKfVk\n9IYT/4e5/zcDH1NKnQ38lfl9veBngOtYybRar8/iN4CPKKWehJ7ReAPr8FmY+N5PAs9QSn0n2gr+\nEdbPs3g3mh9d1N67iJyLjoOea77zWyLSyOGlFXzIRKmFhVLqDqXU583/HwSuR88bWJ4cZn7+y2FK\n2C9E5EzgAuB3WEmtXXfPQkT2AN+jlPpd0LEupdR9rMNngU4/PgpsF5GNwHZ0Qse6eBZKqU+iZ+a6\n8N37K4H3KaWOKqVuQe/V+5ym85cm+JCJUusCRqk8HbgKOM3JNLoTvcPMesCvA/8BVq0Nsx6fxeOB\nu0Xk3SLyDyJymYjsYB0+C6XUt4FfRU8g/Do6C+9jrMNn4cB3749h9b7CrXxamuDnCC4gIjvRa7H8\njFLqAfdvSke5F/45icgPAHcppa5h7cQ4YP08C3T22jOA31JKPQOdfbbKglgvz0JEzgL+L/RuT48B\ndorI69xj1suzqEPAvTc+l9IEfzuwz/l9H9Pd2T4JIrIJTe7vUUr9qfn4ThE53fz90cBdQ5WvRzwf\neIWIfBV4H/C9IvIe1uezuA24TSllNz75AJrw71iHz+JZwN8qpb6llFoC/hi9ld16fBYWvjZR5dMz\nzWdelCb45YlSIrIZHSC4ovA1RwMREeBdwHVKqbc6f7oC+FHz/x8F/rT63UWDUurnlFL7lFKPRwfR\n/lop9XrW57O4A7hVRM42H70UvXXbh1hnzwIdXH6eiGwz7eWl6CD8enwWFr42cQXwIyKyWUQej150\n7e8az6SUKvoPvZTuP6IDAj9b+npj+ge8EO03fx69jsY16Oj3ScBfondi/wtg79Bl7fm5vBi4wvx/\nXT4L9GqknwO+gFate9bxs3gjuoO7Fh1U3LRengV6NPt19P6st6IninrvHb3ZyU3ojvFlbeefJzrN\nmDFjxoJi3rJvxowZMxYUM8HPmDFjxoJiJvgZM2bMWFDMBD9jxowZC4qZ4GfMmDFjQTET/IwZM2Ys\nKGaCnzFjxowFxUzwM2bMmLGg+P8B6nF4FSHM8PMAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(values, '.-')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### to pandas Series" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "obj = pd.Series(values)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.2 , 0.64 , 0.9216 , 0.28901376, 0.82193923])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "obj.values[:5]" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Int64Index([0, 1, 2, 3, 4], dtype='int64')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "obj.index[:5]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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S8GfcTZo4eBdyi6ZMwRfvN5RcEodJPuvWgOuq0utVwUdeU3ZtFIZi0SzqAIUZ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\nAw/BePAtoEyB+Uzo1tTnR4+me4I/gCxYYFBwtAs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "obj.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bifurcation of Logistic Map" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n = 10000\n", "r = np.linspace(2.5, 4.0, n)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "iterations = 1000\n", "last = 100" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x = 1e-5 * np.ones(n)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "lyapunov = np.zeros(n)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x = f(3, x)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 8.99964001e-05, 8.99964001e-05, 8.99964001e-05, ...,\n", " 8.99964001e-05, 8.99964001e-05, 8.99964001e-05])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(3, x)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(array([ 2.5 , 2.50015002, 2.50030003, ..., 3.99969997,\n", " 3.99984998, 4. ]),\n", " array([ 2.99997000e-05, 2.99997000e-05, 2.99997000e-05, ...,\n", " 2.99997000e-05, 2.99997000e-05, 2.99997000e-05]))" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r, x" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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UA2xj3uI4RiImMBIiQgJRDHoZ28wueF/4OZ/GTFKU3ybFaRLb/CsscJ7I4VNO\nmJQQhetpPivEhl6bbZErEahLhLmGyFprKS8iNU2UE1DJBIgadBDkQgRiDSMFj/sazmNKHJgSpTHM\nEGGXIwQBwtfpPl/PKTqdNFVWQOGYCr0UCZXCpFwvhf6t+Joq56xXrPo89mHERGGdUp3a8ETlriln\nTgpev58/CjyNkaW9RB7b0z4vmbtM+LXWCBMXPaPrhKnIIeLeTxPumYLGuUiQTnw8u+gsKaAadFLu\n+pvf9xOkTiqoTFjacFYIFU/r0jOSyCUSiUQikbinUUp5P/AlN6q/lpzd7PNKKd8GvAHbNG7HwhO1\nUR9l8wrhOcwY5AhG4BYIR8RhjGBsx4iejEe653G5lHICI2QrmMIyR4Rxjjb9rmPkEDqLP4vcjWFE\nVOGh2rsqHFNtFLImsxERr3k6FTy5J+4mXBUvY0qMCnJ/GiOJk9jmXsYXur7cLGWC0g2F1UlJmsCU\nuEsYWV3wcahe3DbCUXOvX3sII+HjhHIkArHWrKeIp0oALGOqpEimas+NEUXVoVM13FItM4fCCxVK\nOouZt7QhlC15kfoq7G6+D/uYnsFUuQcIF9GzBClSyKZKEKzR6Vyq3Ez125qutDlrcwTZmsTu1/PY\nMyFFsB9b72XsGRMR7nbCFKHUv0HVnhvH/m1dIp5DuFK12xSSyCUSiUQikbgnsFXFq1eCdjNRa/15\n4Oc3+q2U8v1EbbLjWOjdGBsX81ZuWj8WWnaYzlyhGSIkb7Dpo9K1nyylyF1ykFCW+ghFa5EwGBn3\nvrZh4ZYQNcPwthcIO/oxInRQ9cpGsM08hDIli34RLylDql826Ne46OsiYw0RAoVNThMbeTlZakxt\nWFxb160tej1JqEif93WUqcY8Ubh8kVCzlI+35m1lxHLR74FIBATJGyOUOOWJiVzI4l9r2yqTInJb\nUeSGCNJygcg53O1jOEeQZxErjVtreIhOoi2l6yi2hnsJwqU2bbim+moJ/QDhLKr+TtCpQGv+Kjew\nRLiaPo2t28sIQieCpj9gfBZT3Y401x/FnudlQhmcpDO3TgplKnKJRCKRSCQSQinlI/Twl+7bkaht\nBbXWHwd+XN9LKW8Hvp4gTC20J9yBqUeD2GZUCscikRcncw0ZkExgKp4wiSmBMttYJtSpU9jmVjlO\n60QxZryNDEZUN22VyJFSqKXCCxUWpwLeCk2cIAxDLhOukQqr2+l9nmyO9WHhi8qPW8EIxLqfv9/b\nrXOlSYXoqUphAAAgAElEQVRKGchE41HMFOU+jKgd9TErz20QUzx305mreMb7P920m8HImMaIr8t+\nIpxylbDvl8Plfv/tOEEuRVSlHknV2oprJYQhiUIdZS6iZ0D5atAZcilSOYrdswnCtGQe+BPgMTr/\nsCDHSNn8y8Clre03ShSZ17V2eFs5fY4Toa/6g4WKurcGK1qzAeweyr1SRFVKNXTWhmvDOGWSonsq\nQpuKXCKRSCQSiXsXmzEZudvI2vWglDIMfCsWgjmOkbARNlbmhoG3YRtPmZxo4zxElB+QkiFDkY36\ngXBXlBvgdmxjvB9TYRYwsiHlTK6My/7bTsIE43NEjTiNR8ocPrfTfs02n04hhKrx9TBG0DSuYwQZ\n0MZ6nnDHlGGJ8tggzC8Ekacl4EHgNT4GrZWMSaQ0qvzBc4SRzAN0Gp2I4C37OkAodyJyMuBQuKXW\n5hhBSNo8NREXWeu31+kVyxhRVY08KX1PY+sqstrWg2uLeqtQtgrFS71TWOu4Hx8giNgwcc8miPBS\nlUFYw4iy5r5EELfTfky1BqfpJPp6BkR8lWO32rxUHw//XfdNJE2EXiQQoizFNBF+mYpcIpFIJBKJ\new8vFCp5L5K2FqWUR4H3E46N2wh1ahojGWOYmqUQw/v89H5sg6xaZCJtIg3rGBFsLeSFee/nJU0b\nOfstEg6Zy4RxiJSwKWyj3dZKmyHcGJXHNICpaZeJDbhC/C5gm22FOsp4QsYaR/z7FLaR30aoWQp9\nlLW/1Mg2/HKBKEjeYhX4IuCNfu1Z70+hpWNEAXIRsAuEernu8xGZUe6cHBnbcgezmLoJofJo3DJq\nOUcYa8gYpK2hhq/1ObZudjLlc34J4dwpFVDEpq2xJuMT5XKu+FpIWVMI7BSR1/Ygdh9UzFvq1yWC\nnCl8UaROz+cSoQSL3F3A1nsQex66x6j+1V7P1B5iTdt6fLPEHx0W6fy3Md98V6hpmyvXE5LIJRKJ\nRCKRuKNQSvkm4Ae6j9/rxK2Fk7gfJHJ5VrGwvWFCFbqMkTmpcyewjfPD3uayt3+EcO0b8LbbiSLd\n3VBtONXOEnGcwQiQNu7PYETlIYy0iDiJkMhWf51Q7UYI10vlTElBWSfyqUSeRggisEa4IPZhm+05\nwiGzHb9C4kSIRB7mfJ2G/ToKF5wEvgn4AiIcUsXNRUTHCNMOOXqqzILGoBBTOU6qvtxo01bEY40w\n/5Das0KEUh6i03lzlgjvkxL3Wa50Hd0slB8IkRPWhnEeJUJwFX4pVUoW/tPEuop09WPGL62C+FIi\n1261OVcK2HDTpxw623BSPS8iVfO+TsvNb3pmWxKmUhIThMLYlhhQ2yPYvVRY5X1EaO6sHz9EZ5hl\nz0gil0gkEolE4rZBD4Yk76u1/tJNGcwdiFLKXwG+Dttw7sHC604QatI2TFFSuN8iYToiAvJz2Ebz\n9d5+FCMKUozWMRVERifdoXlfSOQ6KVxOyptcDaVAyQBFZQKmCCMSmYJIHesjQuyUH/c8oXb0NX1K\nOZPD4HEsFFEbaF1TRcqPEAYhImEiQKpJpo04NIS4lPLPgC/29fgUoUCtN/NfJFw6NT+Rh9M+1/2E\nKqjcLuXEqS7eeYw0PEiQmNPYPTxPZ+6b1KntPgcI9VLk9BBXd9+8XsjpcZUIoRTpP+TXbotfS6mU\nyvgIZijyaew+SR18wNs8Rbh1/n3/7VcIUxyFTUp5G/GXiq0fJGq2ncbu7bdh6/lHzfXaXDkZ6Uxi\nIaLn/VpyRW1rxS01n/XM7iPyD+X4Ok2okHpmu8uCbApJ5BKJRCKRSNxw3Ky6axvgB4B7msiVUnYC\n78bysrZhBG4A27T+DrZx/FJs4yjre4XsySRjiKgnJiLyWWzDPQO8iXCIvIyREoUyiiRQStkGvBUz\n+zhHhFaKFA0C93tz5ZstE3luE4RjpBQwqWvrhO2+asV15xmJnCokT2RpCCM/QxhZEClU+KVC4ZSD\ntkIUuVbNOZE5vM/5LmOdgplzyN1QIZRjhPGKXDWlKO7ByEGfr+Oir/t9RO7XDEaEtX4qAi68GVMH\nn/bvMqlZJUIC5fh5kqjfJsONrRYDH/D+TmGkUYqZnDeVDwZBJFXkXWYiCjWFqDMnF0kI4iscxp5v\n5dzpHs0TpP1B4tm+3LQdJ+5JWzB8X/NdyuAwRjInCVWwzblU2CX+WX9YUIHzM8TzpP5msbBOzbNn\nJJFLJBKJRCJxTdxCUvYXeKEwyXZM7ed7KbyylPIDWDgfmBpUMAJz1j8rf2yHv5SvJFVIDpEzmJHI\no8TecBwz4hD5+LT3u9/P2+HXGCLs9QHehYUXikjIfESkTDXYVN/tISLfbQRTT6Z8TFKzRDTkbLhI\n5EFpEy5StuxzGfWxrvj7N/qY/9ivRdOn3AgPE2Gfqz5/FZk+4Nf9c1/HlwPvpRMnCZMVrbHG3oeF\nBa77tRRGKoOXMeC13u/pZt7rhHOmirD3E7X95KwpxW6b9y/1S7lb8z6/y0SxbSmzW+UDx30uyz6m\n3YSd/58Q1vsKN2zLBYARpCWMOO8n1GEVMIcwn/lN4BVEvqCe6baumxwmdZ5yGZUjKZVtrjk2ToRW\nrhG5jWexQu5tYfH+5jwpvzv8GipKP078QWRpg3NktqOyGT0hiVwikUgkEvcQbnTx6xfCzSJWtdbX\nbeRWuRHpvNvIXSnlAPBThKoBkeM2h20sFc64B1PqKqYOQBAAOUUq9O8MRqYebNroXaGYx4mQuQHg\n1RhB+eellB8FvtzH8hQRYjdK1H97GNvQfg7bzI4S+W+D2Ca9D/ggUQtOKlxrFHKMTqOML/Q+/r3P\n8TBRq22EeE4mmrGc89c+ggi2CuU+wi1SY3zY+3sTV0IFqUcJAxApoC8lCnav+PjnCTMShQiq7ILy\npxSOKTOXCR+XiBzAf/L3NudqiSCAIgtyFx33NVVemchsT+UHaq0XSykDhEp6ik6HT6llpwlVqi0g\n3ubUiYCKVE0SCu048LPYWj5OZ506Ebg1bH10/dYI5wJB/qXu7SMUNtW+09gOeBuRSRkCKe9ULpzQ\nWUphn49VOYn7/HObd6f7pHp6PSGJXCKRSCQSdzBuJTG73QhRrfWvtt+vphxeS1G83ea0EUopv0Yn\naWvx+xjx0mbxvB+X0ce7sP3ep7GNuoiEjD4OEk6Hi1jNrjdiuXUf92P7sY3wFLGpnvFzXu1j7F7j\nJYJ4iSAp300EsY+olyZFaRhTlUQKlolNsvLopMZMELXSVghyMtm0Vx+fxTbh3UqZNtaLmAI30pyz\nhyCDMvEYJ9SUj9Zav6uU8oPA1xL5dUNE6N5OTK1R/1prFbqWk+VJjJw/4Memm3F+jii3IKIno5e2\nDhvN535fzwsEKXrO27RhjnjfM0QYYy8QERaJbUsttCYjyk/UOA/R6SipcU0TCt72pp9l7Fl+FFs/\nkVyFZcpNss2FHMbWVDmQbY6bXCRF6OW0Odq0k6FMWx9Ov8n0RuvXOlhKmRvCnnOFU7b19jK0MpFI\nJBKJuwm3IpTxTiAwm8VGc3qhtbyetb7Va1VK+Vbgb19n87f4+1FMCZPBxhQWzqh8rFk/LiVHpGiZ\nMAoRyQDbYD+PbTy1mZ4mjEa0+f1ZLD+vG21hZ+XjTWCE6mwzBhFOfGwfJsxKRPZ2EsYpCkMcI0jd\nCEZ2VgmnxhlC7dkHPOnXEDlqc86kTC0066A6YXIn7PdxPOTXPgH8gff5Ez6GR4mcOyk1WtOZpm+V\nUNjt11Tbc75GR4jQU41BZEgOkwp51TVasqTfW5VKIajKZ1S4nxTNNv9sU/C8SIXBgj0rE/4uZ0jl\nk7UOkro/NGNrwxfBVGK5eS4Rz/NTxB8YNFeVLVgjlC79YWMHEUraT5DJtiSDQj2lkopgLmPq3DFC\nkR7GnskD2L0UmRTZ17zbeyCiqz+6dJeU2DSSyCUSiUQicQtws8nZ3UjMbgSuti6bUTI3e+96vRel\nlN+jMQ7pwvFa6zu72v8WtpmVoccapiKtErXW/pSwYVfej3LNFBomY46zmOvil/o4tBk+7udexDa4\ne4nN7lOY2cbbgB9qhneYTlMVuflNYZtz5bVBkMl14GOYSniQUNqkyqkswZzPcYEIB1zytRBUF2we\nUyzXiRw2hU9qjZ4n6raJ4MnEQjlOr8NIYh9GmBf8OLXWy6WU3wTeiZGw496PSNLn6AwDVcFrERyN\ntd/PU0F0rZnaqr6ZrPtlLKIwTtnmP0iE9omEKuRPhGWeIBNtQeteIDVuF0GMRFJaYomPf9KvdwZ4\ntmm/1IxJBiaaB0T9QYUN6w8CWhuRpjZ38gBRo647nw6CdOklAqnvu5s2q9i/m5aoTRPlBFpzFghn\nUIVaLhHureNNPz0jiVwikUgkElvAzSRoSc5uHmqt3/dCba5Wr+46zrshz8QL3f9a69vcsfKrsdw0\nkSFt8hcwYraMka9VwuJ+nlA35Ap5Hts0/yLwBJaLJNfIU0Qo3wC2cda19tZa/3Up5TeA/xnLXwLb\n9F72cUCEBb6SMP2Qvf46RhSVZ6YQUBWJHiEMQuab10GiUPhxn+dePyYHT4UqLhP5cQo91Od5/203\noRSK3Dzsa1Ex4gGhyggqHn2AcAyVe2VbN0ykSuGaoz6HnQSRGCIUzHVfg13NOinsT4olRK5b65gp\ncj9KOG62tvnKSROp7ilHjlh/hSeKfF3yObR1/ETSljBnztYFUuvdlhKQ6rhAhGqqNMXnMeJ8iAin\nlKKHny91c5ZwptSaQWdoo5RYhUzK+ETmJ8s+H81jj/er2oh4uxP+u2ostusNQVbH6bz+ppFELpFI\nJBKJDXCzCFqSszsHXp/uuksb3CoC19X2IvBLpZQ14GswwjGI/eW/ejOpBAphPEuUDxBp6SPIgja+\nKlQ9gRE6FZ3W+QpN01iWgO/3YuTfgBG6Pd63CExrXrLbP0NnYeWLfs2JZmxSqRaIED0Ik5Q9GJGT\nujPl89jdXLOt9aVCzWeaeZxs5qjxvgKzn5fBiopQK5RPkBnLBSLsUeGL9xNhresYYVbtM1n1a7zq\nCyLHUC6MygMcI2r6iWgrrO8QUfxdqtQSUTS8LdegcEcd30qOXKuMSRFT7bc2VHK6+SzVU+9yrlwi\niB9+bIwIUxUZncZq0I0QazeIranUvdMEMTxNhHOONn2sNOeK3KoPrYmUwGXsXqlcxzzwCUxllDGO\n8vLY4NqtEg6dfwzYNHoicqWUrwLe7wP6v2qtP9b1+17gFwjJ+n211p/bykATiUQikbhRuBkkLQla\nYivPQCnlP+Eb3Ob5XKy1vmD4ZyllH2aScT9BiJaxEEAI4w+FpB0nHPogzDmkVslh7yRW6PoAQXye\nIQjMToLwtZgBfhfb3L8SUwGVGzaEKRj7MSVqESM/OzAFrR2vxrRIKCLDRIHlHYSqJUKi9ud8fiot\noBwwETGR0zWMwCofqt/nOuh9HfZjyveTc+QMnUQOopTDEEYA5zAl86T3scP7lCKluUKQlmnvY5LI\nkZugk2zIuVOKlYitiItytpQzJ3t9hVHONv1JpdtKLblVTAUVKW1z9URmZSTS1uFb8nMULqo2cneU\niinjmUFC/VP48FHsjxcP+PEFXwMReoWhqg5gf/ObxtPeAymaMiOZ9PNPEGUjBpr2WjeNqV3H7c06\nSJ3bSaiS+oNJz9g0kSul9AP/BybhnwA+Wkr59VrrZ5pm3wN8vNb6Pzip+2wp5RdqrVstOJhIJBKJ\nxDVxo0laErTErUCt9YlSyr/BzDSEkas8z4vYZvWhDX4TdmHKj5wgR4kcsz7CuEQulEN0ugz2Y5vi\nS358u7dV4WyZoGykKEgd+Ty2CX+cyE0bIZwZV+gshA1BNrSJFzlQHpeKNkt9anPkZJCyShCyEWyz\nr829xqB5TBLkRsqcatCpncL+Vv37Wa40B2kLWit0b9TnJoVm3ddExKrNqVJO2Bqm/MmlUmUPWvIw\n4H3NN+e2BctFjkRWtvtcLhDEZYYgiGc2mM9mMUBnzpdIlNSvI9gaTdOZd7bP27cq3CXsjwciWnIO\npWs9VjEuMk6UhVggVLU2lFMKa0veuk1idKxVA6V0ah7HfTwa/yRB2FTe4FBzTT07qrG3nU5HzFtu\ndvIE8HSt9TmAUsovY8mdLZE7hdvRYv9QzyeJSyQSicSNwI0kaknSErcTaq1/TZ9LKe8jHCm7McK1\nSRzYX/6V+7bb20vFUbiiwt9E4Ba9bxlHDGMqhIodq1D1fYRboJwEu6GN8HPe9lHvR7lu2tSr/pj6\nbkPapG7J2l2qoML1+rANv5SrNcJYRcYnp7HNvvLP5rBNtRQ/ETCdL9IxToRBfh7bpIMRZJ3f5jfJ\ncEZGKotE2OdDPq+zWI6dchi10W/zxMCIxpSP7xKh5ijXTJ/bkL19WAioVCfdVxG+GUK9VHkC2Fo4\npSBSJfWtNQJp/zigV5t7Nk+UoAAjYmPE2oj0tEYmEKUYlrE13eXnnsDIlUx8+r1/1ZxrQxql/Kl/\nka95Oh01lSPakkg9T8Nd7zsIEqnnaYkowg6dKtyW+FEvRO4Q9pcC4Tgmu7f458DvlVJOYv8h+fre\nhpdIJBKJewmllI8Q//PcEpKkJe5k1Fo3NFl5AYLXjQNY+OI6tpFVKJiUOOVtKR9NBiMbOQ5KCZLl\n+zqxKdZmnea7jByG/RzlPj2OhXyqHECrCmqTLJVvjNiwq17XMlFj7AwWTjqGEZ923Ae9DylAmofy\nq0a9r2XChv8tmFqosYqI4eeM+VwWsXBJkTuacSmvTe6XIk4yA9G6HCeUUilOZzAioILTWheFG0rh\nE5FVCKDUptb9calpc877EbHRGkCEmaqswVag8FetrUIR5VIpF8g1jHAd8vlILdV4RFj13Om4LPxF\nqBRGq7IMWk8IgtaSytY9UqRSNQe1vm1IqEoFiGTK5GeMUA4VAtqOXyY9u4h/A5NEGZDW5OSWE7n6\nwk34u8Cf1VrfXEp5GPidUsprPCE3kUgkEvcwboSiliQtca+im+B5Da9vwIxOZFbSFlH+0q4ulrFw\nxDUsJ+0coS4p90qmFfuxveJnsQ34ETpDC1sTi+5riFjsxBSyGUyd24uRrB0EARSZE5GTsqFwP5FM\n5eIdJhQmhc7JBAWfj5S5wxhReBbbnB/yMcg8Zd3PezmWzzfgbeWAOYptwmWSIjfLjfLK2rp8Utkg\naqyJcMmIA+9/zscoEw2Fkr6MCOeTccsIUQNQoX0iD3JLFHlTiGp3/TYpkCKCWw2rhCDF4hZDxH1a\nJkxHWsVrmAg1FFnVPKXILTR9rjZ9tyT7qPf1BPbcnGnmKldOPSsH6FxP9aFwVDlWti+Z6WiO0OlC\nCXG/Z3xOerb1x45JwtlU11ohDFJ6Qi9E7gT21w/hfmxBWvxlzH6WWuszpZRnsYfxY22jUsp7mq8f\nrLV+sIfxJBKJROI2wo1Q1ZKoJRLXh1rrZcxg7hd0rJSyC6t79m2Y6UaLAeAl/lJduLPY/k4hcmtE\njtgcoWrJjEQhbcoF6yACtdalUoryjmQMMuX9/Rq2KX4cI3SrGLGcxAjKHLbxHsWMVcAIJD7GYcIE\nRSqH8th20Fmbrq/5rjA6kQMRG6klB7GN9gKRA6jxnCVCOZXrtN/PU2rRKlH3bjcWBqrSCa0rpVQf\nkQSpZ+MY8WmLU8vR8zJRIkD3TE6gEwT5FvlR/ThdQ4qkjrcqnhSrrZI5PRMKH5zB7vNBbO2fx0iU\n5q+SAUfpLG7eojUl0Xilxm0nHFThShKt+e/BlDOIkhl6DtROTpdtSQiFRCpUVWsk99Dh5hyRP4Uk\nLzbjax0yd/vrceC1mDJ9PQLZVdELkfsY8Ggp5QFMVv4G4Ju62jyJmaF8uJRyH0biPt/dUa31PT1c\nP5FIJBIvMjZTTPkqWKm1vuFGjSeRSARqrRcw18jf1bFSytuxvZlMSiawTeQD2D7tPKEEzWHkSeGT\ni1hR6zmMbEhpGSLIxl+glCKCso0oxK1cuEVsnziEbWYHCAv4eaJ4ucLYIGqqSVWRkjZC1H6TeYSK\naMvUReqcwif7m+tN+jxlCX8aIyQPeB8nifIMUuS0kW/D/gSNd745R66JQjsO1TSTuimiJXzC24iI\nXSRIj0JQ133MCtmTMteG+51r+u0uB6Bn4TS9Q+G6cqsX2b1EcI3usgeCHEvlfioyJAK0RBCjYSIM\ntSXIchb9FPAYUWBdYasKgZRLpEJNFT4poxuRM92LFYy/jBJ5nXsJAi6iKaInZ1CFxLbPg9APfBzj\nU6o19x1XWdcXxKaJXK11tZTyPcBv+2D+Ra31M6WUv+m//zTwj4CfLaX8Z+wB/cFa6/RVO00kEonE\nbYmthEGmqpZI3D6otX4A+IC+l1IOAG8FvgwLyRwkyNVrvdnnsU3rM4TqtYopCbKB78M20tocgxEh\n1SZTuzYXCUIBfADbAI8QLpFTGEG5nyBjeDsVyT6GbYIPEaUEjmIb8VGiZIGIjhw2RaKGMbVICpLy\noFaxEFCZwfQRSo5cL9W2Da1b9XFo099HhM2JgIg0rBFhmzKcEYHWvRgkTEBEFEQMpOAtN+drbgo5\nFNEUcVUo5zh2L9aavmZc2d0KVMICv/YYURhcJRsUfihSNerr0Kpdy0SNQSmGA9gfGiBCWmUsM0GQ\n60XifrUE6wRxz2RmozEMY+t8HDPkkVGKxqd289hzqeeoLf+gvEQRTLlYSlmdpdNUSCHA/bwIoZXU\nWn8L+K2uYz/dfJ7CYrUTiUQicZtjK+pakrVE4s5ErfUUTUhmKeWNwGuAt2MhcGBhaZNEmOAFbDM7\n6a9FbEO7p6v7USxf6UGMbLXFrmVUskbUs3vE+9ju/V3ANuhD3r6PqFOm8gH7MOKziiln2mRro99H\nKCMakzblhzEVUnb1xwnFRaUZVCZh2q8j5UwkY5FOZWmIqD2m0EnlZA14H9rUK0dN/V0m6pTtoFO5\nkqqkfDspj7O+XnLLHPd2F5r1FZlQmYXW6EV9tLXQekW3k6OIMtg6LTfjkZrZ5u7pRdf5bTsR8Oex\ndWpDN3WNHX68DyP4uh9Sy8ab/lewZ0hEF18P3Te9t2srwinyLKI46H11O4qqD4V2SjEVOdfnntET\nkUskEonEnYleFbYkbInE3Y1a64eBDwP/zEMj3wK8CcsF20sU29YGtmAb58qVhidHMBI34r+3+W4K\nm5Mz41MYkXjc+1nEVIqDGPm5SJRQkCmKinqPYcqcCjcfJgxbFBIpYxAIUvMyouD2c1ie1UFCyRsh\nlL9FbyflReRrmU7XSilOR4nyBbNEWKicPLXxF5kTUdmHkTnVRRMZmMZUOoULihyc5soi2zpH6pDq\n1YlA0NW38slGSynbtqDKSYU873OVM+U5IndwAFtjPSuah8ilyM7+Zk4twYMrHTb1u3I5L2FGNcp5\nE6mWOrwDu2cKL53GntMjzXX0fIp0t4RM7q4K+WzbK8xTzwZEYXa1o5lbWz6hZySRSyQSibsQvRC2\nJGuJRALMrAQLw/wAQCnl6zCFTZvh7UTO0iGsDNVve9vvB74RI1GfwjbYrcPgOGa0chBT0saxDe2z\n2MZ3gtgY92EkZhUjLpP+WTXWRCrlsLmbcJVcbK6pQugvJwjaaYx4rPp5csZcJpwhFeI5QdTek7LW\nT2fZBYVcSjnqwxQjhf1JlRIxEAlTSKrqwJ0nSOO0vx73uR+jsxabCoq3OVhrBFlT6N8YQTpFWGSr\n/3TX+b1AauYyEZKokgAtdJ22lp2IpwhyW9dOyqLMXGTsMoStbVvYXCGyU8Sz0489F4PeTmplW5Ab\nQuFVXpxCImcIA5q29psUQ7XRc6P2O7BnSiqdSLjyEKWIti6YPSGJXCKRSNzB6CUsMglbIpHYDGqt\nvwr8KvxFuYM3AK/GNs9fA7yzlPLODU4t/r6fsNlXvtwiRlLkDvl5//5uP+ePm3NlqCKSppw5qST9\nWF7fNj9PqlcftunfS5RhOIeZrUx5v1Jv2hp0g0S+lr6rflmrCrUEaIpQo0T0VMBcuYWtcia1RyGf\nInR7iLA7KUEybNlFGLcojBE6SwmcI+qliSTpJUIyjxFwqUhbdayU8Y3KAqgAuciKVCmZlozTafW/\nhoW4jhCkTkXB+wnzFJHFAUx9k9o3hbmzKnftKEHstTZa/7Zm3BE/1m0Oo/unovJSLzU3/bFh3ud8\n0D/LTbOt99f90vMkh88kcolEInEvoBdb/yRtiUTiRsLD7/7QX5RS3kGUIejGHiy0chVTKaRoyYQE\nrOYXGOm5SCg6CjVsSZzyn0YIBWcdI3DK85LKobDKVSwHT5Cio3NVXkBmLiqQPtrMS6qinDVHsLy2\nbuwgwhWVC6h8K5GutuC0SIyUtYu+ZsrNEmH7KBYCeLiZ47rPQYrkEkbipGLpe5sHNt5cU7XsRps+\nt2J4otzEw34NFQMXuVv2ubVFtqeJXDrVzxNpm6PTkVQ5alPe3wxxz1exe6g2YH8YkPOlFFbNXYRa\nqtoJ/y530UsYidO6nSfUV6mO+jzR9NuGUZ4m1Fcda///PUaQup6RRC6RSCRuU2wmPDIJWyKReDFQ\na309QCnlQeD/7fp5J5HXJnVL1v8qHSCyolIG78GiDF5JhMstEqGSCnGEMKkYBT6NbdZVm+6kt3sA\nIwOfw0jjS7xfFSBXmYEzdJqDKBdvvfmuTb8Unbb2mcoliBx0K2QyxtCGX3lrInprhCIlEteSvjWC\nbEppXCcUtrXmfZYgMZMEwVFIoO7DeYxA7+DKMMjNQGYnKgQvZax1lZwgiOReouZeay4iIqf7IrK3\nQoTgiui3Kp2IucYCZoqyEwtXnceInsirCJTWeR9Gos8Q4cPjBBHfTzwPUhrlQqqwX+U6rjR9Q2c+\nIkSunBTgK8p3bAZJ5BKJROI2QJK2RCJxJ6PW+ixWhByAUspbgK/ENu1jhNI0iuUqyexDm2oVapaa\nI+dKbfoV1ihlTHl3rd38PEba1rGN/kHCyfCsv3b6NUaIsgSqoyZzEKl6UtdUdmAbQd7aUDyI/C4p\nbdn3lwAAACAASURBVIf9Gsf8dylnrbPjrI93mChYLjVvH0Hw9jVr1CpD5/wl8iT1RwRl3PvSuq/Q\nqfRNNMe3yglE5maJ0gBS43Tv5wk1bsbPm+3qR6SsJdPKcdxOhDeKSIvQDTTn420ewu7ZJaL2W39z\nrkhiv49xP53rA0G4VZJAJFPvYz7OYTrJuYxpNJZWlb1AhGFuyTE0iVwikUi8CLhe4pakLZFI3Imo\ntf4+8PvugPl24PVYXbiXYyrZc4T6MoCVANjjrz7/fRQjRMoz0wb6rF9GG+kxbKO9lyB6L8WIykXC\nsr4PU1103giR66a6ZQPY5vocFs6oEEvl5invTc6HgkolyNZeuU8yPDlJkD+RF7kpitQdIwihiOUg\n4XYph0aNSSRTBcOFVhWSMjTeHJsmlKgVjFhsJVdLhbL3Nv1P+txnsfy3lvRewJTNNUwVHGjmcJ+/\nzxIETqGg49jz8DTx3Ew0Y5BKJtUM73cEW08pqRDhrCLLKhB/jlB62/ISKn2xjOUX4vOiGYPyHqUs\nirxKSdW19Nxvp9MwZ9NIIpdIJBK3AEncEonEvQh3wPwV4FdKKY8Df4twCDyAbZ5Vm0v5R3OEYqa8\nuIN05hXJAXAvtiE+SxhRjBE11iqmtCinSkRPoYTL2EZboY8QhhzK45NVvNQ/Eb1WTRGRaK3o1zDy\n2oZMygRDhizbiLBMhQ6KKGg8MumgOU/lDNq8r1YlVCkEkcU2pK/FEjDv92kr0Fq0xFLXVF7bdoIg\nKwxR5QakVIr8yCSln7jX6lflHHRNFUJv74eKr8uR8iRhfDLo4xgnHCSV/yii1c5Bz5xChNt1Vq1C\nlZtQqOQuggjuobOOHs38bn1B8EQikUhcG9dJ3D5Ua/2+mz6YRCKRuA1Qa/048DcASimvB96IKXQD\nRC7Xcf/+gJ92EiNmk8RmXzb0fRhRU+035bhtI8iN6twpDFNtpa4oPA86Qxyl5kGnKYWUwT10bsKl\nssgwo58Ir1R+nwww1EZhiPsI8iJ1ajemPCkcUrb5KsegcD3loy3RqcS1amFb9kBj01yWwNxIt1BH\nDqKo+mHvX8RZBFfrfcTXROiuQSilbJkggFKt5giTm/a4Qh7bcE6RQP0h4BKRmziErcUEcAq7L+PY\nM3cBU3Dbum9SGRUOOo7ds2cxRfE48LD3KcKqHDutfWt2ohy77rlvGknkEolE4gYgiVsikUhcP2qt\nH8XcGCmlPAq8DQuHVJmAM9gmWQrNOEaclDclA5GL3u4LsXy4p7CQt+Lv64Ty8hlM7VK4psLtVEtO\n4XAiGrvoLAR+3tsrr60NvVO+nY6PY/vsOcLBUkpOS6REFEQcZPKhY2p7zvt/CCO2c0RZAhFRmbEs\n+1oojLDfx7zN10TXVbjfXow09UTkaq2XSykqli21VaRN+XA7fRwv9eud93bnfGyvwUjUk3TWVxvy\nc9awovLKkVvGiNcgUUJhL53GLlLbWnMZkasd/l3hkKoLuJO450s+Jimt6ltrJ+OaZcJEZYBOhVTm\nN8qzA/ujxE5v1xaV3zSSyCUSiUSPuB7ylqGSiUQicW3UWp8CniqlHAB+ASMEymd6JWF+MoqREbkJ\nylHyAYIoaPO+QJQhqH7sNPCon6cyA3NEkfEFgizOYqRPuVhgSst93me36qU2LVG7QJCH6eb3Vj2T\ng2RrXz+MEQ2ZmOzGlMlzdBbGPk8U9VYu2ZMY4XiAKB6+38d8lE5lTuMYp1OB7AUD3q/Wf5VQo5aJ\nAvL4+FSqQeT3so9lJ0Hk9vr3pabPlruI7Cm0UgXiwRQ4KXta19PEOslwZ5YooP6kn7OTqEEHncrZ\nKpa/+VwzlyOEgY3CJy/6dVQ+QbUB9bkllD0jiVwikUhsAi9E3pK4JRKJRG+otZ4C3gpQSnkjptId\nxIjYPkwp24Zt+vuIos3Ko6rE3nYYI2xSb1awDTeEqqdQvEVMAdQ1RGjavLE2H0sFwducLNU2k5oD\nppxJnTlF1B07SOTJyc1wmDBtOeDtPufjPuztP+ZjVaiiQjVPN3PTWKDTeGOoGcskYbqy1dy49pqq\nuyYVTGrjTNPujM/hGYIoiYzOEEXVW9KmcMtWjROZVd/6TeeoAPg4UYi+DZdsi6irhMMCYZjSEjPl\nT+olU53T/nmSUNwU9qqi4fh8REZF4s4SNeh6RhK5RCKReAEkeUskEolbi1rrh4EPl1L2YWGTX4wR\nsyMY4WqxhoVS9hGhcqpfJ3fKUYxEnMU23QpJVK7Vg8SGfBXbYM97n3u8r+MEQVwkzEggcsC0WVeY\nnfLbFJanHMCdzVhbYiVjErlpDvu11McQUUdu0tvIXXOJKH6+2oxD8xRpFJkQZthCHblSyjY6yy9c\natamzR3UGCHUUzl9SjWbwu7ZqH9WXqByDNt8OK33PJFj2ebVSfWT6tqPqZpSQttQ13N+fYVDql+t\nF97nYYyIq8TCDjpNUnTeBHFfpwnVVaG3+kOCrtsTksglEonEBngB8rZSa33DLRtMIpFI3KOotZ4D\nfruU8h8xY5SvBL6CzpA0qTd9GMlSHbB5jIRtI8IhdxDFwLvrkOm4CJjUpUKYUyikU6F+LXbT6YIo\n8iQSo+tIYZOLpTb32uArN1Ak4gS24VfhbtWG28mVxa1by/sFwsClzdNTyGVrvrFVTjCFEcLDWBjl\ncT8m8qn5LRFETXl/Kz5niPsApnYNY2GQreuoVFGFVk56n/i11FaEco8fbx08l7BQ0zYUdlfze5uf\nqPWUgqu5qKC9Qn3HCEWvzZs7TmftuzYfL+vIJRKJxI3CtQhcKm+JRCLx4qDWerGU8jTwCmzT3xK5\n7XQaW2gjPkbkKvVhYZgPeZs5PyYny3VMrZvBCNkejGStAp/HNuT3Y3vnESK8T9AGXuUFIMIgj2AO\nh6OEeianxCPe5oyfI5VGuVUigsqxa/tdpzNkT0rSHEEyFOop842V5kXze8+cwM1ORHK2+9gXMAID\ntlYK/5Ta2BZPH/Yx7yJs/JVftubrIafQM0SRcClvI97uEvZctGGWa0TdQZWl2EaQ/TWMKK8SZR9U\nZ28Uy00UMWydRUWidV0VYJcSOU8Q1Z2Ee6lqCCqsc0tIIpdIJO55JHlLJBKJ2xullMcwR8vXYQTg\nSWyDLCVmp7+miI37ALbxlgul1DQRgGk6a7hBkB0Vm1YY5rp/XySIVGujr0LlIif7fGxtfbV9GDk5\nTShoKkLebupnm9/b76N0Fj1vr692a4SyJEMNmXqoALiKja8Q9vvz9IhSyi6itlurbs0QYZB7CbIt\nBUtOkmoPUSdPpiEiPnsIBXEZI37KS1QIpsi17vs+ogyAXCZVcL6tt7ebUEaPEvdlmig4f5RQa1Xu\nAeJZaf+AIIgM6h4op28Cu3cK4+0ZSeQSicQ9i6sRuCRviUQicfuglPIqzATlCLYJVy5SW0R8P0YW\n2lpf2nT3Y+Srz78fJRStGe9noTlvmVDnlIu2jpEH5cYpRE4QYZRzo3LTpgnnSak08825p/33JYy0\nrGLKn2zrW7Wtv5mvQkll5CIiON70J7IxSpQF0He1mSZCFHuFSK8MT5Tz9irv/0yzNu11W1Vsmbh3\nKvKuUNN2vPNNWxFwqYEQxi6rdBZBV76hyOQ0psT1Y0rcMHZvRJjx6z/on0WAVQNOzprKw4PO9RYx\nVr8yu9Ez2YZu9owkcolE4p5DErhEIpG4/VFKGcbqi30hpooon03hkFMYuRsGPo1tjhWSuANzf9Sm\nf9DPPYDlvGkjrjpkMuyQSiJFSORJ6o/ynrrdHpe9rYxYtJHvdj9slRypfxCkpd2bS0kSkVG+22mM\nXI4QtfAmCfVHL+VkHcScPj/r41BxdZUemGELihxBqvb6mC8SIZb9Pq+z3uZhgjgqB3GACJXVWp8n\nTFJE+FRSYpVO8qmwR4iC3DKXERlWTqCIO0Qh9nMEGVaxdt173QNdry08PoSFVUoh3OFjFGGeJXIT\nW7VQaJ+XnpBELpFI3DMopbwf+JLu40ngEolE4vZCKWUn8NcwEncWUzT2EW6TY9gm/JOE9b421H3+\nvhfbvE8AL8NMM/YQRhh9ROjkWPNdiozMTxQaqJy0Q36ttu6aXBvPYYRrksihk4onQqcwPIVCtvlS\nq11tVay620FRIZlHiALlEGGY6m+NyEkTwZPypGtIzeoVIrlSwzQPKYyj2HoMY0RHYZUiXzOEsclx\nH9cEodBJUZvyXMmddKpi4jN67ydKPMilUmGcKkmwF7vfTxI5ckPN+SoZoLXSWNowXDAiPeD96d6I\nmJ4hDG30m0JCRc7bUMxNI4lcIpG4J7CRCpcELpFIJG4/eD7cfwF8gR+axjbgO/17n79LYfkM8CaM\nYH3cf1vGSN4DWIifbPlVNPscRsykvin3TBv2NmxRbpiywh9pzhUUViiiMISpSsMEQZwliKKUQ31X\nDtUQQeBate4iQTAOEURoCCOhKh8gZUmukGuEaUpb260lrFvlAwo/ldnJQjOfVYyUPeLXfhojn20x\n8BNYgW0RX+XzCVIO+0spIn9aK+U7HvB5TRHk9xJ2r9oC3OPEvVUO26SfJ2I4QZDm1hRG+W2C2h5q\nriFHToj7INOWE0TYrfrdUh2/JHKJROKuxkYqXBK4RCKRuD1RSvl3wH3An2Gb6+OYkqaC2VK3ZDay\nim2QKxYe2ZKzde/jo4RqdwpT5ca870WMKI4QhO0stkfejSkoc35skDAY6SOMViBysGRx36pcInJ4\nnxCkYqg5XwriIEbCpojC0jsJZW6cqC0nkw+ZiMhIpLXQb8lCG+bZ1kcbwMIve4EIrZwcFU65TGdY\n6DpBUtvXPqKemvLbFI7YGpdAJ/kcaj6vEOYqYPdLobRat8Hm/TQR3trf9NUSMeW+rWL3TUTvMFEW\nYojI31P4pkhjW6duxa+tEhVnseduS2poErlEInHXIlW4RCKRuDPQ5MMdJJSxs9jGWWqSDErOYORq\nNxFK+KfYJrwlWxcxMjQM/IS/7wFeiZEhFdQW6TtJFAFX7hPEZrt1U+x2GxT5kNLW5mzNYJt+hT+u\nESYok0QY4gxGPKScSYEbptM0ZQ04RpCbWUJdaknDKJ1hm3qXkYoIK2yNE8iNcQC7BxvZ6rdjlLGL\n1MFBn5fI7g4iZ1DOn6foNDbRurZ5hXKVXCMInNS8B4l8OZEs/X4eu9fjRBik7p/m0pI9lRpYwwjh\nc806iASKvM4Sz+gQ9ty26zPDFpBELpFI3JXoJnFJ4BKJROL2RCllG/AW4AngNwglZ4Aofr2bCB/c\n58dXCKXqBLZhPkS4U7b5ZDK8UGjlYeCl3tdLiDptY0RRaikscqDUmEQgWqgW3CzmOilSqGLVhwgi\nMev9q/7ZGkYmWlWtJXN6iRyI8IggKEyyLfKtcMp+guBeIHLtRFSk5m3FBl8EqnVxlLKGj+tpgsgO\nN8elWEmpk/mJcgAXmzG21xnC1Mp57H4otFNzkdGKwhlHCHMVETYRyhGivIHW5jkf4yimEEslFXeS\noqrr01xbKuQ+wqFT96Ilccrz6xlJ5BKJxF2HUspH2u9J4hKJROL2hOfDvRZ4DCMcT2LlAR4hzEVk\nMCEDkyHCCv6wn6dN+T4iRHIAU/jwPqWYATyPhVY+hOXRTQBv8PNOePvdhJPlFEG+8HbtplwW/PsI\nq/1+H4vC6Y4Rm3oRu2mMEOzB8ssu+bF9dOZoifzItl/FvxU2qfm3xh5aOzlzipTK6GTEf5cT5lbQ\nhjqKhEEY04jEiBC1JFVjVft5IhdN/S4378q724WR09b1UgS1zW0Du9/T2D0UCROJVtF1Ebm15rpS\nB1X2QM+D/jDQEuDW6EUunSKB0831+rF73Y6vJySRSyQSdyP0F8kkcYlEInGbopTyKPAOjIxNA5/D\nSNQSRqQgCJHqvE0RSptMQNYJdWeeKwt2X/B3EQcpJvOYOconMDXwi/34doLkQJAD1f9a5cp8siGs\nlp0KPY/7+aeBZ7xNW2dMdeXa8gTjhDIoEjZO5I+JBAw3544SypxULbWVmjmPrafWUoRlkchn2wq6\nTUKmCPUUTPHUONuwRhVPHwY+T6hsUvbakgtSuk4T1v/nvK3MX5aa31qSplpuInfnMAV4Gfg9TM2b\nJcJfB7HQTJpxS2FVPt4atn4K7VQ+336iVIJMehRCqnDRZaIA+qXrWeCrIYlcIpG4q9CGVCaJSyQS\nidsTpZSvxIyo9mMbXikms9hmWirIg0RukTbVyv9qjSRECmTwIVJ1lFDB9BKUe3cO29AfxUxRJjAl\npY9wIoQgJ3KtbAs6D2E10hQOuN/bKAS0NdqQKiWzDZE4ETbNYzdGKkXq2rlKWWwNNhS2SXOdNSI/\nrQ01VX9LXFm/blOotV4upUhJa9dD/SrMs1slbNu3+Ygai9rP0hmCuEq4TConThjAiOMwdj+7zUdE\nwqYJJ1KFpeo3GdYoFFMKnUpDyIBGpF3P4UWC6GsOei6VA9iGseqe9YwkcolE4m7FlmqzJBKJROLG\no5TyIPA1GGFaxJSOGWzTPYptok8ThhLaZIuMKS+pDTEcIoiNcpzOYkqLHCNbN8fW6OIQtlF/irDH\nfxAjA3ux0MztmNnGDOG8OEEnKcTHMOH9niU29gqt/CwRSin7fZErERbNe54IdxQZEBlTCCWEE6LC\nFhUaqGuI3A0353T//1EmIluBVCmFu6qO2hdipHiOcHcUOcLHttD0I9ULOk1PZKgiDGHrt4O4lyJc\ng813hZ9qvbVGHyaU0XNEWK7uh0j/lF9DJSIU5itlU8XYJzFF7wJRQkLGLi1hF7m+6PNJ18pEIpHo\nRq31DS/2GBKJRCIRKKV8HfAtWFjZnwJ/RJCQ1smxVdZWMZJ3yrvRpl0bcilQ2mjr3E9ipEskT4Rm\nH5aPJtLRTWqk+n0MI0Ovx8xLZKbxJEHk9nWdq+MKE11rrq350Lxroy/V7pz32ZI0tRfpE0E7Sjgs\nquh1ew0INa51wJSiqfDM01ih7Z7rmXmBbhnBKGz1IrbGaxiJO8eVpiatw2Or4Km4uMil3hV22RYB\nl5o569dZBZ4lng/ozM+DCHEdJ8IuNabuGn5qp8LqGqOeQ4Xbqk+FTrYGO4u+HiN0qpP3N2PqCUnk\nEonEHQ03NtnSfwgTiUQicfPgrpRvAr4CU7mUc6S8JilI05iKcz+mio1je9UHCOIBoU5JmdtHECbZ\n/y9hCthj3tcUocANYMRQoYXzGLmD2MyLIH0AeDWWQzeEKYmrfl3lswG8HAunXMYI5GGMkLTEQDlv\nEKGVcuSEMCERIVOIqTb/qnXX5n7hcxwCPtXMR+REZEkujq3T5SARMrgVDDXvE35dkS25cEqJFKlq\n8wR1X1uTGIgSEPf590GMED1JGJ6oULrqzmkuDxKKZKvC6nlTgXaRK6252ijMdoxQ92R2oja6p2vY\nek/TWctugU7SCUbqpBpuee+SRC6RSNxybFTf7QbjQze5/0QikUhcB0opu4B3Aa/CNuYfwja8Cqfr\nJmer2Kb45VhYY2uaoTBLCAVFZEakTptrbbClyikUb50oLSB3x3MEabrY9KmN/ccx4vcgRtZ2YQRg\n3Of4IPBf+/E/JHKvZGQh4jKEETE5J57GSKjGIdVNYXga12P++wU6cwSVcyWHzsHm3DaPTu2liil0\nU2UCBkop22qtvRYEhyA5Wjvl3k1iJSKeolNhBLtfbf6a1kHrLqInsjtL5BGKtEnBU5H4HU3/bU5c\nm1/YrQDrjwL6I8A0dq8VLnmcKH0g0jpHhFwuEcYnE3SqkgoHVUim6uDp+Uyzk0QicfNxC8jXllBr\nfV0zxi95UQeTSCQSCblSvhl4HNssH8NMTZQjJVKmzfZFbKM7iG2Mj2LKnazbJ72f1oRCm++V5jeR\nIikrUrLu8+PHiQ39aWwzLeVsgk7lCCK36yOYSvNG4IuA15dSfqiZ8iy2SV/EyNU4RjjkxPkQYaqh\nQt+6Vj9G6pTT1YYhrmB7diltEMrePPCbWLkGmjF3r+9RP/YgoSBJWVJYaq9EbgBTIDUXhbseoDN8\nVWuq+SlkVPOY9baXCHdIkTIVMD+N3SOFWco8RAYkbeiizHNaZbQte9CSTo1pFFNt26Lp3SUGpKwO\nNnMdwXIptf5SRpU7qDGqL93fJHKJRGJj3Ank60b3d7vPOZFIJO4FlFK+HHg7Ucj7NBGSqA26crsE\nqR4q6v0cnZb90Jkv1m7yIXKeRPTU93k/vtf7FQk8jYVyPkCoQRAKmjblrVnFOSy/bxemGraQAiir\nfBEkkbuLhCq1jyAubemAFTpJ2Jpf7wix+ac5T3lap72NwgmXCDt9qY1tSKAMU25EeKVywvBxTBH5\ncm0OoHLNWqOalpiLHGmsC0Q+2rOEc6VULblI7sVIvkjj7mae0FnEWy9dRzXu9CwOEQ6ixwilUfNR\nuKjOX2r61v1pyxKAEbjHvM1ZooacVMuekUQukbgNcTuTkTvF0r+U8id3ylgTiUTibkH5/9l78yC9\n0uu873enexpbY+sBMMBgBpyhuJNaKIqS6CWWZDuiygstqxSVbKkc2lHZqXISJaXYqfzhUjmqVFxh\n2XJFSUnlJYmXoh1FTmxVWaKXSBEVk9ESUSLFRRzOcIbADGYaSzemgW5gGrj547y/Oed+aGCA7tnn\nfaq+6u+7373vfe97L1Dn+Z5znjMM3wf8SSLtTFfKrzJNZ4NUb55tnx9sfyVBR8i6NpgSlyWSeFnz\n9V1EXPuv2v6zjpI/0v7+U5KorRLpm7pKQjpFqn7pPijJOE/2n/u7M+dYItSf2jT8eLvmQ+1aH2/j\nPdT2+QypIrkWbynXXAmr815v89TWnjJHlTvXScKhSnW2bDOdcEfOiQ1X22uTuHeSOwnwKmlYM8+U\nYEIqXdbu+d1K+b6an2yUsbxmyft6O+4Ysf7LZENvifQh8v5WB9EbbZ+vlWup59PcxObwriskgbze\nvrNlxn1kausm+XzsSI3z4js6Ol4ivFYJWCc0HR0dHR0vN4Zh+GWiHgoioP01wj1SwmAAvKttU3GR\nRF0BfqKN8Ssk2bMWTKVKMqL6NEeqbaoiqmHVURBCgVGxOkiagKhWOe5sg23ruebbvI8AP9S++0dl\n/G8jgnXVN8nsItMm4+eYmpE4X89nLZsEWFVQu/w1st/Z2TLWDdLoxNYKZ5iSwZpeOMfO+cA8SWq8\nr/e38y+T7RPWSQMQyVqthTMN0sbiNX10N1PjkN0keTN9EdIFVdRG3PNtbBXIDVIp3sXUabKez9o4\nlcaTZVwV1Eo8VfE2ifRSnTFNA71Q5rCjte9ErqOj4bVIwjoBu3vU9MquynV0dHS8/BiG4UcJQ5OK\npwlF4gBJjOaIwBZSGVks32+SKtLTTNPgauBfm2lbd/XbBAE8RToIOv414MeAbySVK4mNRE/SVMmh\nBON62eZ8rwFr4zh+DfjAMAwPAd8LfBNB8g4RaZsrbQ00WankRCJVXSjtJ6cydbztf4bss1dTA9fL\n302yNm+xbDcds66nBLk2sN5ujZwqldfiNVsnZh2e6phmLxfKXK60sRZJFU5XUwmVNWYrZc426JbT\nSMjvY9qEXaLmuljPCFkXaRqo16QD5ZH2vWYltZ3ENYLgHSnHuQ9MSfNiuxb7x+1YCe1EruMNgdca\nCevk4dVFJ3MdHR0drwyGYfgEGcRWrBJB8Y32WRMMTT2s0TK90jS2T5B1bDB1HTQ9zd5h62WfM4RS\nUptBQ5Kw0+3vOwlCsdG2Pdn2MxVTMxEVMhtW7yvztYaqNqheAT4OfBb4Q4T5yJE2zvNESuUlss2C\naYf2jbP1gs2kF9qYJ4n0T407JHALTOvcVJMuk8ShOnNeKPvOEjnVrO1Cdcs0ykWCmFUlzmuGINyz\ndYASskWCdHkcJAGqKZSVvKnYWb9WVUy4eY2syfP4o8Qaf42pe6i1eKZPVhIJqebWms19BIlVCb3E\nlHRvkPWTzn3b6ESu41VHJ2EdLxP8NbOTuY6Ojo6XAc12fysSJ0wjM6jW9KJavptyeIWsW5sNbldJ\nJUVSJ86RwXFVzQzoVdRMlXuyzfkIQTJVvyj7SnL2lPNCEii3LRIplGKRqAc8C3wnYYayRKZU2mPu\nEEFWdei8px2/QZiovLt9/lybn4SwtlqwZk/ytEa0JzjYxrjElNBIiqypW2Xas20nkNiorJpqqULn\nenp919v8TC/0pSOlaZMqkKYt7iHTFl0HHSwhCKL3xnq8vWTt4f42R9U8yZT33+fPHwogFdAz5HN2\nnCB0l4h7c38bw7RK0zG9Fh1Zz5GGKa5bNzvpeHXxWiJiPVjvEOM4fqg2C/c57c9IR0dHx87Q2gq8\nizDs+CJwZhzHv9K++y8I45G9pHEEJKHbJNMELxOB8xJhTGEaZFXtzpJ1b/aNq06P1h1dK9/X2iWJ\nxOE2D4nGIhGIHyXbA/gDoHM4yDQ1EZIczjoOaqRxpI35BeD3gPcR6twJgrA9SdayOf+nSGK4hyR5\nc+X7SmbtESfZqOTWuWoCoxJm+wfVKQmsNXIvRZ2cRNj1lVBLsudJEqdb5NPt+/vJ3oK066+1jape\nkOqb57EeTVJ7gVD1FsoxkrXjJOGEJOf3kMTOZ8FjKoF2nfaTz8usQ2atf/MZ2UsSTrFTJbQTuY7X\nDhHrAXbHS41xHD8E02e8q3MdHR0d28cwDF9P9Oo8RgTQTxD91cTfIQLiR0hlY5lIG6yE4SQRZH+B\nCKZPEWTrq2RK3qwpB0zTKU2p2yRVM2uwDpX9rpDGKhBpjveQaZ8aZNT6sWqA4njVgVHiZSompFrj\nefe067kIfLBd4xGCzD1Lkl3J17H2/okyF5i2UpAYvVCnR6aA2n5BsifpNaX1IZI8ConcTpQhUyvr\nODW1cY1w+7QNg83L7dtnP72Dba66OS4QKtYK6YR5upzzOJnueIRMx9SUpN5PIUGrSqFk13VdLcdU\nl0+vT+XXNNbrpGPnYfKZv0q2GvB4a/Wu0IlcB0BVHV5N9OC447WK2f5yXZ3r6OjouDsMw/BuJ2rp\nHAAAIABJREFU4ANEz7UFMgi9QJAVAMZxfG4Yhn9HNsU+TLr0zRNBd019tC5qPxHo6w5ZCYe1ZKZd\nHm3bVwlCeJ4kL9dIcqDiZPC92ObzWNv+ABno24sOIg2uOljClEhK4haZotY9qSDVNgbfRZDGsa3F\nFbImy35pzttjJB4atCyVfaqKJ5FVlXwrma5Y53qtjGO64hHgUXYGa8d2k2qbjbZdW3u0uS7XSTfT\n1fJXwrS/jbVBplQeYkpED7S/rsEqmQJZj9OQZK2999g5gnCpGM8xXU+vw2uThF4i1naNeI6OkWsr\nsZ4n6wHPt/H8geECL4HhSSdyrxG8FlSxHtR2vJHRyNzkR4/27+6T4zj+6Ks3s46Ojo7XNoZh+CHg\nW8igc4MMqC+QgbH4XUKRO0HWxVU1TmVl18w22wdcItPZXqh3Jm31a72XaZaX2hgPte3VHOQISQ5U\niVSwtO+XuBm072JqyKLCtkoSsNnrrjb5c2Qj9IcJFe6TpCr3EKHoPNbOuZckbrplSsqcg2rcrNvl\nNYLcVvv8fUzTAytRlaxcKPvsRJGTJK6QqYtCQmQa5FGS4M0qrbo5HmBqWCMp29/GOU3eU1sFuB6m\nn6rq1ecL8lncRd5TSEfRWtfn+s4qaP4gcZxcZ4j7tkr8sLHR5ni9HWsfu0redGjdNjqRewnxapOx\nTsQ6Om6PrVItgT/Y0y07Ojo6bsYwDPuBfx/4I2QArZKgFfwCN6sK1aL9KhEM23vL73UmVDF6niQu\nG0RAbJ802nlV5q6345bbuKcIoqQboeSgkkEVI+ucdrXjTzF1wLxO1GvVudnoWeL3JGmXL2pa4QGC\nWJryt0AQtseAt7c5P0SoOA+QKZbPtvPolHiBTJd0bqtt3tbw7SIt8yV8S209axsDSUutp/O6Hmfn\nqI25JdPW9UGSNpVG5yn5FJtETeD9pPmIpiAXmTYFh6yR9DzV0XM32ZjbFMyFtu068ZyZFrpGEMWj\n5I8DrpOqbn2dJGsUnyLu3Vo5lyYopnpaM6cyaBrnjsxmtkXkhmH4MPCT7eR/dxzHv7HFPt8B/C3g\nXuDcOI7fsf1pvnJ4tdMUezDZ0fHyw39nPd2yo6OjY2sMw/DvAd8BPEgEp48RAatpgypDmodUzBNk\nR7VHl0XVNuupLhPtAB5un60Xs6+XNVMw7Z1G++7p8n4PmZ5I21dl6xlSIVExOz9z7FGSZBxn2idM\n4qRCJ7GaJbCqaEeJFM6aYmirguU2708TdXPf2uZwkayvs77rVFuLFZK4qf7MthNQgZQYOU9TN2dT\nGmvaqOfcSR85m2ZvtOs4RDwD3i9TOU+T98n1fY6pG6X35ypBruaIezcHfIkk5NUhsq7zrnLNKqwP\nkmmRC2TLi93lr33vJGjWQtpWwPu7RKb6Xm/fXSXI/bl2/XvJZ6z2ojPlUvW3Ni+/a9w1kRuGYQ74\nKeLXmTPArw/D8C/GcfxC2ecQ8D8C3z2O4+lhGG5nTfuy4NVUx3og2NHx+kBLt/xJonAfmPzf0VMu\nOzo63nQYhuGvAR9pH79EkK3PE+qUpEozB4nPLEx5M9VNgwqbPUtqVFL2tm22A9CxUMdKg/TzhIoF\n6UxoPVKdR02PWyCD8KqozBPBt6ocpIqoMqjb4oV2zDHS9l/yJCQXpm9qdKHtfk0/dL9Ptu8lbO8m\nCN3n2/hvIx0sNWexcbjK5BNlDs5bddFr0PjkENmI2/uzh0iD3SjHbQfVRdJ7ooImSbpG3Gva+8fb\n96pU+0lCq4Lm/tX8xfvn+0PlevaTBLYSXUnUVimbVdG7UI51LTdJ18n5sp/r5zUvk8qsih9l2+Xy\nuaZ/bhvbUeS+FXh0HMevAgzD8E+If/BfKPv8GeDnxnE8DTCO42wO8R3j1SJknYx1dLw5UMnaVimX\nbZ/+/0FHR8cbHsMwfDvw9WXTaSKY1tVPk5FqCrFV8F+DWT+r4KnczBPW/HPAZ0h14zzZhuAKcB9Z\np3SeaRPrI0yNMqxdkriYumawfY6bLeC16K/29BLVOobKFiSBfaGubBzH54dh2EM29D5PEpR9pPKj\niqRt/m8TRiPfBfzhNtxTBGk7Qvbiu9TmYP87TUQulHlJ8iqpNa2ymrastbWtJGmn8J6eaOd6kqx1\nm31WlgiSbk2c62gK7JF2rD3YLpPrJjnaLJ/PEapuPUcl5F5jrS2EbLousd4NvIX84WCuHF+befvZ\n87i2dW72LpQkel6VYue3I2yHyJ0k+lCI08C3zezzduDeYRh+iWDGf3scx384O9ArQdJ6ANbR0XGn\n2Crlsn7u/590dHS8EdEae/8xQgE6D3yZVM0uEmThPBH4n2zbTS/7LDebftik2/otVSpdKiHUrbe3\n7WcI8mRgW40/qjq2lyAAEIRLtWm5nfN+biYuBu3V6l1VTqJwgax5Mn3zOql6abBiDzmdN18YcxiG\ne9u1HW7fvaWtmYqRRimQDa8h0/I+C3y47fcw2Vxa4mrKqCmIrs1sU2sNUfYQMfg97fqWySbgGoKY\nLiqp2i7my+sosY5nypyskzxKpOg6B9NFd5OqrTWMkrv7219Jn+fTNESy6zVdJBVR0y/3kc+Bpjab\nBJmtYy6W11kiJfcA6aCqwckegljbkFyCDvlsnWtje39miXRNLd02tkPkxjvY517gm4lfFvYCnxqG\n4dPjOH55Zr8T5f1z3IaZ9gCqo6PjlcKLEbq6T0dHR8frFc3M5M8SMZs26Y8RrnuSBy3W10iDkqpq\nzHFzPyw/XyaML/aQpGM/2QPMFEyD4wtEPOjYV9o5Nfm4Tta0VSdJ1TIVKUlX7b0mEdAAw/Gfa59N\nPXyM7A1n43LKeiwQKqHNzYXkQmI41+buWthXbRdBMmrvswXgc8B3A98IfDvRcP1eIv1QF8xrxP3Q\noMXG5AskAam92/aUbaqUS+14HUBtJXGO7dfIeY26MFoDplmMTeA1Z1GVqnOQ4FeSrbq6ULbLXRzX\ntEmfg01ifb3Hnk/VdqWNUWs2F0lCdpYg9ZJ4nzXvr2m/m2V8YZsD31szKOFzrb4Z+FAb855bLeqd\nYDtE7gzxj1I8RLJo8TXC4GQdWB+G4VeIB3NC5MZxfGAb5+/o6Oh4RVAI3U0mSIXUXdMNs6Ojo+P1\ngtYX7ruJtgIaM5xpL2u0dA28TihoNW2vKj+TeLKlGZpSKLSelyTtKd/Nka6U9xFKyFUiKD5JKmEG\n6JpYaNxxnTQWcWwJjfN1jruY2syfb+N8nvB/eA/wm9ycWimJWyAVwEpga3sD2yscIevSVHTq/htb\nbPsS6fb4XkLZM/WvtluoSk6tB1Opq+mDp0hHT1P+DpaxdtqYWjVOYxiI9bItwAMkmbeJtkrjc+1Y\njV4kQ5K2p9rxbyUMSiAJl6mO7yTrMd/JtAef7qeux1vbX1VWU3SXiHTQZ0jC6357yH52MDWQuUwK\nUfeTZO++9t0+QqV1nHXg19pLMvojt17a22M7RO43gLcPw/Awsbg/APzgzD7/HPipZoyyi0i9/Jvb\nnWRHR0fHq4lK1LZICV/oBikdHR2vF8ykUWoCogonOTpDBMTa06+QpMb0wNX20hFyFpXAaOl+lkyN\nvN6ONSiedQhUBdG9cp1UPyRvprdV1UwVSmt7t9kM2v08l/3wniYUugfbfNfKGJ7vApk6uFUWmSl+\nSwQZWSEbnpuyeb5dlwrQaVJNq9b6v9Lm80B7SdyOEYRmmSRtujvSPpt2eqbtV9MY7eG2UN7vFKpN\nkmZNatwuibdf33XgKwTxUQmWMGsSYk1cHfs+Mm3RlFVbNVCutaZCbpAulBsk4T1L1lXWthSey/RK\na+iE90hif5Wsv3yGJOg6Vh5uf33eqpum92DbuGsiN47j5jAMfxn4RJvQ3xvH8QvDMPzF9v3PjOP4\nxWEYfhH4HaIg8++M4/j5nUy0o6Oj47WAmlK5Ban7g53UdXR0vBYxDMMJ4HuJlD1t+J8kSJw92SQo\nBv41RXCJUKtWCNL3LNOAe6u0PM0i7Mn2VNv/97VzPE6m/pm+qfq11OZzsmy36fU6ETRvkiYXy2QK\novb7jq1FPIRKcrkda02cKsrvkP3hPHaVbDi+wrT5doXqkAH+W4ggv6ahQqbomTJaa7QOlfV8Dvgl\n4n79QbIG7DlSSfM6HyFJtgqmTp61Z5stHqpDpeu0097SngOS+HjfJJ2utz8CmCqrOlddNs8Sz+l9\nBCly32rpX2vjvOaaWuo8JIr2Qqz9/ubLvhrQ6F5qWiVkCZjPiueeJ58tlcn7SEX5YvvOxuHeD89X\nlem7xrZu2jiOvwD8wsy2n5n5/DHgY9ufWkdHR8drG3dB6nr6ZUdHx6uC5qT4J4g0yuqWpxul/ccq\nodokiJqOkdfbsdb82AvLwNdaJs95Lxmomm4naXkHkTJ4gazbkmzZKPxqOecyYbG/RqhRc0RQba2T\nxK4S0KqgPU0G/ab6qYoZ/NOOP9fGeoRsYH6GJK0eb4ribBy9u4wFqZLVVEjt7q031Bb/HFN16Aih\n5jwJ/BahkB4mSch+UgG7l6i1UmFbJusL97TjrA+TEKkQ1vqz7UJSc1+5/toSQkJsOmN1q5Ts1bYU\n/kBgk27NRCSd/hBhzzjv9WzvPMgU2Nmm3hrGbJBmNBdJgxRr73xGVPe85/47OUI8r/PcrC7Ol+31\nuTxb5nXgThb4Vtgp++7o6Ojo4EVJ3UI3Suno6HilMQzDjwI/3D4uE4Hq00QQeYFpQ2uVh6NkQP0O\nQr2y0bTErxKm2kutojr5nSTVlu8n6tx+jSSWVY1ZJk0yamqnczRds7Y0oLyvCk01t1AJcx+dMefa\nNUqiThM1ZQsEOTpKqH+7yTQ551Pj6EPc3NrAeUAqkx4nAa21bjWF7wjZq+7T7fWNhAJpn7VnCaXw\nKaZEfPb+zH4nofJ8O+UDpgsukK0RrpON1SVrT5dz3kfa/9dnRbdHlbFlknz5Y4Ept7PPAGTzdudF\nG+ds2/9b2rZHyTRfVWBTjSFTiW1NUdtmaI4iKff5ujgzf8mqY5laCuk38so2BO/o6OjouD1ehNR1\n98uOjo6XFcMw6H5Y20M9Q/T8nSfUGpWodSIotqlxTfezBq2SjqpU1Cbbs6gNsKsZhWrdRaZ1WtVQ\nRNt2g17bCiyR6W0admhqYYqeYxjQHyLJnGqLtW+mAv4OqbZskmqSQfb9ZS46Ix7m5tqpDWKdIYnY\ns6RrYSUcdf1cb1W/B9vcJMmHCRXyd9vcPkjUzUHcI9r+1nXVfmqLhOpjM/FdpCmLqYM+C9uF9/85\nct1VGiFJpU21qxpIO8aaQWvfIFU6+8pdIe/TVWKtrL/0+Vwhm8ZfJUj5NSIduM6Fdh7rMet6UT7X\n9hUao2isM08QN+sbNX88QtbKqTpqsHOGaV3fjtCJXEdHR8fLiLshdbP7d3R0dNwNmpHJ9wLvJwPj\nn2t/HyQJ0ApZT6TpgiRolQyWHyWCVOvUdN6r+1aTCCEhUq0w1W030S9tub20yD9Kqn3XCeJ0nQi+\nHyDTKVXn1tr1aGphWiIkQTGF8CDpDjlPEizT/SCDdBUXyZBE4yQRgJ8niJB9ySqBNRXQvmaqUo59\ntt2T+wmCcZnpeR8gVSjTN9fKcaZHfrGt07e1Y46167hBEgSVwydJAr2XSPE7zbQ5ttf5UtTISXo0\ni7Hu0h56vq81j4vEvVUdvZ9Q8moDbhuLS3ytTbPPnvdpT1sPldC1dt2mY24Q91GCpUJ7rWyDrBV1\n7apxi+ukomkvO9toWPdWTUyeJYnrcaa9Cl/5GrmOjo6OjrvHDKn7SaKAfYJO7Do6Ou4WrZXAjxAN\ntu8ljEeuEgHyk0QgeoBIFdRRT8IDmd4IqcjZj+sgQRiuELVqdX8Vrq0UuZpypsIlQZE8VhXNcSU3\nBt8HiZQ80y0lmbMNrGv9k4YY9jUTVW1RDTQFcPY6VHiuE8TIFEvbHyxvMYfdpOLk+JXQbrZr3Uso\naZKJmvJ5jiAb1l1J7qxPhCBy/46o5Xsn0ZdZsqD6o1HMKkHIv4kkGZqNqGiqgj7H9qDrJuT9rYY1\nkD8cVKVzue1rvZ8Kp/dFU5hrpPIlKfeHCus7a83kKrnuptjaDkE1dSsiL8m/0saX0B1t1/Jb5Rw+\nK/YOhFRFvYbdZX/J+z4y1fVc27ZtdCLX0dHR8Spg1tFyK7Vui+3dNKWjo+MFDMPwY9zcAsrgcCQC\nZWukNogA9QpJ4nTnM9XQVL7dBHFSQblBpibqZKmaYDpfhQRlH0GqVFEOECTTNMlV0qoekliukDby\nEIF+NZeADL43SRdJXRyda02XkxTMlZeEw9S4Wl/m9c8R/ZGtoapNthdJV0JdJ6vSpaKz2M5dg3aV\nOB0O7bWswmOM/pY2zyvtuwOkAcfn2vs/3ubzz5g2Cjd1VPWzmoFI3DVc2QlU0ZZJC/4T5D3R8MYU\n0rmyTQJ1nVwfSex82b/WH0qKTfFdJshxJWeSZ41UaPtUsn68fe8PFJqi0MY+TvT1U1mEVBPrOBJF\n/114/527tXZnyX8LYvbHgLtCJ3IdHR0drwHMKm+3IHYLndh1dHQADMPws2RzY/Ek2VcMMg1xnegb\nN0+aN0CqTjZNXiQbR0OqNaY9wjQlTJVj0n6gNQSXjEGQjyXSWVEFo6bFGUCbqinp8lwqUta8GRBv\nlDnZNFt1R8IquTGdz7Q43RMhXQS1k9c50xorG4RXI41qFmNdnwR5lVDdNgiyVlWr8+VaalCvEnnf\nzLXXGrZLpKqzQdQ9fhNBOr65rbH3yutfIgiJ/dwkyXMESZ9NE71b2NLiLFlzJlmUzEmUIV0cJc3n\nyliSNO+FJO9qGUNlrdYZHmvXLYGTnD/Vxj1EqsiQJiSeU4XvKvHs+ePE8fZecyCf6832/nh77Wn7\nPNuuT5Ip6Ta9uf5gcICdrXsnch0dHR2vRWyT2PVUzI6ONzi2+L/gk0QK3YNEEKpCdIFs5G0tW00z\nVDkw0DxYPms4YaCs46JK1SWmpGgSjJb2A+eIQPwDRND6OaYKjeqQKZqQxiCSopr+Wc1FbI1QbeF3\nl319v1rGkURKMI4RgX49/yahDO0u63aCqcLn+tX5QCp818i+c67jOlkLKBnxeFMyJaieR3JwliAL\nznM3U8fNf0j0+PtGQnVSQbWGTPXxaFkX136FmxXVO8YwDPvbuS616/SZUKESqpLOW6InaZNIQdac\nabajyupLwlv70llTKMnzefC++sNA/X6lvK/k8QSx7suk42qto5srx8y3671A/NvbINsQWGenK6r/\nhq4RZH4/qZpuC53IdXR0dLwOcIfErtfYdXS8AXEL9U1Ya/s0kU55g6x50mjEpsyqM5KDmmon4am4\nBHw9oUpttHP8HhkwQwa1tSG4CsfuNu9jbV4PEOTOnmKQ6thB0onQ5smSAZUlzU52kapSJUAG7XvK\n+KbrXSeVHwNqVSEJQiVYjvVkm9v97bNrt6ed++ly3TV1slr7S6DPzGy33us4cV9UGRfLGklKJbZe\nlyRJB8Un2zHvaWMdanM90/Z7G3EfXaeqjs42N78bvL/N7RLTdE2bwD9HEjRbDthgfY1op3CMaSsG\njUEOtGs4Sqqqx0kl1XTHp7nZrMYfBCBTLBeI+6hi6j2ojqb2lzNd1zpJ0ymrWcnDZV4qdtYaXiOe\n5402FsS/QevoHLf+uHLX6ESuo6Oj43WI7RI7ejpmR8frBsMw/AJppf4CxnH8wEx93CoRSI6k7fsN\nIliX5Cy3fQ+SjbJt4Kypifb+kDVo9lOzfsgGxqZcOm5FbRC91I690a5F58CF8lKtsDm140ssV8u+\nBr/W3qlm7SEDaJUq0xqPkvVJkhZrkzYJ4qi6omPidbJpuqSg1pbV/m+0ffYRBiTLwFfIFDzJ12mm\nyqGBv9cloaxkTYK3Qqhtc4Ty43GV3D3T1uW9RLqlao/ujZeIe3kPaX7zGDsjcm9r1/kUcZ+qKmlt\nm6QFMt3wAOmy6TXUptkeU9cDpuqrrStU6ExTPUI2lpf82ZPQusXqzup41l8+0+bnMwdJqE2brKoi\n5dz+AADZ6sFr2yDugUY/54nax22jE7mOjo6ONwDulNjR0zE7Ol7zGIbhY8B3zmx+bBzH7/fDOI4f\nAz7W0hg/DHyECIifJ0jTWvu7i0w7symxtVvnmTbK1lnQlLTjbYwniVYABtS7iQC09sqaxQqhxl0n\nzEJ0CrSO6C1MVSWDd50IHyH7we1pc7WJt2mWa20cFQ4Vrr1MmzdLzkw1NaXQOjfXwbomlTXVvscJ\nZVKjk6MkEfB+rA/DMGsn7/hXy+dqne9awjQ9UDJ9lSAOqkyao0hIa/qetWK6N+4Bvq5d+5PtGiWG\nB8gUTNM9KwG5IwzDcJT8ocFm13Veqqaz5He5rIVpnxIsj9XVUaJlDznXQTVuiaxLlASqgta6uvUy\n9kI5vpLHalCiYnj/zGd71x0lTWRgmprrnP3hw7n7PKgMb9W6467QiVxHR0fHGxBbkbO7UO06uevo\neJUwDMMniSBb/M44jh+91f7jOD4P/PwwDIvAH2ZKVO4hgserpLKgAqAzYq2HWyYJEUSQfIMMYiUy\nzzINTGdTK912nAhkf48MlpeJ4N/aPdMb10gCpWqn46Bk5grTGjrIgPw5sibPlDpT6DQ60VVSa/sj\nbZyvtv2vMrWklzhpHnKsvD9YzsMwDKZraql/nCTEkkaVQ9P8rKOrhNg0ytqn7xBZI/cMU+t731cz\nkRXglwmDk28h1ahqLnOhvT9JOpvWGsA7wR8hFLkVspUETFNirxH3TSMRuYekWmOaSkqtuzxEPqOz\nKammCe8h1vxi2VdyvLfND7JRO+S9rc+eqplpvD7bR9t3TzJ1wqxqnerufUyNeqojrN9LUHdkciI6\nkevo6Oh4k2AL1e5T3CI/v5O7jo5XHjMk7so4jjf1mrwVxnH8+DAMh4HvIG3+q3K1n6z70V1QtcTG\n4AbgpqMtkGYgtU5Nd0jTxWbjyU2iYfXXkSYYWrjPlbEfJwmeKZa2GHiujF3VmnouXTg99kjZb7YN\nQe1VB6kW1Xo4Ux0lfKsEuVwjerE90tbAeVfr+EOkY6b1VM7f8Q+SZKle72bZ/wjTdEkJTK3lq7V1\n9XhrE/1e9ekdhLK0SRL5e9pfayoX2TpN9nb4bqLu8SzptGm6rWmfKpe1zxwkGV8l1daL7fsHyvWc\nLPPSoESyW9N7q1umymo1XLGW7TKZNinRv9zO573z+TlJqr2nyLVzXWsPRNNEvW8S9aeYmvDQxnS+\n/jCwLXQi19HR0fEmxVa1crdJyezkrqPjZcQwDP81SeI+3lIn7xbPEEHzLoK4GXiaxmYjbM0XVBYg\nAlD3nyfTGFVyrhL1VKbMaUiiAlKbSZvOqIlKbWvgPFbJlLODbbt9vjT2uEAE2fa+WyLNWgz6VeF2\nk+RyvY1xmKybg0w9lDRtkmmYmwTZkfxKUiVrz7R5PtQ+f5WbbfNhatpBG19HRhtDnyPJSHU/hAz6\nTXf0s6TwENl7zjpGr62mbUr6vkT0SfseQlE8zdS04wZZK3nHGIbh7QQZlABBqlSqTdeI+2eNWk1F\n9Nky5dVrrymetpaopjw+b7qtatIzm8Jpqu45Ys2OkWRSJU7HywNkeqbE7FnSMMZ/M8vk83WBJG3H\nSBLp/KtZiwpcbSa+Z2b/baETuY6Ojo6OF3A3KZm3+q6Tu46ObeHb2t9f2g6JG4bhBBFYPkoQmwNE\ngKyKZZB7kghEzzJVwxaJoFs7/2pOYcApkYBpb7MX0sRazd6fIhSMx9t5dOo7Q6bO6Rq4RAblBtHV\nCEXly7ovSIMLyRCkoUclBsKUwv0EsbM2aZMkByp5pmjWxs0SjCdJUqz7YSWw1eGw1mDVhuyVtO0i\nyeJsuqi1inuZGmKoSG2SRPJhUgFS/TpE9spbAz5DpFkeIV0rDxAGObM98e4E30Oovp8n7vHptt1U\n0NqvT6XqOqnKqgwvEcqtBE9SuYtYp0dJpVL4DFrXJiG0TnAvU0OTWoumgY/7QypxkjHJ9lfbce8g\nn0WJ3FWiTYHPrv39ar3nVfJ58XlS0bZedLaFxV2hE7mOjo6OjtvipSB3txqno+PNitv8O/mxbQ5p\nLdTvAu9kmuJX2xBYi6Q6V23QVXhUWVQNIAL9XWSPtc3yuQaj/yGR3vkcoQapcuiKudzOZxqiSqBk\n0HS32u/NmjsDcImdY6wQgbcKn+pXTZkzhfQEQehMcax96EyztHWCCppz02zDHmZHCLIKQVyPEmSP\nstZVnVsj1JvDhKJoyqjr7vklKKZier210bWESUKqKua6uOaLbc7LxLNxiuy/p8HLXfGBYRjeTzQB\np41jU3GfLZVTW1xImtzHZwgyFRLS3MU0Xq9prY3lGhwoY6mk1T5vu8hnx3YFkvsNgnDVnm6mFl8n\n74PKn2sjMfOZqo3cVUcPk83LJel1X8e13hOmBPWu0YlcR0dHR8dd4xbk7ifJnlY3oat3HW9WDMPw\nzwh3xTvZ94PjOP76XY5/mFRVrBk6DNxLqBMStVVC4VAlqOloQmIhNH6QsFnDZgCtsvb8MAzfTig1\ne4DfJhS46hZ4qn0+TRp/rBFB76EyvumY1ZbewHyBXEvJwV4yVXAXWSNlIG0dUlVddET0etz3Aaaq\nixbyEARA8jBXttOu7QTwxbb9MBGsm+ZqWl11ZjxLKnGuuc2wJTPWCmpOYy2aBGGurfMLxiskqTlQ\ntq0RpjO/RzQOfw9BwO7l5pTGF8MfI4ja59qcHiSIaa15fJysPztcjpWILrQxnmW6jh4vaq8/UxV9\nJqz/9Bk7UL7zWHsOeo5DZUwI4r1E1tDVJuHWTPrc7WL6fPlcObakW3ObB8hnbZFUUynb7lYJnaAT\nuY6Ojo6OlwTjOP7oVtu7etfxZsPtnvkZvNDXsbQc+Gngbp//h8ng/QEiQN8k0udURCQf1o9pFFFT\nK+cI4wmDelWr62SwWgmWdWrivyNIyxnStdK6KANuiaPEqSoeKjCew/0NzCshkwwdZNp07q2AAAAg\nAElEQVRPzTF0MYQkhjoUnuHmdD1VRomWBhu7yneec41Q33YBDMOwvx3nuqv4PEeqcnWONTW01sZV\nt0qVOVMlNeiATFE0rc/1pLxX9XGN1wjCtasdc5Z4Po6SxisvimEY/gpB5C6ShEVSZNpgrVuTWNU6\nuvvK/ro8LrQxqxqnS6ew/u9tRIrwZ8v459u4s7VuV4n7QZtX7dtnjSVMjUhcC01k/PfhDweeo/6b\nmXXW9FrniH+Te8hm85tl/x25V3Yi19HR0dHxsuKlUu9uNVZHx6uNOyVut3t+x3H8Mcdpf//SnShz\nrTbuXWRgv0AEp6tkQ27bCkAGyBI8jzEgloDZqNljTpXj1ojecC+YhgzD8B8QJA6ScKnmmb65TJIq\na7xUJTRXkeDU+r1qCjHrMAlBAGqjaOel+uJLYnqSJEmQgbVzlexWEw1Jq3PbVdbnbe3aV8o4e9p8\nzrXzqCKuk+0cjjBVD00rPNv23Uc2eL/AzWYuEicVRYlBJammbVaCsgL8FkFobwDfR7SuuJP/X/8U\n2d9PVGdQyVF9hiQ8kCR8tc1VJ1WvxdYC6wQRVal13JOEe6htDaydPEGmop4jyJNrW3sDSvxNx1Tp\n9N5CPo/Xyn5rxH22xYRN6n1+fYZUWOsPFKrA1amU9veujWYqOpHr6Ojo6HjFsR317nbfd4LX8Uri\npSBut8BfIhQ5gJ8ehuH0OI4feZFjvoMIbE1jtI+ZJK0qcfW9geVsmtoG8Cfad7/O1La/qma1h9k8\n8Ffb+/+VCKKXiRq5OaaGFKpSF8o4Eq51Iu1PtcR9JUiqVva9q+qNdVizKWuSOOvRDKop11tTC12H\nxXJcJX2H27mOEE3Cfwn4Q8B7CYXoeJl/TdGr85BkzhNqjuvwNqatIKpT46zqVdsmeA+87rNkLZ/w\nXtUar2eBXyWIHMMw/ONxHP8st8AwDL9IENhLwFdIZXelzfcU2VS+Nvr23nhNNcX0KPHsfoWsTaxq\nquunq+kPt/f/R7kmnwPv1cMk6VUlU5VbnDnGeaiSes98XpbIZ+I4QXyfJAnyHPEsrLe1NWXUMf0h\n4FIb9zDTe1obyN81OpHr6Ojo6HjN4FaBbyd4Ha8m7pC4ffJWP1DcKZoC94Fyvgfb+58bx/G/3WJe\n/4AkEI+SZKv2wnqQTAWzps00MZttq1QdJGrcPgA8TQbBa6Q5Q3V0lKz8apnWe4igtQbzEsZHiKD3\nGZKkSBRNW/uThJPix8v1QBIzg2zdInW3VLmSwBwux28SJiOnCAKpQ6ZkVDfO/QSJ8DxXyRpDFT+/\nXwK+fRiGtxKK6F6C+EIG9fvamBq8VAIz2zpgDfjmNs4aSch1Ha2pkq6XJKfWF6oMOv6Rds5zZa2r\n86VmLZAGJjdh5t/ACkE6d7U5/Sb5vFkHqZLlsyiBhCBErpNpmF9XxveezKbLXgc+2N7/PZLg+UOB\nrQJ8NuuPGT4LF4hnZ1cbpxqvzCq0VZE9ThD3DeDfkmt4jSkhqw6tkLV3psDWZ6ASzW2hE7mOjo6O\njtc8XmqCd7sxOzrgjsjbE+M4/umX49zjOH5gGIZ/TpAwgO8bhuH7KIRuGIa/SZA4iCDymwgS8yWy\n7uk48CEiiP83RJBZUywp20wVe5AgUs+SKto7CbLwRYKESQLWgP9mZvofJALdC2QQD2lGcoyb0ztV\n6lSUDOJVdwzsDb4lmaYPnm/X+Qjw5batpmYeBH6EMPb4GdKEpPZb2yRI6HXCql/XS9M6dQL9ctv/\nN4HfT/bkO8+05161vNfoRLXOIH6TdGx8pK2Nzpirbew9bV7LBGGv7pWO/wFCKfqtNrYER4XyEKl6\n1rX0Hv4BGhlvz/0XqzK3xb+FU4Q1v0rjbrKlxSNM1bh3tu+/RpJ1SEVxDfhWgnh/lSRjz5XjrxEq\nWG3DYIqkymxNw7VH4QpBEA+243Xq3CRUVID/u9yDcyRBU/V1nj9KGsq4vySs7vf1xHP2KEkG50iV\nTmIpud4RF+tErqOjo6PjdYvbELzb1uC1fbqK1/EChmH4QeC21v+v5LNhSuXMcyqhWyXIwgj8s/bd\nbiKYhyRr1sbNk3VV2sLr9ghJuC4QqYLvJnvQabpxD0kONKbYAN7fxvgkodKcIFWRaySphCCZphSq\nAtKuhbbf58iA3CbM5wmSIwmodUYSvRvt5RxVq0wHNbXOgNtXVeUMzJ27gb+GHnNkc+9/Cfyn5Roe\nbddu0+j7yIbVuwliYSAvcV0oxy8QZOOxdr1vYWqPTzt3VY2qK2dNTzV9sF7TEaamNefL+83244HP\n2ruGYfjNtq2qzL/X5vLOds6hXcchgtwst9fJdj1XyHozlSjTKy8AT7VrWCXuT035FRI1Vb7PMnWS\ntN5OZUyoTEIqka7bPPE8u5+Ktc+M62bN2yZB6iVy/vghUbtOKsGmDFdzlJrOqSp4uV37jmrkhnEc\nd3L89k88DOM4jsOrcvKOjo6Ojjct7sJR8CZ0kvfGwh2Qtx2nS75UuMVz+4+B/wH4MPAQ6fBnKtdV\n4geNB4gaJAlcrXczLc1aNPuQQZKZar8v6TOA/c+Aq+M4/pnWX+x7iMD1820O1XnyXJvnKdIwwvSy\nS+081ok9RdQ6rROko5JOyJomg2HJ18V2nQ8SgfcKoT79gXa9n2GaNqqy5VpYy3UdeIII7G23oOok\n+fso4eAI8PMEcfkc6aYJGdhbkzXHVBnaTyqT1mNJCuxjpxHHYUKp0i0SkqxUAquyaZPweTJt1Pup\nAcoicG4cx2W47f+Py+M4fngYhkeAHyDuoQTzQlvTs2V/VTINSCS4knxTXIWmJ/5QcKVcd8W72/GP\nlzU4TTpf2pdugVQNaz9EUyndtzqn1t6IqmU6Za4B/4D4N/A/MSXl9Z75b8dnyF5+y2RrghVCnfU5\n+p3tcqKuyHV0dHR0vKlwOzLWUzXfHHg93kfnNQzDPyKCWYAr4zg+PwzDEkFa7PU2R6giZwkFA9J5\nT1QTEwPsa+WvZEMnShtYG2QvEml0v05LZxzH8beGYXgL8D4yxa3WOGlNv16+t0G1aXOqGJtkcGyD\nZ9U9669UpK6SPd/2keRMsnkN+BSZ3lnNQ1SyzhOkZ9ZABNLUYoVU9OaB/54gpt9ApNT9IqkO1RQ6\ne/hdJIL3Y23cp8o2SV6tn6sKk/dA4jFPkFvXSTMYFSWbolciIjE6Xt7vIi34mVHmKNs/3P4+PgzD\nFYI8XyJSJh1/iXheTrfrPU7c668RPyYstO9Mf9UxctaC31pA3U1r+qvrC1OFFoLk6oQ563Tqeu0j\nnhVJpyS9pkfuJhRRlWfn8jjZqw6yb9yuNo7PrqmhKs9rZG2laa86avYauY6Ojo6OjpcC263Fe7F9\nXqvk4M2EN8r9GcfxhwCGYfhZ4KPDMNxTvlZZM9DcQ5guHCSVgsXyvWleB9t7U+KeZEoGrLs6SvaP\nc4wVpkqMqXYPkKmFqjD1vJqtHG+fdxGpic7/aDuP5zc1b41MCzTQr2lw+0nzD8nq+XYuiWrt4SYp\nkPDUNgamgUKonbpZ1rTGrxBE7uE2z2dJNU3nTa95pY0psZ0nSdiDxD1yrewbt04qN6qSl8p6q1jV\nPnneO9NnrS10zh5nPZ6qHjD50eCW6hyRmniYrEeDrHf0hwHrJDdIpUxSZk+1+8uaSH4lTw+0MXQi\nPdDOVx1NXS/bPKj2OSddRv1RwB8GagsKHUUXSbK+n3zuT7XxfoU0L9GJcrbm0FRaSCOeC23cI+Rz\nd5543v13uS10ItfR0dHR0fEi2ImKdyf7vJ6IxOsNt1n7j43j+PFXdDIvLX4XeCvwFwiF4ddIt0Kd\nIm0urVNlrRWqPeIMjt9Wvl8i1QSJj3Vt7yMUiw2C4Fwrx50lAlzPf5VMoZTcmG44X767StaOWeel\ncmQKnm6OawTxqb3hVF9Ml9sggvuqUK0Qathi+c7jThJB+jMkoTtE9hOr7Q98f24cx58YhuGbCHXy\nOJmeJ6oSatx9uv2taX27yAbYOoPai02Cs0ASL50fa2sG10hCs7uNdYQ029AAxTXZAHYPw8A4js+X\neavOfRLYOwzDPxzH8YfbV2dIN80VojbRurcnSBJmbds8UUPoc2nfO1McrQWUsB8giNOT5dpUWKvD\nqv316josksqq9WeO4Tl1mbS+DpJ8eozKNKS69xWCeFK+m03T9DmDVJL3kM/GbFpr/bdz1+hErqOj\no6OjYwd4EZL3oqYrbb83hFr0WsIb3cxmHMcfH4YBoufbLiIAPU4oQioGBqCm+L2LCCSfJAjBwfZ6\nnIgJL5BpYAbWBqUah+xpx9xDkBxVIPFpgtTo+vdWIlh+un2vmrIwM6ZtBQyKJS+18bTOh6ZDrpIK\n2iGSnK6WbbOwmfcRpil9KoYqOCpbruFsqqPX/Rzwt4D/GHgHocyJ422e9tPTZdPrN4XUukQVy91k\naquEyybcKniqVNXB0mtWeavEwvOoink9jnUr/L/AdwLvGYbhL4/j+FPAtxDPm8/LZbKNwFsIwrNO\n1oedIsjfpbIGNjKXQPnc7S7f6yB5om2T6PnepuHz5bWrHO9zYMqppF0iq9GJ6beOJcHyx4cnyrH3\nk8q0sL5S9dg6ONf5ULtW1bk14geFdYLgbhudyHV0dHR0dLxMeDGjjK7mvfS4xXq9bK0CXk00Mvdr\nwHcRgfUSEaReJ5Ur09e0/X+WdKjUFMKUPtU7lT2DaUmLdXHzRGBu/Vyd0/owDGeJ4PUomWq3i0yz\nu162GRCrAC4TxACSkFYXzNNk0F7VJ0nXnjaWLQYkQJK2q23f+9r+1lWZAmrtkmsicTrENIXvBZI4\njuP/MwzDBwkid4o0lVFZ3MOUZNY0SNr47nuEqOM6P3uesm/d5vs1ksxLJDbaZ1MoVfkkNb42Z9W4\ncm0/Vv5NfXQYho+Wry8R6tlFpgT9YVLlPUgSItWwWjdpSuM1QsXTGMT9zxL3SKIuyb7QxvEZfKD9\n9VmhrcH9JFH0um1d4bxcq5peW1NQF8tnz+/9tPZtgXi2NknzndOkGrhCps+utPlLGreNTuQ6Ojo6\nOjpeJbyImvcppjbct9qvEz1uuV6vGdfJlwvjOP7LYRi+APwwoYbsJYLnE4QKdo4gBVeIFDgJnrU5\nBtsqQgaoKj41lXCJCNLrOlfnQfE0qVqodpxn2vtMqHTsIQJ2XSEPk9btjjHXzi95WSRTDVWjDM7n\nCUJY57rR1siUzTPt2vaRNXWauUg8D7a5q/ZU85Cq6P0c4WB5ol3L2Ta+So0pdOfb9pPtO+vfJAjC\nNEF7v10niYLXbp2hqYfVqMZ13V1eEjzJg2PNA1sSObi1AQpJfu4n6y19niRnOjpeJkif5BymTeMh\ne9BJqiXq2vxXV1GVtFnTHv/uIsmdzePrvFUhD5E9Bes91ZTGdFQV3Evk+s2R5imQabhzBMGsZi7n\n2nn2EERPN9KtVOM7RidyHR0dHR0dr0GM4/ih231/p20U3gxEb4trfEMqcLdCcxL8V0RjZZs/30OQ\nCuukPk+qQ28j3SMhVZHqLjlPNFNeJ3qbfQPRgHyhjWdqZSUNFRK8WmtnumJVQ/aRhGt/G2uJIILO\nsTpq6kio0ic0JpGEQaowEp2Ncpx9z3QadD723auOgjUVsRqK1DhaYriXdKHUREZnw4Ntnip2rvW+\nds22RbiPTMXThl8F0ibxqj1VLdIpUbOXDZLoua/X4rlnr2NL3ILMHSZI8Tmitk/Sba3jQYLc1XUz\nrXEX6UK6TJK0ZTItU/gjAkwV2ppeWVsvQBI/SaPKnemsPremRWp8ouKp8Y/KGeRaPtQ+q+Dqzlp7\nx83Wvp1sf8+2a/F53cMO0IlcR0dHR0fH6xAvRsDeLERvdv6v9fm+XBjH8dPDMHwF+FNkI22JzEr7\nXE0zDIINOo8S5Mz+bMaI60TQaYqaNXi1f9ZWNVbXy1/d/3SYPEekIc4RgfJhMqA9SAb4tTWCWCcN\nSUyVmy+f7yNr61S03GeNbGqtkYiKicThfPu7v53La5Poeh6YEtg14DfaPifKvM+3MR4hCYg92CQT\n1dIeUuFRIaoNqveSJNNUTNM9jxD3aqmt6xdJcw0JnsRv0rJgGIaNW6VXikbmfpaoe4RME4SsubyH\nuD+1TYC95HwOdHMUki576VHW4wjpFLlKKrsSNs1ONCnxOVon0h59bldIMmdvwJPEs3ahbK+N5Ffb\nGrmeEmbJqUSxNm3XadT04M1ynD8gSFpXmP4YcdfoRK6jo6Ojo+MNiFeK6N3JuV4uzMztTaXCbYVx\nHJeHYfg3wPcRZOLLRKz3dpI82IhZAxQbMFdzh3mCXGne8J1Empoq0AGCUDxB2uPX9LWvtr8nmPYv\no3w2+L1CpLDVvlpnyBS7pTIP1bkDZAxba+XeUq5TonOdDKphWqe1Xq6zzq26CUoWN0m17hDhWPnC\nNTcS9PQwDK6nKZW7SIdJG1fvIQixJO1K23cv2bhbu3yVG9WgK+W9qh3tvY6KXofrA0l8al2eLRZu\nZ3YywTiO3z8Mw18DPgLcSyiE59pf21BUJ8rafkGF0bYW6+VVm2fbZ1CVS5JdW1Doduo1+uz6w4G1\nkOtEvz6dPqvSp4vq0ySZdwzn7nOgC6jnPkr2ljtDqNzOTedNn71NMrV0qY17nlQRt41O5Do6Ojo6\nOt6EuAOid0eOm23fV5zszZzz9d5K4CVDS7P8LNGg2vREA+uaSmnAO0emK9YaLb97P6HA3GgvFYYF\ngjjcFIyO43hxGIZ3kql1c2RzaEnXWSKg1fBE0rJOEFAJzAWmuEKQHQnPPEmUbPRcr01Sc4hMS6ym\nJjU9DzLVUFVskZv7y80Dh5qKdRFgGIZ72/bH2nz2k7VctUbOcVWQIJUaVaADJBEwFfBY288ea6aM\n2gZgH6linSdI42xNYr2/lDFuaj1wO4zj+NcbYf2z7bw3CCVuk7hfVQ2tabGQqa/1HrkG1wkXR0md\n6Y4Q6YzVIEY3UV0tNaZRUT1Bpj3OA+9s268Sa2t6rm0DTKetqJ9naw69VxA/HvhvqF7zOfKHAVXn\nmrKrQrptdCLX0dHR0dHRcRPuxCTkTlW9O913m2Tvk53ETTGO4yeGYXgM+KPAewjFwNTKmtpniiRE\nAHqmDHOFUHneRgTnpuJdIoLlPYSCZOriC2ikxqC11rhdJslQ3WYQX1UvlcENkrxJzKqBhA2eIYL0\nr5EB/j6m7o17SWKoc+IaodjcX+YMST5MBxSqc7N1gRLAc20d30MG95WQ0ear6qdbpbViq6RqdLld\ng+tueqoKXTUWsc7QptaVdNb0PmN/x7pVjeNtMY7j3xyG4RuJnoL3tvFukOt6tO1qGuI14hmSeF8j\nlDBrD02vXCTVKomc6b5rxD1W1fS6KlGENIdR6dOAZp1sJg/TWse9pEpa6yAX23e1llCHVEjSCUns\nvOcHyGdFMi/Zq/dk2+hErqOjo6Ojo2NbuBPi9XKQvaYW+vkN7Uq5XYzj+OVhGL4X+OMEsfhfyMDW\n1D+Jyz6yibLK0/sIEqfl/1NkwGpwLtGZRVU3TE+7xM3pfqa/2abAuqpKnExltO5PhXGBJDQrhJvl\nfiLVbY0gC44/T5IIjUhq6l5tEK0ZyuVyHq/7KknkVBYrDMyfIRuMLzF1aoRMAxSSHFNAJTKHyPoy\n0zhVhGpjacmaDa5NvZRISl5qbV9NGZ0fhuHeu1HlAMZx/HPDMPx5opfhCeK5uEKS33uYKsKmtF4g\nm297LxbLZwm7612dKVVLNdHxHti2QudS76fPqGRPsu1zfoQ033GNjpS1UmWkHON8JI9PtvlURc5r\nrWqfSqUq3G6mz8FdoxO5jo6Ojo6OjpcNLyfZe7Mam9wFvkYEi6cIYlFT3iRVbyMUhxtk/69vJpqH\nQxCwi2RvrwpdJXfPbFex0H1QguQ519p8TpEuhRIog/U9RMC+m6xdquTpKOk8aWBejT3my7bZBtvW\nclUjlWp1LzGqDonrTFUta8O+1rap5Nhr7gxTIrhOWtVfIo1nanuFqtK4pqo8e8s+EhBIpcr0So81\nxrcfWzVO0fK+Xs9tWxDcCuM4/v3WmP67CEMXSesNsgG56a6Sq6fKPCRaXqcKruT6vUR95g2CnK+S\nz4xpqqpt1t75vAnVzIPtVRXVWjso+ZXUzaalaihzlTQNqt/NE3Wabjf903sMSbglcd21sqOjo6Oj\no+P1i+2SvWEYfrIrcrfGOI4fH4bhIPBtBEmDaVrjBhEg1zS97yPq6wD+LZni5jH2qDtPBt+z8eRu\nItithhTHiSD5LBnYWxe23PYx4NUJUWMVa5nmiKD+ONMUPo1RIOuODrVxDNo3y3vVrgPlXBIez0s7\nhw3DVbkkH7ZhqKgE8ittH+v3dDKUbDlfibUpqhJCWwfURtYqab72kaokJCmw39xzRBqi869ErqZc\n1gbY28HH2/V9N/EDgKYs1whVTsItudogav5UYiXMVXGVKC21MWw67nO70q7jGmGu47XpGil5c90g\n1/nQzLWfI4meNWxVdVVdhby/kvB6jyX/PpsLBPHbYFr3V1Xs2TYFd4VO5Do6Ojo6Ojpe86hkrxix\n3JEZy5sZ4zj+9DAMXyKcJ48RdUA3iCDTfmPPEgH0KdKi/VlCOVE9OkWqYs+RBA9uJgG1iXN1kDRt\nTjWi1gwZvFvjVRUyCaSKzippDe98qzujZEvzFJXAjfLXdLqNMraOgypokgYVPJtCw9S0wvNLElV5\nJC6z9vS1YflxgqyYEiqZlDjWHniHiHuo8yNtripAGtqoDu0lXS5NK5W41HYE5+42rXIGm8C/afP4\nI0Rrif+vXZNmOhqPzJEk7gjxfNVU01q/CZG26LOhwchugqB63fMEKa/mMhJB0yld79l+epI2CZ/G\nJNbnaShTU3mrQUltpaAKTbkem4rX7f47stXCttGJXEdHR0dHR8frCuM4/qgK3TAMv9lTLF8UnybS\n3h4m0wRXCUVnL9m8+b2EkvSpdpyBroYcx9r2M2SgPOsq6XErbXx7xT1NBsD+reSmkicVKchm0Cp1\nu0iTjEfIwFgF5ThTa/uqcNUxad9bvyShrClzoio41qeZzilUhCRfXuNCeV1lmjpY0wrXyxg2Ffd8\n+0kyIvmUrElcIIl1NZSx/9lxMsVU8uL4i6Qquh1Iiv434p5/ezuf98SaOBUpiPV+iiTEVWGtzpSQ\n92QPSWyt8fRez9YcapBTWx74PFcTGJW42ptQ9U8DHMer91xSqmGOrqfeG4m29/hCOe8CmQY6+6zd\nFTqR6+jo6Ojo6Hg94gWnuk7mbo9xHNeHYfgksWZLZIBrgHqQaDFwmAhoDbwlOetEoK9iZmrjrdLC\nDpFKhsRjkWwZUANiDUGqHby1VapNqncbbYxjbY6z5zdYr+6TphZaR3ak7C+5UCG5TJAtx5UA3E/W\nY6ksTYxOxnF8fhgGSZGpi2fJ1gs1rU4F0PNUh8aVNseHyb5zs8YukMqa5E9iV9UllTiVxFon53ld\nt53iUDvnz7fP30Ck6D5B3lvTHiVeq2TPN41OvK8a5NxPPJeX2v57SWIsEaruqG6nbJeg2QvOlEzJ\nNO08l0myt0G2PFgl10pVUxJqPzl/CPDZdSzNZs4R9+EYafSyIxIHkXPa0dHR0dHR0fG6wjiOH6qf\n78Yw5c2IcRy/TKS63UMElA8SBOp9RIrqEqF0rZCpbSpHEp3HyXTGWgc0SwRUpSQsi0Rtm8qYSojE\n0mD8VNtHtaKmUtaURdMzzzBN7zxCBP3WSFUcaq99pNplIO11SHRg2hAcslm3/cEWmZJC51BflDk+\nVK6zKpESj7k23iGSANf6uar4aYu/u5xHsrLEVBGs22qNnMYsEr6doI67Afxr4PPEfbhB1u75A8Fx\n8t7aB8/3F8rLus15sj6u9ml7klSLl9rfC0Tqr8pXrTXcRRC2xfKaIwi7dYUS4mrE8hxTMghJ7Kry\nC3k/N9sYqojHyzlVE62n2za2ReSGYfjwMAxfHIbhy8Mw/NXb7PfBYRg2h2H409ufYkdHR0dHR0fH\nzZhV4YZh+M1O6G6LpwgScoM0nHgLmXJnz7ZVItC8Qapk1po9T8SPpruplFXYhBsigH2AqTOjwfB1\npirVAZIYLpT9JGULZbuphkfJINnUwyWC0K0Qasg+giRZJ6WSVVVAWxHsJlsxqHQ9Q9QMXiTTMSdZ\nba13noG6ypn7rLc1sz/ZmfaSpNk0fYkgGidJJVPysr9cI9zcogHSERGCeB4jHURV66oqJyFcbPPf\nCSRLKoe/AHyWuPfvJ+5TteW3FlECZrqvlv0Hga8j2wxYY3aRWC9TMm2poco3R6p29bptY1DP4z0/\n0cb2B4b5tm3WrbSa0UCS0adJVVVTFH/IkLTXZ8EfJtbZIYm+ayI3DMMc8FPAh4lmhz84DMO7b7Hf\n3wB+ERh2MsmOjo6Ojo6Ojq3QyNwn67ZG6D51i0PetBjH8XHCifIaoRA9RBIJU80gnSUvE0GnPcxM\njVsjguW9TBtdi2pSIhGpKhNkU2ybla8BXwAeI4mhpOQA6QxoEKz7YE2vPAs8Sgb6KoMqJKozko5L\nTE1YDrTt9pxT0amtDSAI0m6mBPYFUkSSB50izxLBvmmWS21tbeativNUu57DZMPrWqe4WcaFm102\nzxGkU7XzWtkusfT42vB6R6VWxSjF9aad41HiPh8jUkUfYppmWdNnbVR/nCCtJwmeUfvMnSSIrj8S\naBayTBA8ybBrXI125on7faXt+0w7VvK3i6niqQq9RrqDVlUUMrXyQab30VTYVbJ/oj+U+MOB99Bm\n9tvCdm7ctwKPjuP4VYBhGP4J8BHiH1/FfwL878AHdzLBjo6Ojo6Ojo7bwRYEM2rcgp97/dwEG4Sp\nydsIxe0sEaBeIgnBChGg2vvrGNn77Vj7/lm2NgaBJCDrbXwD9znSfv8g8PY2h6dIMgeZSmew+1ay\nfsp6uZoOaX0ZpCIGGXA/OzOuhKu6Z0oaKzm7QsbKNYCfTbv0mrXEP8K0b90qQduOHhIAACAASURB\nVCwkstZd7SJElaOkKcky0ZtO4ma9lrVztaG0ZjI2Ufd897XjnyXrFa1TfJBp6ueO6+Oamuf5ne/x\nNq9fBd5N9q670a6x9uiz15wkT7VMl0qJ+7Wyv3VpXvsm05pCyPXeRbqSVudSW19YU2crC8n+rDmO\nz4Dq7kXivmrGs97mANM0TWsUJYiXy/eHb7+6t8d2iNxJsvkhxIS/re4wDMNJgtx9F0Hkxu1OsKOj\no6Ojo6PjTiBhm02v7IQuMAzDtwO/j1CeIFMpl4mgf4nsK7dY9qs1S0ukpfp+wjny1+t5mvGHKXzW\nR9UgfZNsH2AdEu29/dGuEsG9LpQStlqjpMpnSptB8wJTV8GzZM+3SvhMv4OpbX+1/JfwqWBR1ucF\nItdUqYvDMFg7V1Mgre96H0lkFkiC6bVX1VHnRM9Ra7pqGmmtnztAkh8VSw04vPbdW3yebeh+t3Ct\nZmsELwH/F/AlghM8TLaz8J5bi/kcWXfpM3OGaYuHZeJ53SDVYcg2E2fI++dzUgnUQhlvgyBUQhW0\nOnqK2oOvNlGvjq6O6fG1BhGCTFYzFcn1TtxCt0Xk7oSU/STwX43jOA7R7r2nVnZ0dHR0dHS8Ingx\nQlf3eTNgGIajwPcTtUr3EKTmChGfbRIpkhpVrBJE5AJTN8k95f0BQvWphhoG1RWOp2K2yc0KhmRs\njghq7Z9Gm8d+so9bPeZ828+6umprbzuFmnZp8Kw6YkBeU/BUtI6QZKLa9M+X/W4yCRmGYT8ZqNeg\nf7PNt66VhKuurQYvYtbUpKo5J8n7ofnMHFubaEjIVTkr0dkA1l6CPnJe20bZJql5glDm5B1eo8TK\nBu0qad47ibvEVEIvsdIhtNbfnSEJqm0jzrZtpkjW9gCHCdL8HDf3HJxtni78UUBF93obw2fndNvn\nwbbf6fbe++i8a4/CbWE7RO4MkeMqHiJlRPEB4J8Eh+MI8D3DMDw/juO/qDsNw/Dj5eMvj+P4y9uY\nT0dHR0dHR0fHTSiEzgbiL+DNQOqGYXgE+AmirmiZCCK119ctENIzwQbSGjZINFS8bCFwhaj5Okxk\naW2VnmfAbErhufKdqsthsseZJE4icIgpyXqEiEElhhCBua6Y1XTlCll7dJUMyqvBB4Q6ZDpdVbZO\nkARDg5LdZN3aCtFE29rBml5Y3SEhYuT62fYNa+VaKpmT0JmCCnlfLs+MVd0vPdbxzxD1hoeIe7fJ\nVFWq7Qp2lF7ZFNjZzVXN3CRKsK4Tjem/laif06BE59JVMnXS/oSS1aNMa95OcLMDqGNBqnv7SWJd\n21LUvny0fe4jCPIC8VyvkM/F7D2UkFlfaYP5dYK01R5x/lvY1455H5HNuEn2n9sWtkPkfgN4+zAM\nDxM5zT8A/GDdYRzHt/p+GIb/Gfj5WRLX9vvxbZy/o6Ojo6Ojo+OOYQ0dbN2m4I1I6oZheDvwnwPv\napseJ1QhiYvOlfuIwPkKEXheat+fbMdphLKHIIT3EKRLle0CN7tWQrYcMLC2nk5FZamNZZNsjzEd\nU/Vlrs35ANN6puoCaLrhbqZqidb7+0m1yKDc4N50Ucmrgb6qked/jnSPXAOODMNAIXOVJFbFx4Df\nuZmyWlsvnCGDfh01VQ9tqO05HF+FbxfZp0wS5PzfStzPJ5gS2KqC6Vi6bQzD4FrVukBf1qXNE+0C\nniFLsj5PrO0e8t7aQkByO0eYoLhOql4HSWOaS0TaprWYElnXbTdJrlSU7RG4h/g3UInZAvHs7iae\nz9m+e7qwOt/aG/AsSSJruq5rfAD4HPBpkkj/ly+yxLfEXRO5cRw3h2H4y8An2gX8vXEcvzAMw19s\n3//MdifT0dHR0dHR0fFyohK15mw5MeuYJXqvN2LXnMQ/QvYke5YI9FXkniMI1I12yL0EGThAqCS2\nHpC8WZdVlS8D1arszabmaYVvfZjrrHJmj7FdRMC9hzBh+RJTwwtIRe9C2babTKlcJZ0CJUGm1Rlk\nXyeIRLXhN81RG/zPt3MYlOtYWRtquw4SQolcVbXqewnlGhE7vwP4xjI/a8RM0ZP4VIONmrpYa7S8\nBzUt9AJpruJ99Lhau1XNZOaHYdgzjuNW6bF3ilm1SlSnx03CzR6i7cWDBKHSFOcqSb4kVd5fnzlN\nU1QuJaKSLMmdJMq1rM/tHGnuo6HP+fY60c5nq4yz5L1yLBXfK8TzWn8E8D5q3uO119pM/z2ts/WP\nIHeMbdmNjuP4C0R/iLptSwI3juNHt3OOjo6Ojo6Ojo6XE3fSVPz1QOyGYTgM/DnCiVLFYp4gP/8n\nETi+s+1uCp61cY8TJO5Ge5nWdp1QNg6QaXEqTQbYBtNb9VSzZ5tqjYTJPnFr7XwG1hI+A11J2kVS\ntasNoU3PNDXxIpnOV41GVEaeJU1KqmLk3Gz8LNmpTpiSvk1CQVoCfptixFEMXqqRSK2vk9Bcaffl\nVLkfKk+2hYBI7TtNNh73Wq+QtVkV82Q65lWmbp6SQtMS98xsr2mDd41xHNeHYThEPC8+d9biVUIq\nsfpF4JsI4r5A/LBwkMj0g1jjE+06dLh0nXYT62I6rNehervZzl8bp0OQ9N1lu3N6luk9kow9R6b6\n1vRTVVKfNRu+H2zz0rl0NoXV1EudV+dmxt0WdtQ3oqOjo6Ojo6PjjYIXU+va9tcEsRuG4QTw06Sh\ngm6QptndIHtYXSecJhdJJWKTTIvcJIjFYSJwvkA6SBogSzQ22drYZBaHSCOSo2RTZxW8o20f0/xU\nYkx1vE6QmUWCcKpeVHUFpn27dLyspNN7uJt0hZRwabCxNrPN65s1RpknUzlnDTCY2a+mV6pSrRFK\nzlvbeb5CEjJJqmT3OZIE6dJog2sVtattvPuI+/4MkfYHUcOokrTJlMxpQnKkjX2aHSpD5TxVUawt\nGyqxAfgMcZ/eR/aQq2rVPUx7ztG2+8OAKZm1FYXrA5n26I8EKnlVJZPA7iN/UPAHg73E2tryYa3s\n71j1umwUL2GbbXXgc6opyjw7X/NO5Do6Ojo6Ojo6ZnEnat2ttr+c5G4Yhp8CPrTFV3OEOnCZ7EEm\nITtFBL5D2X6JIEyzja1rSqSBq+mE95Dk7CukkrSVqmCfLgPt62TPOo1DrhAKxh7SFAWSMG4SxMQ+\nayp2KnXV5dE5GNBrhFINMaoSU9MrTzF15fwaQWoPkG0XIOu3fH+IllpZVEjHlyhUArVBkC/a9v2k\n+ukaXWjXu7ecd7YhufDe6GZp+unBsr+Eoboj1v5om8DGTlwrW42cpF+idISbn61ZfIEkcftJ+38V\nYn9AOEsSN+dtXaMpuK6jx/jMSryPkGmmtZ2AjemrK+YqeS8rQa098mpLinmSiKu6bRB1e7vaeOdJ\ntddWBLW9xLbQiVxHR0dHR0dHx4tglpwNw/CDwI9tte9Oyd0wDB8k1LY7wYeBv0EEts+QNWh7SeXr\nYSKgXSEIgymNqlvXgN8j6rf2tnGXSFc9iQZt2w1S3TrLze0HJEoLbRzdLw+SJh1rRH3RNSKQX23b\njxPmHCpG10gSN1f+Hmaa3mlgvUySpJqeqXvkbNrbJlmDZb2ZNXIG5HX//W2eErIKiZsKmYH/rEr1\nRdKtUIJwkKzdopzbdEANU2abW3scZLPvy219vH7JVFUKNeCQkL4U9XGO6+ddZHPtmu5aieRZ4JvJ\nGk3TgjXU8dp8/qxJXCZV3jVSvfWZqU3FTctcYOoSWcn1LlI1O0iSOdM0TamU1FH2myvvVbx3E/+W\nqjnPfe2zjeaPbLGWd4VO5Do6Ojo6Ojo67hLjOH4c+Hjddqt0zPbdi5K7W6l+t8AqETz+IhGMnmvn\nNvBcIUjRn2j7/zap0GkacaW9VMAuEKrbUbJxte6KtO9UKA6TKWOzqoJpjMcJp8tnSEOTDaKVwCIR\nxC+SxhBeF2R/Lw1GIAJuVTqI+iaJp4F6VUbWSHdC4fytcdpPEoKrbU1PkQRBAiUZqamYW6lNEqn6\nnT3DJLdrRG2ia2TKYDWQcR1NLZXE+nyZ3qnaWInpCrHuxwmDlw2mqYWzCupO+YA99SRxzsF5VbOW\n2mx9k1iH08B72hxvtGvy/qswej8l465VVdwgzUZqbWZtBXCNVMlmG7vbLsMfOVTr7m/bvUbvp8+j\n98/7c5H4d1iJ+AFSIdwkle0X6iy3g07kOjo6Ojo6OjpeAsymY8Ldk7uZ8W6r4g3D8AtE7dtuYGzn\nkdhUMwth/7JNQjm4RBqaXCKI1XuJGq4nCYVkF0HgdJlU0ZPUbJVauUiajJwjUyL9+3DbTyVqtXw+\nRwTO1r29jbR1P0QG6SomNUCHqYnIAkEETpO1Zdbl1fWpis0SaWIxTxAK+8ftaue/Sqz7JkFCIdMp\nqxHG7pnzmG5q6upxwtxkHxH807YdJdb/ibZNZWmznXsvU6MXTUQ0crFu8kwZt5IJWzS8oKQNw3Dv\ndtMrm9FLvUZTCDULqc+hCqdrswb8HFHT9/52bZfI2rX6LEHcD1tB6PxYU25tIq5qWUlWbZLuvBbb\nmIttDldI0nu1vZ8jnjeJvc+7qZG6VEL+cDDrMHqNMHNxbSSir7xrZUdHR0dHR0dHx4tjK3IHtydx\nd5qGOY7j9wzD8N1Es/MHiVYCkp0DBLn7JBEYqwBICHQLvIcMtG8QROZhoo+c9WHH2n6qDOvt8yXS\n5KFig1DLVEc0PDlDKh4X27FLbe4rZJraNYLgHSQVNshg3p5jVYGUQBxkWlO3RPZmgyAHB0iyKBmQ\nlF4o57mfVFH2zqzfLKqpyKwbZLX6P0u2hlhu87mnXbv1cTWNFTI9cr58vl6+P8C0HYNOjTpHmgYr\nVMVqyuO2UZqh17o82xysMFULJbuHyvtNwlUS4A8T9/ArxLp8HXH/lst1Qa7RKklufSZU6mjvnyMJ\nk/ek3kNbHGwS98N77DU92/Zz3aytc+2WmfYinDVT2UU2ptf59CDxLBy+eUXvHJ3IdXR0dHR0dHS8\nwtgirfIfAe9u7yV5/9E4jr/1IuN8YhiG3wF+gOxPtkgYm1wi6tAukWmROvvtJgjaBkHgTB98giAa\n64S6da19fw8RdEv+niENNGaVP1PWDJA1E3mEMGq5DvwqEXhby1dVO0mYhGyZVMtUp7TiV1kxUF8v\nx1wm0jAlUxC1a8dIowzr4ayl0uWzpjpqcOIxKoez7QeqS6MEs87N+qramPsScc+sJax90Kr6I1Fj\nZj7OUwMb2nVXMimRUIkTL9R+jeP4NC8NrEGk/HUdqsmIc5PkrQGPEc/HAwS5P0e2JjhD1lqKdeJ+\nHiKVtyVCSda1UkfO48Q6Scoqyax1c9WMRpKv0ukPGf4Qspd8Tv2Bwmce8r5r5EI750VSlasq4V2j\nE7mOjo6Ojo6OjlcZ4zj+0DAMHwO+s2z+u8Mw+P6xcRy//xbHPj0Mw+cIZe4tbbMtCCRqtL9a0qvW\n1H3OErbwnwA+QPSeGwhyZ8rgPBG0WsukKUeFhMY0M2vQDrbxJEtLZENoVTjVt9Pt7xyRkvZQ29+x\nJDP3EUGxc7hGBPIH2zEGyhKMDYLwXC+vavsPUzJ3ra3LPKkQqiJtVWtmWl5V4yDNMnaTqts1kqQe\naNslK7ZpmCfTCCWwi2Vc66zqfEy1vI8gJqtMFTH31a1xK4XxjtFIbFUMa+uFSmZVwlyX2Zq6TeL5\nUxk2DbQ2YpekS/xPkAqcZMkfBFbb+/uIHxPWyF51QsXZsZ1HnbP3AJKMu01S572RxPlM+uPJ0bb/\nLlL9tT502+hErqOjo6Ojo6PjNYBxHF9wwdwi9fKtt0nHvEH8yn9f2XYPaYihwYLKwgoZ/KvGbRIK\nw0HSIGMTeL79vci0ncBuIoieI1wYZzHfvreWa40IZj8DfJlpLdPse+cCEVxrxFLT61SdTpL1UKtk\noH6KIANrbaxKpDy+KmQG1tdIZQvSGGaFUIWsq5qYVMy0H9jb5uU5TMlTLZUwSsJWSRdO1+AqU/Io\naj2h1yLp87NKnorPbNpnbXD+zOy1bBOmU3ou+6+tkGSsGsfAtDm3hixPtjk/0r6zKbhEbrmcy9YL\nknXbENS+hxqWWE/ovwHJ40b5rpLRatiySNaiQtbN+e/rfDuPytxaGdt1r3WYkMS8poveNTqR6+jo\n6Ojo6Oh4jWGmOfnPEgYkt8I9TEkcBAGwfm2OUHwOMHUtrKmWB0gV5BoRiD5DKHxvJw1OdCg0tewg\nN6dW1ibLkrTjZNCq+qEKB6m0qXjpTLin7XOZrPPzutZIF04JkK0HJI/W6KmQ7GZaL2gN3lOEDf4S\nqa6YtneYtLW/Uq5DtbGiqlHVjl/FUAdQFaR1grwcJsjLMkEY10giXO30Z10fJTEbTM1B1kjXz1q7\nxhZzmt+J2UmpkXNsWwjU2kAJVD235M02BBKkR4nn4/cThPgseX/niNRL+yY6toRulVS89rQ1qKmy\n9zN1wFwjni3NdXxGJGCOT1kvP/sDCQTh1LznOtM0Uk15vC+1fnNH6ESuo6Ojo6Ojo+M1jNmUymEY\nThB95h7c+ggggtXjZKD8MKGu3dO+10K/qnUG1Cobp4necqaebRBq2nmSEKk8VFTjjTWmDZk3iWD6\n/rbvZZKMmGZ2rP3VhMQg/miZO6RrZA3M58k6utqLzDYJ1kQZ6M/WNanyXGtrd7CMJ+m8wIwq19IL\nIZWx2j9Nt0xr4RzfJtY2835Hm4eqkzVwrk91vJR8z5HqnWRBhcn9TFGs5GI2tfGlQFU4N4h7/jBZ\nS+n5arNw5/Eupgris8T6PAx8fZv7Aab1jBfIOk6fndk1kEhaQwdZX+naqLJCKGsQ6cTO1fnUWjuV\nVJ/9I+SPDD7ntkRwfW0MvlbG6O0HOjo6Ojo6OjreLGjGFB+BF0jdXwD+EDf/wj8H/FGCwN1LEAYd\nGDXZMJDdR6hu1YRhoex3gCR9+0kFTwOICpWqJdIx0aD52XbM8TYPUzYlTJ53nQh8j5Iuf5CEq6YS\nQqYLut9BIri/RKhdBteSh3NEoH2MVCWrocZm+860zUsk+ZP8vECAmipVa/VOMK39OkKY2TxPKknX\nyjh7gO8gHBY/38Y6ytR9UVKnuiYxgUx/vUjG99ZDHm6vLzNVnLyOte2qcTCpkVN1Wyvv57iZONq4\ne4U0I/lWUqmVTH2BeE4eJhrW+wPBGdIJVRKv0ckcaRbjjxkbxLNQazBhqpLaBqMaxewm1rC6nkIS\nspoqusGUdHutkCqc24+1+X+NHZLoTuQ6Ojo6Ojo6Ol6naKTuJ9qLYRgeAX6YSId8mCBL97bd97XX\nvWSLgtqDznQv67JOtf0ukkrWcTJIvULW2FVITAy0IU1V7pnZ5nuD8apSXCJVKbhZNdPiXvfJmkIn\n1ggSoyJnjaBQHTvQrq2m6FlvtdDWTWUOkpBcLJ8lbq6PrpC6ctq0fZ0gMLVNwGq5TuevK+LT7b0m\nKKqZs73RKmE63r77MllL+Na2prXHWU1/3AkkpJVbnC3nmTU2MbXS/U1xrff7GkHg3kU8lxeINFTI\ntVsl03e9N/4Y4DPhPGwBYC2fNYOqnBfavseJ+6YCqLKmyurzbl9BnykNfC6Qpjd1rs5RknmAJHjb\nQidyHR0dHR0dHR1vEIzj+Djw1/08DMPfJ5pqr5LOjPZog2warbOlROoE6TKpXfpDRMBq+tgltm48\nDhHQ2rj77QSBe5SpWQokGXuSaQCvI6Bpc2tkg2bfv6XtZwrmOtNaO5W2Wst0kFTvDpVjdadU1VGV\nvNLOZeC/hykREqp9BvD2i6vOi7Vv3W6SqM0Dvwv8U0KteVu7ZkmvY1nbd738vVTm4jXZ648yH3ud\nLZKkcYFQVzeGYTi7gxo518R1gCBD+4HH2/xrfz1IlcuUU0hC5j1cA/51m/vXl/U41dbja6T6Vw11\nbFshsa/OnNYWrpEEbZVszn0ceA9JAE3dtf7whbpCkkR7bT53e9r5TcOUbEoWV4hn17q8baMTuY6O\njo6Ojo6ONyjGcfzzvh+G4d1ECuYHCMIwRwT3J9suzxMKyFNEkDsQAfc5QhVRoXieNDxZYGtS49+j\nRC2fxiM2/d5HkizT5GrdkGmZEjVdCtdJ90gJmIGy6poB9iKZMqcRhWl9+9s+5wiCeo2oi3IcTVbO\nkDWBps8tESmitb5JxUm17In217YNMLXI18nQWjKI5u1vb+NLRtaItV8jXQ6t/9IYpjo/7mtjS3oX\n2/xVA2ut2DrZImKeuK/bgXWY9g80rVKSWlNRq1mL90JjHMmb91ADkd9o330D8azqJCoxkizBND3X\nz3vK313EPVUR3Ff2rQqd5/eHir3lGmFqsHKEfPasCT1KPq/O45l2vPebdv5toxO5jo6Ojo6Ojo43\nAcZx/AJRdwS8QOw+CnwdEeDuBt7bXhDBserTaSJQVWWarX2q2GzHPkyk820SRMJWAcuEAnijfb6H\nCHR3kQRKYrfAtG9YTZtUuaPMQ1KokYtmIBvl+/tIA5TDJBGUXKlc6mgoMbGfnIRg9rpr/zlr8R4g\nG5mfbOe8QNYWHiFIgqRNdao6anq8RHCNSLe0pYFqYCXQa6STqamMKo5eWzU/UVHaDqrKJZHT3bSq\nlJqHSKLc791tXp8h1U/X4nh7b13cj7c1+RTZk+//Z+/dwyw/qzrfz+rqrq7uVF/S6U463elOgkm4\nBojhEoghQR1hGIEZ53gUIT6oM8fHY7zNIGiGEWbMBPFwlHHwMIp4DgaVRwcvoBkQlcQYhIkYIApo\nQi59STrpTqVv6a5UV/V7/ljv6vfdu+uya+/atS/1/TxPPbv2/t3e3++3a9f73Wut75qgUciFa2Wc\nT5xvpPs+mV8PZ1Tw2sRonh6GP3H94n0UfwtxXzfh9yHqQaNGNe7ZgfwT6aLxtxNiMb4waBsJOSGE\nEEKIFUgWdm+HM+lx1wI/iadVgguMy3Ex9gQ+KT2G19iN4BG7Hbjb4kPVrqOmaQs+MX6MEh2bwifl\nU5Sm4RFBO0YRA9H8O1LpJvJ223Gb/j15PCH2om1ACImI9EERqRFNOSfvN4TlHkptW+1yua5puyAE\nWzMx0Y9xxO+RqhnpkHW9HhQDkxCf0Yssopch4Gpb/YtorAkLETeCRxujBUOcV5jLzFBSPWuDkrbr\n5FJKT1V99MJIJqhNP4JwSQ2BHymGz+D3agMl4hrXBfxLiBDu6/D3TkTv6msMJT0zXhuj1DNG5K2O\nmIUwr9s91P376n5805RegyGIa3fVGfy9eozSZ+58/P0W752T+Pt3Jx0gISeEEEIIscJJKZ0E/jz/\nYGbX4o6Xu/DIxHpcPITxx2lKfdampt2di4vCS/EJ62k86vY0ZSJbR/TAxWBYykeaGnn7DfiEdz8l\nlQ4aXR3DvTBq6kIAkreLSE+IuBOUNgLR1uAQjWYbER3cRxEf6/PxI4JWU7tBrs77i/1vytuEuIjI\nWAjCiKw9iU/wd+fjh3V/HHM/pQ4sjDNCPMS9qFsmhBnHpmofdU3dOHAopXSMNqkcO4PmHnF1G4ZY\nFtfpOZRatIjIRkT1CI2RxoiYRhpm9NGLKGjUZUYabVyfUfy9G7VwIRKPUVIn4z38eH6M90m8F2Pd\naJ2wutpX/P4g/iXIeD6n2HeMO1Ivn8HfR/X7vy0k5IQQQgghRAMppbuBuwHMbBvweuAluKg6D580\nn59/EvB7ed3XA/8WF14nKDVBD+KCLkxXIhIxjtferc/7OpHXDXOQmDgDPBsXIiHA6pYFB2hsEQAl\n8hG1STHvjdRQaIzwQBFKEZmJZuJQGlaHKUeYpZBSOmlmF+XxhpFHbcEf+zuWtwsBt6n6PSb1j+AR\ntIgYTVX7iPTSk/k6RKSu7m3WnFYY0aloch5ppiGmNpvZoSzmO6EWsuFuOl29Xjtbxr2IyGtEIqOO\n8jiNzdejDu11uPHJt+Cpu+fj9+whyv0KURbvjdh3mO9EpDdEbkSPD+Dvk8242HqaIujq1gkb8PtY\n90eM/V2Gv5+jdhPKfYx7szaPcwcSckIIIYQQoluklA4Cv5l/MLNr8L5fl+DmKS8wsy/OsmlM0M/B\nJ7zHcTOQEDxhqjJKSZOLyFBEyaJlwXT1egiYuhF0TKrh7HS72M8YLmSepky2w8wESrpfCKOIDkav\nubD0j3YAm/PvEZUKou0AlNS7GO+GvM+nKZP/iJ6FwDqOp3tegQveWqSMVNvtp9SdhXX/o5TU1Eg9\njWOHGUkYt8T5hthqS8jlPnLhBBp1exspTbdpOk4c93Ae7xhFfNaiKFJBp6vXAO7D78Wr8raRnhkR\nuDDMOUnpCxcCOKKgIcbjepKfX0YRfHVqZe0wWRv8jOfzXEt5z4aza7z34n14mBLRDWGtGjkhhBBC\nCLE8pJQ+D3wewMxupzg1NhNmEWEy8jQuUCLVLOqMQjzV0bbaqCPcC+tUuTBNeTzv/2KKtX6kI0a0\naiOl5UAcL5pDH6Sk/EXKXV2TFpb2MfEOQngFUWcWqXQRiYt16tqt6FsXtXARfYw0xM35PEbx1NZI\n44zjT82yfkTsdtDYoqB28gwRGU24o9l1c8PrRZFFbB2NrK9JPNaGLHVK4bnVdTmY19nRdIh6uxCh\n9+djbsSFfkT2ZvL5RdTrCEXARqQu7jH49QjRFkIvhFfUXe6h0YAFSl9BqnMbx5u5x37qZu5x/Y/h\n78+L8rKI2rWFhJwQQgghhGiLlNLr4nczuwp4Fy4+wCeya3CRBR65gDKJjyjKKjxSEc6C0UT7BEUU\nra22j/qnsH6PyElMxmMCHjV347jYrA0rop1BHDOEZG1yEbVaIYpqMVWbcASRflf3GgsBEvuNfUfK\nZtSBRZQnokcjeLRqM0V0jlT7CFfFEL2x/ziPE5QWC0cowvIZitgK05O4Ju1StxioCVfMuIdjFJOV\niNzVaZBhVFNH8iIVtF734bzve/FWGhdR0naP4++VuIaRrhlfBEQfwRDw0c4hIn5P4NctvjSgGncY\nwkSj+ycp79eIPkdNZNyPiPZF9O2pvH4Yn0REuS0k5IQQQgghRMeklO4Fdj9+ZgAAIABJREFU/mU8\nz8Lu1ZS+decCV+XFR/DJdz0XDTOJ8/GJ+z58Ur8Rn0yfrtYNEVUbrRyhpNCNVK/HZB2KeIu0yRBp\nUX8GJaKyhiKiwqgkUuHqaBwUsRKum2HccT7FaKQ2vAiHxBj/QVxYXURJKfwHXASHBX/Ue0WtVfSE\ni0hU7CvE0nqKCcgEHr0M8QIlLXOMEsVsh2lKa4YxXDRHKmeMZzuN9Y5xncKkJqJgI5RWAFGHWAvN\nOEb0IDyAvz925McJPIIGJfoZwr6OkNUCdi2N75cQdkfzcUIQh0g/1vT7efh1PkSp04xU0bq5/OP5\nuM+lRJSjZUFbSMgJIYQQQoglJwu7ewHM7FLgzbgTZqQy7sIn+AkXbWH3HxG6SJsDn3yvz89PUKJT\n4dIY5hIR5YoUzNr0Y6RaP8RcLaTqyXzUWtXtCGqHyWbHwTr1L9L6Ytx1HVwd1alNSsbztSCP6STe\nnD1qr2LiP8LZUaQT+XrGPo9Q6sqgCJKopQsDj0gPnU4ptdsMPAiBFtHHSFUNwRNppyGg4hqcj6dJ\nnqRcmzH83gd1tK82HRkFHsjHuzLvK5rQ1+IwhDr4PYcijkOQx7UN8RuR0xDccd0jjTLGEL3yxilR\nu3PyNmFsU/fti/dn3ZaibSTkhBBCCCFEV0kpPQTcAtySe9a9HrgGn9CG8Dkfn2BHi4H1FDfK0eq1\n9ZQ0wnOBU5Ro2QW4ENqfD12nuIXwuphidlJHyqDRvTIiV1HDFjVtEQ07k0qYUjpmZlE/9ThFxNSm\nGHGMqMWD0hz8HMqkP8w2onH0BkotWQi6aGJetxeIOrMwaImU0Xq+H1GwqM0KYdIJtQtl1ApGXVud\nLlqLmYso9Wwhtmu7/ugFGOIuxl0LxBk8VfRLeZ3n4kI/hHcI/In8GH3eQuSvxq9riPadFNFVtymI\n90iI0jH8npykXLtwtoz3TKTxhuCGYgJTp+/WXx4sGgk5IYQQQgixbGSb+9+jtCy4HPgXwAvw1Mvz\nq9W34WIu+tGFQUo0xH6CItSO4FGnLfiEvq6JqtPcnsHTJi/J+wszi9odMWq2RnFxFJP/EBQxsSef\nQ+0+GGIkUvIibTMEYwiMqNMCr7cKIRgibXs+lxP5vC7HXTKPUKJEE7iYCPONJym1c9HqYTMuiEKQ\nRkpmHZHqhNn0RETook7unPwY57iWIqAiMli3lIj7FVGwEOER0Yt7cCjv8wDew21r3lfdVxA8Ohb7\nfwq/DhdQhHtcl5OU1M44h6h/qyOucW5Q6i3Pw99bISTPpbiLHqr2F9Hh2tmyLSTkhBBCCCFEz0gp\n3Q+8H8DM/hivd/p7XMScg0+QEz7pfQKPeK2i1LmFwBrFxd50Xn46L9+Rt9lDY+PqurH0eTS2LSDv\nP+zo9+DCaHv+OUiZmENjRGojJRoWk/xmO/twWYyo4kFK9K62pT+Zjx3tDuJ8QxSGGUht/x/LQ/BF\nCmD00oum5xF1Gjez4x2mV0b0McZRR9YmKaYuEb2rbf+foTGtMoTYKC6Gwwgm0ldDvMUxwvDm/vz6\n+ZSav+ZWBpH2WTeyb24uvrratu4zGPWF0Uy8NnmpXUIj4hb3sHY4jTTYeJ/U74lFIyEnhBBCCCH6\ngpTSG+N3M3subpayA4+2ROPmrXgrg1q0TOCpceF+uYriSBk90iYo9War8MjMDPCcfMiIWIWZSKTf\nbaUIvDDYqCf8UCI4MUkPoRSRo7olQqR0zlDq9KaAb1AMQWL5E3j08TGKa+dOXPhFmuKzKGYaGyk1\ndLURzAZKZCyabk/RaHzSrpCr69cignaIIuKoHlfj9zN68kV6Yly7uk3EU5RUxOb0zVow7qOIw28A\nz8ev2QR+/eJ+ztAoeJ+hiNqDlHrE2uUyBHucU7wXpimpmM1NxmO9kXwO0SC9TjVdnfffiVuohJwQ\nQgghhOg/UkpfA74GYGYX4mmXL8Mn0CGwLsUnwwfxCFzt2AilR902fOK8La8XjoaRyneQEkWj+v0Z\nqsgVjSYjzRG58ygul3Xz7gP4ZH8bJRIX0UTysicp6YPbKQIBSlrksyl1dLXbYVjZR10YNLo0hpCJ\nerCJatsQTx0JCkqUayd+7R6guHNGOwnwa3YlLqT/iWI6coAi5uroWwgjcKEV+wxxdQC/Ptvz63tx\nsfrivK8Z/LqH2IqWFSGox6sfqtcjchfCnOp5HDv2F6IbivivjWzCjXUjnsobhipH6FCLScgJIYQQ\nQoi+JqX0GB6Vuj03oH4xcD1wBT4xfg4+r30QFwnh1BiT/g345PlcSqphRML2U2rOwkEyJvMncQGx\nisYWBpGOF0SEp06Vi35jQUQAoUTloNT9RX3XRorwJO/jcVy8xTijfgxK2ic0mrGM0miCEuN5IG8b\nEaW6iXe7RDQuasQi9bGO+EUd3Go8iraf0hqhdn6M9cPsBUr6ZIy1bhJeC7FJ4B78foWYajapqfu7\nxXWLNMiopwyzmc2U9gR1Wm40iX+QIlSP45HjaPYdYjtSaCOSFy0KYvxtIyEnhBBCCCEGhlzLdQ9w\nTxZ1VwP/Bo/ERBPtHXhd3XHKZD1SL1fhk+xJSi3TRlwknMSjO5ESeZLSx24Tpen0XGlxU/hEPQTj\naD4ueNrfdLX/EFeXUIxbJilNrCNdL9JDH837/Kb8PAxLQphMUCJbW/MY6qhTRPl2U4RMCJTjdJ5a\n2ZwyWLt+1mmWh/NYV+dzDhOUtRRtEoYiT1Ms/SPaVUftyNtGr7gQVJ8GXohf+z0UMVULuuOUaGSI\ntYi4bsJFaYyjblJep4vWffGiVm5bfi0aktfN6ePLhehlF7WBbSEhJ4QQQgghBpIs6j4PfD6Luu3A\ntwIvwifUG/JrO3GhsgaPBEXkJ2q6TlFS7qBM6iMFcgdF/ET9WfRAg8Y59Tn5eOfiUbgwyoi+eTGp\nj6jYNkoT6+i1NpEft1DSNSNSFMLoKCUldFPe96V45HKS4rYZvfOiTm9nta8QP22nVqaUTplZjCnS\nT0Mk1ZEzKE2+D1IMXjZTUmE3U8R3pDDGPmcoDpxxnaCkYNZ1iiEWX5SXR8uGEUod3Lp8LSYoKZlR\nP7iFIuLifCLNMurlImoInlYbIjDqNkNkz1TL4pzCFbXuRbhoJOSEEEIIIcTAk0XdXuAjAGZ2JXAd\nHpl5abXqOjy6dQCvl4sUwM0U58WIokSa5fn4vPkfKCKorjWbxsXDWlwERDQqxF+0LZjJx402AXWf\nM3CxcCg/hkvlcRpTAQ9RzFzq9MtIGwyL/wOU6NHjuFCpG1JDSe9sW8hlAb05/9QGJkFEz86jsf/e\nJsp1gdLove4Xt6VaVhumQEnTBL+eIawm8ShnpC9ehEf+DlAik2FsEwJrI6V+8XD1ejhO1g6Vmylf\nAET65TaKcN5PiQCOVD/r8nmEe+h5+JcHbSMhJ4QQQgghho6U0n3AfQBm9il8sv11fDK9Hnd7hMZJ\n+xOU+qrduMh6iCKsNlB62zVHUy7Ao2LhjBlpmVDSH/fj6YJjlHRIKKIDGi36o69ZNEGfpkTvzqc4\nK67L+4pIH7gwCaOXOiU0hFPU+YVQ6aT9QAio2gwkjEninDZVYwxhA379n6KkJ0Zz9HCRDNEcxiwR\n5QsxFc/DxTKu40ngDtwgJ9pITFBEVriJxlgicnZhPm5EFbfkdR6ipK7G9iEMJ6rtw6kyonNhOjNO\nifKRl5+z4JWdBwk5IYQQQggx1KSUXhu/5wbk1+FRm+34ZDp+tuBiLyI20Sj6QTyysxmfwG/Fhd7e\nvNvpvN6z8rKjFKfEg5RavPiJKE3dhqBmHBd8YQJylFKD9gguiqIdQ7A9P9btEyIqFFFIKDV5k9VP\nJ0T9W7hHbsrHDcEZeiNSRPdU44rI4HS1nzFcpB7Hr91MtSwE9VZKFDTOPerjIvWRvHwd8Ao81TWu\nTaQ1RkTyJKUp+zYajVKiKXyIxRCP0e8uIrTNkdi4DrXBTawzX51ly0jICSGEEEKIFUNuQH4/gJld\nClyLC7AX4pGvKyimJespEZdo4vwoLrKamcEn6utxsRKT9ajJ2p/Xi0bhER0LUROT+vPz+lELtjr/\nHmJnKy4eTuI1XmN46iQ0tiCIvnnksUSPuYgSNRt1tEvsJwRORCpDbEXvtkijDKFUi9cYc4wlrP0j\nkridIqJWUxp8x/pj1eM4pWn4VjzKeh9+rXbg6bRRwxaiqm4fACWKFoYk+6pz2oBHSeN8QuzHdvvy\neKO+MSKRB/M2kcIZx2wbCTkhhBBCCLEiSSk9hKfMYWZXAS/BJ/xb8AjdBXha3h5KbdoOGvvAgU/c\nX0iJHIVgirqsVZQaqjAgGcGFSrQJmKFY04/ggi5s7iN9MKJERyi96Sab9rUNF40hMM6lOG7Wza5D\nPE7n+sJ2OY4LnOfl/T5JEaARYbsuX4cv5vOpDUyaaw3rKGHU0dUplIeb1o0xhNA9jyIm1+bzfjDv\n6zn4NX6UItrCXTKia5EmGQJ7A0UcRuQ1Im9hZhIumEco4rVuCXEwbx91kpHO2xESckIIIYQQYsWT\nUroXuBfOpF++EHc9vBhPq9yBT9xX4WLhkWrzzXn9c3Ehc5hSQ7WHErGpo3GRVriJUlMXHMdTN8/F\n2xZspQiA2O4AjVb3EWkLkRY95B6mMUUwRM4M2SDEzNZ0IObCZGScYhYStYFh/rIeF11H8OjhGMXB\nE0o0LZqhj+C1ZvX1gGLkUh93dT7GUYqwG8OFU9TphXPlJXlZ1BxO0Jj+GOmeB/N6L6yeh3iboKTH\nHqLUO8b1DNOcvZSWD/vysidpjMR1lNYqISeEEEIIIURFlX758Zx++d14hGwaF3YvBp5nZkeA7wFe\nkDfdi4uX9ZTUzBBg0YB7Ld4iIGq0IkXvJKWVQETNoll4iKTaOCPMOiItse5XFhGvA3ga4EmK6ItI\nFNW2h+i8j1z03YMiVqJVwxN5XFsoaamxbkQdR/DebeDXIdoKRCQsBFKYs0Rj9zinSPEMm/8QebG/\nCeBreB++09XYpiipkxdSattOUlo2RKQ16vCi7rCOlI7iUdxI85ymCOoYW5jC1M3S20ZCTgghhBBC\niDnI6Ze/CGdq6l6DR+TOA36+afVHKaYWEW3anR/Py4+TNFrTR6rhbkrtVGwfEbYQg1BS8qLO7Oq8\n/ZfydtHOIKJGa6sxRBpjpA523H6AIq5qkflMfu1qPJ0xRGv0yHs8bxfNzyPiVjfZjhTVrZTUyTqC\nFcs3Uq5l3fMt1llNibo9REnXDKfMKVxwr6Nck7g/j+LibBOlZnEDjVHUEKZxn6arn/35HDdTes+t\nr8Yakdq2kJATQgghhBCiBbKo++/AfzezL86yyq78GAYfpylpg6vwiF2k5oUQCHdLaGw6HqYYE3g0\nL6JtIe6iDu8ELmZ2UETLgbxORJYi2tfc0mCGpXGtnKbU7EWt3ySeKhnRybguEQWMdFAommQzpUYu\n6uFiWS024/dwyTyJi8e47nUD70hpDCOWdcD34eL2T/FrG60gQsCF8NyKX8cj1b7XVccMjubjrKXc\nw3Mp93AtJaI4SuN9bhsJOSGEEEIIIRZJSulqONMQ+z/g6ZVP48LmXFxkPAOsya/XImYtLr725vXX\nUVwta1GxCRdHIXqiv1lEf0aAu/OxnkvpbxYpfWGCcoDSqiBMTkbzduG02G5q5SQueC7Nx4weexdQ\nWgEcyucUvdmgmLFM0WjIEsvPz9tE0+1Ic6xTK8N9srmdQtSq1f3txikulXvxFNkrcSF8Kr8eRjRU\n41hHEaaHKG0qjlB6AsZ5RKuEiOpFVHY7JVpYNwlv7kW4KNoScmb2WuD9eQC/kVJ6b9PyNwNvBwxX\n/D+SUvpKJwMVQgghhBCi38gmIe+GM6LuauA7cKEQDoebKS0AVlFMOMbw+rGxape7ccF2MD/fUv1e\nN5iO+roZirPlaYpgjKhfLA9nRXDhFamEUY/WLqspdvtHKFG03Xn/YXIS6Zx1A/ZIt4yas0gzhSKC\n1lIiV6urn1rwhUiNerqtlEhhtC+oheIncYfS83ARF1HSqIuL6OXjuMiM9E4obRGioXeI5oO4IN6c\nj30sb3NxtQ3VPupzbYtF3zQzGwE+AHw7/s3BPWb2iZTS16rVHgRelVI6kkXfrwPXdDJQIYQQQggh\n+pks6j4PfL4Sdd+Mux9ejKfxRfPpEHPhhBnNyTdShEotgIJ4HvVVkaZ3EE/tfAEupo7l10OghAlK\niMGI1kVPuVh/scQ+a5v93fm4T1FSO8NxM9YPs5Fw0zxJMYOphdvTlNTIiMRFO4DoBbeten2cIrCi\n71xEv/ZR2iXch+uTC/J1iDrFEHvhQhmCayslSlpH4Ear30NbhaNl3OMQlTGWENkd0Y76fhnwQErp\nYQAz+xjwRtwFBoCU0t9U638Bt2wVQgghhBBiRdAk6rYBP4I7JkYK4yhuBPIsPJIW0aRRPEpXpz7W\nrpZbqtfqGrgJPMIUbo3n4BGlEGszFOfKME8JQdhJnVykNgab8TTLC3F3zqmm9ULQ1AIolsfPpnzu\nVGMPgRXbh5PkJCUttXaFjFTGEIOxPFwl9+OtHS6mRDZH8QjcBN42ItJeI7IZQhRKZDGE9Lp87ufk\n/dQ1fdFqYU/T9vV1WzTtCLmdeF5psA94+Tzr/xBwexvHEUIIIYQQYuBJKR0E/jOAme3CAyOX4hGg\ncXyiH/PpL+JCYiPFzGQ1LvSi/i3EzhZcHIALg3/I+7o0b/uNvGwd3kNtFR6t20ajuUenhNiawSNc\n5+OCabRpWbRWeCYf9xHcDCXq3SLds260HSmJUd8WKY6RYhnCKFwlI50yXC5D3IWTZDxfDTyQt78U\njwoepFzfaP7dfI1GKGYyUbMYIrtOGwW4Ar9H4zQ2Cw/qSOuiaUfIpVZXNLNXAz8IXNvGcYQQQggh\nhBgqUkp7yUGR3M7gRXhN3QV5lXE8PXI1Lk4exkXdNKUJeRigRDpiCAhwQREi6nJcCIJHi05QhEZE\n9Kbo3AAxUhOn8TTS7bh1/9q8PERZPIYoi15rIXxCuE1W53eA0r9vEyVyGWmU0aphktKIPKJhIfYm\nq9fCfTIcMvfj1z5qCEcpTpZRh3gcTxONVNhoH1C3kIiUyRlcqE5TxGlERcPAJbYPN8+2aOem7adY\nq5J/39e8kpm9EPgQ8NqU0lPNy/M6766e3pFSuqON8QghhBBCCDFw5HYGDwF/ZGZvBy7DI2yX4GJt\nCx6xOoELg9MUA5EDNPaFq+u1HsbF1PmUefpRPCK3gdJIO6JlnfSRW01xyLw0H/NEHmM0KQ+R1Jya\nuBqPgoWr5N48ts24+NlCSS8NwVY3+l5L6bdXp1OOUwRc3dpgjNLPjXze9+ftIooZAi1qCyM6eDiv\nvyEvj0buzSmWJykNzKNv3sl8TS4EXomn1D6D34+2sZRaDrD5BmargX8Evg1X2v8LeFNtdmJmu4G/\nBN6SUvr8HPtJKSVrd+BCCCGEEEIMI2b2KuAGXMRswMVcuF0+hs/Bo6F1mIdEpGgCF0eb8MheRKui\nPmwVLgin8r72AF+dK/DSwlgvBJ6fn16Dp4v+HcXApO5nB43W+9E+IIRV7fp4GHgexZRlHDdUPJ7X\nIW8XInQTjQ25Q8SNUSKDkcK5l8Zo3Rh+rXfjNW6HqrFGGuXRvN/tlLq5+jygRBPPqZ5P4+I29hfG\nMLH9Z9rVRIuOyKWUps3sJuDT+eAfTil9zcx+OC//NeDn8ELBD5oZwKmU0svaGaAQQgghhBAriZTS\nXwF/ZWYbgO/E+51FOuUWPPVvEq+JO4ELkXOY3TzkfEoELlohgIumSE/shK2UyNlGiuNjRAujxmwL\nJWJW18OF0ImIVt1aoE7/fIJGkRbHrqNoM5QG5CEQV+MmMGEKE9RRufG87CCNfeIiMhf7ugC/9kfy\n+W3Jx5/AI2zReiGEXN0zL0Rf1ERCh2Yni47ILRWKyAkhhBBCCNEa2fnyBXj06wo8AjWFpwaO45G2\nqKELETeKpwyGw+NqXGxN4mLnNC4G/yqlVIucxYzrVXgk7oq8v7+niLiIOh2hiJboiRd93Z4CduTX\nnqCkjY7h9XajuOiM6FnUux3AU1E30lgjOIK3UohUyM2UyF1E76ZprJ3bXY35xXgK5COU/nJHcMEc\ndXoP4cJvZ95mf3Weq3GBOZW3X42nytZtH+JajAKfWLaInBBCCCGEEGJ5yc6XnwU+a2bnAq/AxdNV\neMTpMCUlEUpftwlK1GwCF3BTFIHzCJ2xLY9jbd5X7HsVxZXxAMW1cl1+jFTIpyiRxLX5XDbhveOi\n911tXnJe/j0ic1Fft4Gz6++il1usdxlFcJFfC3E2ldffjwu0XRSjk4n8eIAiSus+fnXUMSKERyla\nKwxeIq3yUTxq11EvOQk5IYQQQgghBohcz3Y7cHs2SbkEFwc78LS9tbiQuj+/fhwXGZfgUbOIzk3j\n6YLb8SjTojCzdbhvxm48avZIPtY2SjNzKGmK0ZcNYA0lhTHMWiLdchOeqjiZ93UBjcYjI7g43VAd\no3bjhOKKGeIuxFytf1bn49SGK8fwusGtNDb+ns6PJyl96cLMJZxB19MYiYuIX6SbjuRzO5fGNNi2\nkJATQgghhBBiQEkp/SJArqd7Jd50fCtwES7cduCRpqN4NGstLiYMFy2jtK8J/j3ePuEoJTURSlsB\nKGYhWyjRrbpX3CaKe2YIp0g9jMbhYS4yQRE/4W45SqMYjEhdRCZjP9spYi7aD6zGHT7Br1m4XR7H\nr9uq/HMl3nMuxhLEcTdTavSinu5cPNoYQu44RcxGpG/ZG4ILIYQQQggh+oiU0jHcjJCcenkl8M24\ngNqYH0/jAm4jrgNW4QJmbLHHM7Pfxm30wd0kp/AIGfk44/nxQLVZCKEQa3WvtiMUwXaEYvMfqYrH\nKc3RRyimLeGKOUJx8hyjsYH4ZjyVMWrY6nq5zTS2X6gNYMYp7R9i/CFIo6YwxkzTOYCLuRCYUHrO\nxbkrtVIIIYQQQgjh5NTLcL68EG84/ty8eBtwCo+EbQQSLuZawsx2Ae+giLgZzo4shd1+OGNGNA0a\n68Wotj1JSQGNNMQQY3GccH0cz+cRjpHR0iDcIiOlMqJz03jNXYi8yTy2rXjkLYRajOck8GXcWGY8\nr1s7bW6iCEwoqZNP4MJwUzXmGUrPuTp6WG/fFhJyQgghhBBCDCkppceAj5jZGjzV8ircmfE5uNHH\nbuB9wNUL7cvMfh94VtPLkUI5gadqgouUo7ho2VSte5zS6Dvs+I9Xy2coRiQRvTpCibiBi7K6vizW\ni2jdGCW9cQxPsTyEC6yI4tV96IK1eO3boxTny/spjcLDZbMWdHXN3rpq/CHaTuIRya34tYaSEhp9\n/NpGQk4IIYQQQoghJ6V0Chcm95vZXbi1//XAawDM7It5vbMEXSyba9d4imY4Nh7ETU/Car/un7aJ\nEr2CEn2LlMRwdayjVc0iLgxLTlAcLOuIYETjRqp14yeidGGScjSvF3VskWJ5LK//RF6+k9JMvG5z\nED3mpvK5xbIZiqitnTTDTTOimDH+tlAfOSGEEEIIIVYoC4i0VjgC/BNF0EQt21G8vgw8rTHSCbfi\nEbIDlHozaHSIDGH2grzNw7gwfBgXZ5vz4wWUZt6z9cF7itI8fAxvkwDuShmiLZwmD1D6y0VNXQiz\nq/B6w2ngS8A3KFHFgxSzlnCrjHq8EK8hRqM+LtJIdwKfaVcTrWpnIyGEEEIIIcTgk1K6erYo3Cy8\nDRcxzYSeCMFU95Bbj9v7R13cBPA4JWVyPy6AtlEielFTF5Gy1RRTkDBpGcHTRLdQUh1j+4gCkte5\nmJJmGT3spimulicozcPjPCJqFlHBN+PunFfjBi4nKc3Coyn4RD5GjC8MZE7iYq9OyZykMaW0LZRa\nKYQQQgghxAqnWczNEql73xybnsQ1RUTXHsUjYefgImlNte44HvmKmrN4rU6lDJF3Erg37zecIEeq\nfUXkbra6tSlcmNXbHAb+geKsGa+NUQRYpFdGc/FooD6Bty+I8e7Or0U937E8zmgsHoIyBOiepvFt\npRiztI0ickIIIYQQQogGFhGpOx+PvK2hiKjz8uvTuEPmBB59G6WInJ3AZbgAipTDEHRhFnKCUpd2\nHI9sQWniHVGtw/l59HKLCFuIrbH8/BAuMtfibpXROy7EHJRoXLRKmATeCtyHp4iOV8sm8hgupDHF\nsxaXm3DDlHDgPJm3301x7mwLCTkhhBBCCCHErFSC7rPzrPZsXKhswV0tQ6CFg2S0DKj7rM3k5Wvy\n83CSjCbhEbHbROnHFumPkb44hUfMyPsPERiplGE0EtuEqckzFDG5nZLGSd5uhiIu47WfBn6LkjI6\nms9zG4397mIMz+DRx2iIHhG6ME3pqBl4nJAQQgghhBBCzElK6W3xu5m9G3h90ypX4Hb6E7ioOUax\n/F+FC66oiYt0xwgqrcHFUbQWgEbXSnARdH7eT+12uSvv7wBFKMby2Md6PAoXUbfjeKRthMaauhCc\nIRLjtaj/ewCP4k1TBOOBfM478Shb3VLh8bzt1jzObXlMe/K1qIXmolFETgghhBBCCNEyKaV35yjd\nW4G/wAVO9Et7Pu4meQ4e7boIF1Kr8utQUgs3UoTaNC7ALqRE7SLNMaJrYd8fYq0WXlBcJE9Q0izj\n9dF8vI35WA8DX8dbJRyl0ezkKMV4hWrZk8DfURqXP0apf2tulxCOneMUF8sRGpuvr6MDFJETQggh\nhBBCLJqU0n3A2wHM7KXAjXjkaRWeDrkJF0bRrDuE2+m8i8MUY5Rj+XnY809R7PvDcXIEr7+LHnWb\n8GgYNIqi2hFykkZDlU14fVysM930+zQlcjdDicZN5p+DeA++HXndGOsUxclyS97mEkq9HXndSN3c\nXq3XFhJyQgghhBBCiI5IKd0D3GNm64DXAa8ALsejcJvx1MtDlF5wh3EtsonSruDh/LiFYmwSdv1R\nZzZDcYCEIuTCEXJ7/v0IntpIPs4ojWma30RJAY0ecmPVT6SAbqF08Hb1AAAgAElEQVSIuOm87lfw\niNv6vPxA3m9EBycoYi1q5KKtwilc2NYNxNtCQk4IIYQQQgixJKSUTgIfBz5uZm8BXonb+Z+L14iF\nrf8ePDI3TkldjAjVJMVw5CReQxfPD1Eae5+kNOYOp8iZ/NpOXCxFi4BY/yk8ArcLF1aP5WWRprmR\n0th8U/V6CM9x3MFyBHgpHpkjn1OIyuOUNM8pSqon+bVw1Ix0zLaQkBNCCCGEEEIsOSmljwIfzVG6\na4Fvx6341+HulqdxMROtBKIX3XFKO4I11Xrg+mWqWmcTXncWKZlPUyz+T+ZtNuXta6F1jNKqYDOe\nsrmu2m6q2j5cMCfxKNtWXFCOVWM+iYvCSOVcl1+fwSN36/I6xympm08s5no2YymlTrZv/8BmKaVk\nPTm4EEIIIYQQYtkxs6vwGrNduH3/DlyoPYYLukN4BOs0Lspm8jqrgb/Jy6/Bo3yHcXEUDpbx+6b8\n+wFcVEUkcD+lWfhaSkuEcK6M9Myox3sCF2EjFJG2mdLM+3m4sDucxxXiso4ChmlK7J+8PHrdfaVd\nTaSInBBCCCGEEGJZSCndC9ybo3SvwtsY7KCkMZ6PR85OAI/iYm4VJa1xBBeBY/n1E7iICqE0QrH5\nD4OT2lWyNjcZx4VYRMpqsTWajxmpm1+juFhG/dw9eKRxjJIqGX3insLTSeN5TRizqEZOCCGEEEII\nMTjkWrpPA5/OUbprcZfHLXjLgoSLqUcp6YiRsggujk5TGoJvz48RlavdJCNCdyKvE6Ylk3gtXZio\nhOiLlMpIsxylpFauprGFwBQepbsMeCivHxG9SNU8SDFbWZfP7xgdNgWXkBNCCCGEEEL0jFmidC/F\nRd0luNB6ikYxNYaLuO0U45CIvo3iwq/ZTGSU0qPuOC4QD+ffo+l3NO8OIRfRtOO4WBujiL4QZfvz\nupvx3nh78NTJ0Wrf2yiiMtI8n6FE/9pCQk4IIYQQQgjRc5qidC8F/gUu5NbiUbVzcPOT1ZSI2vb8\n/BhFgG2h2PtP0JhKOZLX25F/Ik1ysto2HDDDYTNSL8+hROxiP4fzOi/GhWL0k6vbI2zP4wmBOUIR\niG0jISeEEEIIIYToK6q+dNuAbwauBN5UrTKD94mbpDQY34ILqGhncLpad5wiyEK8QTEmiRq8iOKF\nEIx0S/Do21bc4XIUF3Hrq+XjuPCMnncTeI3fATwS13xspVYKIYQQQgghho+U0kFKlC6E3D48Mvd8\nXCxFw/BoLA4l+jWK16+Fm2SIuqibO4LXzm3DBdYBXJiN531EndtjuEBcnfcxhTtnRm3dQeBq3Kxl\nGheRsW04aoZZStTd7ezk2kjICSGEEEIIIfqelNLVAGa2C/hXeDrjerydwSpcMD1CSZMcwZ0ja9OS\nuu4tTEuOUFImw/kyxNe6vH7sMxwwm/vezeAi8DJczO2jpGLW7Qhm8Hq603SIhJwQQgghhBBiYEgp\n7QV+BcDMXgW8Fm80vhF4CS66HsX7wB3GzVIi/fE4RditxoVevBaplBG9i8jdQUoT77rf3AQeyVuX\n1/kbisA7jUfmQmDGvqEYt8Q+20INwYUQQgghhBADjZk9F/gW4OW4kJrOP4eAB6rfx/GI2DQupB6n\n0fUSXKRFKuQ4Hmnbh9fGbaoOO0Fj+mSIwWtwg5M9uKA8WG0Xhizr8s/vtKuJJOSEEEIIIYQQQ4GZ\nbQCuA54HvACPmB3FUy4P4amY0b5gAo/YgYutk7jgivTJcKecyduvpbQSgFJH9wQeBdyEC7hn4emV\nh/J+Ryg1e1B6yh0E/rpdTaTUSiGEEEIIIcRQkFI6BtwO3G5mrwG+DRdNW4Ar8Ehc9Iw7gadjPk2J\nrI1Qmnmfhwu9/RQnzIikHc/r7cz7PkBpRv4ELhQ343prklInF7V4Ee1rGwk5IYQQQgghxNCRUgq3\nyw3AdwCvxmvirsDF1AQupqbxaNszFBfKDbiwO4aLuUPARXnZBXj0bQ8lihf956IR+SgenRvL64XR\nSkT8og6vbSTkhBBCCCGEEENLjtJ93Mz+DDdDeSueYnkBLuyO5lVP4JG2Y8CTFBfL5+NCbwsegRvH\no2zhbhmRtTBCiXYEY7j424xH/YLVuAnK9k7OS0JOCCGEEEIIMfRkQfdZ4LNmdinwRrzR+BpcoD2J\np0Q+gws6cJE2hkfapihOk1OUXnQRgYPijnmQ4mA5RmksfhKvtxvJy9pGZidCCCGEEEKIFUl2u7we\nF1urgB24wJoCHsajdZO4kBsBduX1ojn4g3h93Pa8PHrUTeHi7lK8t9xRXChG24J1+TgflGulEEII\nIYQQQrSBma3BXS5fiEfpIu3xGTy69jDuRDmOtyII05RoBh7uljPVbg/iYu7V+TFMUJ7CUzpXA/+X\nhJwQQgghhBBCdIiZXQ78M7yFwTm4s+X5uKh7CPgGLsKO4kJuPR6lO0hJs4y2A+DRt8vzetGSYBRP\nzfyvaj8ghBBCCCGEEB2SUrofuN/MduGpkb+cF63H9dN6PE1yLP/+BKUObobSX24Ur4k7gKdkbszb\nj+fXo96uLSTkhBBCCCGEEKKJlNJeYK+ZPQJcnF8+jEfp1uAtCr6Bi7dVFPOSaPh9BK+J24anYZ4G\ntuLCDzrUYhJyQgghhBBCCDEHKaXvit/N7KXAtXgvuvOA5+AC7hAehTuJNxA/mTeJBuNT+XlE6SJi\n1zaqkRNCCCGEEEKIRWBm24B/CVyFR+cATgFfxxuAb6KIt2gafh4lvfIAXnP36zI7EUIIIYQQQohl\nJPejewHwbOAa3NjkMdwIZSI/TlFaGpzI60/mXfyUzE6EEEIIIYQQYhlJKT0EPGRmn8JbErwIj9Dt\nAi7BhdyDeBrlJLAXr5PbSInYtcWqdjYys9ea2dfN7H4ze8cc6/xKXv5lM7uqk0EOImZ2Q6/HINpH\n929w0b0bbHT/Bhvdv8FF926w0f3rPSmlUyml96eUfgC4DfgybnYyjtfRnY+7VG7Ho3KT+bFtFi3k\nzGwE+ADwWry3wptyR/R6ndcBl6WULgf+D+CDnQxyQLmh1wMQHXFDrwcg2uaGXg9AdMQNvR6A6Igb\nej0A0TY39HoAoiNu6PUARCGl9OcppVuAXwL+Eq+ZA3g+cDUeuVuNp2O2TTuplS8DHkgpPQxgZh8D\n3gh8rVrnDcBHAFJKXzCzzWZ2QUrp8U4GK4QQQgghhBCDQErpPuA+MzsXeAXwEjyl8hJgM15P1zbt\npFbuxHM7g335tYXWuaiNYwkhhBBCCCHEwJJSeiqldDvwHuB/AA/jveQ2drLfdiJyrdpcNruvnLWd\nmfXGMnOZMLN39XoMon10/wYX3bvBRvdvsNH9G1x07wYb3b+VRztCbj/uwhLswiNu861zUX7tDGo9\nIIQQQgghhBDt0U5q5d8Cl5vZJWY2CnwP8ImmdT4BfD+AmV0DHFZ9nBBCCCGEEEIsDYuOyKWUps3s\nJuDTwAjw4ZTS18zsh/PyX0sp3W5mrzOzB4CngR9Y0lELIYQQQgghxArGUhrqMjUhhBBCCCGEGDra\nagguHDPbZWafNbN/MLO/N7Mfn2O9G8zs3rzOHcs8TDEHrdw/M9tqZp8ysy/ldd7ag6GKJsxszMy+\nkO/LV83sPXOs9ytmdr+ZfdnMrlrucYrZaeX+mdmb8337ipndbWYv7MVYRSOt/u3ldV9qZtNm9l3L\nOUYxN4v47NS8pQ9p8bNT85Y+xsxG8t/WJ+dYvqh5SztmJ6JwCviplNKXzGwc+KKZfSaldKannplt\nBn4VeE1KaZ+Zbe3VYMVZLHj/gJuAe1NKP5vv3T+a2UdTStM9GbEAIKU0aWavTimdMLPVwF+b2bek\nlP461jGz1wGXpZQuN7OXAx8ErunVmEWhlfsHPAi8KqV0xMxeC/w6un89p8V7h5mNAO8FPsXZLtai\nR7T42al5S5/S4t+f5i39zU8AXwU2NC9oZ96iiFwHpJQOpJS+lH8/jjdF39G02vcBH08p7cvrHVre\nUYq5aPH+PUbp8bEReFIfhv1BSulE/nUUr9edaFrlDcBH8rpfADab2QXLN0IxHwvdv5TS36SUjuSn\nX0C9SPuGFv72AH4M75V0cLnGJVqjhfuneUsf08L907ylTzGzi4DXAb/B7F9wLXreIiG3RJjZJcBV\n+ISj5nJgS07h+1szu3G5xyYWZp779yHg+Wb2KPBl/JsU0QeY2Soz+xLwOPDZlNJXm1bZCeytnu9D\nYqBvaOH+1fwQcPvyjEwsxEL3zsx2Am/Ev02G1vvPimWghb89zVv6mBbun+Yt/csvAz8NnJ5j+aLn\nLRJyS0BOy/sfwE/kyE7NGuCbcQX+GuA/mtnlyzxEMQ8L3L+bgS+llHYALwZ+1czOCoeL5SeldDql\n9GL8Q+5VZnbDLKs1f+OlCWWf0OL9w8xeDfwg8I5lHJ6Yhxbu3fuBn0nupmYotbKvaOH+ad7Sx7Rw\n/zRv6UPM7DuBJ1JK9zL/Z+Ki5i0Sch1iZmuAjwMfTSn90Syr7AX+LKV0MqX0JPBXwIuWc4xiblq4\nf68Efh8gpfQN4CHg2cs3QrEQOf3uT4GXNC3aD+yqnl+UXxN9xDz3j2xw8iHgDSmlp5Z7bGJ+5rl3\nVwMfM7OHgH8N/D9m9oblHp+Yn3nun+YtA8A890/zlv7klcAb8ufi7wLfama/1bTOouctEnIdYGYG\nfBj4akrp/XOs9sfAt2SXmvXAy/EiR9FjWrx/Xwe+Pa9/Af5h+ODyjFDMRXbl2px/Xwf8M+DeptU+\nAXx/Xuca4HBK6fFlHaiYlVbun5ntBv4AeEtK6YHlH6WYjVbuXUrpWSmlS1NKl+LZDj+SUvrE8o9W\nNNPiZ6fmLX1Ki/dP85Y+JKV0c0ppV/5c/F7gL1NK39+02qLnLXKt7IxrgbcAXzGz+EO6GdgNZ5qj\nf93MPgV8Bc+J/dACtSBi+Vjw/gG3Av+vmX0Z/+Lj7Sml2Qr7xfJyIfARM1uF35fbUkp/YWY/DGf+\n9m43s9eZ2QPA08AP9HC8opEF7x/wc8C5wAf9OxdOpZRe1qsBizO0cu9E/9LKZ6fmLf1LK39/mrcM\nBgmg03mLGoILIYQQQgghxICh1EohhBBCCCGEGDAk5IQQQgghhBBiwJCQE0IIIYQQQogBQ0JOCCGE\nEEIIIQYMCTkhhBBCCCGEGDAk5IQQQgghhBBiwJCQE0IIIYQQQogBQ0JOCCGEEEIIIQYMCTkhhBBC\nCCGEGDAk5IQQQgghhBBiwJCQE0IIIYQQQogBQ0JOCCGEEEIIIQYMCTkhhBBCCCGEGDAk5IQQQggh\nhBBiwJCQE0IIIYQQQogBQ0JOCCGEEEIIIQYMCTkhhBBCCCGEGDAk5IQQQgghhBBiwJCQE0IIIYQQ\nQogBQ0JOCCGEEEIIIQYMCTkhhBBCCCGEGDAk5IQQQgghhBBiwJCQE0IIIYQQQogBQ0JOCCGEEEII\nIQYMCTkhhBBnYWYPm9m39Xocon3yPfzWXo9DCCFEd5CQE0IIMRsp/4jBJQHW60EIIYToDhJyQggh\nFsTMRs3sSTN7QfXa+Wb2tJmdZ2bnmtmfmNkTZjZhZp80s53VuneY2XvM7AtmdsTM/sjMzs3LbjCz\nvU3HOxNNMrN3m9nvmdlHzOyomf29mV1drfvcvP+n8rLX59dfbmaPmZlV6/4rM/vyHOe41szeZ2aP\nmNkBM/ugmY3lZX9qZu+r1v2Ymf1G/v2tZna3mf03MztsZl+rI2FmtsPMPpGv3/1m9m+qZQud2w4z\n+3i+rg+a2Y+1sq2Z3QbsBj5pZsfM7G0L32UhhBCDhIScEEKIBUkpTQEfA95Svfwm4M9TSk/ikZ8P\n4+JhN3AS+EDTbm4EfgC4EJgGfmW+QzY9fz3wu8Am4BOxbzNbA3wS+BSwDfgx4LfN7PKU0heAp4E6\nRfT7gN+e45i/AFwGvCg/7gR+Li/7QeBGM3u1mb0ZeAnwE9W2LwMeAM4D3gX8gZltzss+BuzJ5/2/\nAbea2atbOLdV+dzuBXbk8/hJM/uOhbZNKd2Yj/mdKaUNKaX3IYQQYqiQkBNCCNEqv4WLt+BG4DaA\nlNJESukPU0qTKaXjwK3A9dW6CfitlNJXU0ongP8I/O91tGwB7kopfSqllICP4mIL4BrgnJTSL6SU\nplNKnwX+BBds4CLnTQBmtgH45/m1BvI4/i3w71JKh/M5vAf43nx+jwM/kq/B+4HvTyk9Xe3iiZTS\nf00pzaSUfg/4R+A7zWwX8ErgHSmlqZTSl4HfAL6/hXN7KbA1pXRLPreH8rbf28K2QgghhpzVvR6A\nEEKIwSCl9AUzO2lmNwAHgG/Co0CY2Xrgl4HXAOfmTcbNzLLIAKjTJ/cAa4CtLR7+8er3E8BYjljt\naNovwCN4NA1ctN1tZj8CfBfwxZRS8/rg0bz1wBfrTEwav/D8Ezzi9fWU0ueatt8/yxguzD8TTaJv\nDx7RW+jcLgZ2mNlT1fIR4K8W2jaldHqWcxRCCDFESMgJIYRYDB/B0ysfB34/p1wC/HvgCuBlKaUn\nzOzFwN/hYiiE3O5qP7uBU8AhPP1xfSwwsxFcWLXCo8CuJsF4MfB1gJTSV83sETwS933A78yxn0N4\nOujzUkqPzbHOfwG+ClxiZt+bUvpYtWxn07oXA3+cx7fFzMZzlA/83Pe1cG57gYdSSlfMsXwhMxqZ\n1QghxBCj1EohhBBzMWpmY9XPCJ6+913Am/E0w2AcF0JHzGwLXidWY8BbsjHJeuA/40IwAf+ER5Je\nl2ve3gmsbXGMX8AjUW83szU5WvideF1a8DvATwLXAb8/205yBOtDwPvNbBuAme2MejQzexXwVjyd\n9K3AfzOzHdUuzjezH89j+G7gOcDtKaV9wOeA92QzlRfi9XYfbeHc/hdwzMzebmbrzGzEzF5gZhHN\nWygt9XE8aiqEEGIIkZATQggxF7fjIil+3pXTEv8OOJ1S+utq3fcD6/DI1ueA/0ljRCjh9XT/H/AY\nMAr8OEBK6Qjwf+L1X/uA4zSmS87WCiHlbadww49/DhzEUx9vTCn9U7Xu7wKvAv4ipTQxz/m+Azcs\n+byZHQE+A1yRa+s+AvxoSumxfN4fBn6z2vYLwOV5DD8P/OuUUqREvgm4BI/O/QHwcymlv2zh3GZw\nUfpi4MG8718HNi60beY9wDuzm+e/m+e8hRBCDCBWMlG6sHOzh4GjwAxwKqX0sq4dTAghxLJgZh8G\n9qeUfm7Blcs2nwVuSyn95oIrDxhm9lbgh1JK1/V6LEIIIVYO3a6RS8ANC3wDKoQQYkAws0vw1MoX\nt7P5kg5GCCGEWMEsR2ql/nELIcQQYGY/D9wH/GJK6ZE2djGs5huzpTgKIYQQXaXbqZUPAkfw1Mpf\nSyl9qGsHE0IIIYQQQogVQrdTK69NKT2WHcA+Y2ZfTyndBWBm+vZSCCGEEEIIsaJJKbWVwdhVIRe9\neFJKB83sD4GXAXdVy4c27dLM3p1SenevxyHaQ/dvcNG9G2x0/wYb3b/BRfdusNH9G0DMJoFR66AM\nrWs1cma2Pls2Y2bnAN+B11YIIYQQQgghxMrC7BbMTmN2Gm/D0xHdjMhdAPyhmcVxfjul9GddPJ4Q\nQgghhBBC9J4ccVtgrdPASLuH6JqQSyk9RHv21MPCHb0egOiIO3o9ANE2d/R6AKIj7uj1AERH3NHr\nAYi2uaPXAxAdcUevB7BiMbsFuAnYuIitbiWld+bt2/YN6apr5bwHNkvDXCMnhBBCCCGEGEJcvN0I\n7Gph7QR8rjxL1zXuqn1N1G3XSiGEEEIIIYToT8zuAq5h4RTHKVIay/Vt83Ea+JtmwdYNJOSEEEII\nIYQQw4nZKTqoQ6tYPYeIK2mSy0zXXCuFEEIIIYQQYlmoHSHrn8WJuLuBvcBUfryVlFbl349X6/my\nHoo4UEROCCGEEEII0W+46+MI8F7gemA3cNtZwmlxEbe9+TFq2+5uMQXyNtzQZAZ4lJQubvF4XUVm\nJ0IIIYQQQojlxQ1DrgfuJKV3YnaY1pwfbwXeQSs1bfC+WSNmfmwWFU0zeyRvs6QiTmYnQgghhBBC\niP7GbAZoFi3XYnbzIvbyNs4WcTOktCYf4y7gLHfIJeC2Jd5fx6hGTgghhBBCCLG0eM3aLfn3qFdr\nJfK0F095XIVH345SatKO0thkeyavu+bMKyldtxyOkf2AUiuFEEIIIYQYBMymmT0QMwM8TetNqbtn\n0nF2j7XTnD1mj6D5uj+LCzy391943zcDiZSWwomyddpJx2xpt+1rIgk5IYQQQgghesFc4qD1erHO\n8KjX0uEGJaNzLD0KfGCWc12cQIpatUh17KFr5FIgISeEEEIIIUS/UQw9XoFHnY4xt0BLCywP6gjX\nFF4vVkenpoA1+XjNLo2z0apz4/zMLj5THsfSRdBC+J05wjIIuS5F43zXMjsRQgghhBCiPcIgA+7E\nzTTmiioF86cBzh1Rm0+k2SzLU7Vs75yOic2OivMJDz/X3RRx99J5xtQajS0AEvA5/Foy5zjaZcAj\ncEuJInJCCCGEEGJwaYzQzCfC7s6Pr6Q1042FOEpKm5vGchdwbQvbzgDvzbb7t+A9ymoRt7clUVaO\n246d/l34tTjdYBbSDm5kEnS7/m6oxJwickIIIYQQYvgpZhftcA2tN44GT2E8DnyAuiE1/Aye2jg+\ny9iaRVyIx4hO3QQcaYisuZgD7402c1akbyHR0q64Sem6XNPWGaVmDVyADo3I6ncUkRNCCCGEEP3L\n7BGrVkjAKWASGKMxUhf1aPedqQ8LUZPS2ILiyFMnaYjINRp9LOzAePY+2+t/1kmUail6rnlapQG/\nIBG3eGR2IoQQQgghhoeFI2+NBh2l7uu2ecTXDMAZ041mAbQYUTPbuiW9sHuphUvN0gk5Ok7PXKEo\ntVIIIYQQQgwWnpJ3EYurV5tdJLUmRPY1bfPOpueLETN3NjxzUXgad2ccDBFXuBKzuzoQc08v6WhE\ny0jICSGEEEKI5WNxPdLuzrVcnZlc+PZ7aBZgS8dNwPGzzE/6Hb+2dy284rzctyRjEYtGQk4IIYQQ\nQnSH+RtE13izaDcVeSVew1ZqrpYmynVnF6NlR7q03+7TeQ+5boljsQBL281dCCGEEEIMJ2aPYHa6\n+pk+qzlz87rzi7hbSWlV/tmcRdadwHtIaXVXeo/NNd529tc4vj35RwwrZrcs2ftniZCQE0IIIYQQ\nZ2N2uEG4lQbSwSrg5jlS85rXnSGlVcBeYApPmRy0WjLRjNc53tTrYaxU5FophBBCCLHSmL9ObYbF\n9VtrtNpvTKdsbJq9sK3/0DV8HmrCqdNFumgDtR8QQgghhBAL4xGU5mjZQiSaa9Z8X3fhTbafbhJr\nxYYfJMr6nXbFs9//a/O2EnJtovYDQgghhBBibupJdyMh0vZTarxeAUwv2NC6dpNs5GheLgE3rPj7\nKUxpPtfj0axYJOSEEEIIIYaZ2ZwjI4Iye2PrRzo84gc63H7wWIrG2r2iPcEdXwrMDOQ5DwkSckII\nIYQQw4JHyN7B3DVue0np4ur5bNbxt3U4ihvz40qKyF3Z6wEsG43mNp9f5mOrhrJCNXJCCCGEEMOA\n2TRzO5In3Na/uxNgn+RfCdy3YiI1fs4vBR5vEsmL3c9giBSP8K4B9nV0vu0du3fXqEvH7ssaOTN7\nLfB+/Buh30gpvbdbxxJCCCGEWNF4OmQt4qaAe/Lv3WyE3cw1QPsphu0bb/RSBEU0rtNIZndZums0\nApxedhEnzqIrQs7MRvD86G/Hi2fvMbNPpJS+1o3jCSGEEEKsWBojcVPA+wCfsLfTwLi53mtQIkW9\n4whwpOPrMzjX92lg5b0v+vA8uxWRexnwQErpYQAz+xjwRkBCTgghhBBiaQkRd5qUxprE2/XLPJan\n5126kClIu5PlhbbrrujYs/AqLdBtYbR0+z2yRPtZPH0opnpJt4TcTmBv9Xwf8PIuHUsIIbDG5ran\nU0oycxJiSLGqT1kakond58xOAbwypTULrfur2VXyR1O62MxuOQFT62DyTC+3zq9JowFKC/szFyHX\n3w9HLlsqYTNsDGAEK99XUkrvPPP7Ut/f+a7LAF6z5aRbE52WHFTM7N3V0ztSSnd0ZTRCiIHE5i/c\nn49V1UTvDEkNS4UYOJq+pGnmZjO7GdibBrReJz7n7qqeL/RF1OHc0DuuzS8Bz4Z7vtvslmZh+75c\nv/W2uY9/ZqIer/1qdp380TlcJ2fbBrgJGL8cjgN3zjkRXKB2znLELi2xUUo4SbRr8TfHOWNmj/wX\n2DEKT//0LNd/UbS57VxjWyJ+Nj++E39f7DB4NKV0cVtpux2yVOfazn6W8Ng3ADd0so+gW0JuP/lD\nJrMLj8o1kFJ6d5eOL4ToU8y/Sd614IrtkYBTNPdLKsc+S9wxwBNAIYYR88jUXNb5c7Er/33fvdQC\noFs0C9Rq0KvM7HCK6NrZ201XTzfCGbW1m5xGaY0T7DFgci4hN8v+Y9s9PzrL67MImVh/HP/ibc4m\n4l0WHAuxYIppm+Pb8R/8vBdON1xgvz2+PmeR36O1m+Im/G9zh3UqWmvm28/Zy5Y7VXjJj50DV3fE\nczN7V7v76paQ+1vgcjO7BHgU+B7gTV06lhCiD5hDJC0FUymlOScGrTLP+HbNsmxo0rWE6HdajLyn\nlNKs4q7p7/daMzvd79H3WT5zplJKY1Yad88agczRqji3o3m9BBzD091m6wk3yTwiY47Putvm+wyc\nY1kEux7v8PNztnPoOfMI2Kdx8TrvNesmXYxObciPR+vDATMLbNdNluT90eaY++692RUhl1KaNrOb\ngE/jyv3DcqwUYjDplkBb7onWbMeb59wiXWve7YUQi6fFiNtMaqFWDMrfZv33nH+fU/z1ilnSRBvG\nmMXcNB6VOzXLNXhlfpzKj6eBaeC+OhJZT1LN7Prq97Yn3nNtE6/ned85zFM/1eMvyBachLc5viUz\n/ujDLxBDnB/JXyIcwSOvk3XNnOgdXZuYpJT+Z0rp2SmlyxUx9WkAAB7BSURBVFJK7+nWcYQQi8fM\nbjGz0638LHLXe1NKq1r56cqJLZLFjGuWa/PIco5ViEHFzCabPlNmE1dTTX+LLYm4mln+hi0f8645\nN1pG8rnXIu7W2YRmVR/XsCxPmi2vM4ZPqqeBe+ZLJ00pXddGuun1rU7S8/+TmOTPAFd2MsFPKb2z\nDwXNWTSNsXcujl2i+h93LD/uzo/TwH3LP6K+4Hp6m9p5FnJ1E2LI6EYErV+E13LQfK7z1PQ1p2TK\nKVOITAufQy1H3BZLSmlVU+Tr2lYMRLpJ0/VoJVI4A4w01cpFmVukue3Ba5ZmO16DkArR0YpAajPS\nciUuZu6hTPj7keuXtLbLJ/V7qt+HiR358QNk85vM472sQ+2VyM9/E7vpM0fWFTM5E2LQMbPppY6g\nDVL0rFeklC5u8XqsaroXM8s6UCF6iJmdWuBz6HSnEbfFkFLa3PS3OquTbbcxs7uajru3xXTP9+bH\nDdVra3ARGMLuTroQCVps+mVeL8ZxJz2sFZuPPKYlq3GqJvbk/Xa87xzd7Jd0xRlgurqXm8gipnIW\nXTB62mfn1Clz1aH2DH17LEQf0IUJhsw6usgsUbswKGh6edHfwgsxMCz0udUPXwLl6NyZv8/lNEJp\njuYv5rg5KvYzzS/Pss6sUaCl/vyfT9zlZX03wZ2NLv1f3N3FffcLe8htLOiziNRy0er9XW4DGAk5\nIbrILIXtnbIkDo5iaWm+J3Pc92Zhp3spBor8Lfy186zStXTJTsgGImfGnv8Ou/plVyciruI4cE5V\n4zcNPN60Tt+Lp2ElC2nwtMOlsqXviz5yVQRtsnnZYtMqh1zg9hwJOSHaZKlFWj98ey2WhtTU/2mO\n98pok7AbmP5XYuUwT41oMBDR//jbqv7mbjazrkwys/DqVMSB1ya9DY+EjOV99aTn5XzXKQuau3Ax\nsxKFZdejkcsQ5WkWojflxw/kxzubHsUcLPfnoYScELOwxCJNKXUrnFmE3Wx9s66tJpkyThE9Y45U\n4TMM8pdOOdXyjJjjTC/tJeVM1LKTa5UF0k0Lr7m0LHYiWkVv7lyKSWyPepN1wpKcdycswfGbBVp8\ncTAo92DFoomCWJEsYU2aRJpYNM0ibZb3Y4MxwyBPnMVgsMCXV0P1OVeLuaWumevi321zSmVLDKAo\nGjSWxalyGe5f83k0p1ReT6mRE32EhJwYOuaIdrTDUE1eRP9ST/hmi4Y0Cb2BSGUT/c8CNW9DHRVu\nEnMzS/FZn//3nNl/p/vL9H1/sjbbFcy7v6Xal2ib5vdd36RWVo6ZKkVAQk4MIEsVTVOUQ/QjtQFK\nnhzd3LTKzWYWr6muTiyaeT5DV9qXV3fjQtbMbLIT86FcSxj/U+5eisG1wkKiZzlEUf6c6nl9XC+i\nj8Py+Tss59FN+jW6rYms6CvM7JEl6pM2pd5oYtDJPXrme89eW/1tDEufHtEF6j5vzcuq99hKEnEx\ned2bn452+DcU5iZTXZoU72EAbN+HrGfYggzL+dbnkR9nbTTfD6SUrpPwLFhKaeG1unFgs5RSsp4c\nXPSMJTQRUSRCrGjm+1JDX1SIYJ73iT5DM3U6fjt/O9X2Sx7RrKJd0AemGgvRr1GLbjEs51unK+bf\nd9PU2H1YzrUf6UQTSciJJWWphJomokK0jlLlRM08rpN92eetH6j+ho42u8wusN2ZOsNu/d/KaZs9\naz0ghp9apM1Wg1anz0rILT2daCJNlsWiyOH3+dIeWxFxSWmPQiwd8/ztWPX3+UhPBieWjepzuEHE\nVe8Pibi5iRTLxX4R+cr8OLWEYxk4hiXFcLHk875rKc69l9cwxFk+/u7808ydYWyzEu91vyKzE3EW\nS2AmoiiAED0ixNws0fFd8betL0uGhzkMcUDRt0WRUrrYzGbwLz8OtxKVy9fe8vZtG6W0QN/XxrFM\nNvyiq8x5DxWF618k5FYg+Zv5XQuuOA+aCArR39QT0eYvZ6rnamUwoMzzOa7at/b5HJ4m2WpU7h35\n8Wh3hjNQ9NyWvocsSbphH3wWxz2cVdDJ9r8/kZAbUszsFNBJVGyv8vGFGA6qKF3z5D9aGSyqLkj0\njrkEnL5c65xs9BBRubtamLCO5O1W/N9OH4gQIVYkEnIDTKcpkPrHL8TKov5ypunzY2N+PtRNoAeZ\nuYyk9Dm+5OzDhfIr5lsp3w+Ama6PSPQtK0nAKhLXn+gfdp/ToVhTjYQQYlaqKN0Muc4HWJU/c1Tn\n2icoAre85Fq50yxsBrchP763y0MSQog5kZDrA5omUotFKZBCiLYJwdZkWW8SdL1lDhMT3Y/lYQpY\nY2aPLPD/NS1TRGYl15+J5UfvtwFCQm6Z6LBmTWJNCNFVwnWvKYVPgq4HzJaJoQjcsvI+4GeAHbMt\nzFHSBBxfjsEMQvqemkUPP7rH/Yn+MSwh8/VYY2ERd3SevmoScUKIZSGltDmLhr3Vy9GP7lSvxrUS\nMLPpZhGn3prLTzVRnStTZoevtjwmJ+rbJZaZ61E7iYFBEbk2MLNp2hPBqlkTQgwE8QVSU4RuJAsN\nZQksIXMYmag1RG9J+BcYt+g+LMxKvUZDGqVSauUAISE3D+0ajejbUyHEsBBRh6b08F1mdlqfdZ0z\ny/8ZtYLoDz4PXAPcBPR0kj5kIkH0N9ezRH3xxPJgKaXeHNgspZTaNfhYynHchTcAXSxTUVMihBAr\nhVmEh+rn2mCWumldxz4jGwBR/6/P9XE7gEeXKyo9pFEf0Wfk99mNwB61GlheOtFEK+bbVDN7ZI7a\ntXlF3Dx1axJxQogVxyw1W1E/d1fPBjVgzFI3fatE3MBwAV4modRiMYzsQamVA8XQReTm6rmzEEoR\nEkKIxTFbbZc+S+dmluuluuk+Zo6I3OH8mtJfxdCh6O/cdPParMiI3DwRtnlF3FwRtmUathBCDA2V\nw+UZFJ2bnfz/qRZxt0rE9T2PA5NyjFwYOWsOPvn+ya1ywOiKgDGzd5vZPjO7N/+8tsP9SbAJIUSf\nMku7gmuzu++KJ9rSVC+l/P9I33j3P7flxxt7OgrRt0jArhxSSu/sx8/tbrlWJuCXUkq/tJiN2nGJ\nlDgTQojeU7UriM/xVSvd2XKWVEq1bRggUkrvNLObgE1QUquAI70bVX/SjxNcsTjy+73vRanSPxvp\nZvuBBXM9FyPcVvJkQAghBoWU0qpcWzQKZz7n715pLmjN/Ub1P2xgqUVbROZum21FsfIYJjEhgTSY\ndPMfy4+Z2ZfN7MNmtpii4L1KiRRCiMElm0PcWr10bbbbXxFk8Rr/t5L+hw0VR5Z7oqv0vaVB17El\nru/3a9SvKY69ou1/Lmb2GTO7b5afNwAfBC4FXgw8Bvzfs+1jjjo2pZ0IIcSAk//Z1v9jRsxspmcD\nWiaaMk2m1FZgqNiTf4QYOrI4UuuBAaPr7QfM7BLgkymlK5teT8B/ql66I6V0R1cHI4QQYtlpbn49\nrBGqJhGnerghIBxYU0rX5fZG6L4KITrBzG4Abqheele77Qe6IuTM7MKU0mP5958CXppS+r6mdbrS\nR04IIUT/0Wz8MWxirknErbiawGGlFm8ScmKYqdoP3KnUxeWlH/vIvdfMvmJmX8bfFD/VpeMIIYQY\nAHID5bvjeTsuxf1K07ncKhE3VOyBM5NcpVYKIfqKrqdWznlgReSEEGLFkSfEN8fzQY7MDdO5iLlp\nbnAvoS6EWEr6MSInhBBCnEVO2TnjaDngkTmJOCGEED1D/3iEEEIsK8Mg5uoxS8QNPXciNz+xAlCL\nhsFD/3yEEEIsO4Ms5iTiViwSdGJoqcxOxAChf0BCCCF6QhZztQHKdA+H0xJNY7x7zhXFMHE9cCOc\nec8KMazM6VipaF1/srrXAxBCCLFyqfpz7QJWmdlkSmms1+OajdxCIb4A3SvTixXFJhStEEOMvqQY\nTCTkhBBC9JTco2sSGAVGzeyufhNJ+Zvo6IM3pV5iK4o7mx6FGEoi4jabqJPQ60+UWimEEKLn5Chc\n1J5d28uxzEE4VKZ+jRgKIYRYWSgiJ4QQoi9IKa0OIxEzm0kpjfR6TNBYF9cvYxLLzm6UWimGHEXd\nBg9F5IQQQvQT4WRpOd2yp+T6vfhfKXOTlcselFophhiZmQwmEnJCCCH6hvyN8NH8dLQPJha78uNU\nv9XtCSGEWNlIyAkhhOgrUkqbKfVyP9urcZjZqfhddXFCiGEmpfROpVYOHhJyQggh+o6UUtRwW7b9\nX1bM7C4g6uFunW9dsSKYs7+WEP9/e/cfc+1d1wf8/eFpGzYd7RYSGW2REhuTouPHJjLH7O1csWmU\nhhGDUTGM/WFstpkl6mhh0mXPRCfbyDZLHDPGHwGDgoyGQnxEnoIG6iZtqTx0a0G0D2xuaMtQafrj\n+eyP+7rL6c394zznnPucc5379UrunHOd63uu65N8n3Oe7+d8f8GqSOQAWFc7QyyfdmCpo7Gzcubj\nGvAkuXoNhvkCPIlEDoC1NAyx7OTJwxyP2rDAyU4MFy7rvgCrZMGT8ZHIAbDO3jg8nlhiA2NngZMH\nlnQ/1tgwd+jv6pkF1k1192puXNXdXSu5OQCjMfTGnUhybmLu3FHd66EMQzm724+dJNnuqUjsswUs\n3jw5kf+kAFhrE8Mbn7KEXrmd+Xj2jCPJE0mczcCBtaNHDoC1N2wOflGOsFduojeuu/vEYeU5HvTG\nAUdpnpxIIgfAKFTVzt5yP3EUjeqJ6/+Ozb+B48aPFqthaCUAx8HOdgSvXfSFJ1aqbEkcu1nND1hH\nRzppHAAWpbsvGXrNjuJHyMuGx7NHcG1GbGKO3O2rjgWOkp648dEjB8CYPJI8MWduIYaGeiVJd3/t\noq7LRrldIxdYN+bIATAqO3PZFrU9wMRCKv9v2IQcAJbCHDkAjpNzSVJVH17Q9S5KtoduLuh6AHDk\nJHIAjM1Hhse/Pe+FJpLBcwcWBIA1Y2glAKOzqOGVVfVYtn/UtOUA+7IsO3BUDK0E4Lh5JElPb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15, 10))\n", "plt.subplot(211)\n", "for i in range(iterations):\n", " x = f(r, x)\n", " # We compute the partial sum of the\n", " # Lyapunov exponent.\n", " lyapunov += np.log(abs(r-2*r*x))\n", " # We display the bifurcation diagram.\n", " if i >= (iterations - last):\n", " plt.plot(r, x, '.k', markersize=1, alpha=.1)\n", "plt.xlim(2.5, 4)\n", "plt.title(\"Bifurcation diagram\")\n", "# We display the Lyapunov exponent.\n", "plt.subplot(212)\n", "plt.plot(r[lyapunov<0], lyapunov[lyapunov<0]/iterations, '.k', markersize=2)\n", "plt.plot(r[lyapunov>=0], lyapunov[lyapunov>=0]/iterations, '.r', markersize=2)\n", "plt.xlim(2.5, 4)\n", "plt.title(\"Lyapunov exponent\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Ordinary Differential Equations(ODEs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$u''=-\\frac{k}{m}u'+g$$" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "m = 1.\n", "k = 1.\n", "g = 9.81\n", "v0 = np.zeros(4) # initial position is (0, 0)\n", "# The initial speed vector is oriented to the top right\n", "v0[2] = 4.\n", "v0[3] = 10." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f(v, t0, k):\n", " # v has four components v=[u, u']\n", " u, udot = v[:2], v[2:]\n", " # compute the second derivative u'' of u\n", " udotdot = -k/m * udot\n", " udotdot[1] -= g\n", " # return v'=[u', u'']\n", " return np.r_[udot, udotdot]" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 12)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VFIKTv94/4ntNKilbxLRayIIMn4fBax+GoXwMvjFRMTsGCKzYBa8E77FjUP/j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\nRaxJZ8JQ05BXW5QzGUJZhzGsA/DdPXv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import integrate\n", "\n", "# evaluate the system on 30 linearly spaced times t=[0, 3]\n", "t = np.linspace(0., 3., 30)\n", "# simulate the system for different values of k\n", "for k in np.linspace(0., 1., 5):\n", " # simulate the system and evaluate v on the given times\n", " v = integrate.odeint(f, v0, t, args=(k,))\n", " # plot the particle's trajectory\n", " plt.plot(v[:,0], v[:,1], 'o-', mew=1, ms=8, mec='w',\n", " label='k={0:.1f}'.format(k))\n", "plt.legend()\n", "plt.xlim(0, 12)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Partial Differential Equation(PDEs)\n", "##reaction-diffusion systems and Turing patterns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\frac{\\partial u}{\\partial t} = a\\Delta u + u - u^3 - v + k$$\n", "$$ \\tau \\frac{\\partial u}{\\partial t} = b \\Delta v + u - v$$\n", "on the domain $E = [-1, 1]^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "http://ipython-books.github.io/featured-05/" ] }, { "cell_type": "code", "execution_count": 274, "metadata": { "collapsed": true }, "outputs": [], "source": [ "a = 2.8e-4\n", "b = 5e-3\n", "tau = .1\n", "k = -.005" ] }, { "cell_type": "code", "execution_count": 275, "metadata": { "collapsed": true }, "outputs": [], "source": [ "size = 80 #size of the 2D grid\n", "dx = 2./size # space step\n", "T = 10. # total time\n", "dt = .9 * dx**2/2 # time step\n", "n = int(T/dt)" ] }, { "cell_type": "code", "execution_count": 276, "metadata": { "collapsed": true }, "outputs": [], "source": [ "U = np.random.rand(size, size)\n", "V = np.random.rand(size, size)" ] }, { "cell_type": "code", "execution_count": 278, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def laplacian(Z):\n", " Ztop = Z[0:-2, 1:-1]\n", " Zleft = Z[1:-1, 0:-2]\n", " Zbottom = Z[2:, 1:-1]\n", " Zright = Z[1:-1, 2:]\n", " Zcenter = Z[1:-1, 1:-1]\n", " return (Ztop + Zleft + Zbottom + Zright \\\n", " -4 * Zcenter) / dx**2" ] }, { "cell_type": "code", "execution_count": 281, "metadata": { "collapsed": false }, "outputs": [], "source": [ "for i in xrange(n):\n", " # compute the laplacian of u and v\n", " deltaU = laplacian(U)\n", " deltaV = laplacian(V)\n", " # take the values of u and v\n", " # inside the grid\n", " Uc = U[1:-1, 1:-1]\n", " Vc = V[1:-1, 1:-1]\n", " # update the variables\n", " U[1:-1, 1:-1], V[1:-1, 1:-1] = (\n", " Uc + dt * (a*deltaU + Uc - Uc**3 - Vc + k),\n", " Vc + dt * (b*deltaV + Uc - Vc) / tau\n", " )\n", " # neumann conditions, derivatives at the edges are null\n", " for Z in (U, V):\n", " Z[0, :] = Z[1, :]\n", " Z[-1, :] = Z[-2, :]\n", " Z[:, 0] = Z[:, 1]\n", " Z[:, -1] = Z[:, -2]" ] }, { "cell_type": "code", "execution_count": 291, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 291, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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8GWP4rxWQGZjMQDsLFOBVBETXPg1VxEMYHHw3wPcjxm5E25OAS9QQCSGCiYXV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icp60VOEoii1RCyJ09TSBL/IPOmfsDm0OHHB0rRv7nZ4feftjwaHhzZDKD3fmTKe6Q1yxeWKAoy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\n", 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